EDUCAIDE SOFTWARE'S
Sample Database
(Version 3.0)
an add-on to
the )??AI program
Copyright c 1995 99 EAS EducAide Software Inc. All rights reserved. Certain portions
copyrighted by Addison Wesley Longman, Ltd.; Center for Occupational Research and
Development, Inc.; Region #10 Education Service Center (Richardson, Texas); The
North Carolina Department of Public Instruction; North Carolina Council of Teachers of
Mathematics; Illinois Council of Teachers of Mathematics; British Columbia Colleges High
School Mathematics Contest; University of North Carolina Charlotte; Western Carolina
University Mathematics Contest; The North Suburban (Chicago) Math League; or The
MATHCOUNTS Foundation. Unauthorized reproduction of this Sample Database or the
accompanying software is prohibited by law.
Notes on the Sample Database
• This booklet, which may be thought of as a miniature
problem catalog, provides a sampling of EducAide’s 35
database modules. About 1650 problems are shown less
than one percent of all problems now available through
the Acces program! Since the samples are just a
cross-section of each module, you will have to imagine
the great variety of problems that actually exist. (See
the last page for a summary of database modules.)
• Please note that problems have a special arrangement in
categories AA AD: two similar problems always appear
next to each other. This reflects the design of the Core
Subjects. In fact, in the real databases modules, four
similar problems are grouped together, giving you plenty
of extras for review worksheets, make-up tests, etc.
This sort of grouping is done, when possible, in other
modules, though it is not apparent here.
• You may choose any of the problems in this booklet for
your sample tests and worksheets, but please remember
that the material is copyrighted by EducAide Software
(or a third party) and is for evaluation purposes only.
You are not allowed to make copies of this booklet or any
of the computer files that comprise the Sample Database.
Also, documents generated using this database module
may not be distributed to other parties not licensed to
use Acces.
• If you are using Acces on a trial basis, then after 30 days
you must either purchase the program or remove it from
your hard drive. (You can recycle the disks or return
them to your dealer; this booklet is yours to keep.)
Sample Database
Table of Contents
A. Core Subjects
Pre-algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Algebra II/Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
AA
AB
AC
AD
B. State/Provincial Frameworks (Mathematics)
Canadian Math Grades 8 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BA
Canadian Math Grades 10 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BB
North Carolina Standard Course of Study (1993) . . . . . . . . . . . . . BC
North Carolina Elementary Math Testlets . . . . . . . . . . . . . . . . . . . . . BD
North Carolina Algebra I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BE
North Carolina Secondary Math Testlets . . . . . . . . . . . . . . . . . . . . . . BF
New York Regents Math (I III) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BG
Ohio Secondary Math Proficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BH
TAAS (Texas) Elementary Mathematics . . . . . . . . . . . . . . . . . . . . . . . B I
TAAS (Texas) Secondary Mathematics . . . . . . . . . . . . . . . . . . . . . . . . B J
C. State/Provincial Frameworks (Language Arts)
North Carolina Elementary Reading Testlets . . . . . . . . . . . . . . . . . . CA
TAAS (Texas) Elementary Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CB
D. Other Modules (Mathematics)
Mid-level Math Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DA
SAT Math Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DB
Advanced Placement Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DC
E. Publishers’ Modules
Addison Wesley Longman Western Canadian Gr. 10 . . . . . . . . .
CORD Applied Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CORD Applications in Biology/Chemistry . . . . . . . . . . . . . . . . . . . .
CORD Principles of Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
EA
EB
EC
ED
F. Translations
French Translation of MMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FA
Spanish Translation of TX2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FB
Spanish Translation of TX3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FC
G. Competitions
British Columbia Colleges HS Math Contest . . . . . . . . . . . . . . . . . . GA
Illinois Elementary Math Contest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GB
Illinois Secondary Math Contest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GC
MATHCOUNTS Competitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GD
MATHCOUNTS School Handbooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . GE
North Suburban Math League (Chicago) . . . . . . . . . . . . . . . . . . . . . . GF
North Carolina State Math Contest . . . . . . . . . . . . . . . . . . . . . . . . . . . . GG
UNC Charlotte Math Contest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GH
Western Carolina University Math Contest . . . . . . . . . . . . . . . . . . . . G I
Copyright c 1995 99 EAS EducAide Software Inc. All rights reserved.
Certain portions copyrighted by Addison Wesley Longman, Ltd.; Center
for Occupational Research and Development, Inc.; Region #10 Education
Service Center (Richardson, Texas); The North Carolina Department of
Public Instruction; North Carolina Council of Teachers of Mathematics;
Illinois Council of Teachers of Mathematics; British Columbia Colleges
High School Mathematics Contest; University of North Carolina Charlotte;
Western Carolina University Mathematics Contest; The North Suburban
(Chicago) Math League; or The MATHCOUNTS Foundation. Unauthorized
reproduction of this Sample Database or the accompanying software is
prohibited by law.
AA
These items are drawn from EducAide’s Pre-Algebra (PRE) module, which is intended for classroom instruction and
assessment. The module covers a broad range of topics that would normally precede a junior or senior high school
algebra course. It has more than 15,000 free-response questions in 164 categories. While the module was designed
principally for grades 6 9, it may be used for review, remediation, and testing at any level.
1.
+
7,382
623
2.
8,005
+
5,338
466
в€’
5.
68 Г— 59 =
4,012
6.
9.
726 Г· 6 =
121
10. 432 Г· 3 =
13. What is 343 more than 672 ?
3.
5,804
86 Г— 65 =
4347
69
4.
4278
в€’
7 Г— 5 Г— 13 =
5,590
7.
144
11. 2 ) 618
8.
455
2367
6 Г— 14 Г— 4 =
12. 8 ) 872
309
14. What is 784 more than 116 ?
1015
2446
79
336
109
900
15. At the end of baseball season, the Tigers had won
101 games and lost 61 games. How many games did
they play? 162 games
16. Carl and Carrie are twins. Carl weighs 78 pounds.
Carrie weighs 65 pounds. Find the total weight of the
twins. 143 lb
17. Sam placed a bicycle on lay-away. He still owes $120.
If he wants to pay off the bike in 5 equal payments,
how much will each payment be? $24
18. Jerry owes his brother $78. If he wants to pay his
brother back in 3 equal payments, how much will each
payment be? $26
19. 18 = 2 ( ? )
21. 320 = 8 ( ? )
40
1
5
1
4
23. Simplify:
20. 18 = 9 ( ? )
9
14
20
+
14
20
24. Simplify:
1 25
2
23
24
+
7
24
1 14
25. Simplify:
+
22. 340 = 17 ( ? )
+
1
2
26. Simplify:
19
20
1
2
+
20
1
5
+
1
3
31
30
27. Tonya bought 3 21 pounds of ground chicken and a
4 14 pound whole chicken. What was the total weight
of all the chicken she purchased? 7 3 lb
28. Eric has 2 pieces of chain. On piece is 4 58 feet long
and the other piece is 7 78 feet long. How many feet of
chain does Eric have? 12 1 ft
29. Write in standard form:
30. Write in standard form:
4
four hundred-twenty and eight tenths
ten and twenty-five thousandths
420.8
10.025
31. Simplify:
25.8 + 4.69 + 7.12
Г—
33. Simplify: 48.06 в€’ 4.002
32. Simplify:
4.45 + 1.29 + 21.3
37.61
35.
2
34. Simplify: 33.01-2.006
44.058
31.004
27.04
0.005
2.94
36.
0.0147
Г—
0.008
7.18
37. 0.07 ) 2.1056
0.05744
38. 0.03 ) 2.7009
30.08
90.03
39. Steven is trying to decide where to go to college. One
college is 357.5 miles from his home. The second
college is 279 miles from his home. How much closer
is the second college? 78.5 mi
40. Irving weighed 68.3 kilograms before running a
marathon. After running the marathon, he weighed
66.7 kilograms. How much weight did he lose while
running the marathon? 1.6 kg
41. Find the quotient of 0.104 and 2.
42. Find the quotient of 0.426 and 6.
0.052
43. How far apart are points H and F ?
H
E
F
G
C
A
44. How far apart are points G and H ?
3
D
B
в€’4
в€’3
в€’2
в€’1
0
1
NUMLIN01.TEX
2
3
45. Order from smallest to largest: 2, 6, в€’4, в€’8
в€’8, в€’4, 2, 6
47. Simplify: в€’25 в€’ 2(в€’3)
4
4
NUMLIN01.TEX
•−−−−−−−−−
•−−−−•−−−−−•−−−−−−−−−−
•−−−−•−−−−−−−−−•−−−→
←−−−•−−−−−
в€’5
0.071
5
46. Order from smallest to largest: 4, в€’9, 6, в€’5
в€’9, в€’5, 4, 6
в€’19
49. Simplify: (3 в€’ 8) Г— 6 в€’ 4
в€’34
48. Simplify: в€’20 в€’ 3(в€’2)
в€’14
50. Simplify: (1 в€’ 9) Г— 3 в€’ 12
в€’36
SMP rev. 3.0 (PDF) page 3. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AA
51. Round 35,468 to the nearest ten.
52. Round 97,432 to the nearest ten.
35,470
53. Round 36.929 to the nearest tenth.
97,430
54. Round 7.9782 to the nearest tenth.
36.9
55. Darlinda has a bag of candy. She finds a single piece
weighs 8 grams. She weighs the bag, and finds it
weighs 472 grams. She estimates there are 60 pieces of
candy in the bag. Is this a good estimate? Explain.
8
56. Laurel has a box of door hinges. She knows a single
hinge weighs 4 ounce. She also knows the box weighs
763 ounces. She estimates there are 200 hinges in the
box. Is this a good estimate? Explain. answers may vary
answers may vary
57. Rewrite 25,000 using scientific notation.
59. Rewrite 0.00004 using scientific notation.
61. Find:
в€љ
0.25
62. Find:
0.5
в€љ
2.5 Г— 104
4 Г— 10в€’5
0.49
0.7
65. Rewrite as a ratio of whole numbers:
58. Rewrite 78,000 using scientific notation.
7.8 Г— 104
60. Rewrite 0.00006 using scientific notation.
63. Find:
49
81
64. Find:
7
9
6 Г— 10в€’5
81
25
9
5
66. Rewrite as a ratio of whole numbers:
16 ounces to 4 pounds
2.5 pounds to 4 ounces
1:4
10 : 1
67. What is the unit price of 12 ounces of spaghetti for
$0.89? ≈ $0.07 per ounce
68. What is the unit price of 5 yards of ribbon for $2.59?
69. How far is it from Lakeview to Redding?
70. How far is it from Chester to Brighton?
112.5 mi
≈ $0.52 per yard
100 mi
SCALDR01.PCX
71. How long would it take to drive from Chester to
Springfield, if you were driving 60 miles per hour?
about 2.7 hr
SCALDR01.PCX
72. How long would it take to drive from Brighton to
Redding, if you were driving 40 miles per hour? 2.5 hr
SCALDR01.PCX
SCALDR01.PCX
73. The air distance between Boston and Buffalo is
400 miles. Mrs. Voss’ flight left Boston at 2:00 p.m.
and arrived in Buffalo at 2:45 p.m. What was the
average speed of the plane? 533 1 mph
3
76. What percent of the
diagram is shaded?
75. What percent of the
diagram is shaded?
20%
60%
74. The air distance from Chicago to Detroit is 238 miles.
Bob’s flight left Chicago at 11:10 a.m. and arrived in
Detroit 11:45 a.m. What was the average speed of the
plane? 408 mph
77. What percent of the
diagram is shaded?
78. What percent of the
diagram is shaded?
66 32 %
25%
PCTFIG21.PCX
79. Write 1.6 as a percent.
166 23 %
81. Write 525% as a fraction.
21
4
80. Write 2.3 as a percent.
PCTFIG22.PCX
233 13 %
82. Write 325% as a fraction.
13
4
SMP rev. 3.0 (PDF) page 4. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AA
83. Fill in the table.
fraction
decimal
0.2, 20%;
1
4,
0.25;
1
3,
84. Fill in the table.
33 13 %
percent
fraction
25%
2
3
decimal
1
5
3
4,
75%; 0.6, 66 23 %;
1
2,
0.5
percent
0.75
0.3
50%
85. What is 25% of 36 ?
86. What is 25% of 44 ?
9
87. 5 is what percent of 10 ?
11
88. 8 is what percent of 10 ?
50%
89. Mrs. Williams invested $264 at 9.5% a year for
6 years. How much simple interest did she earn?
80%
90. Mr. Botswain invested $983 at 6.5% a year for 8 years.
How much simple interest did he earn? $511.16
$150.48
91. Simplify: x3 + x3
92. Simplify: n6 + n6
2x3
93. Write as an algebraic expression:
2n6
94. Write as an algebraic expression:
the number that is 12 more than the number n
n + 12
the number that is 4 more than the number n
n+4
95. Evaluate z + y for z = 2.2, y = 3.5.
96. Evaluate x + t for x = 1.5, t = 0.9.
5.7
2.4
97. The area of a triangle is given by the formula A = 21 bh.
Find the area if the base b = 4 inches and the height
h = 12 inches. 24 in2
98. The formula A = 21 bh gives the area of a triangle.
Find the area if the base b = 9 feet and the height
h = 6 feet. 27 ft2
99. 7 Г—
= 56
101. 5 Г—
2
103. Solve:
6
7m
104. Solve:
2
11 n
100. 6 Г—
8
= 30
= 54
9
35
105. Solve: в€’5.1n + 4.2 = в€’0.9
x≥
1
4
в†ђв€’в€’в€’в€’в€’в€’
•−
в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в€’
в€’
в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в†’
1
2
109. Solve: 7(x в€’ 5) < 21
3
= 22
4
= 48
4
121
1
108. Write the equation of the graph.
x≤
9
4
в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
−−•
в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в†’
0
1
2
110. Solve: 8(x в€’ 2) > 32
x<8
2
102. 3 Г—
2
106. Solve: в€’2.9 = в€’6.7y + 3.8
1
107. Write the equation of the graph.
0
= 20
3
4
x>6
111. Two numbers when added together are 188. The
larger number is 161. Find the smaller number. 27
112. Two numbers when added together are 224. The
larger number is 131. Find the smaller number. 93
113. In Fort Assiniboine, Montana, the temperature
rose 42 в—¦ F in 15 minutes on January 19, 1892.
The temperature started at в€’5 в—¦ F. What was the
temperature after 15 minutes? 37 в—¦ F
114. The temperature in Rapid City, South Dakota,
dropped from 49 в—¦ F to в€’13 в—¦ F in 2 hours on
January 12, 1911. How many degrees did the
temperature drop in those 2 hours? 62 в—¦ F
115. How many dimes are in $45?
116. How many dimes are in $78?
450
117. Estimate the capacity of a fish tank.
119. Estimate the measure
of the angle. about 30 в—¦
120. Estimate the measure
of the angle. about 70 в—¦
780
118. Estimate the capacity of a water glass.
121. Classify this triangle.
scalene, acute
122. Classify this triangle.
scalene, acute
ANGL01.PCX
TRIANG11.PCX
ANGL02.PCX
TRIANG12.PCX
SMP rev. 3.0 (PDF) page 5. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AA
123. Find the length of the
missing side. 4.5 cm
124. Find the length of the
missing side. 22 km
125. State the types of
symmetry in this figure.
line, reflectional, point,
rotational
126. State the types of
symmetry in this figure.
line, reflectional, point,
rotational
RT-TRI36.PCX
SYMM06.PCX
SYMM05.PCX
RT-TRI35.PCX
127. Find the area.
570 cm2
128. Find the area.
55 ft2
129. Find the surface area.
43.92 ft2
PARALL05.PCX
130. Find the surface area.
75.6 in2
PRISM13.PCX
PARALL06.PCX
PRISM14.PCX
131. Find the circumference of a circle with radius
r = 6 feet. (Use ПЂ = 3.14.) 37.68 ft
132. Find the circumference of a circle with radius
r = 9 inches. (Use ПЂ = 3.14.) 56.52 in
133. What is the area of a trapezoid with one base
B = 3 millimeters, a second base b = 1 millimeters and
height h = 10 millimeters? 20 mm2
134. What is the area of a trapezoid with one base
B = 5 inches, a second base b = 3 inches and height
h = 7 inches? 28 in2
135. A cone has radius r = 3 inches and height
h = 14 inches. Find the volume of the cone.
136. A cone has radius r = 7 feet and height h = 11 feet.
Find the volume of the cone. 564.15 ft3
131.88 in3
137. Find the mean, median, and mode:
138. Find the mean, median, and mode:
17, 28, 19, 21, 14, 26, 25, 14, 20, 14, 22
20, 20, 14
26, 29, 28, 33, 30, 27, 28, 30, 35, 25, 28
29, 28, 28
139. Make a bar graph using the data in the table.
Fat content of foods
140. What types of graphs would be best for displaying the
information in the table? Why? bar graph
(grams per tablespoon)
food
FOODFAT.TBL
fat content
butter
11 grams
corn oil
14 grams
mayonnaise
11 grams
margarine
11 grams
cream cheese
141. Which of the items listed contains the least amount of
fat per tablespoon? cream cheese
FOODFAT.TBL
142. Which of the items listed contains the largest amount
of fat per tablespoon? corn oil
5 grams
FOODFAT.TBL
FOODFAT.TBL
143. John has 5 pairs of pants, 6 shirts and 3 ties that he
wears for work. How many different combinations of a
pair of pants, a shirt and tie can John wear to work?
90
144. Alvin wants to buy a new ski outfit. He has to choose
between 4 jackets, 5 pairs of pants, and 8 pairs of
gloves. How many different outfits can Alvin choose?
160
145. Find the probability of choosing a red card then
another red card from a deck of 52 cards, without
returning the first card to the deck. 25
102
146. Find the probability of choosing a black card then
another black card from a deck of 52 cards, without
returning the first card to the deck. 25
102
SMP rev. 3.0 (PDF) page 6. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AB
These items are drawn from EducAide’s Algebra I (ALG) module, which is intended for classroom instruction and
assessment. The module covers most topics in a traditional one- or two-year algebra course. The large number of
free-response questions (18,630) and categories (170) make it one of the EducAide’s most popular modules. It may
be used for regular lessons and exams, as well as placement tests, competency tests, and review worksheets for a
geometry or advanced algebra class.
1.
1.4 + 0.8 =
5.
5 9
В·
=
21 25
9.
Simplify: d2 В· d4
13. Divide:
2.2
3
35
xy 8 z 2
x2 y 9 z
2.
0.7 + 2.6 =
6.
20 3
В·
=
27 16
3.3
5
36
10. Simplify: h4 В· h3
d6
14. Divide:
z
xy
k 7 n3 r 3
k 2 n2 r 3
17. Rewrite 0.0008 Г— 105 using scientific notation.
3.
6.2 в€’ 12 =
7.
6
2
в€’3 Г· 4 =
7
3
в€’5.8
в€’ 81
98
11. Simplify: p7 (p4 )2
h7
0.5 в€’ 4 =
8.
4
1
2 Г·5 =
5
2
в€’3.5
28
55
12. Simplify: (r)(r3 )2
p15
15. Simplify: (m2 r)в€’3
k5 n
4.
r7
16. Simplify: (aв€’3 b2 )в€’1
1
m6 r 3
a3
b2
18. Rewrite 0.0057 Г— 107 using scientific notation.
8 Г— 101
5.7 Г— 104
19. Japan has a population of about 124 million and
an area of 3.7 Г— 105 sq km. What is the population
density (number of people per square kilometer)?
20. The U.S. has a population of about 240 million and an
area of 9 Г— 106 sq km. What is the population density
(number of people per square kilometer)? ≈ 2.7 × 101
≈ 3.4 × 102
21. Simplify: в€’2 В· 7 + 9 В· 5 в€’ 16 Г· 8
23. Simplify: в€’7 |8| + |24 в€’ 18|
25. Rewrite
3
4
22. Simplify: 9 В· (в€’3) + 5 В· 3 + 35 Г· (в€’7)
29
24. Simplify: 4 |13 + 3| в€’ |в€’52|
в€’50
(12 в€’ 4k) using the distributive property.
26. Rewrite
9 в€’ 3k
27. Evaluate
2
5
в€’17
12
(10a + 20b) using the distributive property.
4a + 8b
3d + 4
for d = 2.
d
29. Simplify: в€’5p2 + (в€’4p2 )
28. Evaluate
5
4c
for c = в€’1.
10 в€’ 2c
30. Simplify: 2a4 в€’ (в€’a4 )
в€’9p2
31. Simplify: 7y 2 в€’ 2y 3 + y 3 в€’ 6y 2 + 3y 2 в€’ 3y 3
в€’ 31
3a4
32. Simplify: 8w4 + (в€’4w2 ) + 6w2 в€’ (в€’w2 ) в€’ 4w4
в€’4y 3 + 4y 2
4w4 + 3w2
33. Multiply: (10d2 )( 53 d5 )
34. Multiply: (в€’ 73 a5 )(в€’12a3 )
6d7
35. Simplify: (15n4 )(в€’n3 )2
36. Simplify: (в€’2c2 )3 (в€’3c2 )
15n10
37. The side of a square is 10xy. What is the area and
perimeter? 100x2 y2 ; 40xy
39. Simplify:
2 2
3x
в€’ 34 x + 1 в€’
41. Multiply: (k + 5)(k в€’ 1)
43. Multiply: (y + 3)2
5 2
3x
в€’xв€’
4
5
в€’x2 + 14 x +
k 2 + 4k в€’ 5
y 2 + 6y + 9
45. Multiply: (3y в€’ 2)2 (y + 4)
9y 3 + 24y 2 в€’ 44y + 16
47. The third side of a triangle is 5 less than twice the
second. The second is 3 more than the first side.
What is the perimeter? 4x + 4, where x is first side
38. The side of a square is
perimeter? 9 k2 ; 3k
28a8
24c8
3
4 k.
What is the area and
16
9
5
40. Simplify:
3 2
4y
в€’ 2y +
2
3
в€’
42. Multiply: (x в€’ 8)(x + 1)
44. Multiply: (a + 7)2
1 2
4y
в€’ 3y в€’
1
3
1 2
2y
+y+1
x2 в€’ 7x в€’ 8
a2 + 14a + 49
46. Multiply: (2k в€’ 3)(k + 6)2
2k 3 + 21k 2 + 36k в€’ 108
48. The third side of a triangle is four times the second.
The second is 1 less than twice the first side. What is
the perimeter? 11x в€’ 5, where x is first side
SMP rev. 3.0 (PDF) page 7. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AB
49. Write a polynomial for
the surface area of this
figure. A = 48x + 24
50. Write a polynomial for
the surface area of this
figure. A = 24x + 70
51. Write a polynomial
for the volume of this
figure. V = 10x2 + 15x
52. Write a polynomial
for the volume of this
figure. V = 7x2 + 7x
3DFIG24.PCX
3DFIG02.PCX
3DFIG01.PCX
3DFIG23.PCX
53. 62 12 % of what number is 0.4?
54. 87 12 % of what number is 1.4?
0.64
1.6
55. There are 26,000 employees at a large corporation,
and 0.75% of them deal with quality control. How
many employees deal with quality control? 195
56. Of the 45,360 commuters who go across a bridge each
day, only 2 21 % are in car pools. Find out how many
commuters are in the car pools. 1134
57. The formula A = p (1 + rt) gives the total amount of
an investment (or loan) with simple interest. Find the
amount A if the principal p is $12,500, the annual
rate r is 7.5%, and the time t is 4 years. $16250
58. The formula A = p (1 + rt) gives the total amount of
an investment (or loan) with simple interest. Find the
amount A if the principal p is $800, the annual rate r
is 4.75%, and the time t is 10 years. $1180
59. The length and width of a rectangle are 1.4 m
and 0.8 m. What is its perimeter and area?
60. The length and width of a rectangle are 6 ft and 9 34 ft.
What is its perimeter and area? 31 1 ft; 58 1 sq ft
2
4.4 m; 1.12 m2
2
61. A bicyclist rides for 40 minutes at 22 21 mph. How far
does she ride? 15 mi
62. Mr. Sornees runs for 36 minutes at 13.75 km/hr. How
far does he run? 8.25 km
63. Solve: b + (в€’24) = 1
65. Solve: 12 = в€’1.2r
64. Solve: x + (в€’16) = 21
25
в€’10
66. Solve: в€’4.5x = в€’27
6
37
67. Solve: в€’2p + (в€’7p) в€’ (в€’5) = 59
68. Solve: 6 = в€’11 в€’ (в€’2k) + (в€’12k)
в€’6
17
в€’ 10
69. 242 is equal to a number increased by 117. Find the
number. 125
70. 37 is equal to a number increased by 65. Find the
number. в€’28
71. The sum of two consecutive integers is в€’75. What is
the smaller integer? в€’38
72. The sum of two consecutive integers is в€’59. What is
the smaller integer? в€’30
73. The perimeter of a square is 16y and each side is
y + 6. Find y. 2
74. The perimeter of a square is 12y and each side is
y + 10. Find y. 5
75. Two angles are complementary. Four times the
measure of the smaller is half the measure of the
larger. Find both angle measures. 10, 80 в—¦
76. Two angles are supplementary. Five times the measure
of the smaller is three times the measure of the larger.
Find both angle measures. 67.5, 112.5 в—¦.
77. Factor 203.
79. Factor 39a5 .
29 В· 7
78. Factor 455.
13 В· 7 В· 5
80. Factor 15c3 .
3В·5В·cВ·cВ·c
3 В· 13 В· a В· a В· a В· a В· a
81. Find the missing factor: x2a+1 = ( ? )(x)
83. Factor: w2 + 7w + 6
85. Factor:
24 + 10nq 2 r
87. Factor: x4 в€’ 49
(x2 в€’ 7)(x2 + 7)
в€’ n2 q 4 r 2
93. Factor:
+1
(x + 1)(x2 в€’ x + 1)
82. Find the missing factor: y 4n+1 = ( ? )(y 3n )
84. Factor: a2 + 3a + 2
(w + 6)(w + 1)
(12 в€’ nq 2 r)(2 + nq 2 r)
88. Factor: 25 в€’ a4
(5 в€’ a2 )(5 + a2 )
91. Factor: r(r + 1)(r в€’ 6) + 8(r + 1)
x3
x2a
(r + 1)(r в€’ 2)(r в€’ 4)
94. Factor:
y3
+ 27
(y + 3)(y 2 в€’ 3y + 9)
86. Factor:
x4 y 2 z 8
(a + 2)(a + 1)
+ 16x2 yz 4
89. Factor: a2 + a +
1
4
(a + 21 )2
в€’ 36
(x2 yz 4 + 18)(x2 yz 4 в€’ 2)
90. Factor: x2 в€’ 5x +
25
4
(x в€’ 25 )2
92. Factor: k(k + 5)(k в€’ 3) в€’ 10(k + 5)
95. Factor:
y n+1
w6
в€’ x9
(w2 в€’ x3 )(w2 + wx3 + x6 )
(k + 5)(k в€’ 5)(k + 2)
96. Factor: c12 + d3
(c4 + d)(c8 в€’ c4 d + d2 )
SMP rev. 3.0 (PDF) page 8. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AB
97. A rectangular patio is surrounded on three sides by a fence (the remaining
side is up against the house). If the area of the patio is 150 ft2 , and the total
length of fence is 35 ft, what is the length and width of the patio? 20, 7.5 ft
98. A rectangular patio is surrounded on three sides by a fence (the remaining
side is up against the house). If the area of the patio is 45 m2 , and the total
length of fence is 19 m, what is the length and width of the patio? 10, 4.5 m
FENCE1.PCX
0.75
x
99. Solve:
=
9
48
56
7
100. Solve:
=
y
0.75
4
6
101. The ratio of apricot to plum trees in an orchard
is 9 : 5. If there are 392 trees altogether, how many of
each kind are there? 252, 140
102. The ratio of women to men enrolled at a private
college is 7 : 9. If the total enrollment is 1504, find the
number of women and men. 658, 846
103. Find the greatest common factor: x2 + 4x в€’ 12,
x2 + 7x + 6 x + 6
104. Find the greatest common factor: y 2 в€’ 254,
y 2 в€’ 2y в€’ 15 y в€’ 5
105. Give the restrictions on p:
25 в€’ p2
24 + 2p в€’ p2
107. Simplify:
n2 в€’ 9n + 14 4n3 + 16n2
В·
n2 + 7n + 12 3n2 в€’ 21n
109. Simplify:
10s + 10t 5s + 5t
Г·
3s в€’ 3t
9s в€’ 9t
111. Simplify:
x2
5
y
+
113. Simplify:
1в€’
4
y2
6
y2
4n(nв€’2)
3(n+3)
6
x+4
xв€’4
в€’ 2
+ 3x в€’ 10 x в€’ 6x + 8
1в€’
p = в€’4, 6
в€’1
(x+5)(xв€’2)
yв€’3
y+2
x2 в€’ 12xy + 36y 2
117. Simplify:
18u3
119. Simplify: в€љ
24u7
123. Multiply: (3 +
125. Find a.
в€љ
в€љ
4 3
в€љ
4a6 3a
3
5 )(3 +
в€љ
a2 в€’ 11a в€’ 12 a2 в€’ 11a + 24
В· 2
a3 в€’ 9a
a в€’ 7a в€’ 8
110. Simplify:
2x в€’ 6y
6x в€’ 18y
Г·
12x + 4y
9x + 3y
112. Simplify:
5)
1
x
1
x2
в€љ
6 2
aв€’12
a(a+3)
1
4
c+5
cв€’6
+ 2
в€’ 5c в€’ 36 c в€’ 11c + 18
2c2 +cв€’34
(cв€’9)(c+4)(cв€’2)
в€’2
в€’
4
x
+4
x
в€’ 2xв€’1
в€љ
4a2 + 20a + 25
в€љ
в€љ
121. Add: в€’2 40 + 90
в€љ
в€’ 10
2a + 5
в€љ
в€љ
122. Add: в€’4 63 + 6 28
0
в€љ
в€љ
124. Multiply: ( 2 + 1)( 2 + 1)
в€љ
14 + 6 5
126. Find c.
c2
t = в€’5, в€’3
116. Working together, Jeanette and her brother can
deliver newspapers in 56 minutes. But, working alone,
it takes Jeanette three times longer than her brother
to deliver the papers. How long does it take her (to
the nearest minute)? 75 min
118. Simplify:
x в€’ 6y
20a9
120. Simplify: в€љ
45a5
в€љ
3 6u
2u
108. Simplify:
114. Simplify:
115. Working together, it takes Stuart and Tracy
48 minutes to stuff some envelopes. Doing the job
alone, Stuart would take twice as much time as Tracy
to stuff the envelopes. How long (in hours and
minutes) would it take him? 2 hrs 24 min
4t3 в€’ 16t
15 + 8t + t2
106. Give the restrictions on t:
127. Find the length AB.
в€љ
5 10
в€љ
3+2 2
128. Find the length EF .
в€љ
2 22
RT-TRI10.PCX
RT-TRI09.PCX
DIABOX03.PCX
DIABOX04.PCX
SMP rev. 3.0 (PDF) page 9. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AB
129. One end of a ramp is raised to the back of a truck, 3 feet above the ground
(see figure). The other end rests on the ground, 9 feet behind the truck.
What is the approximate length of the ramp? ≈ 9.5 ft
130. One end of a ramp is raised to the back of a truck, 1.5 meters above the
ground (see figure). If the ramp is 4 meters long, approximately how far
behind the truck is the other end of the ramp? ≈ 3.7 m
131. Solve for v: F =
mv 2
gr
RAMPTR1.PCX
132. Solve for r: V = ПЂr2 h
F gr
m
V
ПЂh
133. A football is thrown along a path which can be described by the equation
1 2
x .
64
In the equation, y is the height of the football above the ground at a
horizontal distance x. Find the distance of the ball when y = 19 feet (round
to the nearest tenth). 20.7, 43.3 ft
y =5+xв€’
134. A football is thrown along a path which can be described by the equation
FTBALL2.PCX
1 2
x .
20
In the equation, y is the height of the football above the ground at a horizontal distance x. Find the distance of
the ball when y = 4 meters (round to the nearest tenth). 2.3, 17.7 m
y =2+xв€’
135. Solve: 3(2x в€’ 5) > 5x в€’ 3
137. Solve: |y | + 3 > 9
136. Solve: 7(3 в€’ 4n) < 12n в€’ 19
x > 12
138. Solve: |x| + 15 > 0
y > 6 or y < в€’6
139. Find the distance between (5, 5) and (11, 3).
в€љ
2 10
141. Which points are on the line: в€’6x в€’ 3y = 0 ?
A( 12 , в€’2)
IR
140. Find the distance between (в€’2, 2) and (0, в€’2).
в€љ
2 5
142. Which points are on the line: 2x + 8y = 0 ?
A(0, 0) B(8, в€’2) C (в€’1, 41 ) D(1, в€’ 14 )
B(1, 2) C (в€’3, 6) D(6, в€’3)
C
n>1
all
1
5
143. Write the equation of a line with slope = 4 and
y-intercept = в€’1. y = 4x в€’ 1
144. Write the equation of a line with slope =
y-intercept = 2. y = 1 x + 2
145. Given Q(1, в€’11) and R(7, 1). Write the equation of
в†ђв†’
the line which is perpendicular to QR and contains
в€’в€’в€’
the midpoint of QR. y = в€’ 1 x в€’ 3
146. Given E (в€’7, 4) and F (1, в€’8). Write the equation of
в†ђ
в†’
the line which is perpendicular to EF and contains
в€’в€’в€’
the midpoint of EF . y = 2 x
147. Write a set of equations that describes this shaded
region. x ≤ 3, y > −6 and y ≤ 2 x − 4
148. Write a set of equations that describes this shaded
region. x > −9, y ≤ 5 and y ≥ 2 x + 7
2
3
5
3
3
SHDREG15.PCX
149. Solve: y = в€’4x в€’ 3
y=5
(в€’2, 5)
and
SHDREG16.PCX
150. Solve: y = в€’2x в€’ 9
x = в€’7
(в€’7, 5)
151. Solve:
(в€’ 25 , 41 )
1
2 x + 5y
=0
6x + 4y = в€’14
152. Solve: 8x + y в€’ 2 = 0
3x + 41 y = 0
(в€’ 21 , 6)
SMP rev. 3.0 (PDF) page 10. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AC
These items are drawn from EducAide’s Geometry (GEO) module, which is intended for classroom instruction
and assessment. The wide range of topics and question types makes it suitable for use with any textbook or
course of study. The module provides extensive coverage of both synthetic and analytic geometry, and the question
types include: short-answer, definitions, fill-in-the-blank, true-false, sometimes-always-never, and two-column and
paragraph proofs.
1.
What is an endpoint of a segment?
2.
one of two points in a segment not between any other two points in the
segment
3.
What is the definition of a parallelogram?
the point that separates the segment into two congruent segments
4.
a quadrilateral with both pairs of opposite sides parallel
5.
What is the definition of a quadrilateral ?
a polygon with four sides
Define the term right triangle.
6.
a triangle with one right angle
Direction 399
What is the midpoint of a segment?
Define the term equilateral triangle.
a triangle with all sides congruent
Determine whether each of the following statements is true or false.
7.
EAC must be a straight angle.
8.
EAB must be a right angle.
9.
3 and
4 must be complementary.
10.
1 and
EAF must be supplementary.
True
False
False
True
GEO-018.PCX
11. If two lines are cut by a transversal, then alternate
interior angles must be congruent. False
12. If two parallel lines are cut by a transversal, then
alternate interior angles must be congruent. True
13. If ABC is congruent to
be an equilateral triangle.
14. If PQR is congruent to
be an equilateral triangle.
CAB, then
ABC must
True
в€’в€’в€’
15. If DE
AE
AD
в€’в€’в€’
=
.
BC , then it must be that
AB
AC
True
в€’в€’в€’
16. If DE
AD
AE
в€’в€’в€’
BC , then it must be that
=
.
DB
EC
False
RQP, then
PQR must
False
GEO-232.PCX
17. Congruent chords of the same circle must be
equidistant from the center of the circle. True
18. Parallel chords of the same circle must be equidistant
from the center of the circle. False
19. For W (1, 4), X (3, 2), Y (в€’4, в€’3), Z (в€’2, в€’1), it follows
в†ђв€’в†’ в†ђ
в†’
that WX YZ . False
20. For J (2, 3), K (3, в€’1), L(в€’2, 4), M (в€’1, 0), it follows
в†ђ
в†’ в†ђв†’
that JK LM . True
Direction 400
Determine whether each of the following statements is always, sometimes, or never true.
21. If a conditional statement is false, the negation of the
statement is true. Always
22. If a conditional statement is true, the inverse of the
statement is true. Sometimes
SMP rev. 3.0 (PDF) page 11. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AC
23. The two angles in a linear pair are adjacent to each
other. Always
24. The two angles in a linear pair are vertical.
25. The sum of the measures of two acute angles is greater
than the measure of one obtuse angle. Sometimes
26. The sum of the measures of two right angles is greater
than the measure of one obtuse angle. Always
27. In
ABCD,
ABD в€ј
=
CDB.
Always
28. In
ABCD,
AEB в€ј
=
BEC .
Sometimes
Never
GEO-095.PCX
29. Two isosceles triangles with congruent vertex angles
and congruent bases are congruent. Always
30. Two isosceles triangles with congruent vertex angles
are congruent. Sometimes
31. Two cylinders with equal surface areas have equal
volumes. Sometimes
32. Two cylinders with equal volumes and heights have
equal surface areas. Always
Direction 402
Find the degree measures of the following angles.
GEO-026.PCX
33.
JPL
37.
LPQ
45
60
34.
JPN
38.
MPR
90
55
41. Which of the following could represent the sum of the
measures of two obtuse angles?
a) 95 в—¦
в€— b) 182 в—¦
e) all of these values
c) 375 в—¦
d) 520 в—¦
35.
JPK
15
36.
JPM
65
39.
KPQ
90
40.
LPR
75
42. Which of the following could represent the sum of the
measures of two acute angles?
в€— a) 174 в—¦
b) 180 в—¦
e) all of these values
c) 193 в—¦
d) 242 в—¦
43. Which has a greater measure: an acute angle or an
obtuse angle? obtuse angle
44. Which has a greater measure: an acute angle or a
right angle? right angle
45. Two angles that have degree measures that add to 180
angles. supplementary
are called
46. Two angles that have degree measures that add to 90
angles. complementary
are called
SMP rev. 3.0 (PDF) page 12. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AC
47. Estimate the degree measure of this angle.
≈ 40
48. Estimate the degree measure of this angle.
≈ 120
GEO-013.PCX
GEO-012.PCX
в€’в€’в†’
49. You are given that AX bisects BAC and that
m BAX = x + 25 and m CAX = 4x в€’ 11. What is
the measure of BAX ? 37 в—¦
в€’в†’
50. You are given that FH bisects EFG and that
m EFH = 2x + 32 and m GFHX = 4x в€’ 10. What is
the measure of EFH ? 74 в—¦
51. The ratio of the measures of two supplementary angles
is 51 . What are the measures of the two angles?
52. The ratio of the measures of two supplementary angles
is 13 . What are the measures of the two angles?
30 в—¦, 150 в—¦
45 в—¦, 135 в—¦
53. In the diagram, the three vertical lines are parallel, f = 27, g = 18, a = 33 в€’ x,
and b = x. What is the value of x ? 13.2
54. In the diagram, the three vertical lines are parallel, f = 24, g = 16, a = 53 в€’ x,
and b = x. What is the value of x ? 21.2
GEO-253.PCX
55. A triangle with sides of 6, 10, and 12 is similar to
a triangle whose longest side is 36. What is the
perimeter of the larger triangle? 84 units
56. A triangle with sides of 8, 9, and 15 is similar to
a triangle whose longest side is 30. What is the
perimeter of the larger triangle? 64 units
57. Sandy is trying to measure the height of a nearby
flagpole using a mirror as shown in the diagram.
The mirror is 6 meters away from the flagpole and
2 meters away from Sandy. The height to her eyes is
157 centimeters, from which she can clearly see the
top of the flagpole. How many centimeters tall is the
flagpole? 471 cm
58. Raul is trying to measure the height of a nearby
flagpole using a mirror as shown in the diagram.
The mirror is 8 meters away from the flagpole and
3 meters away from Raul. The height to his eyes is
183 centimeters, from which he can clearly see the top
of the flagpole. How many centimeters tall is the
flagpole? 488 cm
GEO-272.PCX
GEO-272.PCX
SMP rev. 3.0 (PDF) page 13. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AC
59. In the diagram, right ABC is similar to 2 other
right triangles. Name the other two triangles.
ADB,
BDC
60. In the diagram, right XYZ is similar to 2 other
right triangles. Name the other two triangles.
XPY ,
YPZ
GEO-233.PCX
GEO-234.PCX
61. The leaning tower of Pisa is approximately 182 feet tall. If an object is dropped
from the top, it will land about 14 feet from the base. At what angle does the
tower lean? (Measure from the horizon.) ≈ 85.6 ◦
62. The height of the leaning tower of Pisa before it leaned was 182 feet. The tower
now makes an angle of 86 в—¦ with the ground. If an object is dropped from the
top of the tower, about how far away from the base of the tower will it land?
≈ 12.7 ft
GEO-317.PCX
63. In the diagram, a = 9, b = 12, and x is the length
of the longest side. For what value(s) of x will the
triangle be an obtuse triangle? x > 15
64. In the diagram, a = 6, b = 8, and x is the length
of the longest side. For what value(s) of x will the
triangle be an obtuse triangle? x > 10
GEO-288.PCX
65. In the diagram, the value of x is 5. What is the value
of y ? 10
GEO-288.PCX
66. In the diagram, the value of x is 12. What is the
value of y ? 24
GEO-292.PCX
GEO-292.PCX
_
_
_
_
67. In the diagram, m ABC = 90, and mAD = 72. What is the measure of CD ?
108 в—¦
68. In the diagram, m ABC = 90, and mAD = 78. What is the measure of CD ?
102 в—¦
GEO-335.PCX
69. Prove the following theorem.
If one leg and an acute angle of one right triangle
are congruent to the corresponding leg and acute
angle of another right triangle, then the triangles
are congruent.
[proof]
70. Prove the following theorem.
If the hypotenuse and a leg of one right triangle
are congruent to the corresponding sides of
another right triangle, then the triangles are
congruent.
[proof]
SMP rev. 3.0 (PDF) page 14. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AC
71. Three parallel lines intersect two transversals.
Prove that the parallel lines divide the transversals
proportionally. [proof]
73. Given
VST is acute, prove that
RSV is obtuse.
72. Three parallel lines cut off congruent segments on
one transversal. Prove that the parallel lines cut off
congruent segments on another transversal. [proof]
74. Given
[proof]
XOB is acute, prove that
AOX is obtuse.
[proof]
GEO-555.PCX
GEO-556.PCX
75. Given:
Prove:
в€’в€’в€’ в€ј в€’в€’в€’ в€’в€’в€’ в€’в€’в€’ в€’в€’в€’ в€’в€’в€’
AB = AE , AB вЉҐ GD, AE вЉҐ FC
76. Given:
CHD is isosceles
Prove:
в€’в€’в€’ в€ј в€’в€’в€’ в€’в€’в€’ в€ј в€’в€’в€’
QP = RP, XP = YP
QZR is isosceles
GEO-610.PCX
[proof]
GEO-609.PCX
[proof]
_
_
77. In circle O, m AOB > m COD. Prove that mAB > mCD.
_
_
78. In circle O, mCD > mAB. Prove that m COD > m AOB.
[proof]
[proof]
GEO-769.PCX
79. Justify the following statement.
If two adjacent angles are not complementary,
then they do not meet at a right angle.
[proof]
81. Given:
Prove:
80. Justify the following statement.
If two adjacent angles are not supplementary,
then they are not a linear pair.
[proof]
m is not parallel to n
1 is not congruent to
82. Given:
4
Prove:
2 is not congruent to
3
m is not parallel to n
GEO-582.PCX
[proof]
GEO-582.PCX
[proof]
SMP rev. 3.0 (PDF) page 15. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AD
These items are drawn from EducAide’s Algebra II/Trigonometry (TRI) module, which is intended for classroom
instruction and assessment. The module covers most topics in a traditional third-year advanced algebra course, as
well as some pre-calculus topics. While the module was designed principally for high school use, it is also appropriate
for a college-level introductory algebra course.
1.
Factor: 225k в€’ 9kx2 y 2
Factor: 588a в€’ 12ar2
2.
7.
9.
(a3 в€’ 9a2 + 27a в€’ 27)5
в€љ
в€љ
2 48 + 5 28 24в€љ7+70в€љ3
в€љ
Simplify:
21
21
в€љ
в€љ
в€љ
в€љ
Simplify: (2 6 + 3i)(2 6 в€’ 3i)
Simplify:
3
13. Solve: (y в€’ 4)(y + 2) = в€’6
15. Solve:
в€’ 13y 2
+ 40 = 0
1В±
17a
= 51
9
4.
27
Solve: 24 =
3m
в€’8
в€’64
в€љ
4 4
c + 4c3 + 6c2 + 4c + 1 c + 1
в€љ
в€љ
3 75 + 2 80 45в€љ5+40в€љ3
в€љ
8. Simplify:
30
2 15
в€љ
в€љ
в€љ
в€љ
10. Simplify: (5 2 в€’ 3 7i)(5 2 + 3 7i) 113
6.
(a в€’ 3)5
27
11. If z = в€’5 + 8i, state the absolute value of z.
y4
Solve:
12a(7 в€’ r)(7 + r)
9k(5 в€’ xy)(5 + xy)
5.
3.
в€љ
89
в€љ
3
Simplify:
12. If z = 9 + 11i, state the absolute value of z.
14. Solve: (d + 5)(d + 3) = 6
в€љ
в€љ
В± 5, В±2 2
16. Solve:
17. In the equation h2 w + 6 = w(2w + 3h), the sum of the
roots exceeds the product of the roots by 5. Find the
value(s) of h. в€’1, 4
w4
в€’ 5w2
+6=0
в€’4 В±
в€љ
в€љ
202
7
в€љ
в€љ
В± 3, В± 2
18. In the equation k 2 x в€’ x(3x + 3k) + 6 = 0, the sum of
the roots exceeds the product of the roots by 8. Find
the value(s) of k. в€’3, 6
19. The figure reprsents a solid rectangular object. Its surface area is 72. What is the
value of x? 3
2
20. The figure represents a solid rectangular object. Its surface area is 22. What is the
value of x? 1
2
в€’в€’в€’
21. The midpoint of JK is (в€’2, 3). If the coordinates of J
are (в€’10, 7), find the coordinates of K . (6, в€’1)
TRI-052.PCX
в€’в€’в€’
22. The midpoint of BC is (3, в€’2). If the coordinates of
B are (в€’3, в€’7), find the coordinates of C . (9, 3)
23. What is the slope and y-intercept for the line
y = 23 x + 5? 2 and 5
24. What is the slope and y-intercept for the line
x
y = в€’ + 2? в€’ 1 and 2
3
3
x y
в€’x y
27. Graph:
в€’ =1
28. Graph:
+ =2
3
4
5
2
3
25. Graph: x + 6 = 0
[graph]
[graph]
29. Write the equation of
this line. y = 1 x
2
TRI-003.PCX
26. Graph: x в€’ 4 = 0
[graph]
30. Write the equation of
this line. y = в€’ 3 x
2
TRI-004.PCX
[graph]
31. Write the inequality of
this half plane. y > 4 x
5
32. Write the inequality of
this half plane.
y ≥ − 65 x
TRI-015.PCX
TRI-016.PCX
33. For what value(s) of k are the points (k в€’ 2, 1),
(k + 3, k), and (3k, 7) collinear? В±4
34. For what value(s) of p are the points (2p, 5), (p + 1, 3),
and (в€’p, p + 3) collinear? в€’2, в€’1
35. A triangle has vertices at D(в€’7, 2), E (3, в€’2), and
F (5, 3). Write the equation of the line that is parallel
в€’в€’в€’
to DF and passes through E . y = 1 x в€’ 9
36. A triangle has vertices at A(в€’6, 0), B(6, 1), and
C (4, в€’4). Write the equation of the line that is
в€’в€’в€’
perpendicular to AB and passes through C .
12
4
y = в€’12x + 44
SMP rev. 3.0 (PDF) page 16. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AD
37. Solve: 4 = 3y в€’ 21 x
3
4x + 6
=
3
2x
5
3y
38. Solve:
1
2y
= 2 + 54 y
3
2
=
в€’
1
2x
40. Graph: 4x < 3y
y ≤ 23 x
[graph]
( 53 , 52 )
(в€’8, 0)
39. Graph: y < 15 x
2x ≤ y
[graph]
41. In the figure, m 1 = (3y + 4) в—¦, m 2 = (6x + 20) в—¦, and m 3 = (3x + y + 3) в—¦. Solve for
x and y, then find the real measure of 2. x = 15, y = 22; 110 в—¦
42. In the figure, m 1 = (4x + y) в—¦, m 2 = (6x + 2y + 10) в—¦, and m 3 = (2y + 2) в—¦. Solve
for x and y, then find the real measure of 1. x = 8, y = 30; 62 в—¦
TRI-335.PCX
43. Find a positive integral upper bound for the real roots
of the function h(x) = x4 в€’ 18x3 + 35x в€’ 28. 18
44. Find a positive integral upper bound for the real roots
of the function f (x) = x4 в€’ 23x2 + 16x + 30. 5
45. Determine the constant c for which 2x3 +3x2 +cx+c+1
is divisible by x + 2. в€’3
46. Determine the constant c for which
x3 в€’ 2x2 + (c в€’ 4)x в€’ (c + 1) is divisible by x в€’ 3.
48. Does this graph
represent a function?
47. Does this graph
represent a function?
yes
no
TRI-071.PCX
51. Graph: f (x) =
49. Does this graph
represent a function?
50. Does this graph
represent a function?
no
TRI-072.PCX
16 − x2 , if x ≥ 2
3x + 12, if x < 2
yes
TRI-085.PCX
TRI-086.PCX
52. Graph: f (x) =
[graph]
2
5x2 в€’ 4,
3 в€’ 2x2 ,
if x > 1
if x ≤ 1
[graph]
53. State all horizontal and vertical asymptotes:
xв€’3
g(x) = 2
x + x в€’ 12 x = в€’4, y = 0
54. State all horizontal and vertical asymptotes:
x+4
h(x) = 2
x + 3x в€’ 4 x = 1, y = 0
55. The profit P of a company for a given time period
is the difference between revenue R and cost C. If
R(x) = 300x в€’ x2 and C(x) = 50 + 80x, find the
profit P (x), the maximum value of the profit function,
and the value of x at which it occurs.
56. The profit P of a company for a given time period
is the difference between revenue R and cost C. If
R(x) = 1000x в€’ x2 and C(x) = 3000 + 20x, find the
profit P (x), the maximum value of the profit function,
and the value of x at which it occurs.
P (x) = в€’x2 + 220x в€’ 50; $12,050; 110
P (x) = в€’x2 + 980x в€’ 3000; $237,100; 490
57. Find the center and radius of a circle described by
(x в€’ 2)2 + (y в€’ 7)2 = 26. (2, 7), r = в€љ26
58. Find the center and radius of a circle described by
(x в€’ 4)2 + (y + 3)2 = 6. (4, в€’3), r = в€љ6
59. Find the equation of the parabola with focus (в€’2, 0),
and vertex (0, 0). y = в€’ 1 x2
60. Find the equation of the parabola with focus (в€’6, 0),
and vertex (0, 0). y = в€’ 1 x2
61. Write the equation of
this graph.
63. Write the equation of
this graph. y2 в€’ x2 = 1
64. Write the equation of
this graph. y2 в€’ x2 = 1
TRI-145.PCX
TRI-146.PCX
8
(x+3)2
1
+
(y+1.5)2
12.25
=1
TRI-139.PCX
62. Write the equation of
this graph.
(xв€’1)2
16
+
(yв€’0.5)2
2.25
24
4
4
=1
TRI-140.PCX
SMP rev. 3.0 (PDF) page 17. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AD
65. Find the center, vertices, foci, and eccentricity of the
x2
y2
+
= 1. (0, 0); (В±4, 0), (0, В±9); (0, В±в€љ65 ); e = в€љ65
ellipse
9
16 81
66. Find the center, vertices, foci, and eccentricity of the
x2
y2
+
= 1. (0, 0); (В±5, 0), (0, В±2); (В±в€љ21, 0); e = в€љ21
ellipse
5
25
4
67. The main cables of a suspension bridge are 50 feet above the road at the towers and
10 feet above the road at the center. The road is 200 feet long. Vertical cables are
spaced every 20 feet. The main cables hang in the shape of a parabola. Find the
equation of the parabola. y = 1 x2 or y = 1 x2 + 10
250
250
68. The main cables of a suspension bridge are 20 meters above the road at the towers
and 4 meters above the road at the center. The road is 80 meters long. Vertical
cables are spaced every 10 meters. The main cables hang in the shape of a parabola.
Find the equation of the parabola. y = 1 x2 or y = 1 x2 + 4
100
100
69. Write 2(log n + log m) as a single logarithm.
71. Solve: e3x = e7xв€’2
x=
TRI-170.PCX
log (nm)2
70. Write 7(log c + log b) as a single logarithm.
72. Solve: e2x+6 = ex+4
1
2
log (cb)7
x = в€’2
73. The Kwan family purchased their house in 1980 for
$100,000. If the value of real estate increases at a
rate of 10% per year, how much would their house be
worth in 1995? $417,725
74. JosВґe owns a rare baseball card which increases in value
at a rate of 15% per year. If the card was worth $3.50
in 1990, how much is it worth in 1995? $7.04
75. The frequency markers on AM radio dials vary
exponentially with the distance from the left end of
the dial. One radio dial is 8 centimeters long, starts
at 530 kHz and ends at 1600 kHz. Write an equation
expressing the frequency in terms of the distance, then
fill in the table below.
76. The population of bacteria in a petri dish vary
exponentially with temperature in the range 0 в—¦ C to
40 в—¦ C. Write an equation expressing the population of
bacteria in terms of the temperature, then fill in the
table below.
distance
0
frequency
temp ( в—¦ C)
0
number
530
600
700
900
1200
1600
N=
40
300
300e0.055t ;
900
1500
2100
2700
20, 29.3, 35.4
f = 530(100.06d ); 0.9, 2.0, 3.8, 5.9, 8
77. State the next 2 terms of this sequence and give a
formula for the nth term.
в€’5, в€’10, в€’20, в€’40, в€’80
78. State the next 2 terms of this sequence and give a
formula for the nth term.
в€’4, в€’12, в€’36, в€’108, в€’324
в€’160, в€’320; an = в€’5(2nв€’1 )
в€’972, в€’2916; an = в€’4(3nв€’1 )
4
79. Simplify:
4
(n + 6)(n + 1)
80. Simplify:
124
n=1
81. In an arithmetic sequence, the first term is 6 and the
common difference is 1 32 . What is the 8th term? the
nth term? 17 2 , 13+5n
3
83. Find sin D.
(r + 1)(r + 3)
85
r=0
3
12
13
84. Find cos D.
5
13
TRI-205.PCX
82. In an arithmetic sequence, the first term is в€’5 and
the common difference is в€’ 56 . What is the 6th term?
the nth term? в€’9 1 , в€’ 25 в€’ 5 n
6
12
13 ,
6
85. Given sin G =
express GI in simplest
radical form. 13
6
12
,
86. Given sin G = 13
express GH in simplest
radical form. 5
TRI-215.PCX
TRI-205.PCX
TRI-215.PCX
87. In PQR, m Q = 90 в—¦, PQ = 1, and QR = 3. Find
tan P. 3
88. In PQR, m Q = 90 в—¦, PQ = 1, and QR = 3. Find
sin R. в€љ10
10
SMP rev. 3.0 (PDF) page 18. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
AD
89. If a = 1.8 and b = 4.7, find m B to the nearest tenth of a degree. 69.0 в—¦
в€љ
в€љ
90. If a = 16 3 and b = 9 5, find m B to the nearest tenth of a degree. 36.0 в—¦
TRI-225.PCX
в€љ
91. A 20 meters long line reaches a point 10 3 meters high on a ship’s mast. What
angle does the line form with the mast? 30 в—¦
в€љ
92. A 20 2 foot long line reaches a point 20 feet high on a ship’s mast. What angle does
the line form with the mast? 45 в—¦
SAILMST1.PCX
93. A swimming pool is 40.0 feet long and 3.0 feet deep at one end. If it is 10.0 feet
deep at the other end, find the total distance along the bottom. ≈ 40.6 ft
94. Refer to the previous figure. A swimming pool is 50.0 feet long and 4.0 feet deep at
one end. If it is 9.0 feet deep at the other end, find the exact total distance along
the bottom of the pool. 5в€љ101 ft
95. Rewrite в€’9 в—¦ in radians.
96. Rewrite в€’10 в—¦ in radians.
ПЂ
в€’ 20
в—¦
98. Rewrite в€’ 7ПЂ
97. Rewrite в€’ 11ПЂ
60 in degrees. в€’33
36 in degrees.
в€љ
в€љ
99. Given AB = 4, BC = 3 2, and CD = 1, find the coordinates of D. 31 , 2 3 2
100. Given AB =
в€љ
TRI-233.PCX
ПЂ
в€’ 18
в€’35 в—¦
в€љ
в€љ
2 5
5
5 , 5
5, BC = 5, and CD = 1, find the coordinates of D.
CIRFIG06.PCX
101. tan x = 1.8. Find tan(ПЂ + x).
103. Graph: y = cot(2Оё)
109. Verify:
104. Graph: y = cot
[graph]
3
2Оё
105. Graph: y = в€’3 sin
107. Simplify:
102. tan Оё = в€’1.6. Find tan(ПЂ + Оё).
1.8
1 + tan2 Оё
tan2 Оё
в€’
ПЂ
4
в€’6
106. Graph: y =
[graph]
108. Simplify:
csc2 Оё
cos2 Оё
cos Оё
=
1 в€’ sin Оё
sec Оё в€’ tan Оё
110. Verify:
[proof]
111. Given ABC with sides a, b, and c, and opposite
angles О±, ОІ, and Оі, solve the triangle.
c = 63, b = 82, ОІ = 61.4 в—¦
1
4
1
6x
sin
cot2 Оё
[graph]
1
ПЂ
4x + 2
1 + cot2 Оё
в€’1.6
в€’5
[graph]
sec2 Оё
sin Оё
sin2 Оё
=
csc Оё в€’ cot Оё
1 в€’ cos Оё
[proof]
112. Given ABC with sides a, b, and c, and opposite
angles О±, ОІ, and Оі, solve the triangle.
a = 12, b = 19, ОІ = 58.9 в—¦
a = 90.7, О± = 76.2 в—¦, Оі = 42.4 в—¦
c = 22.2, О± = 32.7 в—¦, Оі = 88.4 в—¦
113. Two forces of 60 pounds and 80 pounds, respectively,
acting on an object exert a resultant force of
90 pounds. Find the measure of the angle between
the two forces. 78.6 в—¦
114. Two forces of 27 tons and 19 tons, respectively, act
on an object to produce a resultant force of 40 tons.
Find the measure of the angle between the two forces.
119.81 в—¦
115. Fill in the table.
Period
y = cos
3
2x
+
Amplitude
PhaseShift
VerticalShift
Range
5
3
y = в€’ 23 sec 2x в€’
ПЂ
2
SMP rev. 3.0 (PDF) page 19. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BLANK PAGE
BA
These items are drawn from the Canadian Math Grades 8 10 (CM2) module. The 5,800 mostly multiple-choice items
are based on the Western Canada Common Curriculum and place special emphasis on number concepts, patterns
and relations, functions, and data analysis. While the module is designed for a modern integrated curriculum, it
is organized by topic. Therefore, it is useful for most junior and senior high school math courses in Canada and
the U.S.
1.
In the expression в€’5x4 the coe cient is
в€— b) в€’5
a) 5
3.
b) в€’8
Evaluate:
a)
7.
e) 4
c) 8
d) 16
b)
7
8
d) 4
e)
72
10
When (5.9 Г— 108 ) Г— (3.8 Г— 10в€’20 ) is worked out,
rounded to one decimal place, and written in the form
A Г— 10B for scientific notation, what is the value
of B ?
в€— b) в€’11
c) в€’10
d) 11
e) 12
A red light flashes every 12 seconds, a green light
flashes every 16 seconds, and a yellow light flashes
every 20 seconds. If they all just flashed, then how
many seconds will pass before they all flash at the
same time again?
a) 80
b) 120
c) 180
в€— d) 240
e) 260
11. Solve for x: |2x в€’ 3| = в€’7
a) 5 or в€’2
d) 5 only
b) в€’5 or 2
в€— e) no solution
b) 6.4%
d) 640%
c) в€’2 only
c) 64%
в€— c) 81
в€— b) 16
Evaluate:
1
4
c) 6
d) 9
e) 150
(10в€’1 + 30в€’1 )в€’1
(5в€’1 + 3в€’1 )в€’1
b)
1
2
c) 2
в€— d) 4
e)
225
32
When (6.7 Г— 105 ) Г— (6.3 Г— 10в€’31 ) is worked out,
rounded to one decimal place, and written in the form
A Г— 10B for scientific notation, what is the value
of B ?
a) в€’155
b) в€’27
c) в€’26
в€— d) в€’25
e) 26
10. A red light flashes every 15 seconds, a green light
flashes every 20 seconds, and a yellow light flashes
every 25 seconds. If they all just flashed, then how
many seconds will pass before they all flash at the
same time again?
a) 100
b) 250
a) в€’2 or в€’7
d) в€’7 only
в€— c) 300
d) 400
b) 7 or 2
в€— e) no solution
в€— b) 0.81%
d) 81%
e) 450
c) в€’2 only
c) 8.1%
e) 810%
16. What is 40% of 70% of 850?
d) 162
e) 225
17. Evaluate: (64)2/3
a) 8
в€— b) в€’9
a) 0.081%
e) 6400%
b) 22.5
e) 3
14. Express 0.0081 as a percent.
15. What is 30% of 60% of 450?
a) 0.81
d) в€’8y
12. Solve for x: |2x + 9| = в€’5
13. Express 0.0064 as a percent.
в€— a) 0.64%
.
Evaluate: (в€’1)25 Г— (в€’3)2
a)
8.
в€— c) в€’8
b) y
a) в€’14
e) 296
6.
в€— c) 2
In the expression в€’8y 3 the coe cient is
a) 8
4.
(6в€’1 + 4в€’1 )в€’1
(3в€’1 + 2в€’1 )в€’1
3
5
a) в€’12
9.
2.
Evaluate: (в€’1)37 Г— (в€’2)4
в€— a) в€’16
5.
d) в€’5x
c) x
.
a) 23.8
b) 119
c) 225
в€— d) 238
e) 485.7
c) 50
d) 75
e) 83.3
18. Evaluate: (125)2/3
c) 16.2
d) 42.7
e) 96
в€— a) 25
b) 29
19. What
is the perimeter of a rectangle
whose length is
в€љ
в€љ
5 8 cm and whose width is 2 12 cm?
в€љ
в€љ
в€љ
в€— a) 20 2 + 8 3 cm
b) 28 5 cm
в€љ
в€љ
d) 40 5 cm
c) 28 6 cm
в€љ
e) 40 6 cm
20. What
is the perimeter of a rectangle
whose length is
в€љ
в€љ
4 18 cm and whose width is 3 20 cm?
в€љ
в€љ
в€љ
a) 15 18 cm
в€— b) 24 2 + 12 5 cm
в€љ
в€љ
d) 72 7 cm
c) 36 7 cm
в€љ
e) 72 10 cm
21. How many squares can be chosen on a 3 by 4 array of
unit squares?
22. How many squares can be chosen on a 4 by 5 array of
unit squares?
a) 12
b) 16
c) 18 в€— d) 20
e) 24
a) 20
b) 24 в€— c) 40
d) 43
e) 47
SMP rev. 3.0 (PDF) page 21. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BA
23. Between what two times is the temperature change
the greatest?
24. Between what two times is the temperature change
the least?
CM2-016.PCX
a) 4 am to 6 am
в€— c) 12 noon to 2 pm
b) 6 am to 8 am
d) 2 pm to 4 pm
e) 4 pm to 6 pm
25. Use the graph to estimate the median temperature
from 4 am to 8 pm ?
CM2-016.PCX
a) 12
a) 4 am to 6 am
c) 12 noon to 2 pm
в€— e) 4 pm to 6 pm
b) 6 am to 8 am
d) 2 pm to 4 pm
d) 19
e) 23
A
B+y
=
for y.
x
y
Bx
Bx
b) y =
a) y =
xв€’A
A+x
xв€’A
Bx
d) y =
в€— e) y =
Bx
Aв€’x
CM2-016.PCX
в€— a) 11
27. Solve
c) C в€— d) D
b) 16
c) 17
d) 19
A
Bв€’y
=
for y.
x
y
Bx
Bx
в€— b) y =
a) y =
xв€’A
A+x
xв€’A
Bx
d) y =
e) y =
Bx
Aв€’x
e) 23
28. Solve
c) y =
Aв€’x
Bx
29. Select the line that is the graph of the equation
2x + 3y = 6.
b) B
в€— c) 17
26. Use the graph to estimate the range of the
temperatures from 4 am to 8 pm ?
CM2-016.PCX
a) A
b) 14
c) y =
Aв€’x
Bx
30. Select the line that is the graph of the equation
2x в€’ 3y = в€’6.
a) A в€— b) B
e) E
c) C
d) D
e) E
CM2-032.PCX
CM2-032.PCX
32. If the ordered pair (2k, k) lies on the graph of
4x + 3y = в€’33, then what is the value of k ?
31. If the ordered pair (k, 2k) lies on the graph of
3x + 5y = в€’26, then what is the value of k ?
a) в€’ 26
11
в€— b) в€’2
c)
11
26
d) 2
e)
26
11
a) в€’ 33
7
b) в€’ 33
10
в€— c) в€’3
d) 3
e)
33
10
33. Select the graph that represents the inequality y ≥ 3x − 2?
a)
в€— c)
b)
CM2-091.PCX
CM2-092.PCX
CM2-093.PCX
34. Select the graph that represents the inequality y ≤
в€— a)
b)
CM2-096.PCX
d)
CM2-094.PCX
CM2-095.PCX
в€’ 37 x + 2?
c)
CM2-091.PCX
e)
d)
CM2-097.PCX
e)
CM2-098.PCX
CM2-094.PCX
SMP rev. 3.0 (PDF) page 22. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BA
35. The lines 2x в€’ 3y = в€’15 and 3x + ky = 12 have the
same y-intercept. What is the value of k ?
a) в€’ 12
5
5
b) в€’ 12
c)
5
12
в€— d)
12
5
e) 5
37. How many litres of a 50% alcohol solution must be
added to 60 litres of a 40% alcohol solution in order
to produce a 46% solution?
a) 60
b) 80
в€— c) 90
d) 110
e) 120
39. What is the value of the expression xв€’2 + y 2 when
x = 3 and y = в€’3?
a) в€’12
b) 0
c) 1
d)
37
6
в€— e)
82
9
41. From the sum of 5x2 в€’ 8x + 2 and 2x2 в€’ 3x в€’ 7,
subtract x2 в€’ 9x в€’ 4.
в€— a) 6x2 в€’ 2x в€’ 1
c) 6x2 в€’ 2x + 1
b) в€’2
d)
2
13
e)
13
2
38. How many litres of a 40% alcohol solution must be
added to 80 litres of a 70% alcohol solution in order
to produce a 52% solution?
a) 80
в€— b) 120
c) 126
d) 130
e) 150
40. What is the value of the expression xв€’2 + y 2 when
x = 2 and y = в€’2?
a) в€’8
b) 0
в€— d)
c) 1
17
4
e)
25
4
42. From the sum of 3x2 в€’ 7x + 5 and x2 в€’ 4x в€’ 9, subtract
5x2 в€’ 8x в€’ 7.
b) в€’x2 + 3x в€’ 3
d) 6x2 в€’ 20x в€’ 1
c) в€’x2 в€’ 19x в€’ 11
d) в€’x2 в€’ 3x + 11
в€— e) в€’x2 в€’ 3x + 3
44. Multiply: 3(5x2 в€’ 2x + 7)
b) 36x2 в€’ 16x + 20
в€— d) 12x2 в€’ 16x + 20
e) 12x2 в€’ 16x + 5
в€— a) 15x2 в€’ 6x + 21
b) 15x6 в€’ 6x3 + 21
c) 225x2 в€’ 6x + 21
d) 225x2 в€’ 6x + 7
e) 8x2 + x + 10
6x2 + 11x + 4
8x2 в€’ 2x в€’ 3
3
3x + 4
a) в€’
в€— b)
4
4x в€’ 3
3x в€’ 4
3x в€’ 4
e)
d)
4x + 3
4x в€’ 3
4x2 + 23x в€’ 6
6x2 + 37x + 6
4x в€’ 1
x+4
в€— a)
b)
6x + 1
xв€’6
2
4x в€’ 1
e)
d)
6x в€’ 1
3
46. Simplify:
45. Simplify:
c)
4x + 3
3x в€’ 4
47. To the nearest square centimetre, what is the area of
the base of this cylinder?
a) 5 cm2
в€— a) 5 cm2
b) 25 cm2
c) 28 cm2
c) 28 cm2
e) 1087 cm2
в€— d) 61 cm2
4x + 1
6x в€’ 1
c)
48. To the nearest square centimetre, what is the area of
the base of this cylinder?
b) 25 cm2
e)
2
c) в€’ 13
a) x2 в€’ 3x + 3
43. Multiply: 4(3x2 в€’ 4x + 5)
c) 12x2 в€’ 4x + 20
в€— a) в€’ 13
2
b) 6x2 + 2x в€’ 1
e) 8x2 в€’ 2x в€’ 1
a) 12x8 в€’ 16x4 + 20
36. The lines в€’4x + 5y = в€’10 and 5x + ky = 13 have the
same y-intercept. What is the value of k ?
d) 61 cm2
CM2-192.PCX
1087 cm2
CM2-193.PCX
49. A pyramid has a volume of 250 cm3 . What would be
the volume of a rectangular prism with the same base
and height as the pyramid?
a) 125 cm3
b) 500 cm3 в€— c) 750 cm3
e) it cannot be determined
d) 1000 cm3
51. What is the sum of the measures of the interior angles
of a pentagon?
a) 180 в—¦
b) 360 в—¦
в€— c) 540 в—¦
d) 720 в—¦
e) 900 в—¦
50. A pyramid has a volume of 300 cm3 . What would be
the volume of a rectangular prism with the same base
and height as the pyramid?
a) 450 cm3 в€— b) 900 cm3
c) 1200 cm3
e) it cannot be determined
d) 1500 cm3
52. What is the sum of the measures of the interior angles
of a hexagon?
a) 180 в—¦
b) 360 в—¦
c) 540 в—¦
в€— d) 720 в—¦
e) 900 в—¦
SMP rev. 3.0 (PDF) page 23. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BA
53. There are 16 cans of soup in a carton. Each can has
a diameter of 8 cm and a height of 9 cm. How much
paper, to the nearest square centimetre, is needed to
make the labels for the 16 cans?
a)
1810 cm2
d)
7238 cm2
в€— b)
3619 cm2
e)
9050 cm2
c)
4561 cm2
55. In a scale diagram of a kitchen, the space allowed for
1
the stove is 3 cm in length. If the scale factor is 48
,
what is the actual measurement of the space allowed
for the stove?
a) 12 cm
в€— d) 144 cm
b) 16 cm
e) 192 cm
c) 124 cm
54. There are 12 cans of soup in a carton. Each can has
a diameter of 8 cm and a height of 9 cm. How much
paper is needed to make the labels for the 12 cans?
a) 1810 cm2
b) 2503 cm2
d) 3648 cm2
e) 4231 cm2
56. In a scale diagram of a kitchen, the space allowed for
the refrigerator is 4 cm in length. If the scale factor
1
, what is the actual measurement of the space
is 48
allowed for the refrigerator?
a) 12 cm
d) 144 cm
57. Find the exact length of AB in the diagram.
в€љ
в€љ
a) 299
в€— b) 389
в€љ
c) 5 13
d) 18
e) 25
b) 16 cm
в€— e) 192 cm
XYZ and
CM2-413.PCX
PQR.
60. State the congruence relation for
CM2-518.PCX
DEF, which of the following is equal to
a) sin D
в€— d) tan D
b) sin E
e) tan E
PQR and
5
12 ?
c) cos D
CM2-522.PCX
62. In
ABC, which of the following is equal to
a) sin C
d) tan A
b) cos A
e) tan C
в€’в€’в†’
63. What is the angle of rotation of the vector [2, 4]?
b) 28.4 в—¦
c) 56.8 в—¦
d) 59.3 в—¦ в€— e) 63.4 в—¦
65. Determine the height of the tree.
a) 5.9 m
c) 7.5 m
e) 9.3 m
12
13 ?
в€— c) cos C
CM2-592.PCX
a) 26.6 в—¦
XYZ.
в€— a) ASA
b) AAA
c) SSA
d) SAS
e) not necessarily
congruent
a) ASA
b) AAA
c) SSA
d) SAS
в€— e) not necessarily congruent
61. In
c) 124 cm
58. Find the exact length of AB in the diagram.
в€љ
a) 12
b) 2 46
в€љ
c) 2 47
d) 15
в€љ
в€— e) 194
CM2-414.PCX
59. State the congruence relation for
в€— c) 2714 cm2
CM2-593.PCX
в€’в€’в†’
64. What is the angle of rotation of the vector [3, 5]?
a) 31.0 в—¦
b) 36.9 в—¦
c) 57.6 в—¦ в€— d) 59.0 в—¦
e) 63.4 в—¦
66. Determine the height of the monument.
в€— b) 7.4 m
d) 8.4 m
a) 7.8 m
в€— c) 16.2 m
e) 25.5 m
CM2-714.PCX
b) 9.1 m
d) 18.0 m
CM2-715.PCX
SMP rev. 3.0 (PDF) page 24. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BB
These items are drawn from the Canadian Math Grades 11 12 (CM1) module. The 6,400 mostly multiple-choice
items are based on the Western Canada Common Curriculum and place special emphasis on number concepts,
patterns and relations, functions, and data analysis. While the module is designed for a modern integrated
curriculum, it is organized by topic. Therefore, it is useful for most junior and senior high school math courses in
Canada and the U.S.
1.
When (x + 4)3 в€’ (x в€’ 4)3 is factored completely, one of
the factors is:
b) 3x2 + 48
e) x в€’ 4
a) 2x
d) x + 4
3.
5.
4.
c)
b)
18
9
c)
в€љ
7
What is the result when в€љ
4
a)
9.
a) 4a2
x
x+3
Express 0.188 as a rational number.
18
99
в€љ
28
x9
b)
в€љ
15
в€— d)
x3
Rationalize the denominator: в€љ
e)
17
99
8
6в€’2
1
в€љ
28 9
x
в€љ
c) 4 6 + 16
в€’4
в€’2
0
2
4
6
в€’6
в€’4
в€’2
0
2
4
в€’6
в€’4
в€’2
0
2
4
6
6
в€’6
в€’4
в€’2
0
2
4
6
13. Solve:
a)
в€’ 12
13
42x
в€’6
=
в€’4
в€’2
0
2
4
b)
b) 2.7
b) 16
в€— a)
в€љ
15
x2
c)
d)
c) 3.3
в€— c) 32
c)
15
100
в€љ
5
в€љ
5
x4
x2
d)
6
в€љ
в€— a) 2 5 + 2
в€љ
d) 18 ( 5 в€’ 1)
13
12
d) 3.4
d) 64
e)
c) x
в€љ
b) 4 5 + 4
в€љ
e) 18 ( 5 + 1)
15
9
8
5в€’1
в€љ
15
x8
в€љ
c) 8 5 + 8
0
1
2
3
4
5
6
0
1
2
3
4
5
6
в€— c) в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’в—¦
в€’в€’в€’в€’в€’в€’в†’
в—¦в€’
в€’6 в€’5 в€’4 в€’3 в€’2 в€’1
0
1
2
3
4
5
6
•−
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
−•
d) в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в€’в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’в€’в€’в€’в€’в€’в€’в†’
в€’6 в€’5 в€’4 в€’3 в€’2 в€’1
8
0
1
2
3
4
5
6
e) в†ђв€’в€’в€’в€’в€’
−•
в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
•−
в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в†’
в€’6 в€’5 в€’4 в€’3 в€’2 в€’1
8
в€— e)
15
99
is simplified?
x2
в€љ
e) x7 7
b)
d) x
14. Solve:
12
13
14
99
What is the result when в€љ
3
8
12
5
в€— e) 4.4
17. What is the area of the triangle formed by the x-axis
and the lines y = 2x + 8 and y = в€’2x + 8?
a) 8
b)
в€’6 в€’5 в€’4 в€’3 в€’2 в€’1
15. A right triangle has an area of 6 cm2 . Its height is
1 cm less than twice its base. To the nearest tenth of
a centimetre, what is its height?
a) 2.2
14
90
8
83xв€’4
5
12
Express 0.155 as a rational number.
в€’6 в€’5 в€’4 в€’3 в€’2 в€’1
e) в†ђв€’в€’в€’в€’в€’в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в†’
в—¦в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в—¦в€’в€’в€’
в€’8
x
xв€’5
b) в†ђв€’в€’в€’в€’в€’в€’
в—¦в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в—¦в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в†’
в€’в€’в€’в€’в€’в€’в€’в†’
d) в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в—¦в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в—¦в€’
в€’8
в€— c)
−•
a) в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
−−−−−−−−−−−−−−−−−−−−−−−−−−•−
в€’в€’в€’в€’в€’в€’в†’
c) ←−−−−−−−•
−−−−−−−−−−−−−−−−−−−−−−−−•−
в€’в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в†’
в€’8
e) 8a + 25
x
10x
+ 2
x + 5 x в€’ 25
x
x(x + 5)
b) 2
a)
x+5
x в€’ 25
15x
d) 2
e) x2 + 5x
x в€’ 25
8
в€— b) в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в€’в€’
в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в—¦в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в—¦в€’в€’в€’в€’в€’в€’в€’в†’
в€’8
+ 75
c) 4a + 75
12. Which of the following shows the solution for
x2 в€’ 3x < 10?
a) в†ђв€’в€’в€’в€’в€’в€’в€’в€’
в€’в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’в—¦
в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в†’
в—¦в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в€’6
b) 8a
10. Rationalize the denominator: в€љ
11. Which of the following shows the solution for
n2 в€’ 2n < 24?
в€’8
4a2
Simplify:
в€— a)
8.
в€— e)
d) 1
в€љ
в€— b) 4 6 + 8
в€љ
4
( 6 + 2)
e) 17
в€љ
a) 8 6 + 8
в€љ
d) 4 6 в€’ 16
6.
17
90
is simplified?
x3
в€љ
4
c) x x3
x
When (5 + 2a)3 в€’ (5 в€’ 2a)3 is factored completely, one
of the factors will be:
в€— d)
x
6x
+ 2
x+3 x в€’9
x
x(x + 9)
b)
в€— a)
xв€’3
x2 в€’ 9
7x
d) 2
e) x2 в€’ 3x
x в€’9
a)
7.
в€— c) 3x2 + 16
Simplify:
18
100
2.
e) 128
в€— a) в€’2
83x
=
0
1
2
3
4
5
6
42xв€’5
b) в€’1
c) в€’ 12
d)
1
2
e) 2
16. A right triangle has an area of 8 cm2 . Its height is
1 cm more than twice its base. To the nearest tenth of
a centimetre, what is its height?
a) 1.8
b) 2.6
c) 4.5
в€— d) 6.2
e) 7.3
18. What is the area of the triangle formed by the x-axis
and the lines y = 3x + 6 and y = в€’3x + 6?
a) 9
в€— b) 12
c) 18
d) 24
e) 48
SMP rev. 3.0 (PDF) page 25. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BB
19. A worker finds a ball on the roof of a building as he
is doing some repairs. He tosses the ball up and off
the roof so that its height h, in metres, above the
ground is related to time t, in seconds, after it has
been tossed, by the function h = в€’t2 + 4t + 32. After
how many seconds will the ball return to the ground?
a) 1
b) 2
c) 4
в€— d) 8
e) 24
20. A young girl standing on a cliff is throwing stones up
into the air so that they land in the ocean below. The
height h, in metres, of each stone above the ocean is
related to the time t, in seconds, after it has been
thrown by the function h = в€’2t2 + 2t + 40. How many
seconds after it is thrown will a stone strike the ocean?
a) 1
6x в€’ 5y = в€’8
c)
4
87
в€— d)
1
3
a) в€’ 29
3
e) 2
23. If g(x) = 2x3 в€’ 3x + 5, find g(в€’2).
a) в€’53
b) в€’17
d) 8
e) 40
9x + 7y = 17
6x в€’ 5y = в€’8
9x + 7y = 17
b) в€’3
в€— c) 5
22. Solve the following system of equations for y:
21. Solve the following system of equations for x:
a) в€’ 29
3
b) 2
в€— c) в€’5
b) в€’3
c)
4
87
d)
1
3
в€— e) 2
24. If g(x) = 2x3 в€’ 3x + 5, find g(в€’3).
d) в€’1
в€— a) в€’40
e) 27
b) в€’22
c) 32
d) 40
e) 50
25. Which one of the following is the graph of y = |x в€’ 1|?
a)
b)
в€— d)
c)
CM1-085.PCX
CM1-089.PCX
CM1-093.PCX
e)
CM1-094.PCX
CM1-095.PCX
26. Which one of the following is the graph of y = |x в€’ 3|?
a)
b)
c)
CM1-086.PCX
CM1-090.PCX
в€— e)
d)
CM1-091.PCX
CM1-096.PCX
CM1-092.PCX
27. If y varies directly as x and inversely as t, then
which of the following equations is true? Let k be a
constant.
t
xy
ty
=k
b) y = k
c)
=k
в€— a)
x
x
t
d) xt = ky
e) y = kxt
28. Write an equation for m if m varies directly as d and
inversely as the cube of p. Let k be a constant.
kd
в€љ
a) m = kp3 d
b) m = kd 3 p
в€— c) m = 3
p
3
kd
kp
d) m = в€љ
e) m =
3 p
d
29. In a 120-volt circuit having a resistance of 12 ohms,
the power W in watts when a current I is flowing
through is given by W = 120I в€’ 12I 2 . What current
supplies the maximum wattage?
30. In a 120-volt circuit having a resistance of 12 ohms,
the power W in watts when a current I is flowing
through is given by W = 120I в€’ 10I 2 . What current
supplies the maximum wattage?
a) 3
31. If sin Оё =
of tan Оё?
a) в€’ 53
в€— b) 5
3
5
c) 10
d) 25
e) 200
and the cos Оё < 0, then what is the value
в€— b) в€’ 34
c)
3
4
d)
4
3
e)
5
3
33. Find side c in ABC if m A = 72 в—¦, m C = 50 в—¦,
a = 34. Answer to the nearest whole number.
в€— a) 27
b) 28
c) 30
d) 31
e) 35
в€— a) 6
32. If sin Оё =
of tan Оё?
a) в€’ 53
b) 12
3
5
c) 36
d) 360
e) 720
and the cos Оё > 0, then what is the value
b) в€’ 34
c)
3
4
в€— d)
4
3
e)
5
3
34. Find side b in ABC if m A = 72 в—¦, m C = 50 в—¦,
a = 34. Answer to the nearest whole number.
a) 27
b) 28
в€— c) 30
d) 31
e) 35
SMP rev. 3.0 (PDF) page 26. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BB
35. In triangle PQR, PQ = 5, PR = 8, and m QPR = 60 в—¦.
Find the area of the triangle.
в€љ
в€љ
20 3
a)
b) 10
в€— c) 10 3
3
в€љ
d) 20
e) 20 3
36. In triangle PQR, PQ = 4, PR = 6, and m QPR = 60 в—¦.
Find the area of the triangle.
в€љ
6
CM1-217.PCX
a) в€љ
c) 6
b) 4 3
3
в€љ
в€љ
в€— d) 6 3
e) 12 3
CM1-217.PCX
37. Wires of lengths 20 m and 30 m extend from the top of
a tower to the ground on the same side of the tower
as shown in the diagram. The shorter wire makes an
angle of 42 в—¦ with the ground. What angle do the
wires make with each other?
в—¦
в€— a) 15.5
d) 63.5 в—¦
в—¦
b) 26.5
e) 74.5 в—¦
c) 48.2
в—¦
38. A sail has sides of length 8 cm and 10 cm as shown in
the diagram. The longer of these two sides makes a
48 в—¦ angle with the base of the sail. At what angle (О±)
do the two sides meet?
a) 18.4 в—¦
d) 68.3 в—¦
в€— b) 20.3 в—¦
e) 88.1 в—¦
c) 45.9 в—¦
CM1-240.PCX
CM1-239.PCX
39. The tires on an automobile are 80 cm in diameter.
If the wheels turn 10 times per second, what is the
speed in centimetres per second of a point on the tire
tread? Give the answer to one decimal place.
a) 864.8 m/sec
b) 1294.4 m/sec
d) 2387.9 m/sec в€— e) 2513.3 m/sec
c) 2005.4 m/sec
41. Triangle ABC is a right triangle. DE is perpendicular
to AC and bisects AC. If AB = 6 and BC = 8, then
how long is DE ?
в€— a) 3.75
d) 4
b)
e)
20
3
25
3
c) 3
40. The tires on an automobile are 41 cm in diameter. If
the wheels turn 10 times per second, what is the speed
in metres per second of a point on the tire tread?
Give the answer to one decimal place.
a) 864.8 m/sec
d) 2005.4 m/sec
b) 1005.3 m/sec в€— c) 1288.1 m/sec
e) 2387.9 m/sec
42. Triangle ABC is a right triangle. DE is perpendicular
to AC and bisects AC. If AB = 10 and BC = 24, then
how long is DE ?
в€— b)
a) 12
d)
169
5
65
12
c)
156
15
e) 5
CM1-303.PCX
43. What is the measure of
в—¦
в€— a) 58
d) 122 в—¦
в—¦
b) 64
e) 126 в—¦
x?
c) 116
CM1-304.PCX
44. What is the measure of
в—¦
в—¦
a) 32
d) 83 в—¦
в—¦
b) 64
e) 97 в—¦
x?
в€— c) 65 в—¦
CM1-317.PCX
CM1-316.PCX
45. Determine the distance between the points (7, 5) and
(7, в€’3).
a) 6
b) 2
c) 7
в€— d) 8
e) 10
47. What is the equation of the asymptote of y = 3xв€’5 ?
a) x = в€’5
d) x = 0
в€— b) y = 0
e) x = 5
c) y = 5
46. Determine the distance between the points (5, в€’4) and
(5, 12).
a) 6
b) 7
c) 8
d) 10
в€— e) 16
48. What is the equation of the asymptote of y = 3xв€’4 ?
в€— a) y = 0
d) x = 0
b) y = 4
e) x = 4
c) x = в€’4
SMP rev. 3.0 (PDF) page 27. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BB
49. A tunnel is semi-elliptical in shape, with maximum
height of 5 m and a maximum width of 12 m.
Determine the height of the tunnel at point A which
is 3 m from the centre C. (Accurate to one decimal
place.)
a) 2.0 m
в€— c) 4.3 m
e) 4.9 m
b) 3.7 m
d) 4.6 m
50. A tunnel is semi-elliptical in shape, with maximum
height of 6 m and a maximum width of 14 m.
Determine the height of the tunnel at point A which
is 5 m from the centre C. (Accurate to one decimal
place.)
a) 2.0 m b) 3.1 m
c) 3.6 m в€— d) 4.2 m
e) 5.4 m
CM1-463.PCX
CM1-464.PCX
51. Which inequality represents the shaded area?
в€— a)
25x2
52. Which inequality represents the shaded region?
в€’ 9y 2
≥ 225
a) xy ≥ −4
в€’ 25y 2
≥ 225
c) xy = в€’4
b)
9x2
c)
25x2
в€’ 9y 2
≤ 225
e) y ≤ −
d) 9x2 − 25y 2 ≤ 225
∗ b) xy ≤ −4
1
d) y ≥ −
x
1
x
e) 25x2 + 9y 2 ≥ 225
CM1-471.PCX
CM1-470.PCX
53. A particular bacteria population on an athlete’s foot
doubles every 4 days. Determine an expression for the
number of bacteria N after t days, given that the
initial amount is 50 bacteria.
в€— a) N =
50(2)(t/4)
c) N =
50(2)(в€’t/4)
e) N =
50(2)(в€’t/2)
a) N = 500(9)t/9
в€— b) N = 500(2)t/9
b) N =
50(4)(t/2)
c) N = 500(9)t/2
d) N = 500(2)9t
d) N =
50(4)(в€’t/2)
e) N = 500(9)2t
55. If (x + 1) is a factor of the polynomial (x3 + kx2 + x + 6),
then what is the value of k ?
a) в€’8
в€— b) в€’4
c) 2
d) 4
e) 8
57. Find the sum, accurate to 2 decimal places, of the
nine terms of the geometric series having t1 = 15 and
r = 1.2.
в€— b) 311.98
e) 562.58
a) 247.49
d) 482.26
c) 389.38
59. Which equation best describes this graph?
a) f (x) =
в€’3x3
54. A particular bacteria population doubles every 9 days.
Determine an expression for the number of bacteria N
after t days, given an initial amount of 500 bacteria.
56. If (x + 3) is a factor of the polynomial
(x3 + 3x2 + kx в€’ 12), then what is the value of k ?
a) в€’14
b) в€’5
в€— c) в€’4
d) в€’1
58. Find the sum, accurate to 1 decimal places, of the
nine terms of the geometric series having t1 = 17 and
r = 1.7.
a) 879.3
d) 4869.8
b) 1669.8
e) 4871.7
в€— c) 2855.7
60. Which equation best describes this graph?
a) f (x) = в€’3x3 + 12x + 1
+ 12x + 1
b) f (x) = в€’x3 + 3x + 1
b) f (x) = в€’x3 + 3x + 1
c) f (x) = в€’3x3 в€’ 12x + 1
c) f (x) = в€’3x3 в€’ 12x + 1
в€— d) f (x) = в€’x3 + 1
d) f (x) = в€’x3 + 1
e) f (x) = в€’x3 + 3x2 + 1
в€— e) f (x) = в€’x3 + 3x2 + 1
CM1-543.PCX
61. The position of a particle is given by the function
s(t) = 100 в€’ 15t в€’ 4.9t2 . Find the acceleration of the
particle at 8 seconds.
a) 9.8
b) 4.9
e) 5
c) 0
d) в€’4.9 в€— e) в€’9.8
CM1-544.PCX
62. The position of a particle is given by the function
s(t) = 100 в€’ 15t в€’ 4.9t2 . Find the acceleration of the
particle at 4 seconds.
в€— a) в€’9.8
b) в€’4.9
c) 0
d) 4.9
e) 9.8
SMP rev. 3.0 (PDF) page 28. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BC
These items are drawn from the North Carolina Mathematics Standard Course of Study (NC1) module. The 1749
items in this module first appeared in the 1993 Teacher Handbook, published by the North Carolina Department of
Public Instruction. They illustrate objectives for grades 6 8, plus algebra, geometry, advanced math and calculus.
1.
The prime factorization of 42 is 2 Г— 3 Г— 7 and of 35 is
5 Г— 7. What are the greatest common factor and the
least common multiple of 42 and 35? 7, 210
2.
Describe the rule you would use to continue the
pattern. y = 3x + 2
1
2
3
5
8
11
4
The median would be best because $97,980 is unusually high compared
to the other data.
17
12. Use a calculator to find the missing sides of these
right triangles. ≈ 7.14 m, 5 m
NC1-002.TBL
3.
Predict what will happen to the volume of a
rectangular prism when the dimensions of the base
and height are doubled. volume will be multiplied by 8
4.
The local newspaper surveyed students in the eighth
grade and reported that 257 of the students at Town
Middle School had after-school jobs. Why or why not
do you think this statement may be biased?
[answers will vary]
5.
Complete
Original
Price
a. $12.00
b. $36.00
c. $45.00
11. If you were given the following set of data related to
personal income, which would be a better description
of the data, the mean or the median? Explain your
answer.
$20,560 $21,000 $18,345 $27,900 $97,980 $14,300
$25,456 $36,750 $26,456 $24,560 $23,450 $24,500
$23,680 $23,000 $24,300
the table.
$9.60, $9, $27, $22.50, $22.50
Sale
% Off Discount Price
20%
$2.40
?
25%
?
?
50%
?
?
NC1-003.TBL
NC1-013.PCX
13. Which properties are illustrated in these two
examples?
a)
b)
[+W=W+[
([ + W) + _ = [ + (W + _)
a. commutative; b. associative
14. A grain is equal to 0.0648 grams. If an aspirin weighs
5 grains, how many grams do 50 aspirins weigh?
16.2 g
6.
What is the number that A represents on the number
line? в€’2.25 or в€’2 1
15. Find the sum of
4
A
в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
•−−−−−−−−−−−−−−−−−−−−→
в€’3
7.
в€’2
в€’1
Give examples of ways in which knowledge of
geometry helps a carpenter. [answers will vary]
8.
Use your calculator to help you find the distance a
car travels when it is driven at the rate of 86 km/h
for 3.25 hours. 279.5 km
9.
Would two thousand tennis balls completely cover
your classroom floor? How could you decide? Record
you strategy. [answers will vary]
в€љ
10. Find a calculator valueв€љfor 2. Is the calculator
value exactly equal to 2 ? Explain.
1.4142 . . . ; no, [explanations will vary]
1
2
+
1 2
2
+
1 3
2
+ В·В·В· +
1 10
2
1023
1024
16. Estimate the product of the following two factors by
rounding each factor to the nearest whole number.
127.36 Г— 80.9
в€— a) 10,287
b) 10,160
c) 10,319
d) 10,368
17. Approximate x to the
nearest tenth. 13.9
NC1-019.PCX
18. Create a problem for the following equation.
12x + 170 = 770
[answers will vary]
SMP rev. 3.0 (PDF) page 29. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BC
19. Which of the following has the smallest value?
a) 32 в€’ 23
b) 33 в€’ 42
c) (3 в€’ 2)5 в€— d) 42 в€’ 24
20. Give an example which shows that division is not
commutative. [answers will vary]
b) {в€’9}
c) {7}
d) {в€’7}
22. The formula for the perimeter of a rectangle of
length and width w is P = 2( + w). A rectangle is
27 feet long and 16 feet wide. What is its perimeter?
a) 43 ft
в€’2x2 в€’ 2x + 1
30. Divide: (3x3 в€’ 6x2 в€’ 12x) Г· (3x)
в€— a) x2 в€’ 2x в€’ 4
b) x3 в€’ 2x2 в€’ 4x
c) x2 в€’ 2x
d) x3 + 2x в€’ 4
31. Use a graphing calculator to solve 1.4x2 в€’ 0.7x = 0.2.
21. Solve: 7x в€’ 4x в€’ 3 = 24
в€— a) {9}
29. Simplify: (x2 в€’ 9x + 8) в€’ (3x2 в€’ 7x + 7)
в€— c) 86 ft
b) 70 ft
d) 432 ft
23. Video City reduced the price of a video tape from
$6.00 to $4.50. Explain how to use a calculator to
find the percent of decrease. [answers will vary]
{в€’0.2, 0.7}
32. Use the formula D = rt to find the distance (D),
when r = 55 miles per hour and t = 2 hours.
a) 57 mi
в€— c) 110 mi
b) 100 mi
d) 27.5 mi
33. Solve: |x в€’ 5| = 4
в€— a) both 1 and 9
c) 1 only
b) 9 only
d) no solution
34. Which ordered pair lies on the line 2x в€’ 5y = в€’4?
24. In the figure, AB = CD. If segment AC has
length 10, how long is segment BD ? 10
A
B
C
D
a) (в€’3, 2)
x + 2y = 5
3x в€’ 2y = в€’1
NC1-005.FIG
в€— a) (1, 2)
25. Simplify: 2в€’3
b) в€’6
в€— c)
1
8
d) 8
26. The perimeter of a square can be found by the
formula P = 4s. Rewrite this formula to solve for the
length of a side (s). S = P
4
27. Which graph best represents the relationship between
the cost of pizzas of various diameters?
в€— a)
d) (0, в€’2)
35. Solve by the addition or subtraction method:
•−−−−−−−−−−−−−
•−−−−−−−
•−−−−−−−−−−−−•
в†ђв€’в€’в€’в€’в€’
в€’в€’в€’в€’в€’в†’
в†ђв€’в€’в€’в€’в€’
в€’в€’в€’в€’в€’в†’
a) в€’8
в€— c) ( 21 , 1)
b) (3, в€’2)
b) (в€’1, 3)
d) (2, в€’ 21 )
c) (3, 1)
36. The sum of the digits of a two-digit number is 9. If
the digits are reversed the new number is 27 more
than the original number. Find the original number.
36
37. Evaluate to the nearest whole number: A(1 + r)x for
A = 120, r = 0.06, and x = 20.
a) 103
в€— c) 385
b) 525
d) 2100
b)
38. If the outside diameter of a pipe is 4.76 cm and the
inside diameter is 3.82 cm, how thick is the pipe?
0.47 cm
39. Find the pattern in the following numbers and
generate the next three numbers in the sequence:
NC1-060.PCX
NC1-061.PCX
c)
1, 1, 2, 3, 5, 8, 13,
,
,
.
21, 34, 55
d)
40. What period is shown in the graph?
NC1-063.PCX
NC1-062.PCX
28. Multiply:
в€љ
5в€’2
180 в—¦
2
в€љ
9в€’4 5
NC1-111.PCX
SMP rev. 3.0 (PDF) page 30. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BC
в€’в€’в€’
41. The coordinates of the midpoint of AB are:
a) (3, 2)
в€— c) (7, 4)
49. Let A =
b) (2, 3)
d) (5, 6)
a) 35
b) 45
3
0
в€’2
7
6 2
в€’3 4
and B =
1
. Find
в€’1
A + B.
ABC , what is the measure of
a)
6
в€’12
6
0
в€’2
в€’7
b)
1
0
0
0
2
1
c)
в€’5
7
1
в€’4
в€’3
8
в€— d)
7
1
5
4
в€’1
6
50. Solve for x:
NC1-126.PCX
в€’в€’в†’
42. If BD bisects
1
4
ABC ?
c) 60 в€— d) 70
2x в€’ 9 x
5
+ =
xв€’7
2
xв€’7
в€’4
51. The height of a ball is given by h = в€’4.9t2 + 10t + 1
where t is measured in seconds. How high is the ball
in one second? What is the maximum height of the
ball? At what time does it hit the ground?
h = 6.1 at t = 1; Hmax ≈ 6.10; t = 2.14
4
52. What is the value of:
(n + 2)
n=1
43. If the coordinates of quadrilateral ABCD are
A(в€’2, 1), B(в€’3, 4), C (9, 8), and D(10, 5), what type
of quadrilateral is ABCD ?
a) Trapezoid
c) Square
в€— b) 18
c) 12
в€љ
53. Suppose f (x) = x + 1 and g(x) =
a) 10
NC1-138.PCX
в€љ
в€љ x+1
x+1в€’2
equation of g в—¦ f .
d) 6
x
. Find the
xв€’2
54. Two dice are tossed. Classify the following pairs of
events as independent, mutually exclusive, or neither.
b) Rhombus
в€— d) Rectangle
a) One die shows 2. Another die shows 3.
44. Prove that ABC is
isosceles. [proof]
b) One die shows 2. The same die does not show 3.
a. independent; b. mutually exclusive
55. Find the domain of f (x) =
number.
a) x > a
∗ b) x ≥ a
x в€’ a, where a is a real
d) x ≤ a
c) x < a
56. Find lim f (x), if it exists.
x→3
NC1-181.PCX
1
_
в€’в€’в€’
45. RT is a diameter of circle O; mRS = 128.
Find m R.
a) 64
b) 52
в€— c) 26
d) 128
NC1-254.PCX
57. Find the derivative of f (x) = ln(x).
1
x
58. If f (x) = x3 + x and h is the inverse of f , find h (2).
NC1-192.PCX
46. Find the area of the circle formed when a plane
passes 6 cm from the center of a sphere with radius
10 cm. Round your answer to the nearest hundredth.
a)
1
13
48. If f (x) = 2x в€’ x, then what is the value of f (3)?
5
1
4
c) 1
d) 4
59. A man six feet tall walks at the rate of 5 ft/s toward
a streetlight that is 16 ft above the ground. At what
rate is the tip of his shadow moving? 8 ft/sec
201.06
47. Find the equation of a line with y-intercept 3 that is
parallel to the line 2x + 3y = 6. 2x + 3y = 9
в€— b)
60. Find
в€љ
4 в€’ 2t dt.
в€— a) в€’ 13 (4 в€’ 2t)3/2 + C
c)
4
3/2
3 (4 в€’ 2t)
+C
b)
d)
2
3/2 + C
3 (4 в€’ 2t)
в€’(4 в€’ 2t)в€’1/2 + C
SMP rev. 3.0 (PDF) page 31. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BD
These items are drawn from the North Carolina Elementary Math Testlets (NC2) module. The module contains
1316 multiple-choice, free-response and open-ended questions. These first appeared in the Item Bank Testlets for
grades 3 5, published in 1994 by the North Carolina Department of Public Instruction.
1.
Of the numbers in the box, which is the second
largest?
a) 645
в€— c) 701
7.
Which addition problem is shown in the picture?
b) 699
d) 717
+
NC2-009.PCX
2.
NC2-015.AUX
What is another way to name the shaded part of this
picture?
a)
2
2
в€— b)
2
4
c)
4
4
d)
4
2
в€— a) 123 + 54
8.
Solve:
9.
3.
c) 123 + 50
d) 102 + 53
b) 102
c) 108
d) 188
567
в€’ 469
в€— a) 98
1
2
b) 120 + 54
Which figure has the most vertices?
в€— b)
a)
These objects follow a pattern.
_W__WW___WWW
If the same pattern was used with [ and =, what
NC2-260.PCX
NC2-261.PCX
c)
d)
would the pattern look like?
в€— a)
c)
4.
[ =[ [ ==
[ =[ [ =[
Which of these is the best estimate for the length of
a school classroom?
в€— b) 10 yards
d) 100 yards
a) 1 yard
c) 30 yards
5.
b) 75
a) 6 Г— (12 в€’ 7) = 30
c) 6 Г— (1 + 7) = 48
What is located at point (3, 2)?
b) book
d) ball
10. Each floor of an eight-story building has
10 apartments. How many apartments altogether
does the building have?
c) 40
d) 18
11. It is said that 1 human year is equal to 7 years for a
dog. Pat got a newborn puppy named Queenie on
his 6th birthday. Which equation shows how to find
out how old Queenie will be in dog years when Pat is
12 years old?
one dollar and sixty-seven cents
sixteen dimes and seven nickels
one dollar and sixty cents
sixteen dimes and sixty-seven pennies
в€— a) pencil
c) apple
NC2-263.PCX
NC2-262.PCX
в€— a) 80
What is another way of writing $1.67?
в€— a)
b)
c)
d)
6.
[ =[ =[ =
d) [ [ ==[ =
b)
в€— b) (12 в€’ 6) Г— 7 = 42
d) 12 Г— (12 в€’ 7) = 60
12. Which of these numbers would replace the
make this equation correct?
6
5
Z
to
97.01 Г· Z = 9.701
4
a) 0.1
3
b) 0
c) 1
в€— d) 10
2
13. What is the median of this set of numbers?
1
0
2, 4, 6, 8
0
1
2
3
4
5
6
a) 2
b) 4
в€— c) 5
d) 7
NC2-022.FIG
SMP rev. 3.0 (PDF) page 32. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BD
14. How much would 9 tickets cost?
a) $22.00
в€— c) $37.00
b) $25.00
d) $45.00
20. What is the area of this figure?
SAVE MONEY!
The first 5 tickets
will cost you
$5.00 each.
Every ticket
that you but after that
will cost you
$3.00.
NC2-047.FIG
15. Which of the following is the best way to estimate
50
12 ?
в€— a)
48
12
b)
52
12
c)
50
5
d)
55
15
16. About how much will Marco pay for these items?
a) 45 cm
b) 90 cm
5 cm
40 cm
в€— c) 200 cm2
d) 400 cm2
21. Simplify: (22 Г— 4) + (22 Г— 7) + (22 Г— 11)
в€— b) 22(4 + 7 + 11)
d) (4 + 7 + 11) + 22
a) 66(4 + 7 + 11)
c) 22 Г— 4 Г— 7 Г— 11
22. While studying endangered animals in Africa, five
researchers counted a total of 353 elephants. Which
of the following is the best estimate of the average
number of elephants each researcher counted?
a) 80
в€— c) 70
b) 75
d) 65
23. What are the chances that you will spin an odd
number?
a)
1
8
b)
3
8
в€— c)
5
8
d)
9
8
NC2-755.PCX
a) $12.00
в€— b) $10.00
c) $8.00
d) $7.50
17. This figure is an example of which of the following?
a)
b)
в€— c)
d)
a
a
a
a
hexagon
rectangle
parallelogram
rhombus
NC2-602.PCX
24. One summer day Jasmine planned to bike to a park
9
10 of a mile from her home. She stopped at her
3
of a
friend Marie’s house after she had ridden 10
mile. Marie asked her to stay and play basketball.
How much shorter was the trip to Marie’s house than
the trip to the park would have been?
a)
c)
18. The movie theater in Brad’s town is selling discount
movie passes in groups of 3. Brad could buy discount
passes in all of the following quantities except which
one?
a) 3
в€— b) 5
c) 12
d) 21
Day 1
Day 2
Day3
Ship #1
52
104
208
Ship #2
104
208
?
в€— b)
of a mile
d)
6
10
1
10
of a mile
of a mile
25. Draw a time line that shows how you spend a day,
from the time you get up to the time you go to bed.
Include at least six things you do during the time.
в€— c) 416
26. Complete the following pattern.
Make your own geometric pattern. Then write a
sentence explaining your pattern. [answers will vary]
27. Make a set of ordered pairs by using the rule the
sum of the numbers is 9. [answers will vary]
NC2-093.TBL
b) 312
of a mile
[answers will vary]
19. Two spaceships are traveling through space. The
chart shows the total millions of miles each ship
traveled in 3 days. How many millions of miles did
Ship #2 travel by Day 3?
a) 104
9
10
3
10
d) 520
28. Draw two different rectangles each having a perimeter
of 28 cm. What is the area of each? Explain your
answer. [answers will vary]
SMP rev. 3.0 (PDF) page 33. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BE
These items are drawn from the North Carolina Algebra I (NC3) module. The module contains 2126 multiple-choice
questions, which are all original and written specifically for the 1992 and 1998 Algebra I objectives for the state
of North Carolina. This module will prove useful to anyone teaching algebra or wanting to create a modern,
performance-based assessment at the junior or senior high level.
1.
Evaluate: в€’6g + 3h when g = 3 and h = в€’3
a) в€’54
3.
в€— b) в€’27
b) 20 N
c) 90 N
a) 0
4.
d) 120 N в€— e) 180 N
c) 2d
8.
9.
e) 17
b) 15 m/s
e) 300 m/s
c) 30 m/s
Simplify: ( в€’ m) в€’ (m в€’ )
b) 2
c) 2m
в€— e) 2 в€’ 2m
Give a formula for the number of dots in the nth
figure in this sequence.
•
• •
•
• •
•
•
• •
•
• •
•
•
•
•
•
•
• •
•
• •
•
•
•
•
NC3-002.FIG
NC3-001.FIG
d) n2 в€’ 4
d) 14
The formula for the speed of a wave is v = fО», where
v is speed in meters per second, f is frequency in
hertz, and О» is wavelength in meters. If a wave has a
frequency of 30 hertz and a wavelength of 5 meters,
what would its speed be?
d) в€’2m
Give a formula for the number of dots in the nth
figure in this sequence.
••••
••
•
•
•
••
•
• •
•••
••
••
•• •••
•• •••••
•• •••
•
•
b)
c) 5
a) 0
e) 2c в€’ 2d
a) 4n в€’ 2
b) 1
a) 6 m/s
в€— d) 150 m/s
6.
b) 2c
Evaluate: в€’9r в€’ 4s when r = 1 and s = в€’2
в€— a) в€’1
e) 18
Simplify: (c в€’ d) в€’ (c + d)
в€— d) в€’2d
7.
d) 9
The formula for force is F = ma, where F is force in
newtons, m is mass in kilograms, and a is acceleration
in meters per squared second. What would be the
force of an object with mass of 60 kilograms and
acceleration of 3 meters per squared second?
a) 2 N
5.
c) 3
2.
1
2 (n + 1)
c) 2(n в€’ 1)
d) 4(n в€’ 1)
в€— e) 4n
Write the product of 7,240,000 and 2,320,000 in
scientific notation?
a) 1.67968 Г— 10в€’11
b) 16.7968 Г— 10в€’12
в€— c) 1.67968 Г— 1013
в€— a) 4n в€’ 3
d) 16.7968 Г— 1012
b) n2 в€’ 2n
e)
c) 2n + 1
1
2 n(n в€’ 1)
10. Write the product of 25,700,000 and 8,250,000 in
scientific notation?
в€— a) 2.12025 Г— 1014
c) 2.12025 Г— 1042
b) 21.2025 Г— 1013
d) 2.12025 Г— 10в€’12
e) 21.2025 Г— 10в€’13
e) 16.7968 Г— 1036
11. Which of the following is an irrational number?
в€љ
в€љ
в€љ
в€љ
в€љ
a) 4
b) 16 в€— c) 30
d) в€’ 9
e) в€’ 25
12. Which of the following is an irrational number?
в€љ
в€љ
в€љ
a) 36
b) 49
c) 81
в€љ
в€љ
в€— d) в€’ 98
e) в€’ 121
в€љ
в€љ
в€љ
13. Simplify: 6 5 в€’ 80 в€’ 3 20
в€љ
в€љ
a) в€’22 5
в€— b) в€’4 5
в€љ
в€љ
d) в€’4 15
e) 16 15
в€љ
в€љ
в€љ
14. Simplify: 3 8 в€’ 2 2 в€’ 4 50
в€љ
в€љ
a) в€’16 8
b) в€’12 8
в€љ
в€љ
в€— d) в€’16 2
e) в€’12 2
в€љ
c) 16 5
16. Given the formula A = 2ПЂr(r + h), solve for h.
15. Solve the formula E = I(R + r) for r.
a) r = EIR
d) r =
Eв€’R
I
b) r = EI в€’ R
e) r =
ER
I
в€— c) r =
в€љ
c) в€’90 2
E в€’ IR
I
A в€’ 2ПЂr2
2ПЂr
c) h = A(2ПЂr2 ) в€’ r
e) h = A(2ПЂ)
в€— a) h =
Aв€’r
2ПЂr
d) h = A(2ПЂr) в€’ r
b) h =
SMP rev. 3.0 (PDF) page 34. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BE
17. If the m D = 3x в€’ 8 and m L = 2x + 17, find the
value of x that would make D в€ј
= L.
a) 3
b) 5
c) 9
18. If m B = 4x в€’ 18 and m C = 9x в€’ 28, find the value
of x such that B в€ј
= C.
в€— e) 25
d) 16
в€— a) 2
в€’в€’в€’
19. Using the given figure, determine the length of PR if
в€’в€’в€’
the length of QS is 13.
Q
a) 3 units
в€— d) 17 units
R
b) 7 units
e) 20 units
S
E
b) 3 units
в€— e) 7 units
H
c) 5 units
22. This table gives the distances from Charlotte to
several cities and the costs of driving to those cities.
Name the independent and dependent quantities
respectively.
Latitude
Boston, MA
841 mi
$200.92
San Francisco, CA
2742 mi
$429.04
40.43 N
New York, NY
636 mi
$176.32
45.0 в—¦
43.39 в—¦ N
Cheyenne, WY
1624 mi
$294.88
75.6 в—¦
25.46 в—¦ N
Houston, TX
1042 mi
$225.04
Miami, FL
721 mi
$186.52
60.0
68.0
в—¦
New York, NY
54.5
в—¦
Portland, ME
Miami, FL
Jacksonville, FL
G
Cost
в—¦
Charlotte, NC
e) 36
Distance
47.3
в—¦
Boston, MA
F
a) 2 units
d) 6 units
c) 10 units
Avg. Temp.
d) 25
в†ђв€’в€’в€’3в€’в€’в€’в†’
в†ђв€’2в€’в†’
в†ђв€’
•−−−−−−−−−−−−
•−−−−−−−−−−−−−−−−−−−−−
•−−−−−−−−
•→
21. This table gives the average temperatures and
latitudes for several cities. Name the independent and
dependent quantities respectively.
City
c) 12
в€’в€’в€’
20. Using the given figure, determine the length of FH if
в€’в€’в€’
the length of EG is 8.
в†ђв€’в€’в€’в€’7в€’в€’в€’в€’в†’
в†ђ
в€’3в€’
в†’
в†ђв€’
•−−−−−−−−−−−−−−
•−−−−−−−−−−−−−−−−−−−−−
•−−−−−−
•→
P
b) 3
City
42.39 в—¦ N
в—¦
в—¦
в—¦
35.14 N
30.20 N
NC3-007.TBL
NC3-008.TBL
a) Temperature, Latitude b) Latitude, City
c) Temperature, City
в€— d) Latitude, Temperature
e) City, Temperature
в€— a) Distance, Cost
c) Cost, City
e) Cost, Distance
b) City, Distance
d) Distance, City
23. Which data appear to be linear?
a)
в€— c)
b)
NC3-239.PCX
NC3-240.PCX
d)
NC3-241.PCX
e)
NC3-242.PCX
NC3-243.PCX
24. Which data appear to be linear?
a)
b)
NC3-244.PCX
c)
NC3-245.PCX
25. Which ordered pair is a solution of y = 3x в€’ 2?
a) (в€’3, в€’2)
d) (0, 3)
b) (в€’2, 0)
в€— e) (2, 4)
c) (в€’1, 5)
в€— e)
d)
NC3-246.PCX
NC3-247.PCX
NC3-248.PCX
26. Which ordered pair is a solution of y = 2x в€’ 1?
a) (в€’3, в€’1)
в€— d) (3, 5)
b) (в€’9, в€’4)
e) (5, 6)
c) (3, 2)
SMP rev. 3.0 (PDF) page 35. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BE
27. Which of the following graphs represents y < 3x в€’ 1?
в€— a)
b)
SMP-001.PCX
c)
SMP-002.PCX
d)
e)
SMP-003.PCX
SMP-004.PCX
SMP-005.PCX
28. Which of the following graphs represents y > 4x в€’ 2?
a)
в€— c)
b)
SMP-006.PCX
SMP-007.PCX
d)
SMP-008.PCX
в€— c) (3, 5)
b) (1, 7)
e) (10, в€’2)
31. The sum of the digits of a two-digit number is 6. If
the digits are reversed, the value of the new number is
six less than twice the value of the original number.
What is the original number?
a) 15
в€— b) 24
c) 33
d) 42
e) 51
33. Factor completely: 18d4 в€’ 24d3
в€— a) 6d3 (3d в€’ 4)
b) 6d3 (12d в€’ 18)
d) 12d3 (6d в€’ 2)
c) 6(3d4 в€’ 4d3 )
35. Solve: k 2 в€’ 7k в€’ 8 = 0
b) {в€’2, 4}
e) {в€’8, 1}
b) (в€’3, в€’2)
e) (5, 2)
a) (в€’5, 0)
в€— d) (в€’1, в€’4)
c) {в€’4, 2}
32. The sum of the digits of a two-digit number is 11. If
the digits are reversed, the value of the new number
is nine more than the value of the original number.
What is the original number?
a) 38
b) 47
в€— c) 56
b) 8f 3 (2f в€’ 6)
d) 16f 3 (f в€’ 32)
e) 16(f 4 в€’ 3f 3 )
a) {в€’4, 1}
в€— d) {в€’1, 4}
b) {в€’4, 0}
e) {0, 1}
39. Solve for x and y.
a) (в€’5, в€’6)
d) (0, 4)
e) 74
в€— c) 16f 3 (f в€’ 3)
c) {в€’2, 2}
38. The graph shown illustrates what type of function?
linear
quadratic
exponential
absolute value
cubic
SMP-011.PCX
=
d) 65
a) 4f 3 (4f в€’ 12)
в€— a)
b)
c)
d)
e)
linear
quadratic
exponential
absolute value
cubic
8
4x + 3y
c) (в€’2, в€’5)
36. Solve: k 2 в€’ 3k в€’ 4 = 0
37. The graph shown illustrates what type of function?
a)
b)
c)
в€— d)
e)
SMP-010.PCX
34. Factor completely: 16f 4 в€’ 48f 3
e) 2d3 (9d в€’ 12)
в€— a) {в€’1, 8}
d) {в€’8, 0}
SMP-009.PCX
30. Solve: x + y = в€’5
xв€’y =3
29. Solve: x + y = 8
x в€’ y = в€’2
a) (в€’3, в€’5)
d) (4, 4)
e)
SMP-012.PCX
40. Solve for x and y.
2x в€’ 3y
в€’2
b) (в€’3, в€’ 12 )
в€— e) (1, в€’2)
в€’5
x в€’ 2y
c) (в€’1, в€’2)
a) ( 23 , в€’1)
в€— d) (2, в€’3)
=
2x + 3y
8
b) (3, в€’1)
e) (1, 3)
c) (1, 2)
SMP rev. 3.0 (PDF) page 36. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BF
These items are drawn from EducAide’s North Carolina Secondary Math Testlets (NC5) module. The module
contains 1713 multiple-choice, free-response and open-ended questions. These first appeared in the Item Bank
Testlets for grades 6 8 and Algebra I published in 1994 by the North Carolina Department of Public Instruction.
1.
Which figures show more than 60% shaded?
в€— a)
b)
c)
d)
1
1
3
2
and
and
and
and
7.
3
2
4
3
1
What is the volume of the rectangular solid?
a) 14 in.3
b) 48 in.3
c) 52 in.3
в€— d) 96 in.3
2
NC5-115.PCX
8.
3
How much more did the Japanese save in 1980 than
in 1990?
4
2.
What is the prime factorization of 36?
a) 2 Г— 18
b) 3 Г— 6 Г— 2
c) 2 Г— 2 Г— 2 Г— 3 Г— 3
3.
в€— d) 2 Г— 2 Г— 3 Г— 3
The picture given shows a three-dimensional figure.
How many faces does the figure have?
a) 3
b) 4
в€— c) 5
d) 6
NC5-132.PCX
в€— a) 3.6%
NC5-017.PCX
4.
5.
Which of these is an example of translation?
a)
b)
c)
в€— d)
1
2
3
4
5
6
Height of Geyser 50 30 80 60 110 ?
in feet
NC5-007.TBL
Based on the pattern, what is the height of the
geyser on the sixth hour?
a) 70 ft
6.
b) 80 ft
в€— c) 90 ft
d) 140 ft
c) 9.8%
d) 13.5%
Twenty-six out of 50 teachers drive their cars to
school. About what percent of these teachers drive
to school?
a) 10%
A geyser at a national park shoots water into the air
every hour. The height of the geyser follows this
pattern every 6 hours:
Hour
9.
b) 7.2%
b) 25%
10. If 100% of
is
в€— c) 50%
d) 75%
is
and 50% of
, then what is 25% of
в€— a)
b)
c)
d)
?
11. Triangles ABC and ADC are congruent. The length
of segment AB is equal to the length of which other
segment?
в€’в€’в€’
в€’в€’в€’
a) BD
b) AC
в€’в€’в€’
в€’в€’в€’
в€— c) AD
d) CD
Which part of the following problem should be
worked first?
7 Г— (2 + 1) + 4 = 25
a) 7 Г— 2
b) 7 Г— 1
в€— c) 2 + 1
d) 1 + 4
NC5-157.PCX
SMP rev. 3.0 (PDF) page 37. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BF
20. The circumference of a circle is C = ПЂd or C = 2ПЂr.
What is the circumference of a circle with a radius
of 4?
12. If you input 16, what is the output?
Input
2
4
6
8
10
Output
3
7
11
15
19
a) 4
NC5-032.TBL
a) 21
b) 25
13. What is the algebraic expression of this statement?
Lisa worked two more than twice as many hours
as Robert.
2n
a) 2(n + 2) b) 2n в€’ 2
c)
в€— d) 2n + 2
2
14. The volume of a cube is 381 ft3 . What would be the
volume of a pyramid with the same base and height?
a) 42.33 ft3
c) Marissa в€— d) Clair
b) Robert
b) centimeter
d) kilometer
22. Cedric has a bag full of quarters, dimes, and nickels.
How many ways can he make 55/
c using quarters,
dimes, and/or nickels?
a) 1
b) 4
в€— b) 0
a) 24
d) 381.00 ft3
15. Lisa, Robert, Marissa, and Clair were all late for
math class today, but each arrived separately.
Marissa arrived after Clair and before Lisa. When
Lisa arrived, Robert was not there yet. Who got to
class rst?
a) Lisa
a) millimeter
в€— c) meter
в€— d) 11
c) 7
23. Evaluate: 2xy + yz when x = 2, y = в€’3, and z = в€’4
в€— b) 127.00 ft3
c) 254.00 ft3
в€— d) 8ПЂ
c) 8
21. Chris wants to measure the size of her kitchen.
Which of the following would be the most appropriate
unit of measure to use?
в€— d) 31
c) 27
b) 4ПЂ
c) в€’12
d) в€’24
24. Use A = s2 to find the area (A) of a square when the
length of a side (s) is 8 cm.
в€— a) 64 cm2
b) 32 cm2
c) 16 cm2
d) 10 cm2
25. Which is the graph of y = x + 1?
b)
a)
16. A chemist mixed 2 oz of solution x and 2 oz of
solution y in a beaker. He then added 6 oz of
solution z. What percentage of the solution was
composed of solution y ?
в€— b) 20%
a) 2%
c) 40%
d) 60%
SMP-013.PCX
2
5
17. Which point is equal to
A
B
?
в€— d)
c)
C
SMP-014.PCX
D
•−−−−−−−−−−
•−−−
•−−−−−−−−−•−−−−−−−−−−−−−−→
в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в€’5
в€’4
a) A
в€’3
в€’2
в€’1
b) B
0
1
2
в€— c) C
3
4
5
d) D
18. What is x ?
a) 7 inches
в€— c) 35 inches
b) 12 inches
d) 49 inches
SMP-015.PCX
26. Which ordered pair is a solution of 3x в€’ 2y в€’ 5 = 0?
в€— a) (3, 2)
c) (в€’3, в€’2)
NC5-257.PCX
19. A small rug measures 2 feet by 5 feet. A large rug
is 6 feet by 10 feet. How much more area does the
large rug cover?
a)
9 ft2
b)
10 ft2
в€— c)
SMP-016.PCX
50 ft2
d)
60 ft2
b) (1, 1)
d) (в€’5, 5)
27. Find the equation of the line which passes through
the point (в€’2, 1) and has slope в€’ 34 .
a) 3x + 4y = 10
c) 3x + 4y = в€’5
в€— b) 3x + 4y = в€’2
d) 3x + 4y = в€’11
28. Solve: c2 + 3c в€’ 10 = 0
a) {в€’2, 5}
b) {0, 2}
c) {0, 5}
в€— d) {2, в€’5}
SMP rev. 3.0 (PDF) page 38. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BG
These items are drawn from the New York Regents Math (NY1) module. The module includes more than 4,400
questions, which are taken from all Regents Exams (Course I III) since 1986. The module is especially useful
because it is organized by topic and question type (multiple-choice, short-answer, multiple-step). Also, it includes
many topics which are often missing from textbooks, such as frequency tables and histograms, Boolean logic and
tables, probability and combinatorics, and transformations.
1.
If y varies directly as x and y = 32 when x = 4, find
the value of y when x = 5. 40
2.
Solve for x: 2x в€’ 0.3 = 1.7
3.
Express (2x в€’ 3)(x + 5) as a trinomial.
4.
In the accompanying
figure, the measure of
angle AOB is 50. Find
the measure of inscribed
angle ACB. 25
1
10. If a в€— b = a + ba , find 2 в€— 3.
11
11. How many different 6-letter arrangements can be
formed from the letters in the word CANADA ?
120
2x2 в€’ 7x в€’ 15
12. Find the value of O О±(I О± L) in the system defined.
NY1-503.PCX
5.
6.
О±
F
O
I
L
F
O
I
L
I
L
F
O
L
F
O
I
F
O
I
L
O
I
L
F
I
The radius of a circle is 7. What is the area of the
circle in terms of ПЂ? 49ПЂ
13. If f (x) = x2 + 3x в€’ 5, find the value of f (3).
в†ђв†’
In the accompanying diagram, parallel lines AB
в†ђв†’
в†ђв†’
and CD intersect transversal GH at points E
and F , respectively. If m AEG = 4x в€’ 15 and
m CFE = 2x + 7, find the value of x. 11
14. If 100.8338 = 6.82, find the value of 102.8338 .
13
682
15. The rate at which a man travels from City A to
City B varies inversely as the time it takes to make
the trip. If the man can make the trip in 3 12 hours
at 60 kilometers per hour, how many kilometers per
hour must he travel to make the trip in 3 hours? 70
16. In a circle of radius 9, find the number of radians in
a central angle that intercepts an arc of 18. 2
NY1-655.PCX
7.
Let p represent the statement I will win, and let
q represent the statement I practice. Write in
symbolic form: If I do not practice, then I will not
win. в€јq в†’ в€јp
8.
A 20-foot ladder is leaning
against a wall. The foot
of the ladder makes an
angle of 58 в—¦ with the
ground. Find, to the
nearest foot, the vertical
distance from the top of
the ladder to the ground.
17. In the accompanying
в€’в€’в€’
diagram, AD is tangent to
в€’в€’в€’в€’в€’
circle O at D and ABC is
a secant. If AD = 6 and
в€’в€’в€’
AC = 9, find AB. 4
NY1-777.PCX
18. If point A ПЂ2 , 1 is reflected in the line y = x, find
the coordinates of the image of A . 1, ПЂ
2
19. If the transformation T(x,y) maps point A(1, в€’3) onto
point A (в€’4, 8), what is the value of x ? в€’5
3
NY1-576.PCX
17
(2t в€’ 1)
20. Evaluate:
9
t=1
9.
Rectangle PROM has coordinates P(2, 1), R(8, 1),
O(8, 5), and M (2, 5). What are the coordinates of
the point of intersection of the diagonals? (5, 3)
21. In
ABC , a = 10, b = 8, and sin B = 34 . Find sin A.
15
16
SMP rev. 3.0 (PDF) page 39. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BG
22. John’s father weighs 20 pounds more than twice what
John weighs. If John’s weight is represented by y,
then his father’s weight may be represented by
y
a) 2y
b) 2y в€’ 20 в€— c) 2y + 20
d)
+ 20
2
b) {в€’5, 4}
c) {в€’10, 2}
a) y = x2 + 4
b) y = x2 в€’ 4
в€— c) y = в€’x2 + 4
23. What is the solution set of x2 в€’ x в€’ 20 = 0?
в€— a) {5, в€’4}
31. Which is an equation of the parabola graphed in the
accompanying diagram?
d) {10, в€’2}
d) y = в€’x2 в€’ 4
24. Which letter has both vertical and horizontal line
symmetry?
a)
E
b)
M
c)
T
в€— d)
25. If 5 is added to both the length and the width of a
rectangle, then the perimeter is increased by
a) 5
в€— c) 20
b) 10
d) 25
26. In the accompanying diagram, ACD is an exterior
angle of ABC , m A = 3x, m ACD = 5x, and
m B = 50. What is the value of x ?
в€— a) 25
c) 60
NY1-543.PCX
X
32. The translation (x, y) в†’ (x в€’ 2, y + 3) maps the point
(7, 2) onto the point whose coordinates are
a) (9, 5)
c) (5, в€’1)
d) (в€’14, 6)
33. Which is the graph of the solution set of |2x в€’ 1| < 9?
a) в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в€’
в€’
в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’
в€’
в€’в—¦
в€’в€’в€’в†’
в€’5
b) 30
d) 100
в€— b) (5, 5)
в€’4
в€’3
в€’2
в€’1
0
1
2
3
4
5
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’
в€’
в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в€— b) в†ђв€’в€’в€’в€’в€’в€’в€’в—¦в€’в€’
в€’
в€’
в€’
в€’в—¦
в€’в€’в€’в†’
в€’5
в€’4
в€’3
в€’2
в€’1
0
1
2
3
4
5
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’
в€’
−−−−−−−−−−−−−−−−−−−−•
c) ←−−−−−−−•−
в€’в€’
в€’
в€’
в€’в€’в€’в€’в†’
в€’5
в€’4
в€’3
в€’2
в€’1
0
1
2
3
4
5
d) в†ђв€’
в€’в€’в€’
в€’в†’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’
в€’в€’в—¦в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в—¦
в€’5
в€’4
в€’3
в€’2
в€’1
0
1
2
3
4
5
NY1-622.PCX
27. Which open sentence is represented by the graph?
в†ђв€’в€’в€’в€’в€’в€’в€’в€’
в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’в—¦
в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в†’
•−
в€’в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’
в€’4
в€’3
в€’2
в€’1
0
a) в€’3 < x < 2
c) −3 ≤ x ≤ 2
1
2
3
4
∗ b) −3 ≤ x < 2
d) −3 < x ≤ 2
в€— a) 1
28. What is the inverse of в€јq в†’ p ?
a) p в†’ q
в€— c) q в†’ в€јp
b) 6 10
d) 16 20
b)
1
4
c)
2
4
d)
3
4
35. The cabbage harvest (h) from the Stuyvesant Farm
varies inversely as the local population of the
cabbage worm (w). Which graph best illustrates this
relationship?
b) в€јp в†’ q
d) в€јp в†’ в€јq
29. Based on the data in the table below, which interval
contains the median?
a) 0 5
в€— c) 11 15
34. A set contains four distinct quadrilaterals: a
parallelogram, a rectangle, a rhombus, and a square.
If one quadrilateral is selected from the set at
random, what is the probability that the diagonals of
that quadrilateral bisect each other?
Interval
Frequency
0 5
1
6 10
2
11 15
2
16 20
4
30. What are the roots of the equation ax2 + bx + c = 0?
в€љ
в€љ
в€’b В± b2 в€’ 4ac
b В± b2 в€’ 4ac
a) x =
b) x =
2a
в€љ4a
в€љ
2
в€’b + b В± 4ac
в€’b В± b2 в€’ 4ac
c) x =
в€— d) x =
2a
2a
в€— a)
b)
NY1-159.PCX
c)
NY1-160.PCX
d)
NY1-161.PCX
NY1-162.PCX
SMP rev. 3.0 (PDF) page 40. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BG
36. What is the fifth term in the expansion (a + bi)7 ?
в€— a) 35a3 b4
44. Given:
b) в€’35a3 b4
c) 21a2 b5 i
Prove:
d) в€’21a2 b5 i
в€’в€’в€’в€’в€’в€’ в€’в€’в€’
в€’в€’в€’
EAD, ABCD, AB в€ј
= DC , and
в€ј
EBC = ECB.
EAD is an isosceles triangle.
37. Which curve has only one line of symmetry?
a) a circle
в€— c) a parabola
b) an ellipse
d) a hyperbola
38. The graph of which equation is symmetric with
respect to the origin?
a) y = в€’3
в€— c) y = sin x
NY1-596.PCX
b) x = 2
d) y = cos x
[proof]
39. If csc Оё = в€’5 and tan Оё > 0, then Оё must lie in
Quadrant
a) I
b) II
в€— c) III
в€’в€’в€’
45. Construct an angle DEF on segment EF such that
BAC в€ј
= DEF . [construction]
d) IV
40. In the accompanying diagram, the shaded area
represents approximately 95% of the scores on a
standardized test. If these scores ranged from 78
to 92, which could be the standard deviation?
в€— a) 3.5
c) 14.0
b) 7.0
d) 20.0
NY1-213.PCX
46.
a) On the same set of coordinate axes, graph the
following system of equations:
x + y = 10
y=5
b) Find the area of the trapezoid bounded by the
x-axis, the y-axis, and the graphs drawn in
part a. (a) [graph]; (b) 37.5
NY1-076.PCX
41. In the accompanying diagram of rectangle ABCD,
в€’в€’в€’
в€’в€’в€’ в€’в€’в€’
diagonal AC is drawn, DE = 8, DE вЉҐ AC , and
m DAC = 55. Find the area of rectangle ABCD to
the nearest integer. 136
47. In the accompanying diagram, ABCD is a rectangle,
в€’в€’в€’
E is the midpoint of AB, DC = 16, ED = 10, and
the radius of circle O is 2.
NY1-679.PCX
NY1-468.PCX
a) Find, to the nearest tenth, the area of the
shaded region. [Use ПЂ = 3.14]
42. The larger of two positive integers is five more than
twice the smaller integer. The product of the integers
is 52. Find the integers. [Only an algebraic solution
will be accepted.] 4 and 13
43. In ABC , the lengths of sides a, b, and c are in the
ratio 4 : 6 : 8. Find the ratio of the cosine of C to
the cosine of A. [Show or explain the procedure
used to obtain your answer.] в€’ 2
7
b) To the nearest whole percent, what percent
of the area of the rectangle is the area of the
circle? 83.4; 13
48.
a) Draw the graph of the equation y = x2 в€’ 8x + 2,
including all values of x in the interval 0 ≤ x ≤ 8.
b) Find the roots of the equation x2 в€’ 8x + 2 = 0
to the nearest hundredth.
(a) [graph]; (b) 0.26 and 7.74
SMP rev. 3.0 (PDF) page 41. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BG
49.
a) Draw the graph of the equation y = x2 + 4, including all values of x in the interval −3 ≤ x ≤ 3.
b) Write the coordinates of the turning point of the graph drawn in part a.
c) Indicate whether the point in part b is a minimum or a maximum point.
d) On the same set of axes, draw the graph of the image of the graph drawn in part a after a reflection in the
x-axis. (a) [graph]; (b) 0,4; (c) minimum; (d) [graph]
в€’в€’в€’ в€’в€’в€’
50. In the accompanying figure of right trapezoid ABCD, AB = 10, DC = 18, m C = 49, and BE вЉҐ DC .
NY1-214.PCX
a) Find BE to the nearest integer.
b) Using the results from part a, find the area of ABCD to the nearest integer.
c) Find BC to the nearest integer.
d) If a dart is thrown at random and lands in trapezoid ABCD, what is the probability that the dart will also
land in rectangle ABED ? [Use the answers obtained in parts a and b.] (a) 9; (b) 126; (c) 12; (d) 90 or 5
126
7
51. The vertices of quadrilateral ABCD are A(2, 3), B(11, 6), C (10, 9), and D(1, 6).
в€’в€’в€’
в€’в€’в€’
a) Using coordinate geometry, show that diagonals AC and BD bisect each other.
b) Using coordinate geometry, show that quadrilateral ABCD is a rectangle.
(a) and (b) [proof]
52. For a class project, 20 students recorded the number of hours of television that they each watched in one week:
5, 12, 29, 23, 35, 8, 41, 40, 13, 16, 31, 29, 18, 28, 15, 32, 38, 26, 20, 22.
a) Complete the tables below to find the frequency and cumulative frequency in each interval.
Interval
Tally
Frequency
0 9
10 19
II
2
IIII
5
20 29
/
/
IIII II
7
30 39
IIII
4
40 49
II
2
Interval
0 9
Cumulative
Frequency
2
0 19
7
0 29
14
0 39
18
0 49
20
b) Using the cumulative frequency table completed in part a, construct a cumulative frequency histogram.
c) In one week, what percent of the 20 students watched television more than 9 hours but less than 20 hours?
(a) (2,5,7,4,2), (2,7,14,18,20); (b) [histogram]; (c) 25
53. Complete the truth table for the statement (p ∧ q) → [(p ∨ q) ↔ (p → q)]
p
q
T
T
T
F
F
T
F
F
(p ∧ q)
(p в€Ё q)
(p в†’ q)
[(p ∨ q) ↔ (p → q)]
(p ∧ q) → [(p ∨ q) ↔ (p → q)]
last column: (T, T, T, T)
SMP rev. 3.0 (PDF) page 42. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BH
These items are drawn from the Ohio Math Proficiency (OH1) module. The 2,184 original, multiple-choice items
are designed to prepare students for the 9th-grade proficiency test given each year in Ohio. The test measures
students’ knowledge, skills, conceptual understanding, and problem-solving in arithmetic, geometry, basic algebra,
measurement, and data analysis.
1.
Estimate the quotient: 813 Г· 39
в€— b) 20
a) 2
3.
c) 30
b) 5.3819
e) 179.18
e) 300
c) 17.918
в€— d) 0.7 > 0.07
c) 70% < 0.7
H
8.
5
OH1-003.AUX
в€— a) G
d) H and I
9.
c) 2 : 3
в€— d) 3 : 1
в€— b) 756 sec
e) 900 sec
17.
b) 3.5
a) 30
в€— b) G and H
e) none
c) G , H , and I
b) 1 : 3
c) 3 : 2
d) 2 : 3
e) 1 : 4
в€— b) 30.7
c) 30.73
d) 30.74
e) 31
14. Kerrie bragged that she had read 26,800 pages beyond
her summer reading assignments. If she had rounded
to the nearest hundred pages what is the smallest
number of pages that she read?
a) 26,652
d) 26,802
c) 855 sec
b) 26,700
e) 26,850
в€— c) 26,750
16. Find 43% of 300.
c) 18
в€— d) 35
e) 220
a) 1.29
18.
4 ft 10 in.
в€’ 2 ft 8 in.
в€— a) 2 ft 2 in.
d) 4 ft 2 in.
в€— a) 3 : 1
e) 55.0
15. What is 14% of 250?
a) 0.35
Which points are included in the statement
4.3 ≤ x < 5.7?
10. Using the letters in the word PROPORTIONAL write the
ratio comparing the number of O’s to L’s.
e) 2 : 5
13. The number of seconds that a human brain can be
kept undamaged using cool temperatures during
surgery is 800 seconds. If this number has been
rounded to the nearest hundred what might be the
actual survival time?
a) 731 sec
d) 880 sec
e) 0.05 = 0.5
12. Round 30.73 to the nearest tenth.
c) 54.88 в€— d) 54.9
b) 54.8
c) 50% > 5
c) G , H , and I
11. Round 54.87 to the nearest tenth.
a) 50
в€— b) 0.05 < 0.5
a) G
d) H and I
6
b) G and H
e) none
b) 3 : 4
c) 1.868
OH1-003.AUX
Using the letters in the word PARALLEL write the ratio
that compares the number of L’s to P’s.
a) 1 : 3
e) 300
Which statement is true?
I
•−−−−−−−−−•−−−−−−•−−−−−−−−→
в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’
4
b) 1.254
e) 2.658
d) 0.05 < 50%
Which points are included in the statement
4.2 < x ≤ 5.1?
d) 200
Find the correct product: 0.048 Г— 51.6
a) 5% = 0.5
e) 70% < 0.07
G
в€— c) 30
b) 20
a) 0.996
в€— d) 2.4768
6.
b) 0.7 < 7%
Estimate the quotient: 911 Г· 28
a) 3
4.
Which of the following is true?
a) 0.7 = 0.07
7.
d) 200
Find the correct product: 0.034 Г— 52.7
в€— a) 1.7918
d) 53.819
5.
2.
b) 2 ft 6 in.
e) 4 ft 4 in.
c) 3 ft 6 in.
b) 12.9
c) 75
в€— d) 129
e) 343
6 yd 2 ft
в€’ 3 yd 1 ft
a) 2 yd 2 ft
d) 3 yd 2 ft
b) 3 yd
e) 4 yd
в€— c) 3 yd 1 ft
SMP rev. 3.0 (PDF) page 43. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BH
19. The coldest temperature one day was в€’10 в—¦ F. During
the day the temperature climbed 16 в—¦. What was the
higher temperature?
a) в€’26 в—¦ F
в€— d) 6 в—¦ F
b) в€’6 в—¦ F
e) 26 в—¦ F
c) 0 в—¦ F
a) 3.2 в—¦ F
21. How many quarters are there in $7.75?
a) 25
b) 27
c) 29
в€— d) 31
b) 3.4 в—¦ F в€— c) 3.8 в—¦ F
e) 77
a) 26
b) 35
в€— b) 40 в—¦
c) 60 в—¦
d) 80 в—¦
e) 100 в—¦
в€— a) 30 в—¦
D
10
11
XOY ?
b) 40 в—¦
c) 60 в—¦
12
13
M
14
15
d) 80 в—¦
e) 90 в—¦
7
N
8
9
10
11
12
13
centimeters (cm)
centimeters (cm)
OH1-032.AUX
a) 2.5 cm
d) 4.5 cm
в—¦
a) 48
в€— b) 58
в—¦
d) 122
e) 148 в—¦
OH1-036.AUX
в€— c) 4 cm
b) 3 cm
e) 8 cm
27. Find the measure of
в—¦
e) 55
в€’в€’в€’в€’
26. State the length of MN as shown.
C
9
e) 4.4 в—¦ F
SMP-017.PCX
в€’в€’в€’
25. Find the length of CD.
8
в€— d) 51
c) 45
24. What is the measure of
SMP-017.PCX
a) 30 в—¦
d) 4.2 в—¦ F
22. How many nickels are there in $2.55?
WOX .
23. Determine the measure of
20. A person with a fever could have a body temperature
of 102.4 в—¦ F. How much higher is this than a normal
body temperature of 98.6 в—¦ F?
B in the triangle shown.
c) 90
в—¦
в€— b) 4 cm
e) 11.5 cm
a) 3.5 cm
d) 8.5 cm
c) 7.5 cm
28. In the triangle shown, find the missing angle measure.
a) 48 в—¦
d) 90 в—¦
в€— b) 66 в—¦
e) 114 в—¦
c) 88 в—¦
OH1-028.PCX
OH1-018.PCX
29. A curtain is to be draped around the edge of a
rectangular platform that is 10 Г— 6 feet. How long
must the material be?
a) 16 feet
d) 35 feet
b) 20 feet
e) 60 feet
в€— c) 32 feet
30. Students jog around a rectangular gym as part of
physical education courses. If the gym is 40 Г— 25
yards, how long is one lap around?
a) 65 yds
в€— d) 130 yds
b) 75 yds
e)
c) 85 yds
1000 yds2
SMP rev. 3.0 (PDF) page 44. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BH
31. Calculate the volume of the figure shown.
32. The rectangular solid shown will have what volume?
3387.5 cm3
в€— a) 5253.576 cm3
b) 3589.5 cm3
b) 5273.875 cm3
c) 4481.5 cm3
c) 5353.786 cm3
в€— d) 4579.5 cm3
d) 6255.678 cm3
e) 5183.5 cm3
e) 6356.567 cm3
a)
OH1-064.PCX
OH1-065.PCX
33. Students in the pre-algebra class constructed a graph
from data collected in a student survey. Which sport
was the least preferred among the students surveyed?
34. Students in the pre-algebra class constructed a graph
from data collected in a student survey. How many
students surveyed preferred baseball?
OH1-071.PCX
a) 30
в€— c) 45
b) 40
d) 50
e) 55
35. Students in the pre-algebra class constructed a graph
from data collected in a student survey. About how
many students surveyed preferred ice-hockey?
OH1-071.PCX
a) 35
a)
b)
1
4
c)
1
3
в€— a) 30
в€— d)
1
2
e)
3
5
39. Which of these sets of numbers will have an average
of 44?
a) {12, 14, 16, 80}
c) {15, 50, 52, 60}
в€— e) {36, 40, 52, 48}
b) {12, 40, 46, 55}
d) {30, 40, 42, 48}
41. For the last four games of the season, Keith raised his
average to 19 points per game. If he scored 18, 20,
and 22 points in each of the last three games, what
had he scored in the fourth game?
a) 12
b) 14
в€— c) 16
d) 18
e) 20
45. Evaluate
a) в€’64
17
2
b) x =
e) x = 33
в€— c) x = 9
k
в€’ a for a = 8, k = в€’32, and p = в€’4.
p
b) в€’16
c) 40
d) 50
e) 70
в€— a)
1
6
b)
1
5
c)
1
4
d)
1
3
e)
2
3
40. Which set of numbers will have an average (mean)
of 50?
a) {12, 30, 60, 80}
в€— c) {25, 25, 50, 100}
e) {25, 50, 50, 80}
b) {25, 25, 25, 90}
d) {25, 30, 75, 75}
42. At the start of the season, Erica’s average for the first
six basketball games was 15 points per game. If she
had scored 12, 16, 17, 18, and 13 points in five of the
games, what did she score in the sixth game to keep
her average?
в€— b) 14
c) 16
d) 18
e) 20
44. Solve: 6(2x в€’ 5) = 54
43. Solve: 3(4x в€’ 3) = 99
a) x =
d) x = 11
b) 35
38. A number cube (single die) is tossed. What is the
probability that you will roll a 4?
a) 12
15
2
e) 67
OH1-071.PCX
в€— c) Track
b) Swimming
e) Tennis
37. A number cube with faces labeled 1 through 6 is
tossed. What is the probability that an odd number
will land face up?
1
6
в€— d) 53
c) 48
36. Students in the pre-algebra class constructed a graph
from data collected in a student survey. How many
more students preferred football to swimming?
OH1-071.PCX
a) Baseball
d) Football
b) 42
в€— c) 0
d) 16
e) 64
a) x = 2
в€— d) x = 7
46. Evaluate
a) в€’11
b) x = 59
12
e) x = 9
c) x =
53
8
g
в€’ v for c = в€’2, g = в€’44, and v = 11.
c
b) в€’6
c) в€’2
d) 6
в€— e) 11
SMP rev. 3.0 (PDF) page 45. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BI
These items are drawn from the TAAS Elementary Math (TX2) module. This module was designed to prepare
students for the Texas Assessment of Academic Skills for grades 3 6, but all teachers and administrators will find it
useful for creating elementary mathematics assessments. The 2000 multiple-choice problems include those released
by the Texas Education Agency.
1.
Which decimal tells how much is shaded?
в€— b) 0.4
d) 40
a) 0.04
c) 4.0
2.
7.
The graph shows the favorite sports of students in
the third grade at Oak Grove School. How many
students liked soccer best?
Which means the same number as 4 Г— 8?
4Г—8
a) 8 Г· 4
3.
b) 8 в€’ 4
в€— c) 8 Г— 4
d) 8 + 4
Look at the number line.
P
Q
R
S
TX2-027.PCX
в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в†’
33
34
35
36
37
a) 30
38
b) 40
в€— c) 50
d) 70
What letter is at 35?
a) P
4.
в€— c) R
b) Q
d) S
8.
Which letter is inside the triangle and outside the
rectangle?
a) P
в€— b) Q
c) R
d) S
a) 6
в€— c) 13
9.
TX2-139.PCX
5.
Sarah’s mom bought some fruit at the grocery store.
She bought 5 bananas, 1 bunch of grapes, and
8 apples. How many apples and bananas did Sarah’s
mom buy?
5
1
8
Rex had 72/
c. He spent 57/
c. How much money does
he have left?
What time is shown on the clock?
a)
8:55
b)
8:05
в€— c)
7:55
d)
7:05
TX2-036.FIG
в€— a) 15/
c
TX2-442.PCX
6.
b) 9
d) 14
What is the perimeter of the polygon?
a) 28 cm
c) 43 cm
b) 16/
c
c) 17/
c
d) 18/
c
10. In the school parking lot there are 4 rows of bicycles.
There are 7 bicycles in each row. How many bicycles
are in the school parking lot?
b) 36 cm
в€— d) 45 cm
TX2-003.TBL
a) 20
b) 24
c) 25
в€— d) 28
TX2-458.PCX
SMP rev. 3.0 (PDF) page 46. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BI
11. Lupe bought a pencil for 19/c and a notepad for 38/
c.
About how much money did Lupe spend?
18. 0.85 + 0.23 =
+
TX2-103.FIG
a) 0.08
TX2-038.PCX
a) 20/
c
b) 40/c
в€— d) 60/
c
c) 50/c
c) 3 and 7
d) 4 and 6
в€— b) 23 25 27 29
d) 13 36 55 79
в€— d) division
15. What is the missing number in the number pattern?
99, 94, 89, 84,
a) 80
c) 75
.
b) square
d) rectangle
в€— c) 768
d) 774
b) 72 hours
d) 2190 hours
22. What is the remainder when 32 is divided by 6?
в€— b) 2
a) More than 60
в€— c) Between 40 and 50
17. The diagram shows the faces of a cube. If this cube
is tossed 3 times, which of the following sequences of
letters cannot occur?
b) TED
в€— d) PAD
b) 336
c) 3
d) 5
23. A health organization says that 1 out of every
5 people have heart disease. There are 223 people at
the band concert. What is the best estimate of how
many of these people have heart disease?
TX2-255.PCX
a) PUP
c) MUD
d) 621
d) 69
16. The yield sign has the shape of a
в€— a) triangle
c) line
в€— c) 631
48
Г— 16
a) 1
, 74, . . .
в€— b) 79
20.
b) 721
в€— a) 42 hours
c) 312 hours
b) subtraction
c) multiplication
d) 100.08
21. The average person watches 6 hours of television each
day. How many hours does the average person watch
television each week?
14. The inverse operation of multiplication is
a) addition
a) 1371
a) 296
13. Which is a set of odd numbers?
a) 32 33 34 35
c) 51 52 53 54
c) 10.08
19. 3409 в€’ 2778 =
12. If you add Alex’s age and Larry’s age, you get 10.
Alex’s age is greater than 1, and Larry’s age is
greater than 7. How old are the boys?
a) 1 and 9 в€— b) 2 and 8
в€— b) 1.08
b) Between 50 and 60
d) Less than 40
24. During a softball game, Maria got a hit and made it
from home to third base. How far did Maria run?
a) 200 ft
c) 100 ft
в€— b) 150 ft
d) 50 ft
M
P
E
U
T
D
TX2-058.FIG
TX2-561.PCX
SMP rev. 3.0 (PDF) page 47. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BI
25. The graph shows how students at Park View
Elementary travel to school most of the time.
Transp.
No. of Students
31. Jack can remember all the digits in Jill’s phone
number except the last one. If he writes down all the
possibilities before he starts dialing how many phone
numbers will be on his list?
a) 3
b) 5
в€— c) 10
d) 20
bicycle
32. A jar contains 3 red marbles and 2 white marbles.
John chose 1 marble without looking and then
replaced it in the jar. Then Ann chose 1 marble
without looking. What is the probability that Ann
chose a red marble?
car
bus
в€— a)
walk
Each represents 10 students
TX2-009.AUX
How many students either walk or ride a bicycle?
в€— a) 90
b) 50
26. This model shows that
в€— a)
c)
2
3
3
6
b)
d)
c) 40
8
12
d) 10
is the same as
3
5
27. Which shaded region does not represent
figure?
a)
1
2
d)
1
5
b) 15
c) 16
в€— d) 18
в€— c)
d)
28. The product of 2 Г— 3 Г— 5 Г— 5 is equal to
c) 60
d) 15
29. What number is missing?
(3 Г— 9) Г— 8 = 3 Г— (
b) 27
c) 2610 mi
b) 350
c) 300
d) 275
c) 5 R2
d) 5 R12
36. 107 Г· 23 =
a) 4 R9
b) 125
b) 715 mi
в€— e) Not Here
35. Angelo has 15 crates of apples. He has 25 times
as many apples as crates. How many apples does
Angelo have?
в€— a) 375
в€— b) 4 R15
37. At the airport 21 planes can take off each hour.
About how many planes take off in a 48-hour
weekend?
a) 100
b) 400
в€— c) 1000
d) 2000
Г— 8)
c) 24
30. This drawing is an example of a
в€— a) reflection
c) similar
2
5
of the
b)
a) 72
c)
34. The distance from Houston to Washington, D.C.
is 1410 miles. The distance from Tulsa to
Washington, D.C. is 1200 miles. The distance from
Tulsa to Houston is 485 miles. How much farther
from Washington, D.C. is Houston than Tulsa?
a) 695 mi
d) 3095 mi
в€— a) 150
1
2
33. Bonita scored 12, 12, 15, and 17 goals during the
4 seasons she played soccer. Her mean number of
goals was 14 goals. If she had scored 4 more goals
during each game, what would her mean (average)
number of goals be?
a) 14
3
4
1
2
b)
в€— d) 9
.
38. The perimeter of a rectangle is 26 meters. The width
of the rectangle is 5 meters. Which number sentence
could be used to find L, the length of the rectangle?
a) 26 в€’ 5 = L
c) (26 в€’ 10) Г— 2 = L
e) L = (26 + 5) Г· 2
b) parallel
d) translation
в€— b) (26 в€’ 10) Г· 2 = L
d) L = (5 Г— 26) Г· 2
39. According to Nielson Media Research 77% of
American households have at least one VCR. What
percentage of households do not have a VCR?
a) 0.23%
TX2-313.PCX
b) 2.3%
в€— c) 23%
d) 230%
SMP rev. 3.0 (PDF) page 48. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BI
40. How are the factors 5 Г— 5 Г— 7 Г— 7 expressed in
exponential notation?
a) 252 Г— 492
b) 352
c) 55 Г— 77
в€— d) 52 Г— 72
41. What is the smallest number that has both 10 and
15 as a factor?
a) 5
b) 10
в€— d) 30
c) 15
42. What letter is missing from this patterns?
...
jjgpqjjjgpqjjjjgp
a) j
b) g
48. Mike, Mabel, and Hazel decided to go together and
buy one birthday present for Jessica. They spent
$28.20 for the gift. How much did each person have
to chip in?
a) $7.05
b) $7.50
в€— e) Not Here
c) $8.40
d) $9.07
49. A lamppost is 6 feet high and casts an 8-foot
shadow. At the same time of day, a flagpole directly
behind the lamppost casts a 20-foot shadow. Which
proportion can be used to find the height H of the
flagpole?
j j j. . .
в€— d) q
c) p
43. Point P best represents what number?
P
←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−•−−−−−−−−−−−−−−−→
10
11
b) 11 12
a) 11 34
12
3
c) 11 10
в€— d) 11 35
44. Find the area of the isosceles trapezoid shown.
a) 12 cm2
b) 15 cm2
в€— c) 24 cm2
TX2-108.PCX
6
H
=
8
20
20
6
d)
=
H
8
H
8
=
6
20
H
6
e)
=
8
20
в€— a)
b)
c)
H
8
=
20
6
50. Pentagons PQRST and VWXYZ are congruent.
Which statement is true?
d) 36 cm2
TX2-731.PCX
45. If the spinner is spun 80 times, which color would
you expect it to stop on about 30 times?
в€— a) Yellow
c) Green
b) Red
d) Blue
TX2-762.PCX
в€’в€’в€’ в€ј в€’в€’в€’
в€— a) TS =
ZY
в€’в€’в€’ в€ј в€’в€’в€’
d) PQ = VZ
в€’в€’в€’ в€ј в€’в€’в€’
b) QR =
YZ
e) Not Here
T в€ј
= X
c)
TX2-330.PCX
46. Augustus made a cake. The recipe called for 2 23 cups
of flour in the batter and then for another 1 12 cups
of flour to be mixed in later. How much flour did
Augustus use altogether?
3 16
a)
b)
e) Not Here
7
3 12
c)
3 35
в€— d)
4 16
3
5 10
10 51
feet of wire. She has
feet more
47. Rhona has
than Yolanda. How much wire does Yolanda have?
1
ft
a) 5 10
d)
15 45
ft
b) 5 25 ft
c) 15 21 ft
51. Sheila knows that it takes 11 feet of ribbon to make
2 bows for a wall decoration. Which number sentence
could she use to find R, the total number of feet of
ribbon she would need to make 7 bows.
R
7
R
7
2
=
a) 1 11
в€— d)
11
2
=
b) R = 7 Г—
e) R =
11
2
c)
2
7
=
R
11
2Г—11
7
52. Mrs. Alfaro bought new shoes for her 5 children.
The price of the shoes ranged from $14.99 to $29.99.
Which is a reasonable cost for all 5 pairs of shoes?
a) $50
b) $70
в€— c) $100
d) $175
e) $200
в€— e) Not Here
SMP rev. 3.0 (PDF) page 49. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BJ
These items are drawn from the TAAS Prep./Algebra EOC (TX3) module. The TX3 module was designed to
prepare students for the Texas Assessment of Academic Skills for grades 7 8 and exit level, as well as that state’s
Algebra End-of-Course exam. But teachers and administrators everywhere will find it useful for creating secondary
mathematics assessments. The 4000 multiple-choice problems include those released by the Texas Education Agency.
1.
Jupiter has an approximate diameter of
1.43 Г— 105 kilometers. This diameter measures
about
.
a) 1430 km
в€— c) 143,000 km
e) 14,300,000 km
3.
5.
b) 14,300 km
d) 1,430,000 km
b) 99
c) 99.9
9.
6.
в€— c) 0.46
b) 0.046
e) 4.6
c) 3x + y
b) 6x + 6y
в€— e) 3x + 3y
Which equation is equivalent to 2x в€’ 10 = 8?
8.
b) x = 2(8 в€’ 10) в€— c) 2x = 8 + 10
d) x = 12 (8)
e) 2x =
9
10
11. What number should come next in this sequence?
The number 842.3283 rounded to the nearest hundred
is
.
a) 842.33
b) 842.32
d) 742
e) 700
в€— d) 162
e) 192
13. Which is equivalent to x2 + x3 ?
c) 5x
a) 10.1 ft2
b) 15.6 ft2
d) 20.2 ft2
в€— e) 23.4 ft2
d) 6x
c) 17.8 ft2
17. Which figure appears to be a parallelogram?
b)
d)
e)
d) 8.22
e) 82
Use the distributive property to select the expression
equal to a(b + c).
в€— b) ab + ac
e) c(a + b)
a) abc
d) b(a + c)
c) cba
a) 10x в€’ 3 = 5
c) x = 13 в€’ 5
e) x = 8
b) x = 10(13 в€’ 5)
в€— d) 10x = 13 в€’ 5
12. What number should come next in this sequence?
a) 108
b) 112
c) 128
d) 256
в€— e) 324
14. Which is equivalent to n5 + n3 ?
15. The dining table in Mike’s house is 6.5 feet long and
3.6 feet wide. What is its area?
a)
c) 8.02
4, 12, 36, 108, . . .
c) 128
a) x5
b) x6
в€— e) none of these
в€— c) 800
What is the correct way to express 82% as a decimal?
2, 6, 18, 54, . . .
b) 112
c) 60,000,000
10. Which equation is equivalent to 10x + 5 = 13?
a) 2x = 8 в€’ 10
a) 78
b) 6,000,000
e) 6,000,000,000
a) 0.082 в€— b) 0.82
Use the distributive property to select the expression
equal to 3(x + y).
a) x + 3y
d) 3xy
4.
e) 90
What is the correct way to express 46% as a decimal?
a) 0.0046
d) 4.06
7.
d) 99.99
A computer disk drive has a capacity of 6.0 Г— 108
bytes of information. Express this number in standard
notation.
a) 600,000
в€— d) 600,000,000
The number 99.999 rounded to the nearest hundred
is
.
в€— a) 100
2.
в€— c)
a) n8
b) n15
в€— e) none of these
c) 8n
d) 15n
16. The bed in Willie’s dorm room is 6.9 feet long and
4.1 feet wide. What is its area?
a) 11 ft2
d) 33.58 ft
b) 22 ft2
e) 46.23 ft
в€— c) 28.29 ft2
18. Which figure appears to be a trapezoid?
a)
b)
d)
e)
в€— c)
SMP rev. 3.0 (PDF) page 50. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
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BJ
19. Find x.
20. Find y.
a) 15
d) 9.5
b) 12.5
e) 7.5
в€— c) 12
a) 1
в€— d) 0.4
b) 0.8
e) 0.2
c) 0.6
TX3-105.PCX
TX3-104.PCX
21.
ABC в€ј
Find DF .
ADF . BD = 12, BC = 20, AD = 12.
в€— b) 10
e) 16
a) 8
d) 14
c) 12
22.
ABC в€ј
Find AC .
a) 4
d) 8
ADF . BD = 4, AF = 3, AD = 4.
в€— c) 6
b) 5
e) 10
TX3-149.PCX
TX3-149.PCX
23. Given
a)
в€— c)
e)
2,
1
1,
5,
2
3
2,
6
which pair of angles must be congruent?
b)
d)
3,
5,
24. Given
в€— a)
c)
e)
4
4
2,
1
1,
3,
4
4
5,
4
which pair of angles must be congruent?
b)
d)
2,
5,
6
1
TX3-182.PCX
25. This container contains approximately
water.
a)
1
4
в€— d) 1 21
b)
3
4
cups of
c) 1 14
e) 2
TX3-182.PCX
26. This container is filled with
a)
1
2
b) 1
d)
1 21
e) 2
в€— c)
cups of liquid.
1 14
TX3-220.PCX
TX3-219.PCX
27. Jean is preparing a stew that calls for 2 lb 5 oz of
meat. If she doubles the recipe, how much meat will
she need?
a) 2 lb 10 oz
в€— d) 4 lb 10 oz
b) 4 lb
e) 5 lb
c) 4 lb 5 oz
29. Celeste can choose her school attire from 3 blouses,
4 skirts, 2 pairs of shoes, and 3 pairs of socks. How
many different combinations of clothes does Celeste
have?
a) 84
в€— b) 72
c) 64
d) 56
e) 48
28. Harry is preparing barbecue that calls for 4 lb 8 oz of
chicken. If he doubles the recipe, how much chicken
will he need?
a) 4 lb
d) 8 lb 9 oz
b) 4 lb 100 oz
в€— e) 9 lb
c) 8 lb
30. Craig can choose his school attire from 5 shirts,
4 pairs of pants, 3 pair of shoes, and 3 pairs of socks.
How many different combinations of clothes does Craig
have?
в€— a) 180
b) 160
c) 120
d) 90
e) 60
SMP rev. 3.0 (PDF) page 51. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BJ
31. Cards with the names of 30 students in algebra were
placed in a box. Fourteen of the students are boys. If
a name is drawn at random from the box, what is the
probability that it is a girl’s name?
a)
2
3
b)
3
5
в€— c)
8
15
d)
1
2
e)
7
15
33. The chart gives the weights, in kilograms, of a group
of third grade students. What is the mode of the
weights?
a) 26 в€— b) 27
d) 29 e) 30
c) 28
Weight in Kilograms
29
30
27
28
26
30
28
32. The consecutive numbers from 1 through 20 are
written on pieces of paper and placed in a bag. If a
number is drawn at random from the bag, what is the
probability that it is less than 5?
a)
13
25
b)
1
2
c)
2
5
d)
a) 69
d) 80
b) 73 в€— c) 79
e) 85
79
85
27
79
76
90
31
29
73
82
75
27
26
79
80
69
d) 4.1 in.
1
5
Weight in Kilograms
80
TX3-057.TBL
35. The normal annual rainfall for Mario’s hometown is
29.2 inches. The rainfall this year totaled 34.1 inches.
How much above normal was this year’s rainfall?
b) 5.1 in. в€— c) 4.9 in.
в€— e)
34. The chart list the weights, in kilograms, of the
offensive players on the football team. What is the
mode of the weights?
TX3-056.TBL
a) 5.9 in.
1
4
e) 3.7 in.
36. The annual rainfall for one Texas city in 1980 was
35.8 inches. The rainfall in 1990 totaled 37.4 inches.
What was the difference in rainfall for 1980 and 1990?
a) 2.8 in.
b) 2.6 in.
c) 2.4 in. в€— d) 1.6 in.
e) 1.4 in.
37. Mike’s dad has a toll free telephone number for his
business. Seventy-five calls were placed in 18 days to
the toll free number. At this rate, which proportion
could be used to find out how many calls the business
would receive in 30 days?
30
18
x
75
x
18
a)
=
b)
=
c)
=
75
x
18
30
75
30
18
75
75
30
в€— d)
=
e)
=
30
x
x
18
38. Mickey is taking the Amtrak train to visit his cousin
who lives 750 miles away. If the train traveled
334 miles in 4 hours, which proportion could be used
to determine how many hours the entire trip will
take?
334
x
334
334
4
4
a)
=
b)
=
c)
=
x
216
4
750
x
750
x
216
x
750
d)
=
в€— e)
=
4
750
4
334
39. A computer store advertised its computers at a 20%
discount. Roy decides to buy one which originally sold
for $1600. What is the amount of the sale price?
40. A department store advertised a 19 inch television set
with a remote control at 15% off. If the original price
was $250, how much is the sale price?
a) $1200 в€— b) $1280
c) $1300
d) $1400
e) $1450
41. To get to the store from his house, Harry jogged
3 kilometers due west and then 4 kilometers due
north. On the way back he cut across a field, taking
the shortest possible route home. How far did Harry
jog on the round-trip?
a) 19 km
c) 7 km
e) 1 km
в€— b) 12 km
d) 5 km
a) $37.50
d) $225.00
b) $187.50
e) $235.00
в€— c) $212.50
42. Nicky left her house and bicycled due east
8 kilometers, then due north 6 kilometers to the park.
She then bicycled from the park directly back to her
house. How far did Nicky ride on the round-trip?
a) 2 km
c) 14 km
e) 38 km
b) 10 km
в€— d) 24 km
TX3-294.PCX
TX3-293.PCX
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BJ
Algebra End-of-Course Items
43. What is the range of the function f (x) = (x в€’ 5)2
when the domain is {1, 3, 5}?
a) {в€’16, в€’4, 0}
b) {в€’24, в€’16, 0}
d) {24, 16, 0}
в€— e) {16, 4, 0}
c) {в€’4, в€’2, 0}
45. Which equation describes the graph shown?
a) y =
b) y =
c) y =
в€— d) y =
e) y =
в€’ 23 x в€’ 3
в€’ 32 x в€’ 2
2
3x в€’ 2
в€’ 23 x в€’ 2
3
2x в€’ 3
44. What is the range of the function f (x) = (x в€’ 7)2
when the domain is {2, 4, 6}?
в€— a) {25, 9, 1}
c) {в€’25, в€’9, 1}
e) {в€’25, в€’9, в€’1}
b) {в€’10, в€’6, в€’1}
d) {10, 6, 2}
46. Which equation describes the graph shown?
a) y = в€’ 23 x в€’ 3
b) y = в€’ 32 x в€’ 2
c) y = 32 x в€’ 2
d) y = в€’ 23 x в€’ 2
в€— e) y = в€’ 32 x в€’ 3
TX3-444.PCX
47. In a given rectangular prism, the length is represented
by x + 1, the width is represented by x + 4, and the
height is 7. Express the volume of the rectangular
prism in terms of x.
a) x2 + 5x + 4
c) 14x + 35
48. In a given rectangular prism, the length and width
are both represented by 3x + 2 and the height is 4.
Express the volume of the rectangular prism in terms
of x.
b) 2x + 12
a) 24x + 16
7x2
36x2
в€— d)
+ 35x + 28
e) 7x2 + 28
в€— c)
b) 12x + 8
d) 36x2 + 16
+ 48x + 16
e) 36x2 + 24x + 16
49. David has 3 more dimes than nickels. He loses 2 dimes
then counts his money and finds he has $3.10. How
many nickels does David have?
a) 18 nickels
d) 22 nickels
TX3-539.PCX
b) 19 nickels
e) 23 nickels
в€— c) 20 nickels
51. The cost of buying a home is increasing. The graph
represents the average monthly payment on a home.
50. Tyrone has 5 more quarters than nickels. He loses
3 quarters then counts his money and finds he has
$3.80. How many nickels does Tyrone have?
a) 15 nickels
в€— d) 11 nickels
b) 14 nickels
e) 10 nickels
c) 13 nickels
52. Motor vehicle accidents are the main type of accidental
deaths.
TX3-565.PCX
Using this information, what is the expected monthly
payment on a home in the year 2002?
a) $858.10
d) $1090.70
b) $920.30
e) $1139.90
в€— c) $978.50
TX3-566.PCX
Using this information, what is the predicted death
rate in the year 2000?
в€— a) 15
b) 18
c) 19
d) 20
e) 21
SMP rev. 3.0 (PDF) page 53. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BLANK PAGE
CA
These items are drawn from the North Carolina Grades 3 8 Reading (NC4) module. This module contains
104 reading passages and 930 questions. These first appeared in the Item Bank Testlets for grades 3 5, published in
1994 by the North Carolina Department of Public Instruction.
The Legend of Corn
SMP-001.AUX
2.
By Dawn, great-great-granddaughter
of Sioux Chieftain, War Eagle
a)
b)
в€— c)
d)
Here is a poem about corn and how important it has been
to many people throughout the years.
The ancient ones in time of need
Discovered how to use their seed,
The hunters threw aside their bows,
And planted corn in hills and rows.
The blood-drenched corn of sacrifice
The golden song which echoes thrice,
All bow down to the great sun god,
His high priest blesses, smiles and nods.
hunting
worshipping the sun God
finding gold
refining grain
SMP-001.AUX
3.
What color does the author use to show the reader
how valuable corn is?
в€— a) gold
b) yellow
c) red
d) green
SMP-001.AUX
4.
What have the Indians done with corn?
a)
в€— b)
c)
d)
The Spanish conquerors of old
Took home this seed, instead of gold,
To plant it in the old, old soil,
To bring new life to those who toil.
Today the grain is used for feed,
And mills refine the golden seed;
Over the world the tall corn grows,
The gift of the Indian the tall green rows.
In this poem, what did raising corn take the place of
for the Spanish conquerors?
sold it to the rest of the world
given it to the rest of the world
hidden it from the rest of the world
stolen it from the rest of the world
SMP-001.AUX
5.
How does the speaker feel knowing that corn is grown
around the world?
в€— b) proud
d) unconcerned
a) cheated
c) confused
SMP-001.AUX
6.
In this poem, which was most important to the
growth of corn?
a) sacrifice
b) old soil
c) toil
в€— d) sunlight
SMP-001.AUX
7.
How does the speaker feel knowing that corn is grown
around the world?
a) cheated
c) confused
Look again at the question above and your answer
to it. Please explain why you think your answer is
correct. b;[SR-4]
SMP-001.AUX
1.
In this poem, what did raising corn take the place of
for the ancient Sioux?
в€— a)
b)
c)
d)
hunting
worshipping the sun God
finding gold
refining grain
b) proud
d) unconcerned
SMP-001.AUX
8.
Reread the first verse. What does it tell the reader
about the kind of people the ancient ones were?
[SR-4]
SMP rev. 3.0 (PDF) page 55. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
CA
My Wish
by Linnie McKay
This selection is actually an essay written by Linnie
McKay, who is a character in a book. The book is
The Thunder-Pup by Janet Hickman. In it Linnie is a
4th grader, and her teacher has given her a choice of
three topics. Read her essay to see what she chose to
write about.
SMP-002.AUX
11. According to Linnie, what is the best thing about
dogs?
a)
b)
c)
в€— d)
They
They
They
They
are furry and warm.
will sleep with you.
are not as bad as Aunt Em thinks.
make good friends.
SMP-002.AUX
12. Who is Arnold Anderson?
a)
в€— b)
c)
d)
Linnie’s friend who owns a dog
a boy who lives near Linnie
someone who is coming to visit Linnie
Aunt Em’s son
SMP-002.AUX
13. Why is Linnie probably writing about a wish?
a) She has company coming.
в€— b) Her birthday is coming soon.
c) She does not agree with Aunt Em.
d) Aunt Em takes care of the house.
What I want most of all is a dog. Dogs are furry and
warm and they lick your hand and curl up on your bed
if you let them. I have wanted a dog all my life but my
Aunt Em says cats in the barn is one thing but a dog in
the house is something else and that’s why I never had
one. Aunt Em is the one who takes care of our house and
she thinks dogs are dirty, and also that they smell bad
and have germs.
I do not agree. I think dogs are good friends. There
are not many people near my house for me to be friends
with, not counting Arnold Anderson or the girl who is
coming to visit this weekend (Dear Miss Crane, her name
is Darla Champion and her mother and father are coming
too but she might get to stay for a while). That’s why I
would like to have a dog someday, to talk to it and play
with it and teach it things.
Maybe for my birthday I will get one. Everyone says
if things go all right I might get a big surprise for my
birthday, and that is not very far away.
SMP-002.AUX
9.
What was the girl’s wish?
a) to visit a friend
в€— c) to own a dog
b) to play with cats
d) to have some fun
SMP-002.AUX
14. In the second paragraph, why is the information in
parentheses ( ) ?
a)
в€— b)
c)
d)
It
It
It
It
is an exact quotation.
is off the subject.
gives an exact definition.
was written by someone else.
SMP-002.AUX
15. What are two things Linnie could promise Aunt Em
to get her to change her mind about a dog? Explain
how each would convince Aunt Em. [SR-4]
SMP-002.AUX
16. If Linnie gets a dog for her birthday, do you think
she will take good care of it? Explain your answer.
[SR-4]
SMP-002.AUX
17. If Linnie does not get a dog for her birthday, do you
think she will be angry at Aunt Em? Explain your
answer. [SR-4]
SMP-002.AUX
10. What is Linnie’s teacher’s last name?
a) McKay
в€— c) Crane
b) Anderson
d) Champion
SMP rev. 3.0 (PDF) page 56. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
CB
These items are drawn from the TAAS Elementary Reading (TX4) module, a collaborative effort between EducAide
Software and Region 10 Education Service Center (Richardson, TX). The 54 passages and 1475 questions are based
on the Texas Assessment of Academic Skills elementary reading tests.
How Rocks Are Made
We see rocks every day. They are in the dirt, on river
bottoms, and hidden in caves under the earth. Where did
they all come from? Are rocks always old? Are new rocks
made today?
There are three ways that rocks are made. Some are
made from lava that has cooled. Others are made when
bits of material settle at the bottom of beds of water.
Still other rocks are remade from previous rocks. (See
Figure 1.)
SMP-003.AUX
Rocks Made From Lava
Hot liquid called lava comes up through the earth from a
volcano. When the hot lava comes out, the air cools it
and it hardens into rock. These rocks have crystals and
air holes. They sometimes look like Swiss cheese. Rocks
that are made from cooled lava are called igneous rock.
1.
Rocks Made From Water
2.
Sand and mud, and bits of plants and animals settle at
the bottom of beds of water. This material is called
sediment. The sediment is pushed downward as the
water moves. The weight of the water squeezes it
together. Pieces of plant, mud, and sand are pressed so
tightly that they form a new rock. Chalk and coal are
kinds of sediment rocks.
в€— a) made again
c) deep in the earth
It has taken many years to make the rocks we see today.
Some are millions of years old. The earth keeps changing,
and new rocks are starting each day. They start with
sand and material at the bottom of the river. They start
deep in the earth with the pressure of an earthquake.
When a volcano erupts and the lava cools, newer rocks
can be made.
If we dig up marble from under the earth it is a very old
rock. If we pick up a rock a year after a volcano erupted
it is a new rock. When and where we find a rock can tell
us how it was made and maybe even when it was made.
b) changed from rock
d) turned into liquid
SMP-003.AUX
In this passage, the technical term sediment means
a)
в€— b)
c)
d)
strong feelings
materials that settle at the bottom
muddy bottom
fragile rocks
SMP-003.AUX
3.
Rocks Made From Other Rocks
Sometimes underground rocks change because the
earth around them changes. Some are heated by lava
entering a volcano. Others may be pushed together by
an earthquake. Some rocks change when they become
exposed to chemicals in the dirt. New rock is formed
when these changes in the earth take place. Marble is
one kind of rock that has been remade by another rock.
These rocks are called metamorphic.
In this passage, remade means
In this passage, the technical term metamorphic
means
a)
b)
в€— c)
d)
cooled lava forming rocks
volcanoes erupting
chemical or physical changes creating new rocks
very small changes
SMP-003.AUX
4.
In this passage, one of the rocks that results from
material that settles at the bottom of the water is
a) lava
в€— c) chalk
b) igneous rocks
d) marble
SMP-003.AUX
5.
In this passage, we learn that rocks are
a)
b)
c)
в€— d)
sedimentary
metamorphic
igneous
made in three different ways
SMP rev. 3.0 (PDF) page 57. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
CB
SMP-003.AUX
6.
Coal is a rock that is made from
в€— b) sediment in water
d) cooled lava
a) other rocks
c) volcano smoke
SMP-003.AUX
7.
rocks
rocks
rocks
rocks
made
made
made
made
from
from
from
from
lava
sediment
other rocks
hot liquid
SMP-003.AUX
Lava becomes a rock AFTER it
a)
b)
в€— c)
d)
c) heats up
d) covers other rocks
SMP-003.AUX
What is sediment rock BEFORE it is squeezed
together by the weight of water?
a) chalk
b) igneous rock c) lava
в€— d) sand, mud, and bits of plants and animals
SMP-003.AUX
10. What would be the surroundings of sedimentary rock
as it is being formed?
a) a dry, hot desert
c) warm, shaded park
в€— b) under water
d) a science laboratory
14. Igneous rocks are created when
в€— a)
b)
c)
d)
в€— a)
b)
c)
d)
Rocks are made in different ways.
Underground rocks are millions of years old.
Earthquakes make rocks.
Volcanoes create young rocks.
SMP-003.AUX
12. Which of the following is the best summary for this
passage?
a) Rocks start deep in the earth formed by the
pressure of an earthquake and then form from the
heat of the sun.
в€— b) Rocks are made three ways, igneous rocks from
lava, sedimentary rocks from pressed mud, and
metamorphic rocks, which are changed rocks.
c) Some rocks are made from water pressure and
others are made from lava.
d) You can find both old rocks and new rocks if you
know the right places to look.
hot lava cools down after time
sediments are exposed to constant running water
a rock is exposed to heat or chemicals
streams deposit new material on rocks
SMP-003.AUX
15. Sedimentary rocks are formed when
в€— a)
b)
c)
d)
sediment is squeezed together by water
plants, mud and sand wash up on shore
underground streams meet volcanoes
a rock is heated by a nearby volcano
SMP-003.AUX
16. When a volcano erupts, it most likely will create
a)
b)
в€— c)
d)
a fountain of lava for years
a rough and rocky surface
new rocks
the oldest rocks in the world
SMP-003.AUX
SMP-003.AUX
11. What is the main idea of this passage?
new rock is polluted by sediments
sediments are exposed to constant running water
the rock is exposed to chemicals or heat
streams deposit new materials on the surface of
the rock
SMP-003.AUX
в€— b) cools
a) erupts
9.
13. Metamorphic rocks change because
Coal and chalk are two types of
a)
в€— b)
c)
d)
8.
SMP-003.AUX
17. According to the figure, coal is
a)
b)
c)
в€— d)
a rock made from other rocks
formed by chemical reaction
formed as a result of an earthquake
formed from river sediment
SMP-003.AUX
18. From this passage, which is a NONFACT about how
rocks are formed?
a) Lava is cooled and makes new rock.
b) Sand and mud settle at the bottom and form new
rock.
в€— c) Rocks are formed by changing their location.
d) Rocks change chemically and become a new rock.
SMP rev. 3.0 (PDF) page 58. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DA
These items are drawn from EducAide’s Mid-level Math Assessment (MMA) module. This module complements the
Pre-Algebra, Algebra I, and Geometry �core modules’ with 5000 multiple-choice questions suitable for quizzes, tests,
final exams, and school- and district-wide assessments.
1.
Find the quotient and remainder when 653 is divided
by 9.
a) 72 r 1 в€— b) 72 r 5
3.
b) 721 m
в€— e) 6284 m
b) 43 r 3
6.
в€— c) 29.031
d) 45 r 2
b) 18,267 ft
e) 41,928 ft
e) 45 r 5
c) 27,738 ft
What decimal is represented by the phrase
eighty-eight and ninety-six thousandths ?
в€— b) 88.096
e) 88.960
a) 88.0096
d) 88.96
8.
c) 44 r 7
The highest elevation of any point on earth is
Mt. Everest, which is 29,028 ft above sea level. The
Dead Sea is the lowest at 1,290 ft below sea level.
What is the difference in elevations between these two
locations?
a) 2,250 ft
в€— d) 30,318 ft
Simplify 4.08 Г— 10в€’10 7.7 Г— 105 , and write your
answer in scientific notation.
c) 3.1416 Г— 10в€’3
4.
c) 2402 m
b) 29.0031
e) 29.311
в€— a) 3.1416 Г— 10в€’4
Find the quotient and remainder when 345 is divided
by 8.
в€— a) 43 r 1
e) 74 r 8
What decimal is represented by the phrase
twenty-nine and thirty-one thousandths ?
a) 29.00031
d) 29.31
7.
d) 73 r 5
Mt. McKinley, the highest point in the United States,
is 6198 m above sea level. Death Valley, the lowest
point, is 86 m below sea level. What is the difference
in elevations between these two locations?
a) 72 m
d) 6112 m
5.
c) 73 r 3
2.
c) 88.906
Simplify 7.5 Г— 10в€’9 9 Г— 10в€’7 , and write your
answer in scientific notation.
b) 31.416 Г— 10в€’5
a) 6.75 Г— 10в€’16
в€— b) 6.75 Г— 10в€’15
d) 0.31416 Г— 10в€’3
d) 675 Г— 10в€’13
e) 6.75 Г— 10в€’14
c) 67.5 Г— 10в€’14
e) 314.16 Г— 10в€’2
9.
10. What percent of the diagram is shaded?
What percent of the diagram is shaded?
a) 3.75%
b) 12.5%
d) 37%
в€— e) 37.5%
a) 3.75%
в€— d) 62.5%
c) 25%
11. Of D dogs in Mrs. Pace’s kennel, 31 are classified as
large dogs and 14 of the remainder are classified as
medium-sized. How many of the dogs are classified as
small?
a)
1
6
В·D
b)
1
3
В· D в€— c)
1
2
В·D
d)
2
3
В·D
e)
5
6
В·D
13. The distance to Earth from the planet Pluto is
4.58 Г— 109 kilometers. In April 1983, Pioneer 10
transmitted radio signals from Pluto to Earth at the
speed of light, 3 Г— 105 kilometers per second. About
how long (in seconds) did it take for the signals to
reach Earth? (Use the formula d = rt solved for time.)
a) 13,740 seconds
c) 16,244 seconds
e) 18,102 seconds
в€— b) 15,267 seconds
d) 17,587 seconds
b) 6.25%
e) 63%
c) 37.5%
12. Each of N summer campers picks either softball,
soccer, or tennis for the day. If 12 of the campers pick
softball and 13 of the campers pick soccer, how many
campers pick tennis?
в€— a)
1
6
В·N
b)
1
3
В·N
c)
1
2
В·N
d)
2
3
В·N
e)
5
6
В·N
14. The distance from the Sun to the Earth is 1.496 Г— 108
kilometers. About how long does it take light to
travel from the Earth to the Sun if the speed of light
is 3 Г— 105 kilometers per second? (Use the formula
d = rt solved for time.)
a) 5 seconds
d) 200 seconds
b) 20 seconds
в€— e) 500 seconds
c) 50 seconds
SMP rev. 3.0 (PDF) page 59. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DA
15. A grocer sold k pounds of butter for b cents. In terms
of k and b, find number of cents the grocer received
for selling x pounds of butter.
kx
k
ka
a)
cents
b)
cents
c)
cents
b
bx
x
k
bx
d)
cents
в€— e)
cents
bx
k
16. A store sold c yards of carpet for d dollars. Find
the number of dollars, in terms of c and d, the store
received for selling x yards of carpet.
dx
c
cd
в€— a)
dollars
b)
dollars
c)
dollars
c
dx
x
d
cx
d)
dollars
e)
dollars
dx
d
17. Statistics show that 7 out of 10 people surveyed prefer
fruit for dessert. There were 750 people surveyed.
How many said they did not prefer fruit?
18. Three out of four dentists recommend brand X
toothpaste. In a group of 460 dentists, how many
would not recommend brand X?
a) 200
в€— b) 225
c) 355
d) 475
e) 525
19. If x < y, then which of the following is always true?
x2
<
y2
a) xy > 0
b)
d) x2 > y 2
e) 3x < 2y
в€— c) x в€’ y < 0
21. Find the next three items in the pattern 1, 1, 2, 3,
5, 8.
a) 9, 17, 26
d) 14, 22, 36
в€— c) 13, 21, 34
b) 10, 18, 28
e) 16, 24, 40
23. The given cube is cut into 27 smaller cubes. Suppose
you paint the outside of the large cube gray, then put
all the small cubes into a bag. If you pick one of the
small cubes at random, what is the probability that it
will have exactly one gray side?
a)
1
9
в€— b)
2
9
c)
1
3
d)
1
2
e)
7
8
в€— a) 115
b) 298
c) 345
d) 510
e) 613
20. If a > b, then which of the following is always false?
a) a + b > 0
в€— d) a в€’ b < 0
c) a2 > b2
b) ab > 0
e) 5a < 3a
22. What are the next four items in the pattern 5, 10, 8,
13, 11, 16, 14, 19?
в€— a) 17, 22, 20, 25
c) 19, 24, 22, 27
e) 21, 26, 24, 29
b) 18, 23, 21, 26
d) 20, 25, 23, 28
24. The given cube is cut into 27 smaller cubes. Suppose
you paint the outside of the large cube gray, then put
all the small cubes into a bag. If you pick one of the
small cubes at random, what is the probability that it
will have exactly four gray sides?
в€— a) 0
b)
1
3
e)
d)
2
27
4
9
c)
1
9
MMA-086.PCX
MMA-086.PCX
25. Evaluate (11z + 6)(z в€’ 3) for z = 4.
a) в€’35
b) 21
в€— c) 50
d) 70
26. Evaluate (4p в€’ 10)(p + 2) for p = 5.
e) 350
27. Which of the following are factors of h3 + 125?
I.
hв€’5
II.
h+5
III.
h2 в€’ 5h + 25
IV.
h2 + 5h + 25
a) I and II only
в€— c) II and III only
e) III and IV only
b) I and III only
d) II and IV only
a) в€’35
b) в€’10
c) 14
d) 38
в€— e) 70
28. Which of the following are factors of 1 + w3 ?
I.
II.
III.
IV.
1 в€’ 2w + w2
1 в€’ w + w2
1 + 2w + w2
1+w
a) II only
c) I and IV only
e) III and IV only
b) III only
в€— d) II and IV only
SMP rev. 3.0 (PDF) page 60. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DA
29. In the figure, find the difference between the
circumference of the larger circle and the circumference
of the smaller circle?
a)
b)
в€— c)
d)
e)
30. In the figure, find the difference between the area of
the larger circle and the area of the smaller circle?
a) 4ПЂ
3ПЂ
4ПЂ
8ПЂ
x + 4ПЂ
2x + 3ПЂ
MMA-106.PCX
x2 ПЂ
b)
c) (2x + 4)ПЂ
в€— d) (8x + 144)ПЂ
e) (2x2 + 72x + 650)ПЂ
MMA-106.PCX
31. Find the expression that would represent the volume
of the rectangular solid.
32. Find the expression that would represent the volume
of the rectangular solid.
a) x3 + 8x
a) a3 + 5a
в€— b) x3 + 6x2 + 8x
b) 2a2 + 5a + 6
c) 5x2 + 18x + 8
c) a2 + 6a + 6
d) x2 + 6x + 8
e) 3x + 6
в€— d) a3 + 5a2 + 6a
e) 6a2 + 20a + 12
MMA-108.PCX
33. Given (3x + 5)(2x в€’ 1) = x(6x + 1) в€’ 16, what is the
value of 2x ?
a) в€’ 17
2
b) в€’6
35. Solve the equation
a) в€’5
d) в€’3 or 1
в€— c) в€’ 11
3
d)
7
3
34. Given (4t + 1)(2t в€’ 6) = t(8t + 2) в€’ 18, what is the
value of 4t ?
e) 12
1
1
2
+ = 2
.
xв€’1 2
x в€’1
в€— b) в€’3
e) 0 or 1
MMA-108A.PCX
a)
1
2
в€— c) 2
b) 1
36. Solve the equation
a) в€’ 38 or 4
c) в€’5 or 2
d) 4
e) 8
3
1
8
+ =
.
x2 в€’ 16 4
xв€’4
b) в€’4 or в€’ 83
c) в€’14 or
1
4
в€— e) в€’ 83
d) в€’ 16
3
37. Which of the following graphs represent a direct variation?
a)
b)
MMA-161.PCX
в€— d)
c)
MMA-162.PCX
MMA-163.PCX
e)
MMA-164.PCX
MMA-165.PCX
38. Which of the following graphs represent an inverse variation?
в€— b)
a)
MMA-161.PCX
c)
MMA-162.PCX
d)
MMA-163.PCX
e)
MMA-164.PCX
MMA-165.PCX
SMP rev. 3.0 (PDF) page 61. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DA
39. The current I in an electrical conductor varies
inversely as the resistance R of the conductor. If the
current is 12 ampere when the resistance is 240 ohms,
what is the current when the resistance is 540 ohms?
a)
d)
1
10 amperes
2
3 amperes
в€— b)
e)
2
9
3
4
amperes
c)
1
2
amperes
amperes
41. A local library bought 54 books. Some cost $32
each and some cost $44 each. The total cost of the
books was $1,968. How many of the $32 books were
purchased?
в€— a) 34
b) 38
c) 41
d) 45
e) 49
43. Orlando can do a job in 4 days. When Orlando and
Maggie work together, the job takes 2 31 days. How
long would the job take Maggie working alone?
в€— a) 5 35 days
b) 5 34 days
d) 6 87 days
e) 7 16 days
45. Find the solution to
a) в€’4
d) 12
y + 4 = 2.
b) 4
в€— e) no solution
47. In the diagram, if 1 and
following must be true?
a) 1 в€ј
= 6 b) 1 в€ј
= 8
c)
в€— e)
2в€ј
= 3
3в€ј
= 5
d)
c) 6 23 days
2
40. The volume V of a gas varies inversely as the
pressure P upon it. The volume of a gas is 200 cm3
under pressure of 32 kg/cm2 . What will be its volume
under a pressure of 40 kg/cm2 ?
a) 138 cm3
b) 144 cm3
в€— d) 160 cm3
e) 172 cm3
42. Admission prices at a football game were $6 for adults
and $2 for children. The total value of the tickets
sold was $2528, and 454 tickets were sold. How many
adults attended the game?
a) 375 adults
d) 425 adults
b) 400 adults
e) 475 adults
are parallel, which of the
2в€ј
= 5
в€— c) 405 adults
44. A cold water faucet can fill a sink in 12 minutes, and
a hot water faucet can fill it in 15. The drain can
empty the sink in 25 minutes. If both faucets are on
the drain is open, how long will it take to fill the sink?
4
minutes
a) 8 13
9
b) 8 10
minutes
d) 9 98 minutes
2
e) 10 15
minutes
46. Find the solution to
c) 8
c) 154 cm3
a) в€’3
d) 11
m + 7 = 4.
b) 3
в€— e) no solution
48. In the diagram, if 1 and
following must be true?
a) 1 в€ј
= 8 b) 2 в€ј
= 3
c)
e)
2в€ј
= 5 в€— d)
4в€ј
= 7
1
в€— c) 9 11
minutes
2
c) 9
are parallel, which of the
MMA-511.PCX
4в€ј
= 6
MMA-511.PCX
49. The perimeter of an equiangular triangle is 31 cm.
Find the length of each side.
в€— a) 10 13 cm
d) 22 12 cm
b) 11 14 cm
c) 15 cm
a) 7 in.
d) 12 13 in.
e) 45 cm
51. Given the following diagram with m 2 > m P, which
inequality is true?
a)
b)
c)
в€— d)
e)
50. Find the length of each side of an equiangular triangle
with a perimeter of 28 in.
c) 11 23 in.
e) 14 in.
в€’в€’в€’
52. Given the following diagram with SQ bisecting
which inequality is true?
в€— a)
b)
c)
d)
e)
QT > TP
QR > TQ
PT < PQ
PT > QT
QS < QR
в€— b) 9 31 in.
PSR,
RS > RQ
QR > PQ
SR < SQ
SP > QP
SR < SP
MMA-295.PCX
MMA-294.PCX
SMP rev. 3.0 (PDF) page 62. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DA
53. In the given diagram, find the height of the tree to
the nearest tenth.
54. In the given diagram, find the height of the light
house to the nearest tenth.
a) 20.3 m
c) 25.9 m
e) 31.2 m
в€— b) 23.4 m
d) 28.7 m
MMA-332.PCX
a) 44.2 m
d) 47.3 m
b) 46.3 m
e) 52.8 m
в€’в€’в€’
55. Given the figure with RTS a right angle, and TU is
an altitude. If RU = 8 and TU = 4, find the value
of US .
в€— a) 2
d) 10
b) 4
e) 12
MMA-333.PCX
в€— c) 46.6 m
c) 8
в€’в€’в€’
56. Given the figure with RTS a right angle, and TU is
an altitude. If RS = 25 and SU = 5, find the value
of TS .
в€љ
в€љ
b) 5
в€— c) 5 5
MMA-305.PCX
a) 5
в€љ
d) 10
e) 12 2
MMA-305.PCX
57. If the base and altitude of a triangle are 11 and 14
respectively, find the area of the triangle.
a) 25
b) 48
c) 54
в€— d) 77
58. Find the area of a triangle with base 6 and altitude 12.
a) 12
в€— c) 36
b) 18
d) 40
e) 72
e) 108
59. Three metal disks with radii of 10 cm are tangent to
each other. The disks are enclosed by an equilateral
triangle metal frame. What is the length of one side
of the frame?
в€љ
a) (20 3 ) cm
в€љ
b) (18 + 20 3 ) cm
в€љ
c) (20 + 2 3 ) cm
в€љ
в€— d) (20 + 20 3 ) cm
в€љ
e) (2 + 20 3 ) cm
60. Suppose a radio tower is 800 feet tall. Assuming that
the diameter of the earth is 8,000 miles, how far is
it from the top of the tower to the horizon point A
or B ? (Find your answer to the nearest tenth of a
mile.)
a) 28.3 mi
в€— c) 34.8 mi
e) 43.8 mi
b) 30.8 mi
d) 38.4 mi
MMA-410.PCX
MMA-411.PCX
61. Which of the following is a pyramid?
a)
d)
b)
c)
62. Which of the following is a polyhedron with two
congruent bases?
a)
b)
d)
в€— e)
c)
в€— e)
SMP rev. 3.0 (PDF) page 63. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DB
These items are drawn from EducAide’s SAT Math Prep (SAT) module. This module contains 2144 questions
that simulate actual SAT I items in content, style, and format. Both multiple-choice and quantitative comparison
items are included. Many of the multiple-choice items can be automatically reformatted to hide the responses and
substitute answer grids.
1.
In the addition problem, 0 < A < 6 and 0 < B < 6.
How many different integer values of A are possible?
a) 1
2.
в€— d) 4
c) 3
e) 5
AB
+ BA
77
в€’в€’в€’
в€’в€’в€’
In hexagon ABCDEF , AB вЉҐ BC .
m A+m F +m E +m D +m C =
a) 450 в—¦
b) 540 в—¦ в€— c) 630 в—¦
d) 720 в—¦
e) 810 в—¦
It takes a painter 4 hours to paint a room. How
many hours would it take 3 painters to paint a room
2 times larger?
a) 2
3.
b) 2
7.
в€— b) 2 23
d) 4 13
c) 3
SAT-013.PCX
e) 6
8.
в€љ
в€љ
в€љ
3 18 в€’ 48 + 75 =
в€љ
в€љ
a) 3 45
b) 9 2 + 1
в€љ
в€љ
в€љ
e) 9 5
d) 9 2 + 3 3
в€љ
в€љ
в€— c) 9 2 + 3
If P and Q are numbers on the number line, which
of the points shown best represents 2P + Q ?
P
Q
в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’
•..−−•−
.. −−−−−−−−•−
.. −−−•−
.. −−−−−•...−−−−→
... 6
0
1 .... .... 2
3 .... 4 .... 5
A B
a) A
4.
Two conveyors feed coal to a furnace. Conveyor A
feeds 3 pounds of coal per minute and conveyor B
feeds 5 pounds of coal every two minutes. How
many minutes does it take both conveyors to feed
99 pounds of coal into the furnace?
a) 9
b) 11
c) 15
в€— d) 18
e) 21
9.
b) B
d) (2, в€’4)
According to the formula F = 95 C + 32, if the
Fahrenheit (F ) temperature increased 45 degrees, by
how many degrees would the Celsius (C) temperature
be increased?
в€— a) 25 degrees
d) 77 degrees
6.
b) 45 degrees
e) 81 degrees
c) 57 degrees
D
E
c) C
в€— d) D
e) E
In a coordinate graph system, a circle is drawn whose
center is at the origin and whose radius is 5. All of
the points described by the following coordinates will
fall within the circle except
a) (в€’3, в€’3)
5.
C
b) (в€’2, в€’3)
c) (3, 3)
в€— e) (1, 5)
10. In the figure, if the area of the rectangle is equal to
the area of the triangle, then h =
a) 1
в€— d) 4
b) 2
e) 5
c) 3
In the figure, if AC = DF = 12, then BC + DE =
в†ђв€’в€’в€’4в€’в€’в€’в†’
•−−−−−−−−−−−
•−−−−−−−−−−−−−−−−−−−−−•
A
B
SAT-069.PCX
C
в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’12в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в†’
•−−−−−−−−−−−−−−−−−−−−−−
•−−−−−−−−−−•
D
E
11. Of the following numbers, the one which can be
written in the form 3N , where N is an integer, is
F
в†ђв€’в€’в€’4в€’в€’в€’в†’
NUMLIN01.FIG
a) 8
b) 9
c) 12
в€— d) 16
e) 20
a) 44
в€— d) 444,444
b) 4,444
e) 4,444,444
c) 44,444
SMP rev. 3.0 (PDF) page 64. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DB
12. If
a
c
b
2
= ad в€’ bc, then if
d
3
a) в€’3
b) 1
x
x
=
5
1
в€— d) 3
c) 0
2
, x=
1
e) 4
19. How many different 4 Г— 4 squares that can be traced
along existing line segments of the checkerboard
shown?
a) 8
в€— d) 25
b) 10
e) 36
c) 16
13. If a = 2a + 1, for which of the following values of a
does a = 53 ?
в€— a)
1
3
b)
1
2
3
5
c)
d)
2
3
e)
3
2
14. In a school of 500 students, 100 are taking French,
150 are taking algebra, and 75 are taking both
French and algebra. How many students are taking
neither French nor algebra?
в€— b) 325
a) 300
c) 350
d) 375
q
e)
=
pq
q=
pq
p
p
в€— d)
p+q =
p+
q
0
1
2
3
4
5
y
2
3
6
11
18
?
a) 21
b) 23
в€— c) 27
b) 40
c) 45
d) 50
e) 55
18. Employees in a certain company are each assigned
a 4-digit identification number so that no two
employees receive the same number and no number
begins with a zero. What is the greatest number
of employees that can be assigned an identification
number?
a) 3,024
d) 9,900
b) 6,561
e) 10,000
b) 150
e) 168
c) 160
e) 36
17. Three children are each 60 inches tall or less. Their
average (arithmetic mean) height is 50 inches. If one
of them is 55 inches tall, what is the least possible
height, in inches, of a child in the group?
в€— a) 35
c) в€’14
d) в€’7
e) 3
21. In a bag, there are b brown pencils, g green pencils,
and y yellow pencils. If a person selects a pencil at
random from the bag, what is the probability that it
is brown or green?
b+g
y
1
в€— a)
b)
c)
b+g+y
b+g+y
b+g
b+g
y
d)
e)
y
b+g
a) 68
в€— d) 162
d) 31
в€— b) в€’21
22. The table shows the percent correct Sherry received
on each of five 40-question tests. How many questions
total did Sherry answer correctly on the five tests?
16. In the table, what is the missing number?
x
a) в€’32
e) 400
15. If p and q are positive numbers, which of the
following is not always true?
1
q
=
a)
b)
(p + q)2 = p + q
p
pq 2
c)
20. If the average (arithmetic mean) of eight numbers
is в€’4; and the sum of six of the numbers is 10, what
is the average of the other two numbers?
в€— c) 9,000
Test No.
% Correct
1
70%
2
80%
3
75%
4
85%
5
95%
23. In the circle graph shown, the 4 sections represent
the number of fish in a hatchery pond. If there are
1200 sunfish, 800 bass, and 2400 catfish in this lake
and arc PQ measures 45 в—¦, then how many perch are
in this lake?
a) 3,600 в€— b) 2,000
d) 3,000 e) 1,800
c) 2,200
SAT-368.PCX
SMP rev. 3.0 (PDF) page 65. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DB
SUMMARY DIRECTIONS FOR COMPARISON QUESTIONS
Answer: A if the quantity in the column A is greater;
B if the quantity in the column B is greater;
C if the quantities are equal;
D if it is not possible to determine which is greater.
AN E RESPONSE WILL NOT BE SCORED.
Column A
24.
Column B
Column A
1
%
4
0.025
The percent
increase resulting
from changing a
$10 item to an $11
item
32.
A
178 Г— 14
16
25.
30 Г— 178
32
The percent
increase resulting
from changing a
$20 item to an $22
item
C
10 silver pieces and 1 gold piece have
the same value as 3 gold pieces.
B
в€љ
1
в€љ
3
26.
Column B
3
3
Value of 1 gold
piece
33.
Value of 5 silver
pieces
C
C
4 Г— (3 + 3) Г· 2
27.
(4 Г— 3) + (3 Г· 2)
x
B
y
3
y = x2 + 7x + 12
y when x = в€’4
28.
8
4
The product of the three numbers in
the row is equal to the product of the
three numbers in the column.
y when x = в€’3
C
x2 = 16, y 2 = 25
2y в€’ x
34.
0
C
(x + y)(x в€’ y)
29.
9
0 ≤ A < B ≤ 100
B
0<a<b<c<d<e<f
35.
A% of B
B% of A
C
30.
a+d
b+c
D
Andrea has p pencils and Terry has
2 less than twice as many pencils as
Andrea.
SAT-162.PCX
The number of
pencils that Terry
has
31.
A
1
2
2p в€’ 4
x
36.
y
B
SMP rev. 3.0 (PDF) page 66. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DB
Column A
Column B
Column A
Column B
SAT-155.PCX
PQRS is a line segment
в€’в€’в€’ в€’в€’в€’
RT вЉҐ QT
x+w
37.
2(y + z)
SAT-158.PCX
The x coordinate
of point B
42.
The x coordinate
of point A
A
C
a
43.
SAT-185.PCX
1
в€’b
? b = 2a
2b в€’ a
? (2 ? 3)
(1
? 2) ? 3
B
1 liter = 1,000 milliliters
The area of
parallelogram
ABCD
38.
20
1
3
44.
of a liter
333 milliliters
A
B
j, k, , m, and n are consecutive, odd
integers.
average value of j,
k, , m, and n.
45.
C
SAT-138.PCX
the degree measure
of QTS
39.
In a bag containing exactly 20 marbles,
3 are black, 9 are blue, and the
remainder are white.
the degree measure
_
of QS
B
The percent of
white marbles in
the bag
46.
32%
A
40.
AUTOMOBILES SOLD
Surface area of the
rectangular solid
shown
Surface area of the
cube shown
1993
1994
A
CARS-001.TBL
P
Q
R
S
в†ђв€’в€’в€’в€’в€’
•−−−−−−−−
•−−−−−−−−−
•−−−−−−−−
•−−−−→
0
1
2
In 1994 the dealer sold 300 cars.
3
RS > PQ
The number of
cars each
represents
47.
41.
PR
B
QS
60
B
SMP rev. 3.0 (PDF) page 67. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DC
These items are drawn from EducAide’s Advanced Placement Calculus (APC) module. The 1700 questions all
original are useful for regular instruction as well as preparing students for the AP Calculus Exam (AB Level).
1.
Which of the following functions could have the
graph sketched here?
a)
b)
в€— c)
d)
e)
7.
x
f (x) = 12 в€’ 1
f (x) = 2x + 1
f (x) = 2в€’x + 1
f (x) = 3в€’x
f (x) = 3x в€’ 1
Which of в€љ
the following is the graph of
f (x) = ln ( x )?
a)
b)
APC-059.PCX
APC-058.PCX
c)
d)
APC-109.PCX
2.
Which of the following is an approximate root of
y = 12x5 + 15x4 в€’ 8x3 ?
a) в€’0.3791
в€— d) 0.4032
b) в€’0.1020
e) 0.6238
c) 0.2253
APC-061.PCX
APC-062.PCX
в€— e)
3.
Which of the following is an approximate zero of
y = cos(ln x)?
a) в€’4.8115
d) 4.8115
4.
b) в€’4.8105
e) 40.1885
в€— c) 4.8105
What is the domain and range of x2 в€’ 4y 2 = в€’16?
APC-060.PCX
a) domain x в€€ IR; range y = 2
b) domain x ∈ IR; range y ≥ −2
This figure shows the graph of f . Use this figure to
answer the following question(s).
c) domain x ∈ IR; range y ≤ 2
∗ d) domain x ∈ IR; range |y | ≥ 2
e) domain x ∈ IR; range |y | ≥ 4
5.
With respect to which of the following is the graph
of x4 y 2 + 2x2 y в€’ 1 = 0 symmetric?
в€— b) y-axis only
d) origin and the y-axis
a) x-axis only
c) origin only
e) no symmetry
APC-001.AUX
8.
6.
a) 1
в€— b) 2
e) no limit
The graph of which equation listed below has an
asymptote of y = в€’1?
a) y = ex
d) y =
x2
xв€’1
в€— b) y =
в€’x2
x2 в€’ 4
e) y = tan x
lim f is
x→3−
c) y = sin x
9.
lim
x→−2−
a) 1
c) 3
d) 0
x
is
(x + 2)(x в€’ 3)
в€— b) в€’в€ћ
c) 3
d) 0
e) в€ћ
SMP rev. 3.0 (PDF) page 68. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DC
10.
lim
x→−1+
x2
is
(1 в€’ x)(1 + x)
c) 1в€’
b) в€’в€ћ
a) 1
d) 1+
19. The figure shows the graph of f , the derivative of
the function f . The domain of the function f is
−10 ≤ x ≤ 10. For what value(s) is the graph of f
concave downwards?
в€— e) в€ћ
11. Assume f (7) = 0, f (7) = 14, g(7) = 1, and g (7) = 17 .
f (x)
Find h (7) given h(x) =
.
g(x)
a) в€’14
b) в€’2
в€— c) 14
d)
49
2
e) 98
12. Assume f (3) = 0, f (3) = 6, g(3) = 1, and g (3) =
Find h (3) given h(x) =
a) в€’6
b) в€’2
13. If f (x) =
в€— a) в€љ
в€љ
c)
f (x)
.
g(x)
9
2
в€— d) 6
1
.
3
e) 18
4 + e2x , then f (x) =
e2x
4 + e2x
d) ex
1
в€љ
2 2e2x
1
e) в€љ
4 + e2x
b)
APC-018.PCX
в€— a) в€’1 < x < 1
d) 0 < x < 3
b) в€’3 < x < 3
e) Г�
c) в€’3 < x < 0
20. The graph of the derivative of f (x) is shown.
xe2xв€’1
c) в€љ
4 + e2x
14. For any time t ≥ 0, x(t) = e2t and y(t) = e−4t . Find
1
dy
at t = .
dx
6
в€’2
b) 2
c) 2e
d) 4e
e) e
в€— a) e
APC-035.PCX
From the following graphs choose f .
15. For any time t ≥ 0, x(t) = t3 and y(t) = 3 ln t.
dy
Find
.
dx
1
1
в€— e) 3
a) t2
b) t3
c) t4
d) 2
t
t
16. Given the parametric equations x = 2 cos3 t and
d2 y
y = 2 sin3 t, find
.
dx2
a) 31 cos4 t sin t в€— b) 23 cos4 t sin t
c) 23 cos3 t sin t
d)
8
3
cos4 t sin t
e)
2
3
в€— b)
a)
APC-036.PCX
c)
APC-037.PCX
d)
cos t sin4 t
17. Given a function defined by f (x) = 3x5 в€’ 5x3 + 12,
for what value(s) of x is there a point of relative
minimum?
в€— a) 1 only
d) 0 and 1
b) в€’1 only
e) 0 only
c) 0 and в€’1
APC-038.PCX
APC-039.PCX
e)
18. Given a function defined by f (x) = 3x5 в€’ 5x3 в€’ 8,
for what value(s) of x is there a point of relative
maximum?
в€— a) 0 only
d) 1 only
b) 0 and в€’1
e) 1 and в€’1
c) 0 and 1
APC-040.PCX
SMP rev. 3.0 (PDF) page 69. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
DC
21. Find the point on the curve f (x) = x2 + 1 that is
nearest to the the point B(3, 1).
в€— a) (1, 2)
b) (2, 5)
c) (0, 1)
d) ( 31 , 32 )
e) (5, 2)
22. Find a point on the curve x2 в€’ 9y = 0 that is closest
to the point P(5, в€’2).
a) (в€’3, 1)
b) (2, 5)
c) (в€’1, 4)
28. Find the area of the region bounded by the graph
r = 2(cos Оё + 1).
a)
ПЂ
6
b)
4ПЂ
3
c) 3ПЂ
29. Find the area of the region bounded by the graphs of
f (x) = 6x в€’ x2 and g(x) = x2 в€’ 2x.
a)
20
3
в€— b)
64
3
c) 32
d) 36
в€— e) (3, 1)
d) (2, 1)
в€ћ
30. Determine whether the integral
4 + 5x3/2
23. Integrate:
x
c)
в€’2xв€’3/2
e)
4xв€’1/2
a) converges, 1
в€— b) 8
d) 2
x + 25 x2 + C
x+
5 2
2x
104
3
c)
104
9
d)
3
104
e) 104
3
4
0
в€— c) converges,
b) converges, 2
в€’ 12
d) converges,
3
2
e) diverges
1
x2 (x3 + 8)2 dx
0
a)
c) converges,
в€— e) diverges
a) converges, 1
25. Evaluate:
31
9
4
3
1
3
1
dx
3
в€’в€ћ (x в€’ 1)
converges or diverges and evaluate the integral if it
converges.
x(x4 + 4x2 + 4) dx
в€— b)
dx converges
31. Determine whether the integral
+ 5x + C
0
100
3
d) converges,
b) converges,
+C
2
a)
e) 128
or diverges and evaluate the integral if it converges.
dx
+5+C
24. Evaluate:
1
x3/4
1
a) 2xв€’3/2 + 52 x2 + C
в€— e) 6ПЂ
d) 4ПЂ
b)
103
9
в€— c)
217
9
d)
217
3
e) 217
26. Which of the following definite integrals represents
the area of the shaded region?
32. A particle’s motion is described by x(t) = 4t3 − 5t2 ,
t ≥ 0, where t is in seconds and distance in meters.
Find the average velocity in the third second.
a) 19 m/s
d) 51 m/s
b) 38 m/s
в€— e) 78 m/s
c) 48 m/s
2
(4 в€’ x2 )
a)
33. A mold culture doubles its mass every three days.
Find the growth model for a plate seeded with
1.2 grams of mold.
0
2
(4 в€’ x2 ) dx
b)
4
2
(4 в€’ x2 ) dx
в€— c)
0
(4 в€’ x2 ) dx
2
4
(4 в€’ x2 ) dx
e)
0
APC-054.PCX
27. Which of the following definite integrals represents
the area of the shaded region?
4
c) y = 1.2e0.23856t
d) y = 1.2e0.38761t
34. A mold culture doubles its mass every seven days.
Find the growth model for a plate seeded with
0.9 grams of mold.
в€— a) y = 0.9e0.09902t
b) y = 0.9e0.12183t
c) y = 0.9e0.38541t
d) y = 0.9e0.45128t
e) y = 0.9e0.81818t
x2 dx
a)
в€— b) y = 1.2e0.23105t
e) y = 1.2e0.54931t
4
d)
a) y = 1.2e0.10034t
0
10
2
x2 dx
в€— b)
0
i=1
2
a) 81
x2 dx
c)
(i2 в€’ 2i + 3)
35. Evaluate:
b) 83
c) 245
в€— d) 305
e) 865
1
2
10
x2
d)
i=1
4
x2
e)
0
(2 в€’ 3i + 2i2 ).
36. Evaluate:
0
APC-053.PCX
a) 618
в€— b) 625
c) 717
d) 735
e) 1395
SMP rev. 3.0 (PDF) page 70. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
EA
These items are drawn from a module (AW1) that EducAide developed jointly with Addison Wesley Longman for
its Grade 10 Mathematics textbook, Western Canada Edition. The module is sold by AWL to schools throughout
Canada.
1.
Evaluate xв€’2 y в€’1 for x = 4 and y = в€’1.
a) в€’8
3.
1
в€— b) в€’ 16
c)
1
16
2.
d) 8
a)
b)
в€— c)
d)
e)
a) в€’25
e) 16
Calculate the length, x, to the nearest hundredth of a
metre.
Evaluate xв€’1 y в€’2 for x = в€’1 and y = 5.
4.
10.91 m
11.79 m
21.82 m
23.58 m
26.00 m
b) в€’10
1
в€— c) в€’ 25
7.
Calculate the distance between the points J (в€’5, 7)
and K (в€’1, 2).
в€љ
в€љ
в€љ
в€љ
в€љ
b) 89
c) 97
d) 113 e) 117
в€— a) 41
9.
On May 12, 1926, Norwegian Roald Amundsen crossed
the North pole in the air ship Norge. Near the end
of its journey its speed was 30 km/h and it was
descending at 10 m/min. What was the slope of its
descent to two decimal places?
a) в€’0.20
в€— c) 0.02
b) в€’0.02
d) 0.10
AW1-013.PCX
6.
8.
Determine an equivalent form for
в€љ
a) в€’35
b) в€’ 35
в€љ
в€љ
в€љ
в€љ
e) 8 в€’ 15
в€— d) 15 в€’ 5 2
в€љ в€љ
в€љ
5 ( 3 в€’ 10 ).
в€љ
в€љ
c) 15 в€’ 10
Calculate the distance between the points J (3, в€’2)
and K (в€’3, в€’6).
в€љ
в€љ
a) 4
в€— b) 52
c) 8
d) 82
e) 10
10. The airplane Spirit of St. Louis completed the first
non-stop trans Atlantic flight in 1927. At one point in
its descent into Le Bourget Airport, Paris, its airspeed
was 100 km/h and and it was descending at 30 m/min.
What was the slope of its descent to two decimal
places?
a) в€’0.03
c) в€’0.01
e) 0.03
e) 3.00
e) 25
11.49 m
22.98 m
27.42 m
32.25 m
264.00 m
AW1-012.PCX
5.
1
25
Calculate the length, x, to the nearest hundredth of a
metre.
a)
в€— b)
c)
d)
e)
в€љ в€љ
в€љ
Determine an equivalent form for 3( 5 в€’ 6 ).
в€љ
в€љ
a) в€’3
b) в€’ 3
c) 8 в€’ 3
в€љ
в€љ
в€љ
в€љ
в€— e) 15 в€’ 3 2
d) 15 в€’ 6
d)
в€— b) в€’0.02
d) 0.02
AW1-113.PCX
AW1-114.PCX
11. The intersection point of two perpendicular lines
lies on the x-axis. The equation of one line is
2x в€’ y + 4 = 0. Determine the equation of the other
line.
в€— a) x + 2y + 2 = 0
c) x в€’ 2y в€’ 2 = 0
e) 2x в€’ y в€’ 4 = 0
b) x в€’ 2y + 2 = 0
d) x + 2y в€’ 2 = 0
13. Calculate the surface area of a sphere with a radius of
7 cm.
12. The intersection point of two perpendicular lines
lies on the x-axis. The equation of one line is
x + 2y в€’ 4 = 0. Determine the equation of the other
line.
a) y = в€’2x в€’ 8
d) y =
1
2x в€’ 8
b) y = 2x + 8
e) y =
14. Calculate the surface area of a sphere with a radius of
8 cm.
a) 7ПЂ cm2
b) 14ПЂ cm2
a) 8ПЂ cm2
b) 16ПЂ cm2
c) 49ПЂ cm2
d) 98ПЂ cm2
c) 64ПЂ cm2
в€— d) 256ПЂ cm2
в€— e) 196ПЂ cm2
в€— c) y = 2x в€’ 8
в€’ 12 x в€’ 8
e) 512ПЂ cm2
AW1-311.PCX
AW1-312.PCX
SMP rev. 3.0 (PDF) page 71. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
EA
15. The slopes of perpendicular line segments are
Find d.
a) в€’90
c) в€’ 91
в€— b) в€’9
d) 9
1
9
and d.
e) 10
17. Simplify: (x2 в€’ 4x + 4y) в€’ (3x2 + 14x в€’ 10y)
a) в€’4x2 в€’ 18x + 14y
в€— a) в€’ 11
4
4
b) в€’ 11
d) в€’2x2 в€’ 18x в€’ 6y
a) в€’3x2 + 10x + 17y
9m 4m 5m
в€’
+
3
9
6
25m
61m
a)
в€— b)
c) 4m
6
18
6m 3m m
в€’
+
3
6
3
6
11m
2m
a)
в€— b)
c)
11m
6
6
d) 5m
e)
10m
9
a)
d)
b) 6675 m
e) 26 136 m
в€— e)
c)
в€— c) 21 606 m
a) 1581 m
в€— d) 20 554 m
24. For
4
5
a)
d)
b) 5493 m
e) 21 329 m
a) 4.3
в€— d) 14.9
b) 7.9
e) 43.4
в€— b)
e)
5
12
13
5
c)
CAB to 1 decimal
c) 13.4
AW1-392.PCX
26. Calculate the length of AB in
place.
a) 4.3
d) 15.6
27. Two fishing trawlers leave port at the 6:00 am. One
travels at 16 km/h on a bearing of 204 в—¦. The other
travels at 22 km/h on a bearing of 253 в—¦. How far
apart are the two trawlers at 8:00 am?
b) 32.4 km
e) 69.3 km
в€— c) 33.4 km
c) 5915 m
12
13
CAB to 1 decimal
b) 6.8 в€— c) 12.2
e) 24.8
AW1-447.PCX
a) 16.7 km
d) 34.7 km
e) 3m
RAY , determine tan A.
5
13
12
5
AW1-391.PCX
25. Calculate the length of AB in
place.
m
3
AW1-353.PCX
HAM , determine tan A.
b)
d)
22. An Air Canada commuter jet is flying at an altitude
of 5700 m over the Great Lakes. At a certain time,
the angle of depression to the shoreline from the jet
is 15.5 в—¦. How much farther does the jet have to fly
before it reaches the shoreline? Make your answer
correct to the nearest metre.
AW1-352.PCX
3
4
4
3
d) 5x2 в€’ 20x + 17y
20. Simplify:
21. An Air France Concord jet is flying at an altitude of
6400 m over the ocean directly toward a coastline. At
a certain time, the angle of depression to the coastline
from the jet is 16.5 в—¦. How much farther does the jet
have to fly before it reaches the coastline? Make your
answer correct to the nearest metre.
3
5
5
4
e) 44
e) 3x2 в€’ 20x + 17y
19. Simplify:
23. For
d) 15
b) 3x2 + 10x + 5y
в€— c) в€’3x2 в€’ 20x + 17y
e) 2x2 в€’ 10x + 14y
a) 1896 m
d) 22 534 m
11
4
c)
4
11
18. Simplify: (x2 в€’ 5x + 6y) в€’ (4x2 + 15x в€’ 11y)
в€— b) в€’2x2 в€’ 18x + 14y
c) 2x2 + 10x + 6y
16. The slopes of perpendicular line segments are
and d. Find d.
AW1-448.PCX
28. Two bicyclists start from the same place at 8:00 am.
One peddles at 24 km/h on a bearing of 167 в—¦. The
other peddles at 21 km/h on a bearing of 215 в—¦. How
far apart are the two bicycles at 11 am?
a) 18.5 km
d) 59.6 km
b) 41.1 km
e) 123.4 km
в€— c) 55.5 km
SMP rev. 3.0 (PDF) page 72. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
EB
These items are drawn from the Applied Mathematics (CD1) module, which is sold exclusively by ITP SouthWestern.
The module contains all skill drills and test items from the Applied Mathematics series developed by the Center for
Occupational Research and Development (CORD).
Use this chart to answer the following problem(s).
7.
In a triangle, two of the angles measure 25 в—¦ and 65 в—¦.
Is this triangle a right triangle? Yes
8.
How much plastic is required to form a hemispherical
bowl of the dimensions shown? 32.7 cm3
CD1-001.AUX
1.
Match the underlined digit in the numbers on the
left with the decimal place names.
a)
3.141
1)
Tenths
b)
825,651.587
2)
Thousandths
c)
2.892616
3)
Hundredths
d)
0.4
4)
Thousands
9.
3; 4; 2; 1
2.
When you multiply 35 Г— 74 on your calculator, which
answer below is nearest the one on your display?
a) 3.23
3.
в€— b) 84%
10. A loading chute brings grain into a bin as shown in
the drawing. The bin is a cone. How many bushels
of wheat will the bin hold? (There are 0.8 bushels
per cubic foot.) 911.02 bu
d) 1.05
c) 421%
Data can best be defined as
a)
в€— b)
c)
d)
5.
в€— c) 0.34
What is the amplitude of the wave described by the
equation y = 3 sin x ? 3 units
4
Your teacher reports that 25
of the students in your
class failed the last test. What percent of your class
passed the test?
a) 42.5%
4.
b) 16.8
CD1-121.PCX
d) 29%
.
a list of all positive numbers
factual information collected to solve a problem
the batting order for a softball team
a Greek word meaning problem
The graphed line shown is
y = 2x. What relationship
between y and x is shown by
the line and the shaded area
combined?
a) y ≥ 2x
c) y < 2x
CD1-338.PCX
11. What advantage does the more complex multiple
sampling plan sometimes have over the relatively
simple single sampling plan?
Often you need to inspect fewer items with the multiple sampling plan
to make a decision to accept or reject the lot (particularly if the lot is
very good or very bad).
Use this statement to answer the following question(s).
Fill a hose-end sprayer with 6 ounces of
concentrated insecticide to obtain 20 gallons of
spray.
b) y > 2x
∗ d) y ≥ 2x
CD1-019.AUX
CD1-373.PCX
6.
You have a list of temperatures taken every hour. If
you want to show a trend in the temperatures, you
should use a
.
в€— a) line graph
c) stacked bar graph
b) pie chart
d) scatter plot
12. What is the specified ratio of concentrated insecticide
to gallons of spray? 6 oz/20 gal or 3 oz/10 gal
CD1-019.AUX
13. How much concentrated insecticide would be needed
to make 15 gallons of spray? 4.5 ounces
SMP rev. 3.0 (PDF) page 73. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
EC
These items are drawn from the Applications in Biology & Chemistry (CD2) module, which is sold exclusively
by ITP SouthWestern. The module contains all test items from the Applications in Biology & Chemistry series
developed by the Center for Occupational Research and Development (CORD).
1.
What process ensures that after fertilization the
chromosome numbers of the offspring will be the
same as in the parents?
в€— b) meiosis
d) replication of DNA
a) mitosis
c) protein synthesis
2.
Which type of cancer probably results from smoking
tobacco and inhaling certain air pollutants?
в€— a) carcinoma
c) lymphoma
3.
b) leukemia
d) sarcoma
The final step in the electron transport chain
.
is
a)
b)
в€— c)
d)
the
the
the
the
formation
formation
formation
formation
of
of
of
of
ATP
FADH
water
NADH
7.
If two people who are heterozygous for sickle-cell
trait marry, what are the chances that their first
child will have sickle-cell anemia? One in four
8.
During which of the two nightly sleep patterns do
you dream? REM sleep
9.
From your data in Lab 8 How Does Thiobacillus
ferrooxidans Remove Metal from Ore? , what is the
effect of ferric ions (Fe+++ ) on copper metal?
Ferric ions oxidize copper metal and make the copper soluble.
10. The reaction given releases heat to the environment.
Which has a higher heat content, compounds A
and B together or compound AB ? Explain.
A + B в†’ AB
∆ H = −100 kcal
Since the negative value of ∆ H indicates that heat is released to the
surroundings, Compounds A and B have higher heat content than
compound AB.
11. Define: Batch processing
4.
Many cooking oils are extracted and purified from
which part of the plant?
a) leaves
в€— c) seeds
5.
b) roots
d) flower petals
Microorganisms that carry out photosynthesis cannot
.
live for very long without
в€— a) light
c) oxygen
6.
b) organic matter
d) growth medium
The map shown shows currents in an ocean area
that is important as a commercial fishery. At what
points would the supply of nutrients support large
fish populations?
In batch processing, a container called the reaction vessel is filled with
the medium containing the raw materials and nutrients, the biocatalyst
is added and conversion takes place. Product gases may be removed
from the container. Additional nutrients, raw materials, air, and other
materials may be added.
12. Describe the process of oxidation.
Oxidation is the combination of an oxidizing agent such as oxygen
molecules with certain elements or compounds to produce a new
molecule known as an oxide.
13. How do development changes in the nervous system
relate to the progress of mental development?
Development involves more than brain growth. Neurons throughout the
body undergo changes after birth. The development of the myelin sheath
around axons speeds up the transmission of impulses. The myelin sheath
develops at different rates in different parts of the brain. Development
begins in the motor area and continues in the centers of touch, vision,
and auditory function. This process continues throughout childhood and
adolescence.
14. Explain the differences in a vegan diet, a
lacto-vegetarian diet, and a lacto-ovo vegetarian diet.
CD2-061.PCX
a) X and W
в€— c) X and Y
b) Y and W
d) W and Z
The vegan diet excludes all animal products from the diet. Protein is
provided by complementary vegetable sources. Lacto-vegetarian diets
include dairy products adequate sources of vitamin B12 and additional
sources of high-quality protein. Lacto-ovo vegetarians incorporate both
eggs and dairy products in their diets.
SMP rev. 3.0 (PDF) page 74. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
ED
These items are drawn from the Principles of Technology (CD3) module, which is sold exclusively by ITP
SouthWestern. The module contains all student exercises and test items from the Principles of Technology series
developed by the Center for Occupational Research and Development (CORD).
1.
Mirrors reflect 100% of the light.
в€— b) false
a) true
2.
в€— b) false
Efficiency can be calculated by using
4.
b)
What is the quantity moved in a fluid system?
a) weight
5.
d) density
в€— b) reflection
c) diffraction
11. A 0.2-hp air motor is 60% efficient. Find the fluid
energy EIN of the input air each second in units of
lb В· ft. 181.5 lb В· ft
12. What’s the flow rate through a pipe if a flowmeter is
calibrated at 1500 pulses/gallon and registers 60,000
pulses in a 10-minute period? 4 gal/min
13. A CO2 laser delivers a 40-watt beam. The beam is
focused onto a target. The laser spot on the target
is 0.1 centimeter in diameter. Determine the power
density on the target in watts per square centimeter.
5.09 Г— 103 W/cm2
14. Use parallel light rays in the sketch to show how light
rays are bent (refracted) and focused by a concave
lens. [diagram]
Linear momentum is the product of an
object’s
and velocity.
a) weight
7.
b) distance в€— c) volume
When a light ray traveling in a medium strikes the
surface of another medium and is turned back into
.
the original medium, the process is called
a) refraction
6.
.
Work in
Г— 100%
Work out
Work out
в€— d)
Г— 100%
Work in
Work in
Work out
Work out
c)
Work in
Work out
e)
torque
a)
The prime mover or force-like quantity in the thermal
system is
. temperature difference
10. An electrical device that is used to store electrical
. capacitor
energy is called a
Interferometers measure brightness of light.
a) true
3.
9.
b) torque
c) inertia
в€— d) mass
Which statements are true? (Note: there may be
more than one correct answer.)
CD3-068.PCX
15. Is the garage car lift shown more like a hydraulic
jack or a pressure intensifier? Explain your answer in
one or two sentences.
CD3-033.PCX
a) IMA is greater than 1.
b) AMA will be less than the IMA.
c) Output shaft will move slower than the input
shaft.
d) Input force will be smaller than the resulting
output force.
A garage car lift is more like a hydraulic jack. That’s because
pressurized fluid is used as the transfer medium and extends continuously
from the input piston to the output piston. In a pressure intensifier,
the fluid medium does not extend continuously from the input piston
to the output piston . Input and output faces for the pressure
intensifier are connected by a metal rod.
a, b, c, and d
8.
Air molecules nest to a loudspeaker vibrate in a
direction along the path of travel of the sound energy.
[transverse,
This kind of wave is called a
longitudinal] wave. longitudinal
CD3-019.PCX
SMP rev. 3.0 (PDF) page 75. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BLANK PAGE
FA
These items are drawn from the French Translation of EducAide’s Mid-level Math Assessment (MMF) module. This
module is intended for immersion and Francophile schools in the U.S. and Canada. It includes 5000 multiple-choice
problems covering pre-algebra, algebra, and geometry.
1.
Trouve le quotient et le reste quand 653 est divisВґe
par 9.
a) 72 r 1 в€— b) 72 r 5
3.
b) 721 m
в€— e) 6 284 m
c) 3,1416 Г— 10в€’3
b) 43 r 3
6.
в€— c) 29,031
d) 45 r 2
b) 264 m
e) 9 684 m
e) 45 r 5
c) 8 450 m
Quel nombre d´ecimal est repr´esent´e par l’´ecriture
quatre-vingt-huit et quatre-vingt-seize milli`emes ?
в€— b) 88,096
e) 88,960
a) 88,0096
d) 88,96
8.
c) 44 r 7
Le point le plus ВґelevВґe de la Terre est le Mt. Everest
qui se trouve `
a une altitude de 8 848 m au dessus du
niveau de la mer. La Mer Morte est le point le plus
bas `
a 398 m en dessous du niveau de la mer. Quelle
est la diff´erence d’altitude entre ces deux endroits?
a) 22 m
в€— d) 9 246 m
Simplifie 4,08 Г— 10в€’10 7,7 Г— 105 , et Вґecris ta rВґeponse
en utilisant la notation scientifique.
в€— a) 3,1416 Г— 10в€’4
4.
c) 2 402 m
b) 29,0031
e) 29,311
Trouve le quotient et le reste quand 345 est divisВґe
par 8.
в€— a) 43 r 1
e) 74 r 8
Quel nombre d´ecimal est repr´esent´e par l’´ecriture
vingt-neuf et trente-un milli`emes ?
a) 29,00031
d) 29,31
7.
d) 73 r 5
Le Mt. McKinley, le point le plus ВґelevВґe en AmВґerique
du Nord, se trouve `a une altitude de 6 198 m au dessus
du niveau de la mer. Death Valley, le point le plus
bas, est `
a 86 m en dessous du niveau de la mer. Quelle
est la diff´erence d’altitude entre ces deux endroits?
a) 72 m
d) 6 112 m
5.
c) 73 r 3
2.
c) 88,906
Simplifie 7,5 Г— 10в€’9 9 Г— 10в€’7 , et Вґecris ta rВґeponse
en utilisant la notation scientifique.
b) 31,416 Г— 10в€’5
a) 6,75 Г— 10в€’16
в€— b) 6,75 Г— 10в€’15
d) 0,31416 Г— 10в€’3
d) 675 Г— 10в€’13
e) 6,75 Г— 10в€’14
c) 67,5 Г— 10в€’14
e) 314,16 Г— 10в€’2
9.
10. Quel pourcentage du diagramme est hachurВґe?
Quel pourcentage du diagramme est hachurВґe?
a) 3,75%
d) 37%
b) 12,5%
в€— e) 37,5%
a) 3,75%
в€— d) 62,5%
c) 25%
11. Dans le chenil de D chiens de Mme Payette, 31 sont
classifiВґe comme gros chiens et 14 du reste comme chiens
de taille moyenne. Combien de petits chiens y-a-t-il
dans ce chenil?
a)
1
6
В·D
b)
1
3
В· D в€— c)
1
2
В·D
d)
2
3
В·D
e)
5
6
В·D
13. La distance qui sВґepare la Terre de la plan`ete Pluton
est de 4,58 Г— 109 kilom`etres. En avril 1983, Pioneer
Вґemit des signaux radio de Pluton vers la Terre.
Combien de temps faut-il `a ces signaux pour parcourir
cette distance, en sachant que la vitesse de de ces
signaux est de 3 Г— 105 kilom`etres per seconde, soit la
vitesse de la lumi`ere? (Utilise la formule d = rt o`
u
d est la distance, r la vitesse de la lumi`ere et t le
temps.)
a) 13 740 secondes
c) 16 244 secondes
e) 18 102 secondes
b) 6,25%
e) 63%
c) 37,5%
12. Chacun des N membres du camp choisit soit le
football, soit le tennis, ou le volley-ball comme activitВґe
journali`ere. Si 12 des membres choisit le football et
qu’ 31 choisit le volley-ball, combien de membres
choississent le tennis?
в€— a)
1
6
В·N
b)
1
3
В·N
c)
1
2
В·N
d)
2
3
В·N
e)
5
6
В·N
14. La distance qui sВґepare le Soleil de la Terre est de
1,496 Г— 108 kilom`etres Combien de temps faut-il `
a
la lumi`ere pour parcourir cette distance, en sachant
que la vitesse de la lumi`ere est de 3 Г— 105 kilometres
par seconde? (Utilise la formule d = rt o`
u d est la
distance, r la vitesse de la lumi`ere et t le temps)
a) 5 secondes
b) 20 secondes
d) 200 secondes в€— e) 500 secondes
c) 50 secondes
в€— b) 15 267 secondes
d) 17 587 secondes
SMP rev. 3.0 (PDF) page 77. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FA
15. Une Вґepicerie vend k kilogrammes de beurre `
a b cents.
Quelle expression exprime le nombre de cents que
l’´epicier re¸coit pour x kilogrammes de beurre vendu?
kx
k
ka
a)
cents
b)
cents
c)
cents
b
bx
x
k
bx
d)
cents
в€— e)
cents
bx
k
16. Un magasin vend c m`etres de moquette `
a d dollars.
Quelle expression exprime le nombre de dollars que le
magasin reВёcoit en vendant x m`etres de moquette.
dx
c
cd
в€— a)
dollars
b)
dollars
c)
dollars
c
dx
x
d
cx
d)
dollars
e)
dollars
dx
d
17. Un sondage alВґeatoires dВґemontre que 7 personnes
sur 10 prВґef`erent des fruits comme dessert. Sur
750 personnes, combien d’entre-elles ne pr´ef`erent pas
avoir des fruits comme dessert?
18. Trois dentistes sur quatre recommandent une
marque X de dentifrice. Sur 460 dentistes, combien
d’entre eux ne recommandent pas la marque X?
a) 200
в€— b) 225
c) 355
d) 475
19. Si x < y, quel ВґenoncВґe est toujours vrai?
a) xy > 0
b) x2 < y 2
d) x2 > y 2
e) 3x < 2y
в€— c) x в€’ y < 0
в€— c) 13, 21, 34
b) 10, 18, 28
e) 16, 24, 40
23. Le cube ci-dessous est dВґecoupВґe en 27 cubes plus petits.
Suppose que tu peignes l’ext´erieur du cube initial en
gris et que tu mettes tous les petits cubes dans un
sac. Si tu tires un petit cube au hasard, quelle est la
probabilit´e pour qu’il ait seulement un cot´e peint en
gris?
a)
1
9
в€— b)
2
9
c)
1
3
d)
1
2
e)
b) 298
c) 345
d) 510
e) 613
20. Si a > b, quel ВґenoncВґe est toujours faux?
21. Trouve les trois prochains nombres de la suite 1, 1, 2,
3, 5, 8.
a) 9, 17, 26
d) 14, 22, 36
в€— a) 115
e) 525
7
8
a) a + b > 0
в€— d) a в€’ b < 0
c) a2 > b2
b) ab > 0
e) 5a < 3a
22. Quels sont les quatre prochains nombres de la suite
5, 10, 8, 13, 11, 16, 14, 19?
в€— a) 17, 22, 20, 25
c) 19, 24, 22, 27
e) 21, 26, 24, 29
b) 18, 23, 21, 26
d) 20, 25, 23, 28
24. Le cube ci-dessous est dВґecoupВґe en 27 cubes plus petits.
Suppose que tu peignes l’ext´erieur du cube initial en
gris et que tu mettes tous les petits cubes dans un
sac. Si tu tires un petit cube au hasard, quelle est
la probabilit´e pour qu’il ait exactement quatre cot´es
peints en gris?
в€— a) 0
b)
1
3
e)
d)
2
27
4
9
c)
1
9
MMA-086.PCX
MMA-086.PCX
25. Evalue (11z + 6)(z в€’ 3) pour z = 4.
a) в€’35
b) 21
в€— c) 50
d) 70
26. Evalue (4p в€’ 10)(p + 2) pour p = 5.
e) 350
27. Parmi les expressions suivantes, la(es)quelle(s) est
(sont) un (les) facteur(s) de h3 + 125?
I.
II.
III.
IV.
hв€’5
h+5
h2 в€’ 5h + 25
h2 + 5h + 25
a) I et II seulement
в€— c) II et III seulement
e) III et IV seulement
a) в€’35
c) 14
d) 38
в€— e) 70
28. Parmi les expressions suivantes, la(es)quelle(s) est
(sont) un (les) facteur(s) de 1 + w3 ?
I.
II.
III.
IV.
b) I et III seulement
d) II et IV seulement
b) в€’10
(1 в€’ 2w + w2 )
(1 в€’ w + w2 )
(1 + 2w + w2 )
(1 + w)
a) II seulement
c) I et IV seulement
e) III et IV seulement
b) III seulement
в€— d) II et IV seulement
SMP rev. 3.0 (PDF) page 78. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FA
29. Etant donnВґee la figure suivante, calcule la diffВґerence
de circonfВґerence entre les deux cercles.
a)
b)
в€— c)
d)
e)
3ПЂ
4ПЂ
8ПЂ
x + 4ПЂ
2x + 3ПЂ
30. Etant donnВґee la figure suivante, calcule la diffВґerence
de surface entre les deux cercles.
a) 4ПЂ
MMA-106.PCX
x2 ПЂ
b)
c) (2x + 4)ПЂ
в€— d) (8x + 144)ПЂ
e) (2x2 + 72x + 650)ПЂ
MMA-106.PCX
31. Trouve l’expression qui repr´esente le volume du
parallВґelВґepip`ede.
a) x3 + 8x
32. Trouve l’expression qui repr´esente le volume du
parallВґelВґepip`ede.
a) a3 + 5a
в€— b) x3 + 6x2 + 8x
b) 2a2 + 5a + 6
c) 5x2 + 18x + 8
c) a2 + 6a + 6
d) x2 + 6x + 8
e) 3x + 6
в€— d) a3 + 5a2 + 6a
e) 6a2 + 20a + 12
MMA-108.PCX
33. Etant donnВґe (3x + 5)(2x в€’ 1) = x(6x + 1) в€’ 16, quelle
est la valeur de 2x ?
a) в€’ 17
2
b) в€’6
35. R´esous l’´equation
a) в€’5
d) в€’3 ou 1
в€— c) в€’ 11
3
d)
7
3
e) 12
1
1
2
+ = 2
.
xв€’1 2
x в€’1
в€— b) в€’3
e) 0 ou 1
MMA-108A.PCX
34. Etant donnВґe (4t + 1)(2t в€’ 6) = t(8t + 2) в€’ 18, quelle est
la valeur de 4t ?
a)
1
2
в€— c) 2
b) 1
36. R´esous l’´equation
c) в€’5 ou 2
a) в€’ 38 ou 4
d) в€’ 16
3
d) 4
e) 8
3
1
8
+ =
.
x2 в€’ 16 4
xв€’4
b) в€’4 ou в€’ 83
c) в€’14 ou
1
4
в€— e) в€’ 83
37. Parmi les graphiques suivants, lequel reprВґesente une variation directe?
a)
b)
MMA-161.PCX
в€— d)
c)
MMA-162.PCX
MMA-163.PCX
e)
MMA-164.PCX
MMA-165.PCX
38. Parmi les graphiques suivants, lequel reprВґesente une variation inverse?
в€— b)
a)
MMA-161.PCX
c)
MMA-162.PCX
d)
MMA-163.PCX
e)
MMA-164.PCX
MMA-165.PCX
SMP rev. 3.0 (PDF) page 79. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FA
39. Dans un conducteur Вґelectrique, le courant I varie
inversement en fonction de la rВґesistance R du
conducteur. Si le courant est de 21 amp`ere quand la
rВґesistance est de 240 ohms, quel est le courant quand
la rВґesistance est de 540 ohms.
a)
d)
1
eres
10 amp`
2
eres
3 amp`
в€— b)
e)
2
9
3
4
amp`eres
c)
1
2
amp`eres
b) 38
c) 41
d) 45
e) 49
43. Orlando peut faire une certaine tache en 4 jours.
Quand Orlando et Maggie travaillent ensemble, la
tache leur demande 2 13 jours. De combien de temps
aurait besoin Maggie si elle travaillait seule?
в€— a) 5 35 jours
b) 5 34 jours
d) 6 87 jours
e) 7 16 jours
45. Trouve la solution de
c) 6 23 jours
y + 4 = 2.
a) в€’4
b) 4
в€— e) pas de solution
b) 144 cm3
в€— d) 160 cm3
e) 172 cm3
c) 154 cm3
1
d) 12
et
42. Les prix pour un match de football Вґetaient de 6$ pour
les adultes et de 2$ pour les enfants. Si la vente des
tickets a rapportВґe 2 528$ et que 454 tickets ont ВґetВґe
vendus, combien d’adultes ont assist´e au match?
a) 375 adultes
d) 425 adultes
2
sont parall`eles,
3в€ј
= 5
в€— c) 405 adultes
b) 400 adultes
e) 475 adultes
44. Le robinet d’eau froide peut remplir un ´evier en
12 minutes et le robinet d’eau chaude peut le remplir
en 15 minutes. L’´evier se vide en 25 minutes. Si les
deux robinets sont ouverts et que lВґevier se vide au fur
et `
a mesure, combien de temps mettra l’´evier pour se
remplir?
4
minutes
a) 8 13
9
b) 8 10
minutes
d) 9 98 minutes
2
e) 10 15
minutes
46. Trouve la solution de
c) 8
47. Dans le diagramme suivant, si
quel ВґenoncВґe doit etre vrai?
a) 1 в€ј
= 6 b) 1 в€ј
= 8
в€ј 3 d) 2 =
в€ј 5
c) 2 =
в€— e)
a) 138 cm3
amp`eres
41. Une bibiloth`eque a achetВґe 54 livres. Certains coutaient
32$ la pi`ece et d’autres seulement 44$ la pi`ece. La
facture s’´elevait `a 1 968$. Combien de livres `
a 32$ ont
ВґetВґe achetВґes?
в€— a) 34
40. Le volume V d’un gaz varie inversement en fonction
de sa pression P . Si le volume d’un gaz est de 200 cm3
sous une pression de 32 kg/cm2 , quel serait son volume
sous une pression de 40 kg/cm2 ?
m + 7 = 4.
a) в€’3
b) 3
в€— e) pas de solution
c) 9
48. Dans le diagramme suivant, si
quel ВґenoncВґe doit etre vrai?
a) 1 в€ј
= 8 b) 2 в€ј
= 3
в€ј 5 в€— d) 4 =
в€ј 6
c) 2 =
e)
1
в€— c) 9 11
minutes
1
d) 11
et
2
sont parall`eles,
MMA-511.PCX
4в€ј
= 7
MMA-511.PCX
49. Le p´erim`etre d’un triangle ´equilat´eral est 31 cm.
Trouve la longueur de chaque cotВґe.
в€— a) 10 13 cm
d) 22 12 cm
b) 11 14 cm
c) 15 cm
a) 7 cm
d) 12 13 cm
e) 45 cm
51. Dans le diagramme ci-dessous m 2 > m P. Quelle
inВґequation est vraie?
a)
b)
c)
в€— d)
e)
50. Trouve la longueur de chaque cot´e d’un triangle
ВґequilatВґeral dont le pВґerim`etre est 28 cm.
c) 11 23 cm
e) 14 cm
в€’в€’в€’
52. Dans le diagramme ci-dessous SQ bissecte
Quelle inВґequation est vraie?
в€— a)
b)
c)
d)
e)
QT > TP
QR > TQ
PT < PQ
PT > QT
QS < QR
в€— b) 9 31 cm
PSR.
RS > RQ
QR > PQ
SR < SQ
SP > QP
SR < SP
MMA-295.PCX
MMA-294.PCX
SMP rev. 3.0 (PDF) page 80. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FA
53. Utilise le diagramme ci-dessous pour trouver la
hauteur de l’arbre au dixi`eme pr`es.
54. Utilise le diagramme ci-dessous pour trouver la
hauteur du phare au dixi`eme pr`es.
a) 20,3 m
c) 25,9 m
e) 31,2 m
в€— b) 23,4 m
d) 28,7 m
MMA-332.PCX
a) 44,2 m
d) 47,3 m
b) 46,3 m
e) 52,8 m
55. Dans la figure suivante, RTS est un angle droit, et
в€’в€’в€’
TU est une hauteur. Si RU = 8 et TU = 4, trouve la
valeur de US .
в€— a) 2
d) 10
b) 4
e) 12
MMA-333.PCX
в€— c) 46,6 m
c) 8
56. Dans la figure suivante, RTS est un angle droit, et
в€’в€’в€’
TU est une hauteur. Si RS = 25 et SU = 5, trouve la
valeur de TS .
в€љ
в€љ
a) 5
b) 5
в€— c) 5 5
MMA-305.PCX
в€љ
d) 10
e) 12 2
MMA-305.PCX
57. La base et la hauteur d’un triangle mesurent
respectivement 11 et 14. Trouve l’aire du triangle.
a) 25
b) 48
c) 54
в€— d) 77
e) 108
59. Trois disques de mВґetal ont des rayons de 10 cm et
sont tangents entre eux. Les disques sont entourВґes
d’un cadre de m´etal en forme de triangle ´equilat´eral.
Quelle est la longueur d’un des cot´es du cadre?
в€љ
a) (20 3 ) cm
в€љ
b) (18 + 20 3 ) cm
в€љ
c) (20 + 2 3 ) cm
в€љ
в€— d) (20 + 20 3 ) cm
в€љ
e) (2 + 20 3 ) cm
58. Trouve l’aire d’un triangle qui a 6 comme base et 12
comme hauteur.
a) 12
в€— c) 36
b) 18
d) 40
e) 72
60. Suppose qu’une antenne radio fasse 300 m`etres de
haut. Si le diam`etre de la terre fait 12 800 kilom`etres,
quelle distance s´epare le haut de l’antenne du point A
ou B ? (Exprime ta rВґeponse au dixi`eme de kilom`etres
pr`es)
a) 28,3 km
в€— c) 62,0 km
e) 75,7 km
b) 45,5 km
d) 68,4 km
MMA-410.PCX
MMF-411.PCX
61. Parmi les figures suivantes, laquelle reprВґesente une
pyramide?
a)
b)
d)
в€— e)
c)
62. Parmi les figures suivantes, laquelle reprВґesente un
poly`edre avec deux bases congrues?
a)
b)
d)
в€— e)
c)
SMP rev. 3.0 (PDF) page 81. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FB
These items are drawn from the Spanish Translation of the TAAS Elementary Math (T2S) module. This module
was designed to prepare students for the Texas Assessment of Academic Skills for grades 3 6, but all teachers
and administrators will find it useful for creating elementary mathematics assessments. The 2000 multiple-choice
problems include those released by the Texas Education Agency.
1.
ВїCuВґ
al decimal dice cuВґanto estВґa sombreado?
в€— b) 0.4
d) 40
a) 0.04
c) 4.0
2.
7.
La grВґ
afica muestra los deportes favoritos de los
estudiantes de tercer grado en la escuela Oak Grove.
ВїA cuВґ
antos estudiantes les gusta mas el fВґ
utbol?
ВїCuВґ
al de estos enunciados nombra el mismo nВґ
umero
que 4 Г— 8?
4Г—8
a) 8 Г· 4
3.
b) 8 в€’ 4
в€— c) 8 Г— 4
d) 8 + 4
Mira la recta numВґerica.
T2S-027.PCX
P
Q
R
S
в†ђв€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в€’в†’
33
34
35
36
37
a) 30
ВїQuВґe letra estВґ
a en el 35?
a) P
4.
8.
в€— c) R
b) Q
d) S
ВїQuВґe letra estВґ
a dentro del triВґangulo y fuera del
rectВґ
angulo?
a) P
в€— b) Q
c) R
b) 40
в€— c) 50
d) 70
38
La mamВґ
a de Sarah comprВґ
o algunas frutas en el
supermercado. Ella comprВґ
o 5 plВґ
atanos, 1 ramo de
uvas y 8 manzanas. ВїCuВґ
antas manzanas y plВґ
atanos
la mamВґ
a de Sarah comprВґ
o?
a) 6
в€— c) 13
d) S
9.
b) 9
d) 14
5
1
8
Rex tenВґД±a 72/
c. El gastВґ
o 57/
c. ВїCuВґ
anto dinero le
queda?
TX2-139.PCX
5.
ВїQuВґe hora muestra el reloj?
a)
8:55
b)
8:05
в€— c)
7:55
d)
7:05
TX2-036.FIG
в€— a) 15/
c
TX2-442.PCX
6.
ВїCuВґ
al es el perВґД±metro de este polВґД±gono?
a) 28 cm
c) 43 cm
b) 16/
c
c) 17/
c
d) 18/
c
10. En el estacionamiento de la escuela habВґД±an 4 filas de
bicicletas. En cada fila habВґД±an 7 bicicletas. ВїCuВґ
antas
bicicletas habВґД±an en el estacionamiento de la escuela?
b) 36 cm
в€— d) 45 cm
TX2-003.TBL
a) 20
b) 24
c) 25
в€— d) 28
TX2-458.PCX
SMP rev. 3.0 (PDF) page 82. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FB
11. Lupe comprВґ
o un lВґapiz por 19/c y una libreta por 38/
c.
ВїAproximadamente, cuВґanto dinero gastВґo Lupe?
18. 0.85 + 0.23 =
+
TX2-103.FIG
a) 0.08
TX2-038.PCX
a) 20/
c
b) 40/c
в€— b) 1.08
c) 10.08
d) 100.08
в€— d) 60/
c
c) 50/c
19. 3409 в€’ 2778 =
12. Si sumas la edad de Alex y la edad de Larry,
obtienes 10. La edad de Alex es mayor que 1, y la
edad de Larry es mayor que 7. ВїCuВґantos anos tienen
los muchachos?
a) 1 y 9
в€— b) 2 y 8
c) 3 y 7
d) 4 y 6
13. ВїCuВґ
al grupo representa solamente nВґ
umeros
impares?
b) 336
в€— c) 768
d) 774
48
Г— 16
b) 72 hours
22. ВїCuВґ
al es el residuo cuando divides 32 entre 6?
a) 1
в€— b) 2
в€— b) 79
c) 75
d) 69
c) 3
d) 5
.
b) cuadrado
d) rectВґangulo
23. Una organizaciВґ
on de salud dice que 1 de cada
5 personas tienen problemas con el corazВґ
on. Hay
223 personas en un concierto de mВґ
usica. ВїCuВґ
al es
la mejor estimaciВґ
on de cuВґ
antas personas en este
concierto tengan problemas con el corazВґ
on?
a) MВґ
as de 60
в€— c) Entre 40 y 50
T2S-255.PCX
17. El diagrama muestra las caras de un cubo. Si
este cubo es tirado 3 veces, ВїcuВґ
al de las siguientes
secuencia de letras no puede suceder?
a) PUP
c) MUD
d) 2190 hours
, 74, . . .
16. La senal de precauciВґon tiene la forma de un
в€— a) triВґ
angulo
c) lВґД±nea
d) 621
c) 312 hours
15. ВїCuВґ
al es el nВґ
umero que falta en el siguiente patrВґ
on
numВґerico?
a) 80
в€— c) 631
в€— a) 42 hours
b) resta
в€— d) divisiВґon
99, 94, 89, 84,
b) 721
21. En promedio una persona mira 6 horas de televisiВґ
on
cada dВґД±a. ВїCuВґ
antas horas mirarВґ
a en una semana?
14. La operaciВґ
on contraria de la multiplicaciВґon es
a) suma
c) multiplicaciВґ
on
20.
a) 296
в€— b) 23 25 27 29
d) 13 36 55 79
a) 32 33 34 35
c) 51 52 53 54
a) 1371
b) TED
в€— d) PAD
M
P
E
U
b) Entre 50 y 60
d) Menos de 40
24. Durante un juego de beВґД±sbol, Maria pegВґ
o un hit y
llegВґ
o a la tercera base. ВїCuВґ
antos pies corriВґ
o Maria?
a)
в€— b)
c)
d)
200 pies
150 pies
100 pies
50 pies
T
D
T2S-561.PCX
TX2-058.FIG
SMP rev. 3.0 (PDF) page 83. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FB
25. La grВґ
afica muestra como los estudiantes de la escuela
Park View Elementary llegan a la escuela la mayorВґД±a
de las veces.
Transporte
NВґ
umero de estudiantes
a) 20
carro
autobВґ
us
в€— a)
caminar
T2S-009.AUX
ВїCuВґ
antos estudiantes pasearon en bicicleta o
decidieron caminar?
в€— a) 90
b) 50
26. Este modelo muestra que
c)
c) 3
d) 5
b)
d)
c) 40
8
12
3
5
b)
1
2
a) 14
d) 10
es igual que
2
5
d)
1
5
b) 15
c) 16
в€— d) 18
34. La distancia de Houston a Washington, D.C. son 1410
millas. La distancia de Tulsa a Washington, D.C.
son 1200 millas. La distancia de Tulsa a Houston
es de 485 millas. ВїQuВґe mВґ
as lejos esta Houston de
Washington, D.C. que Tulsa?
3
4
1
2
a) 695 mi
b) 715 mi
в€— e) none of these
c) 2610 mi
d) 3095 mi
35. Angelo tiene 15 cajones de manzanas. El tiene
25 veces mВґ
as manzanas que cajones. ВїCuВґ
antas
manzanas tiene Angelo?
27. ВїCuВґ
al de las siguientes regiones sombreadas no
representa 21 de la figura?
a)
c)
33. Bonita anotВґ
o 12, 12, 15, y 17 goles durante las
4 temporadas que ella jugo futbВґ
ol. Su promedio total
de goles fueron 14 goles por temporada. Si ella
hubiera anotado 4 goles mВґ
as durante cada juego,
ВїcuВґ
al hubiera sido su promedio total en goles?
Cada representa 10 estudiantes
2
3
3
6
в€— b) 10
32. Un jarro tiene 3 canicas rojas y 2 canicas blancas.
John escoge 1 canica sin ver y y luego la regresa al
jarro. Entonces Ann escoge 1 canica sin ver. ВїCuВґ
al
es la probabilidad de que Ann escoja una canica
roja?
bicicleta
в€— a)
31. Jack recuerda todos los dВґД±gitos del nВґ
umero telefВґ
onico
de Jill, menos el u
Вґltimo. Si el escribe todas las
posibilidades antes de empezar a marcar, ВїcuВґ
antos
nВґ
umeros de telВґefono habrВґ
a en su lista?
b)
в€— a) 375
b) 350
c) 300
d) 275
c) 5 R2
d) 5 R12
36. 107 Г· 23 =
в€— c)
d)
a) 4 R9
37. En un aeropuerto 21 aviones pueden despegar cada
hora. Aproximadamente ВїcuВґ
antos aviones pueden
despegar en un fin de semana de 48 horas?
28. El producto de 2 Г— 3 Г— 5 Г— 5 es igual a
в€— a) 150
b) 125
c) 60
d) 15
a) 100
29. ВїQuВґe nВґ
umero falta?
(3 Г— 9) Г— 8 = 3 Г— (
a) 72
b) 27
30. El siguiente dibujo es un ejemplo de:
в€— a) reflecciВґ
on
c) similar
b) 400
в€— c) 1000
d) 2000
38. The perВґД±metro de un rectВґ
angulo es 26 metros. El
ancho del rectВґ
angulo mide 5 metros. ВїCuВґ
al oraciВґ
on
nВґ
umerica puede ser utilizada para encontrar L, lo que
mide el largo del rectВґ
angulo?
Г— 8)
c) 24
в€— b) 4 R15
в€— d) 9
.
b) paralelo
d) translaciВґon
a) 26 в€’ 5 = L
c) (26 в€’ 10) Г— 2 = L
e) L = (26 + 5) Г· 2
в€— b) (26 в€’ 10) Г· 2 = L
d) L = (5 Г— 26) Г· 2
39. De acuerdo a una encuesta realizada 77% de los
americanos tiene por lo menos una VCR en sus casas.
ВїCuВґ
al porcentaje de americanos no tienen una VCR
en sus casa?
a) 0.23%
TX2-313.PCX
b) 2.3%
в€— c) 23%
d) 230%
SMP rev. 3.0 (PDF) page 84. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FB
40. ВїCВґ
omo son los factores 5 Г— 5 Г— 7 Г— 7 escritos en
notaciВґ
on exponencial?
a) 252 Г— 492
b) 352
c) 55 Г— 77
в€— d) 52 Г— 72
41. ВїCuВґ
al es el nВґ
umero mВґas pequeno que tiene ambos, 10
y 15 como factores?
в€— a) 30
b) 15
c) 10
d) 5
42. ВїCuВґ
al letra es la que falta en estos patrones?
...
jjgpqjjjgpqjjjjgp
a) j
b) g
j j j. . .
48. Mike, Mabel, y Hazel decidieron ir juntos para
comprar un regalo de cumpleanos para Jessica. Ellos
gastaron $28.20 por el regalo. ВїCuВґ
anto dinero tuvo
que poner cada quien para comprar el regalo?
a) $7.05
b) $7.50
в€— e) none of these
c) $8.40
d) $9.07
49. Un poste con una lВґ
ampara mide 6 pies de altura
y refleja una sombra de 8-pies. Al mismo tiempo
del dВґД±a, un mВґ
astil con una bandera directamente
atras del poste refleja una sombra de 20-pies. ВїCuВґ
Вґ
al
proporciВґ
on puede ser utilizada para encontrar la
altura H del mВґ
astil de la bandera?
в€— d) q
c) p
43. El punto P esta representado mejor por ВїcuВґ
al
nВґ
umero?
P
←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−•−−−−−−−−−−−−−−−→
10
a) 11 43
11
b) 11 12
12
3
c) 11 10
в€— d) 11 35
T2S-108.PCX
44. Encuentra el Вґ
area del trapezoide mostrado.
6
H
H
8
H
8
=
b)
=
c)
=
8
20
6
20
20
6
20
6
H
6
d)
=
e)
=
H
8
8
20
50. Los pentВґ
agonos PQRST y VWXYZ son congruentes.
ВїCuВґ
al opciВґ
on es verdadera?
в€— a)
a) 12 cm2
b) 15 cm2
в€— c) 24 cm2
d) 36 cm2
TX2-731.PCX
45. Si la ruleta es girada 80 veces, Вїen quВґe color crees
que pueda parar aproximadamente 30 veces?
в€— a) amarillo
c) verde
b) rojo
d) azul
TX2-762.PCX
T2S-330.PCX
46. Augustus preparВґo un pastel. En la receta le pidieron
2 23 tazas de harina para empezar y despuВґes otra
1 21 para mezclarla mВґas tarde. ВїCuВґanta harina utilizВґ
o
Augustus en total?
7
b) 3 12
a) 3 16
e) none of these
c) 3 35
в€— d) 4 16
c) 15 12 pies
в€— e) none of these
b) 5 25 pies
d) 15 45 pies
в€’в€’в€’ в€ј в€’в€’в€’
b) QR =
YZ
в€’в€’в€’ в€ј в€’в€’в€’
d) PQ = VZ
e) none of these
51. Sheila sabe que se toma 11 pies de listВґ
on para
preparar 2 monos para una decoraciВґ
on en la pared.
ВїCual oraciВґ
on numВґerica puede ser utilizada para
encontrar R, el nВґ
umero total de pies que necesitarВґ
a
para preparar 7 monos.
R
7
R
7
2
=
a) 1 11
3
pies
47. Rhona tiene 10 15 pies de alambre. Ella tiene 5 10
mВґ
as que Yolanda. ВїCuВґantos pies de alambre tiene
Yolanda?
1
a) 5 10
pies
в€’в€’в€’ в€’в€’в€’
в€— a) TS в€ј
= ZY
c) T в€ј
= X
в€— d)
11
2
=
b) R = 7 Г—
e) R =
11
2
c)
2
7
=
R
11
2Г—11
7
52. La Sra. Alfaro comprВґ
o zapatos nuevos para sus
5 ninos. El precio de los zapatos era entre $14.99 a
$29.99. ВїCuВґ
al serВґ
a el costo razonable de los 5 pares
de zapatos?
a) $50
b) $70
в€— c) $100
d) $175
e) $200
SMP rev. 3.0 (PDF) page 85. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FC
These items are drawn from the Spanish Translation of the TAAS Prep./Algebra EOC (T3S) module. The TX3
module was designed to prepare students for the Texas Assessment of Academic Skills for grades 7 8 and exit level,
as well as that state’s Algebra End-of-Course exam. But teachers and administrators everywhere will find it useful
for creating secondary mathematics assessments. The 4000 multiple-choice problems include those released by the
Texas Education Agency.
1.
JВґ
upiter tiene un diВґametro aproximado de 1.43 Г— 105
kilВґ
ometros. Este diВґametro mide cerca de
.
a) 1430 km
в€— c) 143,000 km
e) 14,300,000 km
3.
5.
b) 14,300 km
d) 1,430,000 km
b) 99
c) 99.9
9.
c) 3x + y
в€— e) 3x + 3y
d) 3xy
d) x =
e) 2x =
ВїCuВґ
al es la forma correcta de expresar 82% como un
decimal?
9
10
11. ВїCuВґ
al deberВґД±a ser el prВґoximo nВґ
umero en esta
secuencia?
b) 112
в€— d) 162
e) 192
13. ВїCuВґ
al es equivalente a x2 + x3 ?
c) 5x
a) 10.1 pies2
b) 15.6 pies2
d) 20.2 pies2
в€— e) 23.4 pies2
d) 6x
c) 17.8 pies2
17. ВїCuВґ
al de las siguientes parece ser un paralelogramo?
b)
d)
e)
в€— b) ab + ac
a) abc
c) cba
e) c(a + b)
a) 10x в€’ 3 = 5
c) x = 13 в€’ 5
e) x = 8
b) x = 10(13 в€’ 5)
в€— d) 10x = 13 в€’ 5
12. ВїCuВґ
al deberВґД±a ser el prВґ
oximo nВґ
umero en esta
secuencia?
a) 108
b) 112
c) 128
d) 256
в€— e) 324
14. ВїCuВґ
al es equivalente a n5 + n3 ?
15. La mesa de comedor en la casa de Mike es 6.5 pies de
largo y 3.6 pies de ancho. ВїCuВґal es la Вґarea de la mesa?
a)
e) 82
4, 12, 36, 108, . . .
c) 128
a) x5
b) x6
в€— e) no esta aquВґД±
d) 8.22
Use la propiedad distributiva para seleccionar la
expresiВґ
on que es igual a a(b + c).
2, 6, 18, 54, . . .
a) 78
c) 8.02
10. ВїCuВґ
al ecuaciВґ
on es equivalente a 10x + 5 = 13?
b) x = 2(8 в€’ 10) в€— c) 2x = 8 + 10
1
2 (8)
8.
в€— c) 800
b) 842.32
e) 700
d) b(a + c)
ВїCuВґ
al ecuaciВґ
on es equivalente a 2x в€’ 10 = 8?
a) 2x = 8 в€’ 10
6.
c) 60,000,000
El nВґ
umero 842.3283 redondeado a la centena mВґ
as
cercana es
.
a) 0.082 в€— b) 0.82
Use la propiedad distributiva para seleccionar la
expresiВґ
on que es igual a 3(x + y).
b) 6x + 6y
b) 6,000,000
e) 6,000,000,000
a) 842.33
d) 742
в€— c) 0.46
b) 0.046
e) 4.6
a) x + 3y
4.
e) 90
ВїCuВґ
al es la forma correcta de expresar 46% como un
decimal?
a) 0.0046
d) 4.06
7.
d) 99.99
Un disco para computadora tiene una capacidad de
6.0 Г— 108 bytes de informaciВґ
on. Exprese este nВґ
umero
en notaciВґ
on normal.
a) 600,000
в€— d) 600,000,000
El nВґ
umero 99.999 redondeado a la centena mВґ
as
.
cercana es
в€— a) 100
2.
в€— c)
a) n8
b) n15
в€— e) no esta aquВґД±
c) 8n
d) 15n
16. La cama en el cuarto de Willie es 6.9 pies de largo y
4.1 pies de ancho. ВїCuВґ
al es la Вґ
area de la cama?
a) 11 pies2
d) 33.58 pies
b) 22 pies2
e) 46.23 pies
в€— c) 28.29 pies2
18. ВїCuВґ
al de las siguientes parece ser un trapezoide?
a)
b)
d)
e)
в€— c)
SMP rev. 3.0 (PDF) page 86. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FC
19. Encontrar x.
a) 15
d) 9.5
20. Encontrar y.
в€— c) 12
b) 12.5
e) 7.5
a) 1
в€— d) 0.4
b) 0.8
e) 0.2
c) 0.6
TX3-105.PCX
TX3-104.PCX
21.
ABC в€ј ADF . BD = 12, BC = 20, AD = 12.
Encontrar DF .
в€— b) 10
e) 16
a) 8
d) 14
c) 12
22.
ABC в€ј ADF . BD = 4, AF = 3, AD = 4.
Encontrar AC .
a) 4
d) 8
в€— c) 6
b) 5
e) 10
TX3-149.PCX
TX3-149.PCX
23. Dado 1
al par de Вґangulos deben ser
2 , ВїcuВґ
congruente?
1,
5,
2,
a)
в€— c)
e)
2
3
6
b)
d)
3,
5,
24. Dado 1
al par de Вґ
angulos deben ser
2 , ВїcuВґ
congruentes?
в€— a)
c)
e)
4
4
1,
3,
5,
4
4
4
b)
d)
2,
5,
6
1
TX3-182.PCX
25. Este recipiente contiene aproximadamente
de agua.
a)
в€— d)
3
4
1
4
b)
1 21
e) 2
c)
TX3-182.PCX
tazas
26. Este recipiente es llenado con
a)
1 14
1
2
d) 1 21
b) 1
tazas de lВґД±quido.
в€— c) 1 14
e) 2
T3S-220.PCX
T3S-219.PCX
27. Jean estВґ
a preparando una sopa que requiere 2 lb
5 onzas de carne. Si ella dobla la receta, ВїcuВґ
anta
carne necesitarВґ
a ella?
a) 2 lb 10 onzas
в€— d) 4 lb 10 onzas
b) 4 lb
e) 5 lb
c) 4 lb 5 onzas
29. Celeste puede escoger su traje de la escuela de
3 blusas, 4 faldas, 2 pares de zapatos y 3 pares de
calcetines. ВїCuВґ
antas combinaciones de ropa puede
tener Celeste?
a) 84
в€— b) 72
c) 64
d) 56
e) 48
28. Harry estВґ
a preparando una barbacoa que requiere 4 lb
8 onzas de pollo. Si el dobla la receta, ВїquВґe cantidad
de pollo necesitarВґ
a Вґel?
a) 4 lb
c) 8 lb
в€— e) 9 lb
b) 4 lb 100 onzas
d) 8 lb 9 onzas
30. Craig puede escoger su traje de la escuela de
5 camisas, 4 pares de pantalones, 3 pares de zapatos
y 3 pares de calcetines. ВїCuВґ
antas combinaciones
diferentes de ropa puede tener Craig?
в€— a) 180
b) 160
c) 120
d) 90
e) 60
SMP rev. 3.0 (PDF) page 87. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FC
31. Tarjetas con los nombres de 30 estudiantes en algebra
fueron puestos en una caja. Catorce de los estudiantes
son muchachos. Si un nombre es sacado al azar de
la caja, ВїcuВґ
al es la probabilidad de que Вґeste sea un
nombre de una muchacha?
a)
2
3
b)
3
5
в€— c)
8
15
1
2
d)
7
15
e)
33. La tabla da los pesos, en kilogramos, de un grupo de
estudiantes del tercer grado. ВїCuВґal es la gama de sus
pesos?
a) 26 в€— b) 27
d) 29
e) 30
c) 28
Peso en kilogramos
29
30
27
28
26
30
28
32. Los nВґ
umeros consecutivos del 1 al 20 son escritos
en pedazos de papel y puestos en una bolsa. Si un
nВґ
umero es sacado al azar de la bolsa, ВїcuВґ
al es la
probabilidad de que sea menos de 5?
a)
13
25
b)
1
2
c)
2
5
a) 69
d) 80
b) 73 в€— c) 79
e) 85
79
85
27
79
76
90
31
29
73
82
75
27
26
79
80
69
в€— c) 4.9 pulg
37. El papВґ
a de Mike tiene un lВґД±nea de telВґefono gratis
para su negocio. Setenta y cinco llamadas fueron
hechas en 18 dВґД±as al nВґ
umero de telВґefono gratis. A
esta proporciВґ
on, ВїcuВґal proporciВґon podrВґД±a ser usada
para encontrar cuВґantas llamdas el negocio recibirВґД±a en
30 dВґД±as?
18
x
75
x
18
30
=
b)
=
c)
=
a)
75
x
18
30
75
30
18
75
75
30
в€— d)
=
e)
=
30
x
x
18
39. Una tienda de computadoras anunciВґo sus computadoras
con 20% de descuento. Roy decide comprar una la
cual se vendia originalmente por $1600. ВїCuВґ
al es la
cantidad del precio de promociВґon?
a) $1200 в€— b) $1280
c) $1300
d) $1400
e) $1450
41. Para llegar a la tienda de su casa, Harry trotВґ
o
3 kilВґ
ometros directamente al oeste y entonces
4 kilВґ
ometros directamente al norte. En su camino de
regreso Вґel acortВґ
o la distancia cruzando un campo,
tomando la ruta mВґas corta a su casa. ВїCuВґanto trotВґ
o
Harry en su viaje de ida y regreso?
a) 19 km в€— b) 12 km
d) 5 km
e) 1 km
Peso en kilogramos
80
35. La lluvia anual normal para el puebo de Mario
es de 29.2 pulgadas. La lluvia este ano totalizВґ
o
34.1 pulgadas. ВїCuВґanto arriba de lo normal fue este
ano la lluvia?
b) 5.1 pulg
e) 3.7 pulg
1
5
в€— e)
34. La tabla lista los pesos, en kilogramos, de los
jugadores ofensivos en el juego de fВґ
utbol americano.
ВїCuВґ
al es la gama de sus pesos?
SMP-001.TBL
a) 5.9 pulg
d) 4.1 pulg
1
4
d)
c) 7 km
SMP-002.TBL
36. La lluvia anual para una ciudad de Texas en 1980 fue
de 35.8 pulg. La lluvia en 1990 totalizВґ
o 37.4 pulgadas.
ВїCuВґ
al fue la diferencia para 1980 y 1990?
a) 2.8 pulg
в€— d) 1.6 pulg
b) 2.6 pulg
e) 1.4 pulg
c) 2.4 pulg
38. Mickey estВґ
a tomando el trВґen para visitar su primo
quien vive 750 millas de distancia. Si el trВґen viajВґ
o
334 millas en 4 horas, ВїcuВґ
al proporciВґ
on podrВґД±a ser
usada para determinar cuВґ
antas horas tomarВґ
a el viaje
entero?
334
x
334
334
4
4
=
b)
=
c)
=
a)
x
216
4
750
x
750
216
x
750
x
d)
=
в€— e)
=
4
750
4
334
40. Un departamento de una tienda anunciВґ
o un televisor
de 19 pulgadas con un control remoto con 15% de
descuento. Si el precio original era $250, ВїcuВґ
al es el
precio de venta?
a) $37.50
d) $225.00
b) $187.50
e) $235.00
в€— c) $212.50
42. Nicky saliВґ
o de su casa y manejВґ
o su bicicleta
directamente al este 8 kilВґ
ometros, despuВґes directamente
al norte 6 kilВґ
ometros al parque. Luego ella manejВґ
o
desde el parque directamente de regreso a su casa.
ВїCuВґ
anto manejВґ
o Nicky en su viaje de ida y vuelta?
a) 2 km
c) 14 km
e) 38 km
b) 10 km
в€— d) 24 km
T3S-294.PCX
T3S-293.PCX
SMP rev. 3.0 (PDF) page 88. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
FC
Algebra End-of-Course Items
43. ВїCuВґ
al es el rango de la funciВґon f (x) = (x в€’ 5)2 cuando
el dominio es {1, 3, 5}?
a) {в€’16, в€’4, 0}
b) {в€’24, в€’16, 0}
d) {24, 16, 0}
в€— e) {16, 4, 0}
c) {в€’4, в€’2, 0}
45. ВїCuВґ
al ecuaciВґ
on describe la grВґafica mostrada?
a) y =
b) y =
c) y =
в€— d) y =
e) y =
44. ВїCuВґ
al es el rango de la funciВґ
on f (x) = (x в€’ 7)2 cuando
el dominio es {2, 4, 6}?
в€— a) {25, 9, 1}
c) {в€’25, в€’9, 1}
e) {в€’25, в€’9, в€’1}
b) {в€’10, в€’6, в€’1}
d) {10, 6, 2}
46. ВїCuВґ
al ecuaciВґ
on describe la grВґ
afica mostrada?
a) y = в€’ 23 x в€’ 3
в€’ 23 x в€’ 3
в€’ 32 x в€’ 2
2
3x в€’ 2
в€’ 23 x в€’ 2
3
2x в€’ 3
b) y = в€’ 32 x в€’ 2
c) y = 32 x в€’ 2
d) y = в€’ 23 x в€’ 2
в€— e) y = в€’ 32 x в€’ 3
TX3-444.PCX
47. En una prisma rectangular dada, la longitud estВґ
a
representada por x + 1, el ancho estВґa representado
por x + 4 y la altura es 7. Exprese el volumen de la
prisma rectangular en tВґerminos de x.
a) x2 + 5x + 4
c) 14x + 35
48. En una prisma rectangular dada, la longitud y el
ancho estВґ
an representados por 3x + 2 y la altura
es 4. Exprese el volumen de la prisma rectangular en
tВґerminos de x.
b) 2x + 12
a) 24x + 16
7x2
36x2
в€— d)
+ 35x + 28
e) 7x2 + 28
в€— c)
b) 12x + 8
d) 36x2 + 16
+ 48x + 16
e) 36x2 + 24x + 16
49. David tiene 3 dimes mВґas que nickels. El pierde
2 dimes despuВґes cuenta su dinero y encuentra que
tiene $3.10. ВїCuВґantos nickels tiene David?
a) 18 nickels
d) 22 nickels
TX3-539.PCX
b) 19 nickels
e) 23 nickels
в€— c) 20 nickels
51. El costo de comprar una casa estВґa incrementando. La
grВґ
afica representa el promedio del pago mensual en
una casa.
50. Tyrone tiene 5 quarters mВґ
as que nickels. El pierde
3 quarters despuВґes cuenta su dinero y encuentra que
tiene $3.80. ВїCuВґ
antos nickels tiene Tyrone?
a) 15 nickels
в€— d) 11 nickels
b) 14 nickels
e) 10 nickels
c) 13 nickels
52. Los accidentes de motocicletas son el tipo principal de
muertes accidentales.
T3S-565.PCX
Usando esta informaciВґon, ВїcuВґal es el pago mensual
esperado en una casa en el ano 2002?
a) $858.10
d) $1090.70
b) $920.30
e) $1139.90
в€— c) $978.50
T3S-566.PCX
Usando esta informaciВґ
on, ВїcuВґ
al es la proporciВґ
on de
muertes predictas en el ano 2000?
в€— a) 15
b) 18
c) 19
d) 20
e) 21
SMP rev. 3.0 (PDF) page 89. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
BLANK PAGE
GA
These items are drawn from the British Columbia Colleges High School Mathematics Contest (BCC) module. The
module, a collection of all 1600 problems since the contest began in 1973, includes multiple-choice and free-response
items involving algebra, geometry, trigonometry, and calculus.
1.
A farmer weighed 5 bales of hay two bales at
a time and recorded the weights for all possible
combinations. These were 110, 112, 113, 114, 115,
116, 117, 118, 119, and 129. The weight of the
heaviest bale was:
b) 56.75 в€— c) 60.5
a) 55.5
2.
d) 60.75
b) 24
e) 60
b) 13
e) 16
b) 5
c) 6
100
в€— e) 8
d) 7
100
i2 and S =
Let N =
i=1
a) 9
d) 30,300
(i + 3)2 then S в€’ N equals:
i=1
b) 609
в€— e) 31,200
c) 900
2 в€’6x
If f (n) is the minimum value of f (x) = 2x
n
is:
the value of
f (n)
a) 0
b) 1
2
5
Antonino is of the way across a railroad trestle
when he hears a train coming behind him. The train
is travelling at 100 km/h. If Antonino can run to
either end of the trestle just in time to save his life,
how fast does he run?
в€— a) 20 km/h b) 16 km/h c) 10 km/h
e) not enough information given
a) 99,490
b) 994,900 в€— c) 995,000
e) none of these
в€— a) 24
b) 25
c) 29
e) none of these
c) 8
B
E
A
C
F
D
BCC-005.FIG
a)
9.6 Г— 104
d) 4.8 Г— 54
9.6 Г— 108
is equal to:
в€— b) 4.8 Г— 108
c) 4.8 Г— 104
e) 4.8 Г— 58
13. 1984 may be written in the form 2n Г— p, where n is a
positive integer and p is prime. The value of n + p is:
a) 3ПЂr2
3ПЂr2
2
в€љ
3 3r2
в€— c)
2
в€љ
3 3r2
2
d) ПЂr в€’
2
в€љ
e) (3 3 в€’ ПЂ)r2
b)
a) 35
b) 36
e) none of these
в€— c) 37
d) 38
14. Prove that the sum of 3 consecutive odd integers is
divisible by 3. [proof]
BCC-158.PCX
The number of points of intersection of x2 + 16y 2 = 16
and y = 1 + 3 sin x is:
b) 3
d) 35
, then
The radius of the given circle is r, and the radius of
each of the arcs in the diagram is r. The area of the
region that is not shaded is:
a) 2
d) 998,992
11. In the diagram the area of the square AEFD is
25 and the area of rectangle ABCD is 35. The
perimeter of rectangle ABCD is:
12. One half of
7.
d) 8 km/h
10. The value of x2 в€’ x в€’ 6, if x equals 998, is:
в€— e) 3 Г— 29
d) в€’8
6.
c) 14
BCC-253.PCX
9.
в€— c) 36
If Ann gets 90 on her next test, her average mark will
be 86. If she gets 72 her average mark will be 84.
The number of tests that Ann has already taken is:
a) 4
5.
a) 12
в€— d) 15
e) 67.75
BCC-015.FIG
4.
In the diagram AD = 5, DC = CB = 3,
m ADC = 120 в—¦ and m CBA = 60 в—¦. Then AC + AB
equals:
The cut out shown may be used to cover exactly
three of the squares on the 4 Г— 4 checkerboard shown.
The number of different choices for the three squares
covered is:
a) 16
d) 48
3.
8.
c) 4
d) 5
в€— e) 6
15. Three men, Able, Baker, and Charlie, make
comments about each other. Able says, Baker is a
liar ; Baker says, Charlie is a liar ; and Charlie
says, Both Able and Baker are liars. Who lies and
who tells the truth?
Able and Charlie are liars while Baker tells the truth
SMP rev. 3.0 (PDF) page 91. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GB
These items are drawn from the Illinois Elementary Mathematics Contest (IEC) module. The 2000 free-response
items originally appeared in the regional and state contests for grades 3 8. The module is updated annually.
1.
The distance b is how much more than a ?
9
IEC-002.PCX
2.
3.
The jersey numbers of the five starters on the team
are 14, 23,
, 41, and 50. The numbers form a
pattern. What is the missing number? 32
The spinner is spun 6 times.
One number is recorded
3 times and the other
3 numbers are recorded one
time. What is the largest
possible sum? 42
8.
I am a number between 20 and 200. I am a multiple
of 2 and a multiple of 13. How many different
numbers can I be? 7
9.
Find the area of the figure
shown. 250
IEC-105.PCX
10. Julia has three times as many ribbons as Sara.
Together they have 124 ribbons. How many ribbons
does Julia have? 93
11. Solve for n:
7
m
nв€’m
=
=
8
24
96
105
12. A rectangular pen is 22 38 long by 15 78 wide. What
is the perimeter of the pen? 76 1
2
IEC-019.PCX
4.
5.
The Burger Barn has burgers that cost $1.80 each.
They are having a special where you get 3 for $5.00.
How much will 10 burgers cost? $16.80
13. If Friday is 3 days after the day before yesterday,
what is the day after tomorrow? Saturday
14. What is the input if 34 is the
output? 7
Number of hot dogs served in the cafeteria:
Number of
Hot Dogs Sold
Day
Monday
Tuesday
Wednesday
Thursday
Friday
132
151
222
129
83
IEC-147.PCX
15. Find the number closest to 2000 that is divisible
by 7, 11, and 13. 2002
16. Find (a + c) Г— b if
IEC-007.TBL
How many hot dogs were sold during the week?
6.
717
How many lines of symmetry
does the pentagon shown
have? 5
9a5
в€’ b3c
394
15
17. Christina bought 200 shares of stock for $1600. She
later sold the stock for $2200. How much did each
share of stock increase in value? $3
18. Find the smallest number larger than 2 that will have
a remainder of 2 when divided by 3, by 4, and by 5.
62
IEC-077.PCX
7.
Tito decided to enter a tournament, It cost $60 to
enter the tournament and $10 per game played. If he
played only 3 games, what was the average cost of
each game played? 30
19. If I am divided by
I? 48
4
5
I become 60. What number am
20. The numbers 15 Г— 17 and 16 Г— 20 + 20 have perfect
squares between them. What is the sum of these
perfect squares? 869
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GB
21. If a jar holds 10 ounces of water, how many jars of
water would it take to fill a 5 gallon bucket? 64 jars
22. How many paths from A to B?
12
34. Stockie bought 100 shares of BIM stock at $80 a
share. Stockie sold 30 shares at $90 a share and used
the money to buy 90 shares of Rotormola stock. To
the nearest cent, what is the average share value of
Stockie’s stock? $50
в€’в€’в€’
в€’в€’в€’
35. Segments AB and CD are parallel. Find x.
16
IEC-211.PCX
23. Find the whole number nearest to 1000 that is
divisible by 13. 1001
24. Let a # b = 6a в€’ 2b Find the value of 3 # (3 # 8)
IEC-277.PCX
14
25. If one tac equals four tecs and two tecs equals seven
tics then how many tics equal one tac? 14
36. I am a multiple of 3 and 4 and a factor of 240. How
many natural numbers can I be? 20
37. If a : b = 4 : 5 and b : c = 3 : 8, then what is a : c?
a
b
= .
3
5
26. How many cubic inches are in a brick
8 by 4 by 2 21 ? 80
38. Find the ratio of a to b if
27. How many whole numbers less than 100 are divisible
by 2 or by 3? 66
39. What is the largest possible
value of a + b + c + d in the
factor tree? 26
3
10
3:5
28. The area of the entire trapezoid is 48. What is the
area of the shaded region? 24
IEC-284.PCX
40. What is the units digit of 3! + 5! + 2! + 6! + 1! + 7! ?
9
IEC-245.PCX
29. Find the sum of all the integers between в€’43 and 46
on a number line. 132
30. Pane Terr can paint 100 square ft per hour. How
long would it take Pane to paint both sides of a
125 foot long fence that is 6 feet tall? 15
31. How many diagonals does a 10 sided polygon have?
35
32. A 100 pound set of Lifter Weights is priced at $49.99.
Additional weight plates may be purchased at 45/
c per
pound. Luke’s parents buy him a 250 lb weight set
for his birthday. How much did the weight set cost
before taxes? $117.49
33. If A = {1, 2, 3} and B = {3, 4, 5} then A в€Є B (read
A union B ) = {1, 2, 3, 4, 5} and A ∩ B (read A
intersection B ) = {3}. What is the set described by
{1, 3, 5} в€Є {3, 5, 7, 9}? {1, 3, 5, 7, 9}
41. An oil tanker holding 750 gallons of oil, releases 13
of its remaining volume every 3 hours. How many
gallons remain in the tank after 12 hours? 148.148
42. A fly randomly lands on one
of the numbered squares.
What is the probability that
the number on the square is
a multiple of 2 or a prime
number? 3 or 75%
4
43.
1 4 7 9
12 14 17 19
22 24 27 29
32 34 37 39
IEC-011.FIG
3
a+b
a
=
=
. What is the value of b ?
4
20
60
в€’30
44. The ratio of two supplementary angles is 5 to 7.
Find the complement of the smaller angle. 15
45. Connie Sumer mixes 1 gallon of alcohol with every
five gallons of gasoline. She pays $1.24 per gallon for
the gasoline and $0.45 per gallon for the alcohol.
How much does Connie save if she uses 570 gallons
of fuel in a year? $75.05
46. If 5(x в€’ 4) + 7(y в€’ 2x) = 20 is graphed then the slope
of the line is? 9
7
SMP rev. 3.0 (PDF) page 93. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GC
These items are drawn from the Illinois Secondary Mathematics Contest (ISC) module. The 5000 free-response items
originally appeared in the regional and state contests for grades 9 12. The module is updated annually.
1.
2.
3.
4
Find k if 6
k
1 2
3
3 1 + в€’2
5 0
4
0
1
в€’k
в€’4
2 = в€’10.
в€’1
9
An object travels along the path described by
x = 0.25t, y = 3 cos t + 1, with t ≥ 0. What is the
smallest value of t where the object is 2 units from
the origin? 1.239
5
2
2
,
A dog is tied by a 6 leash to the middle of the long
side of a 4 Г— 8 out-building. What is the area, in
square feet, of the region the dog can visit while tied
up? 20ПЂ
3
x
5
x
=
y
3
x
y
find the ratio .
5
y
3
5
or 0.6
в€љ
14. In the diagram shown, the length of AB is 2. Also
FAE = CAB = AED = 30 в—¦ and DAC = ADC .
Find the length of AF . 16
3
Find the sum of all solutions to the equation
sin x + sin 2x + sin 3x = 0,
with 0 ≤ x < 2π.
6.
p(x + 1) в€’ p(x в€’ 1)
2
2
13. If
find the maximum value of x2 + y 2 .
5.
p(x) =
+ 3y 2
+ 5xy
=2
6x2 + 8xy + 4y 2 = 3
4.
12. A quadratic polynomial, p, satisfies
for all real x. Find the value of
[p(0) в€’ p(в€’1)] + [p(0) в€’ p(1)]. в€’ 1 (or в€’0.5)
If (x, y) is a solution to the system
2x2
11. A textbook is opened at random. To what pages is
it opened if the product of the facing page numbers
is 3.192? 56 and 57
ISC-132.PCX
5ПЂ
в€’в€’в€’
в€’в€’в€’
ABCD is a trapezoid with bases AB and DC .
AD в€ј
= BC . If AB = 8, AC = 34, and EF = 30, find
the perimeter of the trapezoid. 32 + 4в€љ241
15. Find the sum of the following infinite series:
1 1
1
1
1
в€’ +
в€’
+
в€’ В·В·В·
3 6 12 24 48
2
9
(or 0.2)
16. For what value(s) of k does the line with equation
y = kx + k pass through the vertex of the parabola
with equation y = 3x2 + 24x + k ? 12
17. How many ways are there to go from point A to
point B, if one is only allowed to move along the
indicated edges and either to the right or downwards?
ISC-193.PCX
14
7.
8.
x6 y 11
Find the coefficient of
expansion of (2x в€’ y)17 .
A
в€’792,064
Evaluate: 1 + 2 + 3 + [4 в€’ 5]в€’1
7
5
9.
in the binomial
в€’1 в€’1
(or 1 52 or 1.4)
Suppose f (x) = 3ax + 9 and f (3) = 25. Find f (10)
rounded to four significant digits. 804.2 (or 8.042 Г— 102 )
10. On the video game Space Mites , the player receives
50 points for every 3 termite ships that are destroyed.
How many ships would a player have to destroy in
order to obtain a score of 1650 points? 99
B
ISC-002.FIG
18. Solve for n: 3n 32n 33n В· В· В· 358n = 310000 .
5.845
19. Gem Food Stores sells Swift Peanut Butter for $2.48
for a 16 ounce jar. Antonio’s Food Stores sells the
same peanut butter for $3.60 for a 24 ounce jar.
Which food store has the better buy and by how
many cents per ounce?
Antonio’s by
1
c
2/
per ounce ($ answer not acceptable)
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Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GC
20. A rectangular solid as shown contains a liquid that is
4 in depth. The container is then tilted so that the
level of the liquid is even with the base edge. How
far, in inches, from the upper edge is the liquid? 2
30. For what value(s) of k will the following system fail
to have a solution?
2x + y = k + 1
(k + 2)x + (k в€’ 1)y = 8
4
в€љ
31. If a b is defined by a b = |a| b and a b is defined
by a b = a2 в€’ b2 , what is the value of [(в€’3) 4] 5?
11
32. For the rectangular solid
shown, determine the
length of HB. 17
ISC-319.PCX
ISC-318.PCX
8
21. What is the units digit of 8(8 ) ?
6
ISC-199.PCX
22. Jim was disappointed by his math SAT score and
decided to take a review course and then re-take the
test. His second score was 767, an 18% improvement
over his original score. What was his original score?
650
33. Find the largest four-digit perfect square that is
divisible by 7 and the sum of whose digits is 25.
5929
34. Find the fractional value of
1
23. How many integral values of x satisfy the inequality
8 < |3x + 4| < 32? 15
24. Two semi-circles and one circle, all having the same
radius, are inscribed in the rectangle ABCD, as
shown. Let O, Q, and P be the centers of the two
semi-circles and the circle, respectively. If AB = 20
what is the area of that portion of the plane inside
the rectangle but outside the circular regions?
200 в€’ 50ПЂ (or equivalent)
2+
2+
1
+
1
3+
1
2
95
132
1
3+
1
3
35. Let r be the radius of the circle inscribed in a
10-17-21 triangle. Find r. 7 or 3 1 or 3.45
2
2
36. Let x and y be as shown.
Determine the value of the
product xy. 24
ISC-111.PCX
37.
ISC-055.PCX
в€љ
x=
в€љ
2 x в€’ 3.
8
3x в€’ 5
b) Solve for x:
25. The sequence x1 , x2 , x3 , . . . is defined by x1 = 1,
xn = (xn в€’ 1)1/8 + 5, n > 1. It can be shown that the
sequence converges to a limit L. Find L. 6.258
26. Solve for x: 3 в€’
a) The weights of five packages are five consecutive
odd numbers totaling 115 lbs. How many
pounds does the lightest package weigh?
c)
x2
в€’ 4x + y 2
2
3
= ANS в€’ 10.
+ 6y = ANS is a circle. What is its
radius?
d) What is the y value of the point at which
y = x2 в€’ x + 1.2(ANS) intersects the y-axis?
4
19; 12; 5; 6
27. Let a#b = a2 в€’ ab + b2 for all real numbers a and b.
Find all values of x such that x#7 = 93. 11, в€’4
28. By using all the letters available from the word
HYPERSPACE exactly once, how many different
arrangements can be formed? 907,200
29. Give the common fraction equivalent to (0.23 + 0.012).
38.
a) What is the largest prime factor of 50141?
b) If f (1) = ANS and f (n) = f (n в€’ 1) + 8, for
n ≥ 2, what is the value of f (10)?
c) Find the last three digits of (ANS)25 .
ANS
ik . Note: i =
d) Evaluate:
в€љ
в€’1.
29; 101; 501; i
k=1
11
45
SMP rev. 3.0 (PDF) page 95. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GD
These items are drawn from the MATHCOUNTS Competition (MCC) module. MATHCOUNTS is a nationwide
program in the U.S. that promotes math excellence among middle and junior high school students. The 6000 short
response items included in this module are taken from the four competitions (school, regional, state, and national)
sponsored each year by the MATHCOUNTS Foundation. The module is organized topically and updated each year.
1.
The product of the first 1001 primes is divided by
the product of the first 1000 primes. How many
factors exist for the quotient? 2
7! 5! 3! 1!
6! 4! 2! 0!
2.
Simplify:
3.
If trapezoids ABCD and ABCE are isosceles and the
degree measure of angle BCF is 70, then find the
number of degrees in the measure of angle ECD.
105
1b 1a
10. If a x b =
+ , find 2 x 3. Express your answer as
a
b
a common fraction. 17
72
11. Compute the quotient:
40 (degrees)
(172 в€’ 102 )
(17 в€’ 10)
27
12. The whole numbers are written consecutively in rows
as shown. Each row contains two more numbers than
the previous row. What is the number of the row in
which the number 120,000 is listed? (row) 347
Row
Row
Row
Row
Row
1
2
3
4
5
8
10
22
9
23
24
0
2
6
12
20
1
7
11
21
3
5
13
19
4
14 15
18 17
13. What is the units digit of 19971997 ?
16
7
MCC-131.PCX
4.
2A farmer and his son, both heavily loaded with
sacks of grain, were walking side by side. The farmer
said to his son, If I take one sack from your back,
my load will be twice yours. But if you take one
sack from my back, your load will equal mine . How
many sacks was the son carrying? 5
5.
Evaluate (35 )(23 ) в€’ (24 )(34 ).
6.
A set of cards consists of 8 red and 7 black cards.
Three cards are dealt at random. What is the
probability of obtaining three cards of the same
color? Express your answer as a common fraction.
14. The first three hexagonal numbers are represented
as shown. Find the sum of the first four hexagonal
numbers. 95
648
1
5
7.
2.8 Г— 1023 is what percent of 5.6 Г— 1024 ?
8.
How many triangles are in this figure?
5 (%)
35 (triangles)
MCC-281.PCX
3
15. Express in scientific notation: 0.57 Г— (1 Г— 104 )1Г—10
5.37 Г— 103999
16. Give the letter(s) corresponding to the fraction(s)
given which, when written as decimals, will not
terminate.
a)
3
150
7
75
b)
c)
11
250
d)
15
48
b
17. Express in simplest form and without negative
exponents:
1
1в€’
1
1в€’
MCC-350.PCX
9.
I have 99/
c in change, and I do not have a half-dollar.
What is the least number of coins I could have?
9 (coins)
1
x
1
1в€’
1
x
18. The coordinates of three vertices of a parallelogram
are (в€’3, 1), (2, 5), and (4, 1). Find the sum of the
coordinates of the fourth vertex which is in the third
quadrant. в€’4
SMP rev. 3.0 (PDF) page 96. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GD
19. Three tennis balls are tightly sealed in a right
cylindrical can, so that the balls cannot move inside
the can. If the radius of each ball is 4 cm, find the
number of cubic centimeters in the volume of the
space within the cylinder, not taken up by the three
tennis balls. Express your answer in terms of ПЂ.
128ПЂ (cm3 )
20. The diving pool shown is in the shape of a
trapezoidal right prism. How many cubic feet are in
its volume? 4,800 (ft3 )
29. What are the coordinates of the point which is the
reflection in the y-axis of the point whose coordinates
are (5, в€’3)? (в€’5, в€’3)
30. Kristie had $250 in her savings account. She made
deposits of $25, $52, and $38, withdrawals of $30 and
$15 and earned interest of $2.15. To the nearest cent,
how many dollars were in her account after these
transactions? $322.15
31. For what digit(s) x will the 7-digit number 3x6xx2
be divisible by 4? 1, 3, 5, 7, and 9
32. The notation a в‰Ў b (mod n) means (a в€’ b) is a
multiple of n where n is a positive integer greater
than one. Find the sum of all possible values
of n such that both of the following are true:
171 в‰Ў 80 (mod n) and 468 в‰Ў 13 (mod n). 111
MCC-463.PCX
21. What is the smallest prime the sum of whose digits
is 19? 199
33. Each of the triangles in the cross-section of a shell of
a chambered nautilus has a shortest side length of
1 inch as shown. Find the number of inches in the
length of the hypotenuse of the tenth right triangle.
Express your answer in simplified radical form.
в€љ
11 (inches)
1
2,
x3
22. Variable y varies inversely as
and, when x =
1
y = 3. Find x when y = 3 . Express your answer in
simplest radical form. в€љ3 9
2
J
2A в€’ B
23. If A B =
, what is the value of (3
2
Express your answer as a common fraction.
в€љ
24. Simplify:
55 + 55 + 55 + 55 + 55
J 4) J 5 ?
в€’ 23
MCC-570.PCX
125
25. What is the area in square centimeters of the shaded
region in the figure? Express your answer as a
decimal. 3.375 (cm2 )
34. Two angles are supplementary. The difference of
their degree measure is 100 в—¦. Find the measure in
degrees of the smaller angle. 40 (degrees)
35. The union of sets A and B contains 12 elements. If
A contains 9 elements, and B contains 8 elements,
how many elements are in the intersection of A
and B ? 5 (elements)
36. Express the product in scientific notation:
(48200)(0.0045) 2.169 Г— 102
MCC-361.PCX
26. Seventeen is 17% of what number?
100
27. Four friends shared a bottle of water. The first
drank 14 of the water. The second drank 13 of the
remainder. The third drank 12 of what was left. The
fourth friend drank the last six ounces. How many
ounces of water were originally in the bottle?
24 (ounces)
28. What is the value of 6% of 5% of $1200?
37. A salesman buys a coat at $64 less 12.5%. He then
sells the coat at a gain of 25% of his cost after
allowing a 20% discount on the marked price. What
is the marked price, in dollars, of the coat? $87.50
38. Twenty-six people, numbered consecutively 1
through 26, are seated equally spaced around a
circular table. Which numbered person is seated
directly across from person number 9? (person) 22
$3.60
SMP rev. 3.0 (PDF) page 97. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GE
These items are drawn from the MATHCOUNTS School Handbook (MCH) module. MATHCOUNTS is a nationwide
program in the U.S. that promotes math excellence among middle and junior high school students. The 4500 short
response items included in this module are taken from School Handbooks that the MATHCOUNTS Foundation
produces each year. The module is organized topically and updated each year.
1.
The numbers a and
в€љ b are consecutive positive
integers, and a < 200 < b. What is the value of the
product ab ? 210
2.
Twenty-seven points are equally spaced on a circle.
If two points are randomly selected, what is the
probability that both are contained on some 90 в—¦ arc?
Express your answer as a common fraction. 6
11. In the figure shown, all arcs are semicircles, and
those that appear to be congruent are. How many
square units are in the area of the shaded region?
Express your answer in terms of ПЂ. 2ПЂ
13
3.
How many squares are needed to build the tenth
shape in the pattern? 55
MCH-400.PCX
12. Suppose the points A, B, C , D, E , and F are the
vertices of a regular hexagon with sides of length
1 unit. What is AD ? 2
1st
4.
5.
6.
2nd
13. Simplify, expressing your answer in scientific notation:
Given that A is the set of all integral solutions of
|x в€’ 4| < 5, what is the median of all the members of
set A ? 4
How many nickels will I receive from a $20 bill if I
request twice as many dimes as nickels and three
times as many quarters as nickels? 20
If x В« y =
tenth.
7.
3rd
xy
, find 4 В« (9 В« 1) to the nearest
|x в€’ y |
0.3
Jane is going from home to school. If she always
goes in either a northerly or easterly direction how
many different paths are there from her house to the
school? 20
3.5 Г— 10в€’3 1.44 Г— 106
В·
1.75 Г— 10в€’3 1.2 Г— 10в€’4
2.4 Г— 1010
14. Each card has either a circle or a star on one side
and either a triangle or a square on the other side.
In order to verify the statement every card with a
star on it also has a triangle on it, which numbered
card(s) must be turned over? 2 and 3
_ [
1
2
?
W
3
4
MCH-001.TBL
15. Simplify:
1.1 + 2.2 + 3.3 + В· В· В· + 8.8 + 9.9
16. If g(x) = 2x в€’ 4 and h(x) =
h(g(10)) в€’ g(h(10)). 0
MCH-269.PCX
8.
Which is largest: 3100 , 650 , 475 , or 850 ?
9.
Let N = 43 в€’ 52 and M = 5 13 в€’ 1 61 . Find the value of
the product MN . Express your answer as a common
fraction. 35
3100
1
2x
50
+ 2, find
17. A cone with altitude 8 and slant height 10 is
attached to one end of a cylinder with height 10.
A hemisphere with the same circumference as the
cylinder is attached to the other end of the cylinder.
Find the number of cubic units in the total volume
of the solid in terms of ПЂ. 600ПЂ
24
10. Find the largest possible product of two prime
numbers whose sum is 100. 2491
MCH-379.PCX
SMP rev. 3.0 (PDF) page 98. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GE
18. Given x = в€’3 and y = 12 , evaluate
в€’y в€’3
.
(2x + y в€’1 )в€’2
в€’128
19. Joe’s French poodle, FooFoo, is tied to the corner of
the barn which measures 40 × 30 . FooFoo’s rope is
50 long. In terms of ПЂ, over how many square feet
can FooFoo wander? 2000ПЂ
26. Four points have the coordinates A(3, 3), B(5, 7),
C (8, 7), and D(12, 3). The points A , B , C , and D
are found by multiplying the abscissas of A, B, C ,
and D respectively by в€’1. Find the difference in the
numbers of square units in the areas of quadrilaterals
ABCD and A B C D . zero
27. How many distinct diagonals does a regular hexagon
have? 9
28. A square nut is placed on a bolt in the position
pictured and tightened clockwise 37 43 turns where a
turn is one complete 360 degree revolution. Which
в€’в€’в€’ в€’в€’в€’ в€’в€’в€’
в€’в€’в€’
edge (AB, BC , CD, or AD) will be in the same
в€’в€’в€’
в€’в€’
position as AB is now? в€’
BC
MCH-336.PCX
20. Find the number of degrees of the acute angle of a
parallelogram whose obtuse angle is 125 degrees. 55
21. Trapezoid ABCD has an area of 45 cm2 and was
created by truncating an equilateral triangle with an
area of 60 cm2 . How many square units are in the
area of AND ? 20
MCH-268.PCX
29. Alice was born 2000 days ago. Today is Sunday. On
what day was she born? Tuesday
30. The average of a set of 4 numbers is 80. If one of the
numbers, 92, is removed from the set, by how much
will the mean drop? 4
MCH-363.PCX
22. Cassette tapes regularly priced at $9.60 are on sale
for $7.68. What is the percent of discount? 20
31. How many more distinguishable arrangements are
there of the letters TALK than of the letters TOOT?
18
23. The first three terms of an arithmetic sequence are
x в€’ 1, x + 1 and 2x + 3. What is the value of x ? 0
24. Students earned the test scores in the table below.
If x is the mean of the scores, y is the median of
the scores and z is the mode of the scores, find
x+y+z
. 84
3
Number of
Students
Score
4
8
7
3
1
2
100
90
80
70
60
50
MCH-016.TBL
25. Some of the keys on Nancy’s typewriter do not print
correctly. For example, when the A key is pressed
it types a W . When she typed the following
problem the sum was correct but the two addends
were wrong. Which number key on her typewriter
printed incorrectly?
32. How many rectangles are in the figure shown?
45
MCH-029.FIG
33. When grouping symbols are inserted into the
expression 2 + 3 В· 45 , what is the largest possible value
that can be obtained? 3,200,000
34. How many three-digit numbers are there such that
no two digits differ by more than 3? 270
35. Sue drove to town travelling 40 miles per hour.
How fast would she need to drive home to average
48 miles per hour for the entire trip? 60 miles per hour
36. What is the greatest common factor of 32, 48,
and 72? 8
34,729 + 37,543 = 76,312
8
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Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GF
These items are drawn from the North Suburban Math League Contest (NSM) module. The 2000 free-response items
that appeared in this Chicago-area contest cover most high school mathematics topics. The module is organized
topically and updated each year.
1.
Solve for x: 48x2 = 168x + 360
2.
Find the inverse of the following matrix.
3
7
3.
в€’5
в€’12
12
7
11. When a sector of a circle is rolled into a right circular
cone as shown, the arc of the circle becomes the
circular base of the cone, and the radius of the circle
becomes the lateral edge of the cone. If the length of
the circular arc is 20ПЂ, find the total surface area of
the cone. Round your answer to three decimal places.
в€’ 32 , 5
в€’5
в€’3
In the World Series the teams play the best of 7.
That is, when one team wins 4 games the series ends.
If we assume the probability of either team winning
in a single game is 12 , then what is the probability
that the series will go a full seven games? 5
1570.796
16
4.
What is the minimum value of the following function?
f (x) =
x2 в€’ 6x + 9
|3x|
NSM-201.PCX
0
x3 в€’ 5x2 + 7x в€’ 3
x→3 x3 − x2 − 5x − 3
12. Evaluate: lim
5.
ABCD is a rectangle with AB = 12 cm and
в€’в€’в€’
BC = 7 cm. Point E is on AD with DE = 2 cm.
в€’в€’в€’
Point P is a point on AB. How far to the right
of point A should point P be placed so that the
shaded area comprises exactly 40% of the area of the
rectangle? 8.4
1
4
13. The number 2342631143a4 is divisible by 12. What
are the possible values of a ? 0 and 6
14. Bill pays $100 for a stock. Its value increases 25%
the first year. It increases 20% the second year. It
decreases in value by 20% the third year, and finally
it decreases by 25% in the fourth year. He now sells
the stock. How much does he receive for the stock?
$90
15. Find all solutions (in radian form) that are in the
interval 0 ≤ x ≤ 2π:
tan2 x в€’ 3 = 0
NSM-391.PCX
6.
Express the following in the rectangular form a + bi,
where a and b are real numbers.
в€љ
в€љ 57
в€’ 2 i 2
в€љ
в€љ
+
в€’ 22 + i 22
2
2
7.
How far will a ball travel before coming to rest if it
is dropped from a height of 32 feet and rebounds 45
of its previous height on each bounce? 288
в€љ
Solve for x: x в€’ 3x в€’ 6 = 2 {2, 5}
8.
9.
Point A has coordinates (10, в€’7). Point B has
в€’в€’в€’
coordinates (в€’1, 0). If point C lies on AB and has
coordinates (4, q), find the exact value of q. в€’35
ПЂ 2ПЂ 4ПЂ 5ПЂ
3, 3 , 3 , 3
16. The candles are initially the same height. The faster
one burns at a rate equal to 32 of the slower one. If
the faster burning candle will burn completely in one
hour, in how many minutes will it be 12 the height of
the slower burning candle? 45 minutes
в€љ
4 в€’ 16 + m
17. Evaluate: lim
в€’ 18
m→0
m
18. Circles with centers O, O , and P are each tangent
to line L and also mutually tangent. If the radii of
circle O and circle O are equal, and the radius of
circle P is 6, then what is the radius of the larger
circles? 24
11
10. Find all solutions (x, y) to the following system of
inequalities.
|x в€’ 3| = 7 + y
|x| + |y | = 6
{(в€’5, 1), (1, в€’5)}
NSM-069.PCX
SMP rev. 3.0 (PDF) page 100. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GF
19. Let f and g be functions defined on the same
interval. If f and g are both increasing functions, is
f В· g necessarily an increasing function? No
27. Let r1 and r2 be the roots of the equation
x2 + bx + c = 0. If r2 в€’ r1 = 6i and r2 В· r1 = 2, then
what is the sum of b and c ? 2 + 2iв€љ7, 2 в€’ 2iв€љ7
20. The rectangular solid shown, has a height of 5
(AD = 5), a length of 12 (DC = 12) and a depth of 4
(AE = 4). Find the area of EDF . 6в€љ41
в€’в€’в€’
28. AC is the hypotenuse of right triangle ABC . If
the length of median AD is 4 and the length of
в€’в€’в€’
median CE is 3, find the length of AC . 2в€љ5
29. Which of the following has the greater area?
A) (x в€’ 3)2 + (y + 5)2 = 25
x2
y2
B)
+
=1 B
25 36
30. What are the real values of x that solve:
NSM-101.PCX
21. A number is picked at random from the counting
numbers. This number is then squared. What is the
probability that when this squared number is divided
by 8 the remainder is 4? 1 or 25%
4
в€’в€’в€’
в€’в€’в€’
22. In the figure, BC is parallel to AD. If BC = 4,
AD = 6, and ED = 8, find CD. 8
3
9
2x
+
=1
xв€’2 x+2
1 or в€’14
31. Assume the universal set under consideration, is the
set of positive integers less than 100. If A is the set
of even integers, B is the set of integers divisible
by 3, and C is the set of integers divisible by 5, then
how many elements are in the set, (A ∩ B) ∪ C ? 32
в€љ
32. Factor completely: 6x2 + 3x в€’ 3
Write your answer in the form (ax В± b) В· (cx В± d)
where a, b, c, and d are integers, roots of integers, or
opposites of roots of integers. (в€љ2x + в€љ3 ) В· (3x в€’ в€љ3 )
33. Two Holstein and three Gurnesy cows give as much
milk in three days as two Gurnesy and four Holstein
give in two days. Which cow gives more milk per
day? Holstein
NSM-031.PCX
23. A rifle bullet is shot with an initial velocity of
900 ft/sec. The rifle was at a height of 6 feet
and was angled up 30 в—¦ from the horizontal. The
parametric equations which describe this motion are:
x = 900 cos(30 в—¦)t, y = 6 + 900 sin(30 в—¦)t в€’ 16t2 . Find
the distance traveled horizontally before the bullet
strikes the ground. Give your answer to the nearest
foot. 21,932 ft
24. Simplify the following (use for modulo K the integers
{0, 1, 2, . . . , K в€’ 1}):
3(5 + 7 Г— 2) в‰Ў
(modulo 9)
3
25. Solve for all values of x for which det A = det B.
пЈ®
пЈ№
0 5 0
1 2x
A=
B = пЈ° в€’2 0 x пЈ»
в€’ 27 , 6
x в€’8
в€’1 0 в€’5
26. What is the probability that if a divisor of 540
is picked at random, that the divisor will be a
single-digit number? 7
в€’в€’в€’ в€’в€’в€’
34. In the trapezoid shown, AB DC , and E and F are
the midpoints of the two diagonals. If DC = 60 and
в€’в€’в€’
EF = 5, then what is the length of AB ? 50
NSM-328.PCX
35. A train 0.5 km in length is travelling at a uniform
speed of 90 km per hour. How many seconds will it
take for the train to go completely through a tunnel
1.5 km in length? 80
36. The St. Louis (parabolic) arch is 352 feet high at its
highest point. The arch is 240 feet wide at ground
level. How wide, to the nearest foot, is the arch at a
height of 100 feet above the ground? 203 feet
24
SMP rev. 3.0 (PDF) page 101. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GG
These items are drawn from the North Carolina State Math Contest (NCC) module. The module features 2500
mostly multiple-choice items from the regional and state contests since 1981. The module is organized topically and
updated each year.
1.
A silversmith mixed 100 g of a 40% silver alloy with
40 g of a 12% silver alloy. What is the percent silver
concentration of the resulting alloy?
a) 30%
b) 25%
e) none of these
2.
3.
b) 7
9.
в€— d) 18
c) 12
e) 72
в†ђ
в†’
In the sketch, RS is a tangent line to circle with
в†ђв†’
в€’в€’в€’
center O and RU is a secant line. The length of TR
is:
a) 16
в€— b) 9
c) 2
d) 7
e) none of these
The value of 3 в€’
A man took a five hour hike, the first part of which
was level but the second part was uphill. He then
returned on the same trail. If he walks 4 mph on
level ground, 3 mph uphill, and 6 mph downhill; how
long was the entire hike?
6.
в€— d) y = 23 x в€’ 2
c) x в€’ 2y = 1
e) x + 2y = 1
10. 16x2 в€’ 48xy +
will be a perfect square trinomial
if the third term is:
a) e
c) в€’144y 2
e2x в€’ ПЂ в€’2e
+
ПЂ в€’e + eПЂ
b) в€’e
1
n
d) в€’36y 2
e
в€— c) ПЂ
d) в€’ПЂ
e) eПЂ
12. A store owner found that if she charges x dollars
each for a certain toy, she can sell 400 в€’ 100x of
them. The toys cost her $2.00 each. What should
she charge for each toy to maximize her profit?
a) 50
d) 11
b) 0 < x < 3
d) 0 < x < 1
b) 1 : 11
d) 1 : 14
b) $2.50
в€— b) 49
4
e) 28
c)
c) $5.00
d) $4.25
53
7
NCC-384.PCX
14. If kx5 в€’ 6x3 + 5x2 + 4x в€’ 4 is exactly divisible by
x в€’ 2, then k must be:
b) в€’ 12
a) 21
e) none of these
Which of the following is the largest?
b) 344
d) 14
13. If the vertices A, B, and C in the 3 adjacent squares
are collinear, then the value of x is:
NCC-377.PCX
a) 255
is:
b) 3y в€’ 2x в€’ 6 = 0
D and E are the midpoints of sides AB and BC ,
respectively, in ABC . The ratio of the area of
DEF to ABC is:
a) 1 : 10
в€— c) 1 : 12
e) 2 : 25
7.
25
e) cannot be determined from this information
x4 в€’ 40 < 41
в€— a) в€’3 < x < 3
c) в€’1 < x < 1
e) none of these
в€љ
4
c) в€’16
a) в€’x + 2y = 1
в€— a) $3.00
в€— b) 20 miles
d) 30 miles
a) 10 miles
c) 24 miles
e) none of these
Solve for x:
3+
a) 64y 2
в€— b) 36y 2
e) none of these
NCC-097.PCX
5.
25
The equation of the reflection of the line having
equation 2x + 3y = 6 about the line having equation
x = 3 is:
11. Simplify: ln
4.
в€љ
4
в€— a) 4
b) 8
e) none of these
в€— d) 36%
c) 26%
The degree of (x3 + 1)4 (x2 + 1)3 as a polynomial in x
is:
a) 5
8.
в€— c) 533
d) 622
e) 711
в€— c)
3
4
d) в€’ 43
=
15. If the operation
is defined by the equation
x y = 2x + y, what is the value of a in
2 a = a 3?
=
=
a) 0
=
b) в€’1
в€— c) 1
d) 1.5
e) 4
SMP rev. 3.0 (PDF) page 102. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GG
16. Solve the formula r =
Aв€’P
for P .
Pt
A
Prt
rt
c) P =
A
e) none of these
b) P = A в€’ r
a) P =
в€— d) P =
A
rt + 1
17. What is the remainder when 299 is divided by 5?
a) 0
b) 1
в€— d) 3
c) 2
24. Each side of triangle ABC is 20 units. D is the foot
в€’в€’в€’
of the perpendicular dropped from A on BC , and E
в€’в€’в€’
в€’в€’в€’
is the midpoint of AD. The length of BE , in the
same unit, is:
в€љ
a) 10
b) 5 6
в€љ
в€— c) 5 7
d) 5
в€љ
20 3
e)
3
e) 4
18. Given a right parallelepiped as shown where AE = 4,
в€’в€’в€’
AD = 5, AB = 6, then length of AG is:
в€љ
в€љ
a) 2 13
b) 4 + 61
в€љ
в€љ
d) 61
c) 41
в€љ
в€— e) 77
NCC-180.PCX
25. If 7x в€’ 5y = 13, and 2x в€’ 7y = 26, then 5x + 2y =
a) в€’39
в€— b) в€’13
c) 13
d) 19.5
e) 39
26. What is the number of solutions of
2 cos2 Оё в€’ cos Оё в€’ 1 = 0 for Оё in [0, 2ПЂ]?
a) 2
в€— c) 4
b) 3
d) 5
e) more than 5
27. If 9xв€’2 = 81x+1 find the value of 2x .
NCC-112.PCX
19. Let h be the height of a tin can and let ПЂ be the
ratio of the height of the can to the diameter of
the top of the can. What are the dimensions of the
label?
a) ПЂ Г— ПЂ
в€— c) h Г— h
b) h Г— 2h
d) h Г— 2ПЂ
20. Find the sum of the fifth term of the geometric
progression 6, 4, 83 , . . . and the 11th term of the
2
4
6
arithmetic progression 27
, 27
, 27
,....
31
27
c)
52
27
d) 1
в€— c)
1
16
d) 8
28. By the Rational Zero Theorem, all of these except
which could be a possible rational zero of the
equation y = 2x4 в€’ 9x3 + 2x2 + 21x в€’ 10?
в€— a)
e) none of these
в€— a) 2
b)
e) none of these
a) в€’8
b) 16
e) none of these
1
5
b)
1
2
c) 1
d) 2
29. Two circles of radii 4 inches and 14 inches have a
common external tangent of length 24 inches. The
distance between the centers of these circles is:
a) 24 in.
b) 25 in.
в€— c) 26 in.
d) 27 in.
e) none of these
NCC-103.PCX
21. The last digit in 410 is:
a) 0
b) 2
c) 4
в€— d) 6
e) 8
22. A ladder 10 ft long leans against a wall. The bottom
of the ladder is 6 ft from the wall. The bottom of the
ladder is then pulled out 3 ft farther. How much does
the top end move down the wall?
в€љ
в€љ
в€љ
в€— b) 8 в€’ 19
c) 19
a) 8 + 19
в€љ
в€љ
d) 4 + 19
e) 4 в€’ 19
30. Using the Binomial Theorem in the expansion of
(2x + 3y)9 , what is the numerical coefficient of the
x6 y 3 term?
в€— a) 145,152
d) 5,376
31. Simplify:
23. If the graph of the equation 2ry = 5x + 9 has slope 1,
then the value of r is:
2
5
b)
2
9
c) 2
в€— d)
5
2
e)
9
2
x2
b) 237,123
e) 84
c) 2,268
1
1
в€’
x+1 x+4
5
+ 5x + 4
3
в€— c) 2
x + 5x + 4
e) none of these
a)
a)
e) 5
2x + 5
+ 5x + 4
в€’3
d) 2
x + 5x + 4
b)
x2
SMP rev. 3.0 (PDF) page 103. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GH
These items are drawn from the UNC Charlotte Math Contest (UNC) module. This contest, a preliminary to
the NC State Contest (see NCC), has generated 1100 multiple-choice items since 1980. The module is organized
topically and updated each year.
1.
2.
If the point D is between the points A and B on
line AB and C is then between A and D, then which
of the following is false?
в€’в€’в€’ в€’в€’в€’ в€’в€’в€’
в€’в†’ в€’в€’в†’
a) AB = AD в€Є DB
b) DA ∩ DB = {D}
в€’в€’в†’ в€’в†’
в€’в€’в†’ в€’в€’в†’ в€’в€’в€’
c) DC = DA
d) AC ∩ BD = AB
в€— e) none of these
A factor of x3 в€’ 6x2 в€’ 6x + 1 is
в€— a) x + 1
3.
b) x в€’ 1
e) x +
1
2
If the operation вЉ— is defined for positive real numbers
ab
as a вЉ— b =
, then 4 вЉ— (4 вЉ— 4) =
a+b
e) 16
3
в€љ
10. A sphere is inscribed
in a cone of radius 3 3 and
в€љ
slant height 6 3. What is the radius of the sphere?
в€љ
в€љ
a) 6 3
b) 3 3
в€љ
3 3
в€— c) 3
d)
2
e) none of these
a) 2
b) 4
c) 8
в€— d)
4
3
The smallest distance d separating the lines 3y = в€’4x
and 3y = в€’4x + 25 satisfies
a) d ≤ 3
d) 5 < d ≤ 10
4.
d) x в€’ 2
c) x
9.
b) 3 < d ≤ 4
e) 10 < d
∗ c) 4 < d ≤ 5
UNC-053.PCX
Find the measure of angle y in the figure if P is the
center of the circle
a) 53 в—¦
в€— c) 109 в—¦
b) 35 в—¦
d) 90 в—¦
11. How many kilograms of pure acid must be added to
8 kilograms of a 40% acid solution to produce a 50%
solution?
a) 5 31 kilograms
b) 13 13 kilograms
в€— c) 1.6 kilograms
d) 9.6 kilograms
e) none of these
в€љ
в€љ
12. If lim ( n2 + an + 2 в€’ n2 + 2n + 3 ) = 3, then a =
e) 37 в—¦
n→∞
a) 5
UNC-077.PCX
b) 6
c) 7
в€љ
5.
x3
Let P (x) =
+ 23x в€’ 15. Note that P (5) = 0.
Identify the true statement. The sum of the roots of
P (x) is
a) 8
6.
b) 1
c) 3
d) 4
в€— e) 9
A pair of fair six-sided dice are tossed. What is the
probability that either the same number appears on
both or the sum of the two numbers is less than 5?
a)
7.
в€’ 9x2
6
36
b)
8
36
в€— c)
10
36
d)
11
36
e)
12
36
A lead ball of radius 24 cm is melted down and recast
into smaller balls of radius 6 cm. Assuming that no
metal is lost in this process, how many complete
smaller balls can be made?
a) 2
b) 4
c) 16
d) 36
13. The square of 2
a) 22
в€— b)
2
в€љ
4 2
в€— d) 8
e) 9
equals
в€љ
c) 42
d) 42
в€љ
2
e) 4
2
2
14. When x4 в€’ 3x2 + 1 is divided by x в€’ 4, the remainder
is:
a) в€’209
b) в€’207
e) none of these
в€— c) 209
d) 207
15. In the figure shown, a circle is inscribed in a right
triangle with sides of length 5, 12, 13. The radius of
the circle is
в€љ
a) ПЂ
b) 12
c) 8
5
в€љ
в€— d) 2
e) 3
в€— e) 64
UNC-070.PCX
8.
Given that 32x+y = 729 and 32yв€’x = 27, then y is
equal to:
a) 3
b) 2
в€— e) none of these
c) 1
d) 4
16. If
a
c
b
d
1
3
2
5
=
5
0
a) в€’98
в€— b) в€’10
e) cannot be determined
1
2
then det
c) 0
a
c
b
d
equals
d) 10
SMP rev. 3.0 (PDF) page 104. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
GI
These items are drawn from the Western Carolina University Math Contest (WCC) module. This contest, a
preliminary to the NC State Contest (see NCC), has generated 2700 multiple-choice items since 1981. The module is
organized topically and updated each year.
1.
The complex number (в€’1 + i)5 is equivalent to:
a) в€’16 в€’ 4i
d) в€’5 + 5i
2.
c) 14 в€’ 4i
в€— b) 20
c) 10
d) 35
в€— b) 12.5
в€љ
e) 3 15
d) 17.5
c) 15
9.
The simplest form for:
is:
x+9
xв€’1
=
.
2x
x
в€— b) {11}
c) { }
e) {в€’10, 11}
a) 88
в€— b) 5
6.
d) 1
1
4
в€— b)
3
4
c)
3
8
d)
1
2
e) 2
e)
1
8
в€’в€’в€’
In ABC , M is the midpoint of side BC ,
в€’в€’в€’ в€’в€’в€’
в€’в€’в€’
AN bisects BAC , BN вЉҐ AN and Оё is the measure
в€’в€’в€’
в€’в€’в€’
of BAC . If sides BA and AC have lengths 14
в€’в€’в€’в€’
and 19, respectively, then the length of MN equals:
a) 2
в€— b)
c)
d)
e)
5
2
5
2
5
2
5
2
b) 85
в€— c) 89
в€— b) 24
c) 25
d) 30
a)
в€— b)
d)
e)
c)
13. When 2x3 в€’ x2 + 7x + 2 is divided by x2 + 1, the
remainder is:
a) 9x + 1
d) 5x + 1
b) 2x + 1
в€— e) 5x + 3
a) 3
в€— b) 2
e) none of the above
в€’ sin Оё
в€’
1
2
1
2
sin Оё
sin
e) 100
12. Which of the following patterns of squares cannot be
folded into a box with an open top?
14. The value of x in the solution of
в€’
d) 75
11. With how many zeros does the number 100! end?
If three distinct coins are tossed in the air, what is
the probability that exactly two heads or exactly two
tails appear?
a)
7.
c) 6
c) 6x4 y 6 z 6
e) none of the above
Which of the following values of k would guarantee
that the equation 2x2 в€’ kx + 3 = 0 will have rational
roots?
a) 0
в€љ
81x2 y 4 z 4 256x8
10. Ed scored 85 on his first test. The average of his first
two tests was 9 less than his score on his third test.
The average of all three tests was 83. What was the
score on Ed’s last test?
a) 10
5.
4x5 y 10 z 8
b) 124 y 6 z 6
в€љ
e) 12x4 y 6 z 6
d) 24x4 y 6 z 6
Find the solution set of
a) {10}
d) {в€’11}
WCC-203.PCX
в€— a) 12x4 y 6 z 5
WCC-197.PCX
4.
c) 54
e) 2
Each of the circles with centers shown is tangent to
the other two circles. If AB = 10, AC = 15, and
BC = 20, then the radius of the circle with center C
is:
a) 12
If ABCDE is a regular pentagon and BAF and DEF
are straight lines intersecting at F , then the degree
measure of angle AFE is:
a) 30 в€— b) 36
d) 27 e) 15
A child has $8.50 in quarters and dimes. The
child has 15 more dimes than quarters. How many
quarters does the child have?
a) 5
3.
в€— b) 4 в€’ 4i
e) 0
8.
c) 2x в€’ 1
3x в€’ 2y = 6
is:
4x + y = 8
c) 1
d) 0
15. For f (x) = в€’2x2 + x + 10, find f (f (f (в€’2))).
1
2Оё
WCC-052.PCX
в€— a) в€’180
b) в€’200
c) в€’160
d) 140
e) в€’2
SMP rev. 3.0 (PDF) page 105. Copyright c 1999 EAS EducAide Software Inc. All rights reserved. You may distribute this document freely, provided you do not alter it in any way or remove this copyright notice.
Note: this document was produced by EducAide’s Acces program. It contains problems from the SMP database. For more information, please call 800-669-9405 or visit www.educaide.com.
Summary of EducAide’s Modules, February 1999
Code
Title
Problems
Categories
Pictures
PRE
Pre-Algebra
15020
164
334
ALG
Algebra I
18630
171
105
GEO
Geometry
5104
139
863
TRI
Algebra II/Trigonometry
16440
162
332
CM2
Canadian Math Grades 8 10
5824
66
732
CM1
Canadian Math Grades 11-12
6382
107
570
NC1
NC Math Objectives
1749
103
264
NC2
NC Elementary Math Testlets
1316
24
924
NC3
NC Algebra I
2126
52
608
NC5
NC Secondary Math Testlets
1713
33
638
NY1
NY Regents Exams
4788
56
795
OH1
Ohio Proficiency
2184
20
112
TX2
TAAS Elem. Math (gr. 3 6)
1945
52
800
TX3
TAAS Sec. Math/Algebra EOC
4012
53
580
NC4
NC Elem. Reading Testlets
929
104
84
TX4
TAAS Elementary Reading
1475
54
30
MMA
Mid-level Math Assessment
5000
112
545
SAT
SAT Math Prep.
2144
60
388
APC
AP Calculus
1767
68
51
AW1
Addison Wesley W. Canada 10
2476
67
503
CD1
CORD Applied Mathematics
2716
88
544
CD2
CORD Applications in Bio/Chem
2222
131
71
CD3
CORD Principles of Technology
2725
96
120
MMF
French Translation of MMA
5000
112
545
T2S
Spanish Translation of TX2
1945
52
800
T3S
Spanish Translation of TX3
4012
53
580
BCC
BC Colleges HS Contest
1591
94
380
IEC
IL State Elem Math Contest
1928
26
390
ISC
IL State Sec Math Contest
4759
84
600
MCC
MATHCOUNTS Competitions
5752
51
615
MCH
MATHCOUNTS Handbooks
4540
51
475
NSM
NSML Math Contests
2075
42
355
NCC
NC State Math Contests
2612
50
455
UNC
UNC Charlotte Math Contest
1108
50
135
WCC
WCU Math Contests
2742
38
540
Note: All modules require the Acces database and publishing engine . For more information,
please call EducAide Software at 800-669-9405 or visit www.educaide.com.

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