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Math Analysis CP - Spring Midterm REVIEW
Multiple Choice - Identify the choice that best completes the statement or answers the question.
1. What is the complete solution to the equation |9  2x| = 15?
a. x = 3; x = 12
c. x = 3; x = 12
b. x = 12; x = 3
d. There are no solutions.
2. What is the solution to the system of equations shown below?
9x + 3y + 3z = 12
27x + 9y + 9z = 36
3x  y  z = 4
a. no solutions
c.
b. infinitely many solutions
d. (0, 4, 0)
2
3. What is the sum when (6x  2x + 5) is added to (3x2 + 4x  9)?
a. 9x2  6x + 14
c. 3x2 + 2x  4
2
b. 3x  2x + 4
d. 3x2 + 2x + 4
4.
a.
5.
6.
7.
8.
9.
10.
2x  3 +
c. 2x + 3
b. 2x  3
d. 2x2 + 3x + 12
(3a2 + 3a  6)  3(4a2  7a + 6) =
a. 9a2  18a + 12
c. 15a2  18a + 24
b. 15a2 + 24a  24
d. 15a2  4a
What is the remainder when x2  6x + 9 is divided by x  4?
a. 0
c. 5
b. 1
d. 17
2
Which product of factors is equivalent to 16y  24y + 9?
a. (4y  3)(4y  3)
c. (4y + 12)(4y + 12)
b. (4y + 3)(4y + 3)
d. (4y  9)(4y  1)
2
2
What is the complete factorization of 9m  36n ?
a. (3m  6n)(3m  6n)
c. 9(m  2n)(m + 2n)
b. 27(m  n)(m + n)
d. 3(3m  6n)(m + 6n)
2
The total area of a rectangle is 3n + 9n + 6. Which factors could represent the length times width?
a. (3n + 2)(3n + 3)
c. (n + 3)(3n + 2)
b. (n + 3)(3n + 3)
d. (n + 2)(3n + 3)
(7  i)(2 + 3i) =
a. 17 + 23i
c. 11  23i
b. 12i
d. 11 + 23i
11. What is an equivalent form of
?
a.
c.
b.
d.
12. What is an equivalent form of (20  4i)  (16 + 3i)?
a. 36  7i
c. 36  12i
b. 4  i
d. 29
13.
a.
c.
b.
d.
14. What is the simplest form of
a. 2a2b11c3
b. a2b11c3
15.
?
c. a2b5c2
d. a2b6c2
=
a.
c.
b.
d. x2  23
16. What is the simplest form of
a. (x  3y)2
c. (x + y)2
2
b. (x + 3y)
d. x2 + 9xy + 9y2
17. What amount must be added to each side of x2 + 12x = 9 to solve by completing the square?
a. 6
c. 45
b. 36
d. 144
18. What are the solutions to the equation 5x2  20x  25 = 0?
a. x = 5; x = 1
c. x = 5; x = 1
b. x = 25; x = 5
d. x = 5; x = 1
2
19. What are the solutions to the equation 3x + 144 = 0?
a.
c. x = 4
, x = 4
x=
,x=
b.
x=
,x=
d. x = 4i
, x = 4i
20. There are two numbers with the following properties.
1) The second number is 8 more than the first number.
2) The product of the two numbers is 13 less than their sum.
Which of the following represents possible values of these two numbers?
a. 5, 3
c. 8, 8
b. 9, 1
d. 5, 3
21. What are the x-intercepts of the graph of the equation x2 + 3x + 2 = y?
a.
c. 2 and 1
and
d. 1 and 2
b.
and
22. What is the minimum value of the quadratic function f(x) = 2(x + 3)2  5?
a. (3, 5)
c. (3, 5)
b. (3, 5)
d. (3, 5)
23. Which equation is graphed on the coordinate grid shown below?
a. y = x2  2x + 1
b. y = x2 + 4x  3
24. Which is the graph of y = 2(x  3)2 + 1?
a.
b.
c. y = x2  4x + 3
d. y = x2 + 2x + 1
c.
d.
25. Which equation is equivalent to
?
a.
c.
b.
d. 5 = 25x
26. Which expression is equivalent to log436?
a.
b.
27. Which expression is equivalent to
c.
d.
?
a. log53x  log52y
c. (log53x)(log52y)
b. log53x + log52y
d. log5(6xy)
28. What is the solution to the equation 10log5x  4log5 25 = log5 25?
a.
c. x = 5
x=
b. x = 30
d.
x=
29. If the equation y = 3x is graphed, which of the following values of x would produce a point closest to the x-axis?
a. 3
b. 2
c. 0
d. 3
30. A certain radioactive element decays over time according to the equation
y=
, where A = the number of grams present initially and t = time in years. If 5000 grams were present
initially, how many grams will remain after 1200 years?
a. 4204 grams
b. 625 grams
c. 50 grams
31.
d. 25 grams
=
a.
c.
b.
d.
32. Which equation is true for all real numbers?
a.
log5 x  log5 y = log5
b.
(x + y) = 1
c.
=x
d.
= x3
33. If x is a real number, for what values of x is the equation log30 = x true?
a. for some values of x
c. for all values of x
b. for no values of x
d. impossible to determine
34. A train is made up of a locomotive, 5 different cars, and a caboose. If the locomotive must be first and the caboose
must be last, how many different ways can the train be ordered?
a. 120
b. 122
c. 2520
d. 5040
35. From a list of 12 books, each student must choose 3 books for book reports. The first report is a traditional book
report; the second is a poster, and the third is a diorama. How many different ordering of books can be chosen?
a. 79,833,600
c. 2640
b. 15,840
d. 1320
36. Mindy has a collection of 6 CDs. She wants to bring 2 of them on a road trip. How many possible choices does she
have?
a. 15
c. 30
b. 24
d. 360
37. How many different ways can the letters of the word MISSION be arranged?
a. 630
c. 2520
b. 1260
d. 5040
38. Brenda has 5 male kittens and 3 female kittens. If she picks up 2 kittens to give to a friend, what is the probability
that she will pick up 1 male and 1 female kitten?
a.
c.
b.
d.
39. Which figure is a counterexample to the statement below?
For any quadrilateral, the lengths of its diagonals are equal.
a.
c.
b.
d.
40. Given: ABCD is a parallelogram with diagonals
a.
c.

b.
d.

and
. Which of the following must be true?
||
bisects
.
41. Given parallelogram ABCD, which expression represents mB?
a. mA + mC + mD
c. 180°  mC
b. 90° + mA
d. mA  mC
42. Jasmine wants to prove that MNP  OPN in the parallelogram MNOP.
Which of the following supports Jasmine’s assertion that 1  2?
a. If two parallel lines are intersected by a transversal, then alternate interior angles are
congruent.
b. If two parallel lines are intersected by a transversal, then corresponding angles are
supplementary.
c. If a quadrilateral is a parallelogram, then its opposite sides are congruent.
d. If a quadrilateral is a parallelogram, then its opposite angles are congruent.
43. In the quadrilateral ABCD,
, and
.
Which postulate can be used to prove ABD  DCA?
a. SAS
c. SSS
b. ASA
d. AAS
44. In the figure below, line m is parallel to line n. Find the measure of BCA.
a. 40°
c. 90°
b. 50°
d. 140°
45. A cylinder has radius 2 inches and height 8 inches.
If you needed to paint the entire cylinder, with the exception of the two bases, what area would you paint?
a. 10 sq in.
c. 32 sq in.
b. 16 sq in.
d. 64 sq in.
46. In circle X, the midpoints of
and
are 5 inches from the center. Which of the following statements is true?
a. The length of
is equal to the length of
.
b.
must be a diameter.
c.
and
are perpendicular bisectors.
d. The measure of
is equal to the measure of
.
47. Circle A has area 81 square inches. Find the circumference of circle A.
a. 9 in.
c. 81 in.
b. 18 in.
d. 162 in.
48. A truck tire has a diameter of 3 feet. How far will the truck travel in 20 rotations?
a. 30 ft
c. 120 ft
b. 60 ft
d. 180 ft
49. Find the area of trapezoid ABCD.
a. 24 sq in.
c. 29.25 sq in.
b. 28.5 sq in.
d. 40.5 sq in.
50. A runner wants to jog around the perimeter of the field. How far will the runner go in one lap?
a. 720 ft
c. 1005 ft
b. 960 ft
d. 1097 ft
51. One side of an equilateral triangle is 10 inches long. Find the area, to the nearest square inch.
a. 30 sq in.
c. 50 sq in.
b. 43 sq in.
d. 100 sq in.
52. Figure ABCD is a rhombus. Find its area.
a. 12 sq in.
c. 24 sq in.
b. 20 sq in.
d. 60 sq in.
53. If the base of parallelogram MNOP is 1 inch less than twice its height, which expression represents the area of the
parallelogram?
a. (x)(2x  1)
c. (2x  1)2
b. 2(2x  1)
d.
54. In the figure below, sin B = 0.8.
What is the length of
a. 9.6
b. 12
?
55. In a right triangle, cos x =
a.
b.
sin x =
, and tan x =
sin x =
, and tan x =
56. In a right triangle, cos x =
c. 12.8
d. 15
. What are sin x and tan x?
c.
d.
sin x =
, and tan x =
sin x =
, and tan x =
. Which correctly shows the triangle?
a.
c.
b.
d.
57. Triangle RST is shown below.
Which equation should be used to find the length of ?
a.
c.
sin 56° =
cos 56° =
b.
sin 56° =
d.
cos 56° =
58. The figure below shows a 10-foot ladder leaning against a wall. The ladder makes a 62° angle with the ground.
Which is closest to how far up the ladder reaches on the wall?
a. 4.7 ft
c. 8.8 ft
b. 6.2 ft
d. 18.8 ft
59. In the circle below,
and
are chords intersecting at M.
If HM = 6, JM = 6, and LM = 9, then what is the length of
a. 3
c. 12
b. 4
d. 36
60. In the figure below,
and m
is tangent to circle M at point D,
= 96°.
What is mDAB?
a. 68°
b. 100°
c. 136°
d. 200°
?
intersects circle M at points B and C, m
= 64°,
61. In the figure below, secants
and
What is mSPT?
a. 18°
b. 36°
intersect at point P, m
= 63°, and m
= 81°.
c. 72°
d. 144°
62. In the figure below,
is tangent to circle B at point C.
What is the length of
?
a. 7
c. 9
b. 8
d. 17
63. Which inequality is equivalent to 3(4  5x)  x + 7?
a. 5  6x
c. 5  6x
b. 5  16x
d. 5  16x
64. Which equation is equivalent to 7(x + 4)  2(x + 4) = 15?
a. 5x + 4 = 15
c. 5(x + 4) = 15
b. 5 + x + 8 = 15
d. 5x + 8 = 15
65. Which inequality is equivalent to
?
a. 6  22x
c. –4x  12
b. 6  22x
d. –4x  12
66. The cost of admission C to a museum exhibit for one teacher and s students is given by the
equation C = 8s +
+ 12. If the cost of admission for a teacher and his students is $183, how many students
went to the museum?
a. 20
b. 18
67. What is the solution to this inequality?
c. 17
d. 15
–6x – 5  2x + 7
a. x  –0.25
b. x  –0.25
c. x  –1.5
d. x  –1.5
68. During a recent fundraising event, Oscar raised $7.50 more than Anna, who raised $12 less than twice the amount
Marissa raised. The three students raised $96 altogether. How much did Marissa raise?
a. $22.50
b. $25.13
c. $32
d. $33
69. What is the x-intercept of the graph of 8x + 12y = –32?
a. –4
c.
b.
d. 4
70. Which graph shows the inequality 4x – 3y  –9?
a.
c.
b.
d.
71. What is the equation of the line that passes through points (7, –4) and (–3, 5)?
a.
c.
y+4=
(x  7)
y5=
(x )
b.
y4=
d.
(x  7)
72. 3xy2(2x2y) 
a. 6x2 y2
b. 3x3 y5
73.
y5=
(x )
c. 6x3 y3
d. 3x2 y4
=
a. 4x3 y2
b.
c. 6x3 y2
d.
74. (9x2 + 16x  1)  3(x2 + 8x  2) =
a. 6x2 + 24x 3
c. 6x2  40x 7
2
b. 6x  8x 5
d. 6x2  8x 7
75. The area of the rectangle shown below is 65x4y cm2. Find x.
a. 156
b. 40
c. 15
d. 2.4
76.
a.
c.
b. 6x4 + 4x3  2x2  8x
d. 6x4 + 4x3  10x
77. What is
reduced to lowest terms?
a.
c.
b.
d.
78. Simplify
to lowest terms.
a.
c.
b.
d.
79. What value should be added to both sides of this equation to complete the square?
x2 + 6x = 10
a. –9
b. –4
c. 4
d. 9
80. Which of the following shows x3 – 3x2 – 28x in factored form?
a. (x2 – 7)(x + 4)
c. x(x – 7)(x + 4)
b. (x2 + 7)(x – 4)
d. x(x + 7)(x – 4)
81. Geraldo can paint a house in 14 hours and Orlando can paint a house in 8 hours. How long would it take the two of
them to paint a house together?
a. just over 6 hours
c. just over 5 hours
b. just under 6 hours
d. just under 5 hours
82. In mixing some fuel, a scientist combines a 50% ethanol solution with a 90% ethanol solution to get 40 liters 80%
ethanol solution. How much of the 50% solution did the scientist use in the mixture?
a. 10 liters
b. 12 liters
c. 14 liters
d. 30 liters
83. LaJon buys 3 bags of peanuts, 2 drinks for $2 each and 4 hot dogs for $2.75 each. He spends a total of $24.75.
How much does each bag of peanuts cost?
a. $11.25
c. $3.25
b. $6.70
d. $2.80
84. What is one of the solutions to the quadratic equation 3x2 – 8x –2 = 0?
a.
c.
b.
d.
85. Which statement best explains why there is exactly one solution for the quadratic equation
16x2 – 8x + 1 = 0?
a. The value of 82 – (4)(16)(1) is equal to 0. c. The sum of 16, –8, and 1 is greater than 0.
b. The value of 16 is greater than –8.
d. The value of 8 – 4  8  1 is less than 0.
86. A right triangle with a base length of 5x and a height of x – 4 has an area of 350 square centimeters. What is the
value of x?
a. 10
b. 14
c. 66
d. 70
87. Aisha opens a savings account with $1200. After two years during which she makes no withdrawals and no
additional deposits, she has $1323 in her account. Use the equation A = P(1 + r)2, where P is the initial amount in
the account, to determine the interest rate r.
a. 1.10
b. 0.91
c. 0.05
d. –0.047
88. Jennifer has 9 Canadian quarters and 7 American quarters in her pocket. She randomly selects one coin, looks at it
and puts it back. What is the probability that the coin she chose and the next coin she chooses randomly will both
be Canadian quarters?
a.
c.
b.
d.
89. Four cards are drawn from a standard deck of cards without replacement. What is the approximate probability of
drawing a diamond, a club, a spade, and a heart in that order?
a. 0.4%
b. 4%
c. 8%
d. 40%
Math Analysis CP - Spring Midterm REVIEW
Answer Section
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STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
(Key)7.0
(Key)8.0
(Key)7.0
(Key)8.0
(Key)8.0
(Key)8.0
(Key)8.0
(Key)10.0
(Key)10.0
(Key)10.0
(Key)18.0
(Key)18.0
(Key)18.0
(Key)19.0
(Key)19.0
(Key)21.0
(Key)21.0
(Key)21.0
(Key)21.0
(Key)4.0
(Key)4.0
(Key)4.0
(Key)5.0
(Key)5.0
(Key)5.0
(Key)6.0
(Key)6.0
(Key)7.0
(Key)10.0
(Key)10.0
(Key)10.0
(Key)10.0
(Key)10.0
(Key)12.0
(Key)12.0
(Key)14.0
(Key)14.0
(Key)15.0
(Key)15.0
(Key)15.0
(Key)20.0
(Key)20.0
(Key)23.0
(Key)23.0
PS 1.0
PS 2.0
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
Key
Key
Key
Key
CAHSEE | Key
CAHSEE | Key
CAHSEE | Key
Key
Key
Key
Key