SESSION: 44 PAGE: 1 3/20/06 11:33 LOGIN IS-joer PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
VIRGINIA STANDARDS OF LEARNING
Spring 2005 Released Test
END OF COURSE
ALGEBRA 1
CORE 1
Property of the Virginia Department of Education
䉷 2006 by the Commonwealth of Virginia, Department of Education, P.O. Box 2120, Richmond, Virginia 23218-2120.
All rights reserved. Except as permitted by law, this material may not be reproduced or used in any form or by any
means, electronic or mechanical, including photocopying or recording, or by any information storage retrieval system,
without written permission from the copyright owner. Commonwealth of Virginia public school educators may
reproduce any portion of these released tests for noncommercial educational purposes without requesting permission.
All others should direct their written requests to the Virginia Department of Education, Division of Assessment and
Reporting at the above address or by e-mail to [email protected].
2006_Alg1FormulaSht1
12/2/05
10:02 AM
Page 1
Algebra I Formula Sheet
Geometric Formulas
b
l
h
h
h
h
b
b
A=
1
2
bh
A = bh
s
l
r
1
3
w
V = lwh
S.A.= 2(lw + lh + wh)
b1
r
s
h
h
h
p = 4s
A = s2
V = 13 Bh
S.A.= 12 lp + B
b2
A=
1
2
h(b1 + b2 )
w
l
B
c
a
r
b
l
c2 = a2 + b2
p = 2(l + w)
A = lw
Abbreviations
Pi
milligram
gram
kilogram
milliliter
liter
kiloliter
millimeter
centimeter
meter
kilometer
square centimeter
cubic centimeter
mg
g
kg
mL
L
kL
mm
cm
m
km
cm2
cm3
ounce
pound
quart
gallon
inch
foot
yard
mile
square inch
square foot
cubic inch
cubic foot
oz
lb
qt
gal.
in.
ft
yd
mi.
sq in.
sq ft
cu in.
cu ft
volume
total surface area
area of base
V
S.A.
B
year
month
hour
minute
second
yr
mon
hr
min
sec
Copyright © 2006 by the Commonwealth of Virginia Department of Education
22
7
Quadratic Formula
x=
–b ± b2 – 4ac
2a
2006_Alg1FormulaSht1
12/2/05
10:02 AM
Page 2
SESSION: 40 PAGE: 2 1/13/06 6:34 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
Algebra I
2
DIRECTIONS
Read and solve each question. Then mark the
space on the answer sheet for the best answer.
For this test you may assume that the value of a
denominator is not zero.
What is the solution to
4(2x ⴑ 3) ⴔ 2(3x ⴐ 1)?
F
AY010417
墍
⫺5
C
L
1
H 7 墍
J 10
G
SAMPLE
2044537
If f (x) ⴔ x2 ⴐ 2x ⴐ 3, what is the value
of f (x) when x ⴔ 6?
27
B 42
C 51 墍
D 60
A
1
2044552
AY010508
墌
C
3
x
B x
C x
D x
A
Ron paid $75.00 for 5 compact disks
and a case. If the price of each
compact disk was $12.60, what was the
price of the case?
$12.00 墍
B $12.50
C $15.00
D $63.00
A
2006 Commonwealth of Virginia Department of Education
What is the solution to 8 ⴑ 2x ⱖ ⴑ4?
2
ⱖ
ⱖ
ⱕ
ⱕ
6
2
2
6墍
2044558
AY010516
墍
C
SESSION: 40 PAGE: 3 1/13/06 6:34 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
4
2044936
What property makes this equation
true?
y ⴔ ⴑ2x ⴐ 3?
AY060605
墌
C
The
B The
C The
D The
A
y
5
4
3
2
ArtCodes
AY060605.AR1
AY060605.AR2
AY060605.AR3
AY060605.AR4
6a2 ⴑ 2a ⴔ 2a(3a ⴑ 1)
5
Which of the following is most likely a
graph of
F
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
1
2 3 4
5
x 墍
1
2 3 4
5
x
1
2 3 4
5
x
1
2 3 4
5
x
y
5
4
3
2
G
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
y
5
4
3
2
H
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
y
5
4
3
2
J
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
2006 Commonwealth of Virginia Department of Education
3
reflexive property
associative property
commutative property
distributive property 墍
2044688
AY030201
墍
C
L
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6
2045014
7
Which of the following is most likely
the graph of a line with a slope of
zero?
What is the y-intercept of
4x ⴐ 8y ⴔ 12?
AY070612
2044940
AY060609
墌
y
C
墍
A
3
B
3
墍
2
C
L
5
4
3
2
ArtCodes
AY070612.AR1
AY070612.AR2
AY070612.AR3
AY070612.AR4
F
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
1
2 3 4
5
x
C
D
⫺1
2
⫺4
y
5
4
3
2
G
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
1
2 3 4
5
8
x
What is the slope of the line through
(1, 1) and (4, ⴑ1)?
F
y
G
3
H
2
H
1
2 3 4
5
x
J
墍
C
⫺2
5
⫺2
3
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
AY070751
5
5
4
2183534
⫺1
墍
⫺3
2
y
5
4
9
3
2
J
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
1
2 3 4
5
x
墍
2006 Commonwealth of Virginia Department of Education
What is the slope of the line
3y ⴔ 4x ⴐ 5?
A
4
2044984
AY070413
墍
C
4
B
2
C
5
3
D
4
墍
3
SESSION: 40 PAGE: 5 1/13/06 6:34 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
10
2045045
AY080306
墌
12
Which is an equation for the line with
1
a slope of that passes through the
2
origin?
C
F
y⫽
Which graph best represents a line
with a y-intercept of 4 and slope ⴑ3?
2044931
5
H
y⫽
J
x⫽0
C
L
4
3
2
F
y ⫽ 2x
墍
y
1
x墍
2
G
AY060522
1
2
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
ArtCodes
1 2 3 4 5
x
1 2 3 4 5
x
1 2 3 4 5
x
1 2 3 4 5
x
AY060522.AR1
AY060522.AR2
AY060522.AR3
AY060522.AR4
y
5
4
3
2
G
11
Which is an equation for the line
which contains (3, 4) and the origin?
2045053
AY080406
墌
A
y⫽
3
x
4
y⫽
4
x墍
3
C
B
y
5
4
3
2
H
C
y ⫽ 4x ⫹ 3
D
y ⫽ 3x ⫹ 4
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
y
5
4
3
2
J
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
2006 Commonwealth of Virginia Department of Education
5
墍
SESSION: 40 PAGE: 6 1/13/06 6:34 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
y
13
2045093
7
AY080612
6
墌
15
5
C
L
Mrs. Crews bought 4 pencils and
3 pens for $5.60. Miss Houston bought
2 pencils and 3 pens of the same kind
for $4.60. What was the price of each
pencil and each pen?
4
$1.70
B $0.50
C $0.17
D $0.80
A
3
ArtCodes
2
AY080612.AR1
1
- 7 - 6 - 5 -4 - 3 - 2 -1 O
-1
-2
1
2
3
4
5
6
7
x
per
per
per
per
pencil,
pencil,
pencil,
pencil,
$0.20
$1.20
$1.64
$0.80
per
per
per
per
pen
pen 墍
pen
pen
2045118
AY090406
墍
C
L
-3
-4
-5
-6
16
-7
墍
Which equation most likely represents
the line shown on the graph?
y⫽
B
y ⫽ 3x ⫹ 3
C
y⫽
D
y⫽
20
G 21
H 40
J 42
F
3
x⫹3
2
A
⫺2
3
The perimeter of a rectangular playing
field is 244 feet. If its length is 2 feet
longer than twice its width, what are 2045105
AY090204
the dimensions of the field?
x⫺3
17
2
x⫺3墍
3
墌
3 2
x ⴑ 12 ⴔ 0
4
x
B x
C x
D x
ⴐ y ⴔ 11
再3x
yⴔxⴐ3
Which is the solution to the system of
equations shown?
C
F
(4, 7)
G
(2, 17)
H
(2, 5) 墍
J
1 1
,3
2 2
冉 冊
2006 Commonwealth of Virginia Department of Education
ft
ft
ft 墍
ft
C
2183516
2045116
AY090403
41
40
82
80
What are the solutions to the equation
below?
A
14
ft,
ft,
ft,
ft,
6
⫽
⫽
⫽
⫽
⫺4 or x ⫽ 4 墍
⫺12 or x ⫽ 9
⫺3 or x ⫽ 3
3 or x ⫽ 9
AY140702
墍
C
SESSION: 40 PAGE: 7 1/13/06 6:34 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
18
2045497
AY140502
墌
C
21
Which is the solution set for
x2 ⴑ 5x ⴑ 14 ⴔ 0?
x+8
2x
{⫺7, ⫺2}
G {⫺7, 2}
H {⫺2, 7} 墍
J {2, 7}
F
2045280
AY110502
墍
5x + 1
C
L
ArtCodes
AY110502.AR1
What is the perimeter of the triangle
shown in the drawing?
7x ⫹ 9
B 8x ⫹ 9 墍
3
C 8x ⫹ 9
3
D 10x ⫹ 9
A
19
2045316
AY110615
墌
C
L
20
2045293
AY110515
墌
C
If z ⴔ
/ 0,
24y2z3
ⴔ
6z
A
18y2z2
B
16y2z2
22
3
C
4yz
D
4y2z2 墍
ⴑ
3.81 ⴒ 10 4 may be written as —
0.0000381
G 0.000381 墍
H 3,810
J 38,100
F
2045183
AY100305
墍
C
(3xy)(5x2 ⴐ 2xy ⴐ 3y2) is equivalent to —
15x3y ⫹ 6x2y2 ⫹ 9xy3 墍
3
2
G 15x y ⫹ 2xy ⫹ 3y
2
2 2
2
H 15x y ⫹ 6x y ⫹ 9xy
2
2
J 15x ⫹ 5xy ⫹ 3y
F
2006 Commonwealth of Virginia Department of Education
23
7
Which is equivalent to p6p2?
A
p8 墍
B
2p8
C
p10
D
p12
2045221
AY100604
墍
C
L
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24
If y ⴔ
/ 0, which expression is equivalent
to the one shown below?
冉 冊
2183537
2
xy
y4
AY100713
墌
C
26
x2 ⴑ 7x ⴐ 10 equals —
6
(x
G (x
H (x
J (x
F
6
F
x
墍
y12
G
x
y2
H
x7
y8
J
25
When completely factored,
27
6x
y2
⫺
⫺
⫹
⫹
5)(x
3)(x
5)(x
4)(x
⫺
⫺
⫺
⫹
2) 墍
4)
2)
6)
2045347
AY120403
墍
C
L
When 5x2 ⴑ 5 is completely factored,
which is one of its factors?
2045396
x⫹1墍
B x ⫺ 5
C 5x ⫹ 1
D 5x ⫺ 1
A
AY120625
墍
C
A board that is c feet long supports the
stairs as shown below.
2045428
AY130502
墌
28
C
Which is the simplest radical form
of 公52?
2183639
c
ArtCodes
13公2
G 公52
H 4公13
J 2公13 墍
12 ft
F
AY130502.AR1
18 ft
AY130710
墍
C
To find the value of c, Britney used the
following expression.
公122 ⴐ 182
29
What is c to the nearest tenth of a foot?
36.0
B 30.0
C 21.6
D 13.4
A
A ⫺4 墍
B 0
C 5
D 16
ft
ft
ft 墍
ft
2006 Commonwealth of Virginia Department of Education
What is the value of a(3 ⴑ b) if a ⴔ 2
and b ⴔ 5?
8
2044627
AY020414
墍
C
SESSION: 40 PAGE: 9 1/13/06 6:34 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
30
2044677
AY020626
墌
32
The base of a triangle is 3 units more
than h, its height. Which expression
represents its area?
F
C
L
G
Input
x
f (x) =
x2
–5
Output
f (x)
2045670
h(h ⫹ 3)
1
When the input is , what is the
3
output?
1
h(h ⫹ 3) 墍
2
AY150R23
墍
C
ArtCodes
H
h(h ⫺ 3)
F
J
1
h(h ⫺ 3)
2
G
H
J
31
2045875
AY180R30
墌
C
Trina’s paycheck earnings, p, varies
directly as the number of hours, h, she
works. If she works 19 hours and earns
$187.15, what should she earn if she
worked 40 hours?
33
$394.00 墍
B $443.25
C $472.80
D $512.20
A
2006 Commonwealth of Virginia Department of Education
⫺ 29
AY150R23.AR1
6
⫺ 44
9
墍
⫺ 14
3
46
9
The ordered pairs in the sets shown
below are of the form (x, y). In which
set is y a function of x?
2183577
AY050750
{(1,
B {(1,
C {(1,
D {(0,
A
9
3), (2, 6), (3, 1), (6, 3)} 墍
3), (3, 1), (3, 4), (4, 3)}
⫺2), (1, 0), (1, 5), (1, 7)}
3), (1, 4), (2, 4), (2, 8)}
墍
C
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34
2044857
AY050507
墌
The table shows the relationship
between a, the area of a rectangle, and
h, its height, when the base remains
constant.
C
L
h
2
5
7
12
a
8
20
28
48
35
ArtCodes
The total number, n, of employees at a
company depends on the company’s
yearly gross profits according to the 2045607
equation n ⴔ 10p ⴐ 20, where p is the AY150R10
墍
yearly gross profit in millions of
C
dollars. If the yearly gross profit
declined from 20 million dollars to
15 million dollars, what was the
decrease in the number of employees?
50 墍
B 70
C 120
D 220
A
AY050507.AR1
Which equation represents the
relationship between h and a?
a
G a
H a
J a
F
⫽
⫽
⫽
⫽
h⫹6
3h ⫹ 2
4h 墍
2h ⫹ 4
36
Which of these pairs of the form (x, y)
could not lie on the graph of a function
2045599
of x?
AY050R29
(1,
G (1,
H (1,
J (1,
F
2006 Commonwealth of Virginia Department of Education
10
1)
1)
1)
1)
and
and
and
and
(3,
(2,
(1,
(2,
1)
1)
2) 墍
2)
墍
C
L
SESSION: 40 PAGE: 11 1/13/06 6:34 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
37
38
Which of the following represents the
graph of a function of x?
The function below contains ordered
pairs of the form (x, y).
2045554
2183630
AY050R04
墌
f ⴔ {(6, 5), (2, 3), (1, 4)}
y
5
C
What is the range of the function?
4
AY050744
墍
C
3
{4}
G {1, 2, 3, 4, 5, 6}
H {1, 2, 6}
J {3, 4, 5} 墍
F
2
ArtCodes
AY050R04.AR1
AY050R04.AR2
AY050R04.AR3
AY050R04.AR4
A
1
–5 –4 –3 –2 –1 0
–1
1
2
3
4
5
x
–2
–3
–4
–5
y
5
4
39
3
Which is a zero of the function
2
B
f(x) ⴔ 2x ⴑ 10?
1
–5 –4 –3 –2 –1 0
–1
1
2
3
4
5
x
2045641
AY150R07
墍
10
B 8
C 5 墍
D ⫺5
A
–2
–3
–4
–5
C
L
y
5
4
3
2
C
1
–5 –4 –3 –2 –1 0
–1
1
2
3
4
5
x
墍
40
–2
⫺2
G ⫺1 墍
H 1
J 2
–3
F
–4
–5
y
5
4
3
2
D
1
–5 –4 –3 –2 –1 0
–1
If f(x) ⴔ
1
2
3
4
5
x
–2
–3
–4
–5
2006 Commonwealth of Virginia Department of Education
11
3 ⴑ x2
, what is f(2)?
3ⴑx
2183460
AY150704
墍
C
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41
The point (q, 0) lies on the graph of the
following function.
43
2183489
AY150755
墌
f(x) ⴔ
C
ⴑ3
4
These are box-and-whisker plots of
four different groups of test scores.
Which has the greatest range?
2045778
AY170R10
xⴑ6
40
50
60
70
80
90
100
墍
C
A
What is the value of q?
⫺8 墍
B ⫺6
C 6
D 8
A
ArtCodes
AY170R10.AR1
AY170R10.AR2
AY170R10.AR3
AY170R10.AR4
40
50
60
70
80
90
100
40
50
60
70
80
90
100
40
50
60
70
80
90
100
B
42
In the table, y varies directly with x.
2183579
AY180707
x
10
15
20
25
C
y
6
9
12
15
墌
C
Which equation best describes the data?
F
xy ⫽
5
3
3
5
G
xy ⫽
H
y⫽
5
x
3
J
y⫽
3
x墍
5
2006 Commonwealth of Virginia Department of Education
D
12
墍
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44
2045757
AY170R13
墌
C
A student scored 85, 49, 67, and 83 on
four tests. What score would the
student need to make on the next test
to have a mean score of 75?
46
Sam and Max sell bags of peanuts and
popcorn at baseball games. This matrix
2044777
shows the number of bags they sold
AY040504
during the July 1st game.
墍
75
G 79
H 86
J 91 墍
F
Sam Max
Peanuts 136 154
Popcorn
冋
0
册
C
38
This matrix shows the number of bags
each sold during the July 2nd game.
45
2045789
AY170R04
墌
C
L
Sam Max
Peanuts 154 167
{5, 6, 6, 8, 9, 10}
Popcorn
For the data set shown, which measure
is the greatest?
冋
册
47
Which matrix shows how many more
bags were sold during the second game
than in the first?
Mean 墍
B Median
C Mode
D Range
A
F
Sam Max
Peanuts 290 321
Popcorn
冋
册
82
85
Sam Max
G Peanuts 18 13
Popcorn
冋 册
2
9
Sam Max
H Peanuts 18 13
Popcorn
J
13
冋 册
4
7
Sam Max
Peanuts 18 13
Popcorn
2006 Commonwealth of Virginia Department of Education
2
冋 册
2
7
墍
SESSION: 40 PAGE: 14 1/13/06 6:34 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
冤 冥
2
47
2311284
If A ⴔ 3
C
6 and B ⴔ
4
AY040703
墌
4
8
ⴑ1
5
2
7 ,
ⴑ6
冤 冥
3
48
A delivery service company maintains
several vehicles. The table summarizes
the cost for auto insurance related to 2084929
AY160718
the number of vehicles insured.
墍
what is A ⴑ B?
A
B
C
冤 冥
1
9
5
13
7
2
冤
⫺2
20
6
42
⫺48
12
冥
4
9
9
⫺3
3
⫺1
1
⫺1 墍
1
14
$5,050
G $5,200 墍
H $5,500
J $5,950
F
冤 冥
2006 Commonwealth of Virginia Department of Education
C
Cost ($)
1,700
2,200
2,700
3,200
3,700
4,200
Using the equation of a line of best fit
for the data, which is the closest
estimate of the total cost of insuring
eight vehicles?
冤 冥
6
12
D
Number of
Vehicles
1
2
3
4
5
6
14
SESSION: 41 PAGE: 15 1/13/06 11:33 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
49
An engine is tested for torque output
at different revolutions per minute.
50
3078422
x
y
70
4
AY160812
墌
C
75
7
80
8.5
85
12
90
11
260
95
13.5
250
100
15
310
300
290
Torque (ft–lb)
ArtCodes
3078422.AR1
2183661
AY160727
280
270
240
Which equation defines the linear line
of best fit for the data in the table?
230
220
210
y
G y
H y
J y
F
25 30 35 40 45 50 55 60
rpm (×100)
Which equation most closely defines
the line of best fit for the data?
y
B y
C y
D y
A
⫽
⫽
⫽
⫽
4.1x ⫹ 414
⫺4.1x ⫹ 414
3.1x ⫹ 383
⫺3.1x ⫹ 383 墍
2006 Commonwealth of Virginia Department of Education
15
⫽
⫽
⫽
⫽
19.5x ⫺ 0.35
⫺0.35x ⫹ 19.5
⫺19.5x ⫹ 0.35
0.35x ⫺ 19.5 墍
墍
C
SESSION: 40 PAGE: 16 1/13/06 6:34 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11alg1-1
Answer Key
Test
Sequence
Correct
Answer
Reporting
Category
1
A
003
Equations and Inequalities
2
H
003
Equations and Inequalities
3
D
003
Equations and Inequalities
4
F
003
Equations and Inequalities
5
D
003
Equations and Inequalities
6
J
003
Equations and Inequalities
Reporting Category Description
7
B
003
Equations and Inequalities
8
H
003
Equations and Inequalities
9
D
003
Equations and Inequalities
10
F
003
Equations and Inequalities
11
B
003
Equations and Inequalities
12
G
003
Equations and Inequalities
13
D
003
Equations and Inequalities
14
H
003
Equations and Inequalities
15
B
003
Equations and Inequalities
16
H
003
Equations and Inequalities
17
A
003
Equations and Inequalities
18
H
003
Equations and Inequalities
19
D
001
Expressions and Operations
20
F
001
Expressions and Operations
21
B
001
Expressions and Operations
22
G
001
Expressions and Operations
23
A
001
Expressions and Operations
24
F
001
Expressions and Operations
25
C
001
Expressions and Operations
26
F
001
Expressions and Operations
27
A
001
Expressions and Operations
28
J
001
Expressions and Operations
29
A
001
Expressions and Operations
30
G
001
Expressions and Operations
31
A
002
Relations and Functions
32
G
002
Relations and Functions
33
A
002
Relations and Functions
34
H
002
Relations and Functions
35
A
002
Relations and Functions
36
H
002
Relations and Functions
37
C
002
Relations and Functions
38
J
002
Relations and Functions
39
C
002
Relations and Functions
40
G
002
Relations and Functions
41
A
002
Relations and Functions
42
J
002
Relations and Functions
43
D
004
Statistics
44
J
004
Statistics
45
A
004
Statistics
46
G
004
Statistics
47
D
004
Statistics
48
G
004
Statistics
49
D
004
Statistics
50
J
004
Statistics