Benchmark Post-Test (8.11)

Transcription

Holt Math
TAKS Prep Workbook
for Exit Exam
AGA07_TAKS_WKBK11_i-iv i
4/13/06 7:36:36 PM
Copyright © by Holt, Rinehart and Winston
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ISBN 0-03-092711-0
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AGA07_TAKS_WKBK11_i-iv ii
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CONTENTS
Pre-Test TAKS
Pre-Test TAKS
Pre-Test TAKS
Pre-Test TAKS
Pre-Test TAKS
Pre-Test TAKS
Pre-Test TAKS
Pre-Test TAKS
Pre-Test TAKS
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Copyright © by Holt, Rinehart and Winston.
All rights reserved.
AGA07_TAKS_WKBK11_i-iv iii
Pre-Test TAKS Obj 6, (G.10)(A) . . . . . . . . . 41
Pre-Test TAKS Obj 7, (G.6)(B) . . . . . . . . . . 42
Pre-Test TAKS Obj 7, (G.6)(C) . . . . . . . . . . 43
Pre-Test TAKS Obj 7, (G.7)(B) . . . . . . . . . . 45
Pre-Test TAKS Obj 7, (G.7)(C) . . . . . . . . . 46
Pre-Test TAKS Obj 7, (G.9)(D) . . . . . . . . . 47
Pre-Test TAKS Obj 8, (G.8)(B) . . . . . . . . . 49
Pre-Test TAKS Obj 8, (G.8)(C) . . . . . . . . . 50
Pre-Test TAKS Obj 8, (G.8)(D) . . . . . . . . . . 51
Pre-Test TAKS Obj 8, (G.11)(B) . . . . . . . . . 53
Pre-Test TAKS Obj 8, (G.11)(C) . . . . . . . . 54
Pre-Test TAKS Obj 8, (G.11)(D) . . . . . . . . . 55
Pre-Test TAKS Obj 9, (8.3)(B) . . . . . . . . . . 56
Pre-Test TAKS Obj 9, (8.11)(A) . . . . . . . . . 57
Pre-Test TAKS Obj 9, (8.11)(B) . . . . . . . . . 58
Pre-Test TAKS Obj 9, (8.12)(A) . . . . . . . . . 59
Pre-Test TAKS Obj 9, (8.12)(C) . . . . . . . . . 60
Pre-Test TAKS Obj 9, (8.13)(B) . . . . . . . . . 61
Pre-Test TAKS Obj 10, (8.14)(A) . . . . . . . . 62
Pre-Test TAKS Obj 10, (8.14)(B) . . . . . . . . 63
Pre-Test TAKS Obj 10, (8.14)(C) . . . . . . . . 64
Pre-Test TAKS Obj 10, (8.16)(B) . . . . . . . . 67
Post-Test TAKS Obj 1, (A.1)(A) . . . . . . . . . 68
Post-Test TAKS Obj 1, (A.1)(B) . . . . . . . . . 69
Post-Test TAKS Obj 1, (A.1)(C) . . . . . . . . . 70
Post-Test TAKS Obj 1, (A.1)(D) . . . . . . . . . 71
Post-Test TAKS Obj 1, (A.1)(E) . . . . . . . . . 72
Post-Test TAKS Obj 2, (A.2)(C) . . . . . . . . . 75
Post-Test TAKS Obj 2, (A.2)(D) . . . . . . . . . 76
(A.1)(A) . . . . . . . . . . . 1
(A.1)(B) . . . . . . . . . . . 2
(A.1)(C) . . . . . . . . . . . 3
(A.1)(D) . . . . . . . . . . . 4
(A.1)(E) . . . . . . . . . . . 5
(A.2)(A) . . . . . . . . . . . 6
(A.2)(B) . . . . . . . . . . . 7
(A.2)(C) . . . . . . . . . . . 8
(A.2)(D) . . . . . . . . . . . 9
(A.3)(A) . . . . . . . . . . 10
(A.3)(B) . . . . . . . . . . 11
(A.4)(A) . . . . . . . . . . 12
(A.4)(B) . . . . . . . . . . 13
(A.4)(C) . . . . . . . . . . 14
(A.5)(A) . . . . . . . . . . 15
(A.5)(C) . . . . . . . . . . 16
(A.6)(A) . . . . . . . . . . 17
(A.6)(B) . . . . . . . . . . 18
(A.6)(C) . . . . . . . . . 19
(A.6)(D) . . . . . . . . . 20
(A.6)(E) . . . . . . . . . . 21
(A.6)(F) . . . . . . . . . . 22
(A.6)(G) . . . . . . . . . 23
(A.7)(A) . . . . . . . . . . 24
(A.7)(B) . . . . . . . . . . 25
(A.7)(C) . . . . . . . . . 26
(A.8)(A) . . . . . . . . . . 27
(A.8)(B) . . . . . . . . . . 28
(A.8)(C) . . . . . . . . . . 29
(A.9)(B) . . . . . . . . . . 30
(A.9)(C) . . . . . . . . . 31
(A.9)(D) . . . . . . . . . 32
(A.10)(A) . . . . . . . . . 33
(A.10)(B) . . . . . . . . . 34
(A.11)(A) . . . . . . . . . 35
(G.4)(A) . . . . . . . . . . 36
(G.5)(A) . . . . . . . . . 37
(G.5)(B) . . . . . . . . . . 38
(G.5)(C) . . . . . . . . . . 39
(G.5)(D) . . . . . . . . . . 40
iii
Holt Mathematics Exit Exam
4/13/06 7:36:37 PM
CONTENTS, CONTINUED
Post-Test TAKS
Post-Test TAKS
Post-Test TAKS
Post-Test TAKS
Post-Test TAKS
Post-Test TAKS
Post-Test TAKS
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AGA07_TAKS_WKBK11_i-iv iv
Post-Test TAKS
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(A.4)(C) . . . . . . . . . 81
(A.5)(A) . . . . . . . . . 82
(A.5)(C) . . . . . . . . . 83
(A.6)(A) . . . . . . . . . 84
(A.6)(B) . . . . . . . . . 85
(A.6)(C) . . . . . . . . . 86
(A.6)(D) . . . . . . . . . 87
(A.6)(E) . . . . . . . . . 88
(A.6)(F). . . . . . . . . . 89
(A.6)(G) . . . . . . . . . 90
(A.7)(A) . . . . . . . . . 91
(A.7)(B) . . . . . . . . . 92
(A.7)(C) . . . . . . . . . 93
(A.8)(A) . . . . . . . . . 94
(A.8)(B) . . . . . . . . . 95
(A.8)(C) . . . . . . . . . 96
(A.9)(B) . . . . . . . . . 97
(A.9)(C) . . . . . . . . . 98
(A.9)(D) . . . . . . . . . 99
(A.10)(A) . . . . . . . 100
(A.10)(B) . . . . . . . 101
(A.11)(A) . . . . . . . 102
(G.4)(A) . . . . . . . . 103
(G.5)(A) . . . . . . . . 104
(G.5)(B) . . . . . . . . 105
(G.5)(C) . . . . . . . . 106
(G.5)(D) . . . . . . . . 107
iv
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6, (G.10)(A) . . . . . . . 108
7, (G.6)(B) . . . . . . . . 109
7, (G.6)(C) . . . . . . . . 110
7, (G.7)(A) . . . . . . . . 111
7, (G.7)(B) . . . . . . . . 112
7, (G.7)(C) . . . . . . . . 113
7, (G.9)(D) . . . . . . . . 114
8, (G.8)(A) . . . . . . . . 115
8, (G.8)(B) . . . . . . . . 116
8, (G.8)(C) . . . . . . . . 117
8, (G.8)(D) . . . . . . . . 118
8, (G.11)(A) . . . . . . . 119
8, (G.11)(B) . . . . . . . 120
8, (G.11)(C) . . . . . . . 121
8, (G.11)(D) . . . . . . . 122
9, (8.3)(B). . . . . . . . . 123
9, (8.11)(A). . . . . . . . 124
9, (8.11)(B). . . . . . . . 125
9, (8.12)(A). . . . . . . . 126
9, (8.12)(C). . . . . . . . 127
9, (8.13)(B). . . . . . . . 128
10, (8.14)(A). . . . . . . 129
10, (8.14)(B). . . . . . . 130
10, (8.14)(C). . . . . . . 131
10, (8.15)(A). . . . . . . 132
10, (8.16)(A). . . . . . . 133
10, (8.16)(B). . . . . . . 134
4/13/06 7:36:37 PM
Name
OBJECTIVE
1
Date
Class
Ready for TAKS?
Benchmark Pre-Test (A.1)(A)
1. The total amount c charged by a
public boat dock for docking b boats for
one month is given by the equation
c ⫽ 500 ⫹ 150b. In this relation, which
of the following is the best interpretation
of what the independent variable
represents?
4. When a weight is attached to the spring
shown, the length of the spring is
determined by the equation given.
ᐉ = 0.4g ⫹ 15
A the total amount charged by the boat
dock
B the number of months for which the
boats are kept
C the number of boats kept
In this equation, what might the
dependent variable represent?
D a $500 flat fee charged by the dock
for docking the boats
F
2. A clothing store had a 25%-off sale on
all its winter items. Which statement best
represents the functional relationship
between the sale price of an article of
clothing and the original price?
F
G the original length of the spring
H the maximum length of the spring
J
The original price is dependent on
the sale price.
H The original price and the sale price
are independent of each other.
y
It is not possible to determine the
relationship without knowing each of
the prices.
3. Which of the following does not
represent a relation in which the first
quantity depends on the second?
x
A the volume of a cone; the radius of
the base of the cone
A As x increases, y decreases at a
constant rate.
B the surface area of a rectangular
prism; the length of the base
B As x increases, y decreases at a
variable rate.
C the lateral area of a cylinder; the
radius of the base of the cylinder
C As x increases, y increases.
D the length of the side of a cube; the
volume of the cube
D As x increases, y sometimes
decreases and sometimes increases.
AGA07_RTAKS11_001-005.indd 1
the length of the spring when g
grams of weight are attached
5. The graph shows a function in which
the variable y is the dependent variable.
Which statement is the best description
of the functional relation between x
and y ?
G The sale price is dependent on the
original price.
J
the number of grams of weight
attached to the spring
1
4/14/06 9:49:00 AM
Name
OBJECTIVE
1
Date
Class
Ready for TAKS?
Benchmark Pre-Test (A.1)(B)
1. Which equation best describes the
relationship between x and y shown in
the table?
3. Which function could be used to
describe the data set shown?
{(⫺2, ⫺24), (⫺1, ⫺6), (1, ⫺6), (2, ⫺24)}
x
y
A y⫽x⫺7
1
5
B y ⫽ ⫺7x ⫹ 1
2
20
C y ⫽ 6( ⫺ x)2
5
125
D y ⫽ ⫺6x 2
10
500
4. Which function represents the data set
shown?
A y ⫽ 5x
Domain
Range
-1
25
0
16
1
9
2
–5
–4
–3
B x ⫽ 5y
C y ⫽ 5x 2
D x ⫽ 5y 2
2. The graph shows the relationship
between two variables, t and h. Which
function represents this relationship?
F
y ⫽ ⫺
x
G y⫽
x
H y ⫽ ⫺x2
t
J
7
y ⫽ x2
5. The table shows the distance, d, in feet
that an object falls freely in t seconds.
Which equation best describes the
relationship between d and t?
6
F
h
Distance, d (ft)
Time, t (s)
16
1
64
2
144
3
7t
h ⫽ ⫺__
6
7t ⫹ 7
G h ⫽ ⫺__
6
7h
H t ⫽ ⫺__
6
J
A d ⫽ 16t
B t ⫽ 16d
7h ⫹ 7
t ⫽ ⫺__
6
C d ⫽ 16t 2
D t ⫽ 16d 2
2
4/14/06 9:49:01 AM
Name
OBJECTIVE
1
Date
Class
Ready for TAKS?
Benchmark Pre-Test (A.1)(C)
1. A towing company charges $45 to hook
up to a disabled vehicle plus $1.50 per
mile that the vehicle is towed. The chart
shows the cost of several typical tows.
3. A saline solution is described by the
percent of the solution that is salt. A
chemist mixed 30 grams of a 50% saline
solution with x grams of a 30% saline
solution. Which equation describes
S, the amount of salt in the chemist’s
mixture?
Towing Costs
Number of
miles, m
Cost, c
1
$46.50
5
$52.50
10
$60.00
20
$75.00
A S ⫽ 30(0.5) ⫹ 30x
B S ⫽ 30(0.5) ⫹ 0.3x
C S ⫽ (30 ⫹ x)(0.8)
⫹ 0.5
________
D S ⫽ (30 ⫹ x) 0.3
2
Which equation best represents the
relationship between the number of
miles towed, m, and the total cost, c, to
tow a vehicle?
4. Ms. Jones invested $12,000 in two
savings accounts. She put part of the
money into an account that earns 3.75%
interest per year and the rest into an
account that earns 4% per year. Which
equation describes i, the total amount
of interest earned by both accounts for
one year?
A c ⫽ 45 ⫹ 1.50
B c ⫽ 45m ⫹ 1.50
C c ⫽ 45 ⫹ 1.50m
D c ⫽ 45m ⫹ 1.50m
F
2. A community center is having the bottom
and sides of its pool resurfaced. The
length of the pool is 3 times the width,
and the depth of the pool is 4 feet
everywhere. The pool is shown.
i ⫽ 0.0775(12000)
G i ⫽ 6000(0.0375) ⫹ 6000(0.04)
H i ⫽ 0.0375x ⫹ 0.04(12000 ⫺ x)
J
i ⫽ 12000(0.0375x ⫹ 0.04x)
5. In most graduate schools, the lowest
passing grade point average is a B⫺,
which is equivalent to a GPA of at least
2.7 but less than 3.0. If z represents a
student’s GPA, which inequality best
expresses this requirement?
If w represents the width of the pool,
which expression best represents the
area of the portion of the pool that will
be resurfaced?
32w ⫹ 3w
2
G 20w ⫹ 6w
H 32w ⫹ 6w
2
J
F
A 3.0 ⬍ z < 2.7
B 3.0 ⱕ z < 2.7
C 2.7 ⬍ z ⱕ 3.0
2
D 2.7 ⱕ z ⬍ 3.0
5(3w ⫹ 4 ⫹ w)
3
4/14/06 9:49:01 AM
Name
OBJECTIVE
1
Date
Ready for TAKS?
Benchmark Pre-Test (A.1)(D)
3. Which of the following equations does
NOT represent a function?
1. The function
_
f (x ) ⫽ {(⫺1, 1), (1, 1), (2, 0.25), (3, 0.1)}
can be represented in a variety of
different ways. Which of the following is
NOT an accurate representation of f (x )?
A y⫽x
⫺2
A y ⫽ x(x ⫹ 4)
2
⫹x
_______
B y ⫽ 4x
x
with domain ⫽ {⫺1, 1, 2, 3}
C x2 ⫹ y2 ⫽ 4
_
1 with range ⫽ {1, 0.25, 0.1}
B x ⫽ ___
y
C
x
⫺1
1
2
3
y
1
1
0.25
0.1
D y ⫽ x ⫹ 4
_
D Domain
4. Which of the following best describes the
graph of the inequality 2x ⫺ y ⬎ 3 ?
F
Range
–1
1
2
3
H the area that is shaded above the
dotted line y ⫽ 2x ⫺ 3
J
8
6
4
2
–6
–4
–2
2
–2
4
6
8
the area that is shaded above the
solid line y ⫽ 2x ⫺ 3
5. A function is defined as follows: x is an
even integer between, and including,
⫺2 and 2, and y is always 3 times x.
Which of the following is NOT a correct
representation of the function?
y
–8
the area that is shaded below the
dotted line y ⫽ 2x ⫺ 3
G the area that is shaded below the
solid line y ⫽ 2x ⫺ 3
1
0.25
0.1
2. Which inequality best describes the
graph shown?
A y ⫽ 3x for ⫺2 ⱕ x ⱕ 2
x
B f (x) ⫽ {(⫺2, ⫺6), (0, 0), (2, 6)}
–4
–6
C
–8
F
Class
2x ⫺ 5y ⱖ 15
x
⫺2
0
2
y
⫺6
0
6
y
D
G 2x ⫹ 5y ⱖ 15
6
4
H 2x ⫺ 5y ⱕ 15
J
2
2x ⫹ 5y ⱕ 15
–6
–4
–2
2
–2
4
6
x
–4
–6
4
4/14/06 9:49:01 AM
Name
OBJECTIVE
1
Date
Class
Ready for TAKS?
Benchmark Pre-Test (A.1)(E)
4. The net profit, p, that a shower head
company makes from producing s
shower heads is represented by the
equation p ⫽ 3.5s ⫺ 7000. Which is the
best interpretation of this information?
1. Which of the following is true for the
parabola y ⫺ 1 ⫽ (x ⫺ 2)2?
A The vertex is (⫺2, 1).
B The axis of symmetry is x ⫽ 2.
C The minimum value is at (0, 5).
F
D The maximum value is at (0, 5).
The company’s profit is always at
least $7,000.
G The company needs to sell more
than 2,000 shower heads before it
makes a profit.
between speed and time during Erin’s
morning jog.
H The company has sold more than
7,000 shower heads.
J
Speed
5. A ball is thrown straight up from a flat
roof of a building that is 192 feet tall with
an initial velocity of 16 feet per second.
If there is no air resistance, the height
of the ball at any time t is given by the
function h(t ) ⫽ ⫺16t 2 ⫹ 16t ⫹ 192. The
graph of the function is shown.
Time
Which of the following might describe
the same jog?
F
Erin jogs along a flat road. She then
jogs up a hill at the same pace.
y
200
Height (h)
G Erin jogs at a steady pace along a
flat road. She then runs up a hill and
her speed decreases.
H Erin jogs at a steady pace up a hill.
She then runs down the hill and her
speed increases.
J
160
120
80
40
Erin jogs at a steady pace up a small
incline. She then jogs up a steep
incline.
1
2
3
Time (t)
3. If x ⱖ 1, which is always a correct
conclusion about the quantities in the
function y ⫽ x⫺1?
4
x
Which statement is true about h(t )?
A After one half of a second, the ball
fell at a constant rate.
A As x increases, y increases.
B As x increases, y decreases.
B The height of the ball decreased for
all values of t.
C The variable y is always less than
the variable x.
C After one second, the height of the
ball returned to the height of the roof.
D The variable y is always greater than
or equal to the variable x.
D After four seconds, the height of the
The company’s profit last year was
$7,000.
5
4/14/06 9:49:02 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
1. Which of the functions is linear?
3. The graph of which function would pass
through the points (⫺1, 10) and (5, 10)?
2
A y ⫹ 2(x ⫺ 3) ⫽ 5
A y ⫽ ⫺6x ⫹ 4
B y⫽x⫹5
1(x ⫹ 2) ⫺ 3x
B y ⫽ ⫺__
2
C 2y ⫹ 3 ⫽
C y ⫽ x2 ⫺ 4x ⫹ 5
x
D y ⫽ x2 ⫺ 4x ⫹ 11
4. Which statement best describes the
2
graph of y ⫽ ⫺(x ⫹ 1) ⫺ 2?
1 ⫹ 3x
D y ⫽ x__
F
2. Which is the best representation of the
function y ⫽ 2x ?
G a parabola whose vertex is at (1, ⫺2)
y
F
H an upside-down parabola whose
vertex is at (2, ⫺1)
2
x
J
an upside-down parabola whose
vertex is at (⫺1, ⫺2)
5. Which equation is the parent function of
the graph shown?
y
G
a line with a slope of ⫺1 and
y-intercept ⫺2
y
2
x
x
y
H
2
x
A y ⫽ x
B y⫽x
C y ⫽ x2
y
J
D y⫽
x
2
x
6
4/14/06 9:49:11 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
4. What is the range of the function
graphed?
1. What is the domain of the function
given?
f(x) ⫽ x⫺ 3
y
A all real numbers
B {3, 4, 5, … }
C x⬎0
5
x
D xⱖ3
2. Identify the domain of the function given.
–5
{( ⫺2, 3), ( ⫺1, 5), (3, 4), (5, ⫺4)}
F
all real numbers
G {⫺4, ⫺2, ⫺1, 3, 4, 5}
H {⫺2, ⫺1, 3, 5}
J
F
{⫺4, 3, 4, 5}
yⱕ0
G ⫺2 ⱕ y ⱕ 0
3. What is a reasonable domain for this
function?
H y ⱕ ⫺2
J
all real numbers
5. What is the domain, written in interval
notation, of the function graphed?
y
1
1
5
x
–5
A ⫺2 ⬍ x ⬍ 1
B ⫺2 ⬍ x ⱕ 2
C ⫺2 ⱕ x ⱕ 1
A [⫺4, 2]
D ⫺1 ⬍ x ⬍ 2
B (⫺2, 4)
C [⫺2, 4)
D (2, 2)
7
4/14/06 9:49:11 AM
Name
Date
Class
Ready for TAKS?
OBJECTIVE
2
A quarterback throws a football to a wide
receiver. The points in the figure show the
height of the football, in feet, above the
ground in terms of its distance, in feet, from
the quarterback.
1. The graph shows the decrease in value
of a tractor over a period of 36 months.
Value ($ in thousands)
y
14
12
10
(45, 18)
8
6
4
Height
(ft)
2
6
12
18
24
30
36
x
6
Time (in months)
What is a reasonable conclusion about
the value of this tractor during the time
period shown on the graph?
(90, 6)
Distance from
Quarterback (ft)
A Its value at 18 months was twice its
value at 36 months.
Use the diagram above to answer
questions 3 and 4.
B Its value at 36 months was half its
value at 8 months.
3. Which of the following is NOT a
reasonable conclusion?
C It depreciated $3,000 every 12 months.
A The height of the ball when it leaves
the quarterback’s hand is the same
as the height of the ball when the
receiver catches it.
D It depreciated $9,000 every 12 months.
2. The graph shows the value, in dollars, of a
certain stock over a seven month period.
B The maximum height of the ball is
45 feet.
C The ball travels 90 feet from the
quarterback.
1
2
3
4
5
6
D At its maximum height, the ball is
3 times as high as its original height.
7
4. What is the approximate height of the
football, in feet, when it leaves the
quarterback’s hands?
Which is a reasonable statement about
the value of the stock over this period?
F
The stock lost value for the first four
months.
F
G 18
G The stocks most rapid increase in
price was between months 3 and 4.
H 45
J
H The stock only lost value between
months 4 and 6.
J
6
90
The value of the stock more than
tripled in price by month.
8
4/14/06 9:49:12 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
1. The scatter plot shows the number of
new highways built in a city for several
different years since 1970.
Use the scatter plot to answer questions
3 and 4.
Walking Times to School
70
New
Highways
Time (minutes)
60
50
40
30
20
10
0
1.5
2.0
2.5
A The number of new highways
continues to grow at a steady rate.
3. Predict the approximate walking time for
a student who lives 5 miles from school.
B Fewer and fewer new highways are
being built each year.
A 70 minutes
C The number of new highways built
has leveled off since 1970.
B 85 minutes
C 90 minutes
D No conclusion can be drawn
because there is no pattern.
D 100 minutes
2. The table shows the retail price of
Tiffany lamps based on the wholesale
price.
4. Which statement BEST describes the
relationship between distance and time?
F
As the distance increases, the
walking time remains the same.
Wholesale ($)
Retail ($)
200
300
250
400
300
500
H The distance does not affect the
walking time
350
600
J
G As the distance increases, the
walking time decreases.
Use the data to predict the wholesale
price of a Tiffany lamp with a retail price
of $850.
$250
G $475
3.0
The scatter plot shows the relationship
between distance from school and the
walking time to school in a large city for the
students in Mrs. Reed’s class. The plot also
shows the line of best fit for the data.
What conclusion can be drawn about the
number of new highways built in this city
since 1970?
1.0
Distance (miles)
Years Since 1970
F
0.5
The walking time consistently
increases by 10 minutes per half
mile.
H $600
J
$1,600
9
4/14/06 9:49:12 AM
Name
OBJECTIVE
2
Date
Ready for TAKS?
4. Pedro began the month with 120 trees
to trim. If he trims 5 trees per day for the
first d days, which expression represents
the number of trees per day, t, that he
must trim for each of the remaining days
to complete the job in 30 days total?
1. Mark makes x dollars each week
mowing lawns. If he saves 25% of his
pay each week, which of the following
represents the amount of money Mark
does NOT save each week?
A 0.25x
B 0.75x
F
C x ⫺ 0.25
⫺ 5d
________
H t ⫽ 120
30 ⫺ d
2. Let w represent the number of gallons
of water being poured into a pool every
minute and let f(t ) represent the number
of gallons of water in the pool t minutes
after the pool has started filling. The
function f (t) is best represented by
wt
⫺ 5d
________
t ⫽ 120
d
⫺ 5d
________
G t ⫽ 120
30
D 1.25x
F
Class
J
⫺ 5d
________
t ⫽ 120
5d
5. Which equation represents the
perimeter, P, of the rectangle shown?
2
x⫹1
2y
G w⫹t
H wt
J
w ⫹ t2
3. The table shows the cost of buying
2
concert tickets at Music .
Number of
Tickets
Total Cost
($)
3
54
5
90
10
180
20
360
2
3x ⫹ y
5x ⫹ __
3y
A P ⫽ __
6
4
2x2 ⫹ __
2xy ⫹ __
1y2
B P ⫽ __
3
3
2
5x ⫹ __
3y
C P ⫽ __
3
2
Which equation represents the total cost
if a customer purchases n tickets.
10x ⫹ 3y
D P ⫽ ___
3
A c ⫽ 54n
B c ⫽ 18n
C c ⫽ 18 ⫹ n
D c ⫽ 54
10
4/14/06 9:49:13 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
4. Greg wants to write an expression that
will always produce a perfect square.
Which of the following will NOT always
produce a perfect square for any given
integer, n?
1. What is the sixth term in this pattern?
8x , ...
4x , ___
2x, ___
4
2
3y 9y
16x
A ____
27y8
F
128x
C ______
729y12
H n2 ⫹ 2n ⫹ 1
G n2 ⫺ 2n ⫺ 1
J
14x
D ____
8y12
n4 ⫺ 2n2 ⫹ 1
5. The figures show a pattern between the
number of rows, r, and the number of
blocks, b. Which equation relates the
number of rows to the number of blocks?
2. Which algebraic expression best
represents the relationship between the
x- and y-coordinates in the coordinate
pairs given?
Figure 1
{(1, 3), (2, 8), (3, 15), (4, 24)}
F
n
2
64x
B ______
243y10
y ⫽ 3x
G y ⫽ 2x ⫹ 1
Figure 2
2
H y⫽x ⫹2
J
y ⫽ (x ⫹ 1)2 ⫺ 1
terms in the following sequence and
their position, n, in the sequence?
Figure 3
4, 7, 12, 19, …
A 4n
A b ⫽ (r ⫺ 1) ⫹ 1
B n⫹3
B b ⫽ (r ⫺ 1)2 ⫹ 1
C 3n ⫹ 1
C b ⫽ 2r ⫺ 1
2
D n ⫹3
r(r ⫹ 1)
D b ⫽ _______
2
11
4/14/06 9:49:13 AM
Name
OBJECTIVE
2
Date
Ready for TAKS?
3
⫺ 4x ⫺ 5
1. If f(x) ⫽ x__________
, what is f(⫺1)?
x
4. Solve the equation y ⫽ ax ⫹ b for x.
A 4
F
B 2
D ⫺3
y⫺b
H x ⫽ _____
a
2. What is the missing value in the function
table?
x
f(x) ⴝ 3 ⴚ x
⫺2
⫺1
0
3
1
2
?
⫺13
J
x⫽y⫺b⫺a
2
5. Twice a number is 9 less than five
times the same number. The algebraic
equation 2x ⫽ 5x ⫺ 9 represents this
situation. Use the equation to find the
number.
A ⫺6
4 ⫺1
9
B ⫺__
7
G 2
H 10
J
x ⫽ ay ⫹ b
y⫹b
G x ⫽ _____
a
C ⫺2
F
Class
C ⫺3
4
D 3
3. A rhombus has four equal sides. One
of its sides is labeled. What is the
perimeter, in simplest form, of the
rhombus?
6. The rectangle shown has an area of
x2 ⫺ 7x ⫺ 18.
3x 2 ⫹ 2x ⫹ 5
x⫺9
A (3x2 ⫹ 2x ⫹ 5)4
Which expression represents the width
of the rectangle?
B 12x2 ⫹ 2x ⫹ 5
F
2
C 3x ⫹ 2x ⫹ 20
G x⫺3
2
D 12x ⫹ 8x ⫹ 20
H x⫹2
J
2x
12
x⫺2
4/14/06 9:49:13 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
1. Which real number property is illustrated
by the equation 4(5x ⫺ 6y) ⫽ 20x ⫺ 24y?
5. What is the perimeter of the pentagon?
3x 2⫺ 2x
A the Commutative Property of
Addition
4x ⫹ 1
B the Associative Property of Addition
C the Distributive Property
x
D the Multiplicative Identity Property
of 1
4x ⫺ 6
5x 2 ⫹ 3
2. Which expression is equivalent to
(4x ⫺ 3)(2x) ⫺ (x ⫹ 5)(2x ⫺ 5)?
F
A 8x2 ⫹ 7x ⫺ 2
3x ⫺ 3
G ⫺5x2 ⫹ 25
B 15x2⫺ 2
H 6x2 ⫺ x ⫺ 25
C 15x6 ⫺ 2
J
D 15x5 ⫺ 2
6x2 ⫺ 11x ⫹ 25
6. The table shows the factored form and
the simplified form for several products.
3x ?
5x2 ⫺3 __
1x2 ⫺ __
__
2
2
2
2
3x
A x ⫺ __
2
Factored Form
9x
B x2 ⫹ __
2
9x
C x2 ⫺ __
2
9x
D 1 ⫹ __
2
4. Which expression is equivalent to ⫺3x y
2
2
2
⫺ 7xy ⫺ 4xy ⫹ 8xy ⫹ 5x y ⫹ 3xy ?
G 2x y ⫹ xy ⫺ 7xy
2
H 2x y ⫹ xy ⫹ xy
4 2
2
x ⫹2
(x ⫺ 2)(x ⫺ 1)
x2 ⫹ 2
(x ⫹ 3)2
x2 ⫹ 9
(x ⫺ 3)(x ⫹ 3)
x2 ⫺ 9
2 2
x(x ⫹ 2)
G (x ⫺ 2)(x ⫺ 1)
H (x ⫹ 3)2
2
J
2
(x ⫺ 3)(x ⫹ 3)
2 4
2x y ⫹ x y ⫺x y
F
2x2y ⫹ xy ⫺ xy2
2
J
x(x ⫹ 2)
Which product is correctly simplified?
2
F
Simplified Form
13
4/14/06 9:49:14 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
4. The graph of a function is shown.
1. Which function notation would represent
the same relationship as the quadratic
2
equation y ⫽ (x ⫺ 2) ?
y
A f(x) ⫽ x ⫺ 2
8
B f(x) ⫽ x2 ⫺ 2
6
4
C f(x) ⫽ x ⫹ 2
2
D f(x) ⫽ (x ⫺ 2)2
–8
–6
–4
–2
2. Which quadratic equation would
represent the same relationship as the
2
function f (x) ⫽ ⫺(x ⫺ 5) ?
F
2
–2
4
6
8
x
–4
–6
2
y ⫽ ⫺(x ⫺ 5)
–8
2
G y ⫽ (x ⫹ 5)
H y ⫽ ⫺(x ⫺ 5)
J
Identify the function.
y ⫽ x ⫺ 5
F
3. The table shows several values
generated by the function
2
f(x) ⫽ (2x ⫺ 3) .
x
f(x)
0
0
⫺1
25
⫺2
49
⫺3
81
f (x) ⫽ y2 ⫺ 1
G f (x) ⫽ x2
H f (x) ⫽ x2 ⫺ 1
J
f (x) ⫽ x2 ⫹ 1
5. A chemistry class monitored the
temperature of a liquid that was being
cooled. The initial temperature of the
liquid was 20°C and the temperature
decreased by 2 degrees every minute.
The results can be represented by the
function f (m) ⫽ 20 ⫺ 2m, where m is
the number of minutes that have passed.
Which equation would represent the
temperature, t, after m minutes have
passed?
Which equation represents the same
relationship?
A y 2 ⫽ 2x ⫺ 3
B y ⫽ ⫺2x ⫺ 3
A t ⫽ 2m
2
C y ⫽ (2x ⫺ 3)
B t⫽m⫺2
2
D y ⫽ 4x ⫹ 9
C t ⫽ 20 ⫺ 2m
D t ⫽ 20 ⫺ m ⫺ 2
14
4/14/06 9:49:14 AM
Name
OBJECTIVE
3
Date
Ready for TAKS?
1. Which of the following is NOT a linear
equation?
3. Which set of coordinate points
represents a linear function?
A {(⫺5, 1), (0, 2), (5, 3), (10, 4)}
A y ⫽ 4(x ⫹ 3x)
B {(0, 2), (2, 4), (3, 6), (4, 8)}
B y ⫽ 5x ⫹ 2(x ⫹ 3)
C {(3, 1), (6, 2), (9, 3), (12, 5)}
4
C y ⫽ _____
x⫹3
D {(⫺2, 4), (⫺1, 1), (1, 1), (2, 4)
4. Which situation can be represented by
a linear function?
D 2x ⫹ y ⫽ 7x ⫹ 2y ⫹ 9
F
2. Which table of values does NOT
represent a linear function?
F
G
H
J
x
y
1
5
2
7
3
9
4
11
x
y
⫺2
2
⫺1
3
0
4
1
5
x
y
⫺2
⫺8
0
⫺2
2
4
4
10
x
y
1
2
3
4
5
8
7
12
A person’s heart rate while riding
a stationary bike if the resistance
increases every 10 minutes.
G The area of a rectangle whose
length is x and whose width is twice
its length.
H The total amount of money saved if
a person deposits $50 each month
for 12 months.
J
Class
The amount of tips a waitress makes
each hour during an 8-hour shift at
a restaurant.
5. Which of the following functions would
NOT have a graph that is a line?
A y ⫽ 0.5x ⫺ 0.16
x⫹2
B y ⫽ 4兹
3x ⫹ 2
C y ⫽ ___
5
1
D y ⫽ 2x ⫹ __
2
15
4/14/06 9:49:25 AM
Name
Date
Class
Ready for TAKS?
OBJECTIVE
3
1. What is the equation of the line shown?
4. Which linear equation represents the
statement “y is 5 more than 3 times x”?
y
F
10
G y ⫽ 3x ⫹ 5
8
H 3y ⫽ x ⫺ 5
6
J
4
–6
–4
–2
2
4
6
8
10
–2
3y ⫽ x ⫹ 5
5. Which is the graph of the equation
1x ⫺ __
1y ⫽ 1?
__
2
3
y
A
2
–10 –8
y ⫽ 3 (x ⫹ 5)
x
10
–4
8
6
–6
4
2
–8
–10 –8 –6 –4 –2
–10
–2
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
–4
–6
–8
–10
2x ⫺ 4
A y ⫽ ⫺__
5
5x ⫹ 4
C y ⫽ ⫺__
2
2x ⫹ 4
B y ⫽ ⫺ __
5
5x ⫺ 4
D y ⫽ ⫺__
2
y
B
10
8
6
4
2
–10 –8 –6 –4 –2
2. The table shows several points that lie
on a given line. Which of the following
could be the equation of the line?
x
y
⫺2
0
⫺1
0
–2
–4
–6
–8
–10
y
C
3
10
8
6
1.5
4
2
F
y ⫽ 2x
–10 –8 –6 –4 –2
H __x ⫺ y ⫽ 0
2
–2
–4
–6
–8
G y⫽x⫹1
J
–10
y ⫽ ⫺2x
y
D
3. Which linear equation is equivalent to
3?
1x ⫹ __
the equation y ⫽ __
2
4
A x ⫺ 4y ⫹ 3 ⫽ 0
10
8
6
4
2
–10 –8 –6 –4 –2
–2
–4
B 2x ⫺ 4y ⫹ 3 ⫽ 0
–6
–8
C 2x ⫺ 4y ⫹ 12 ⫽ 0
–10
D x ⫺ 2y ⫹ 6 ⫽ 0
16
4/14/06 9:49:25 AM
Name
Date
Class
Ready for TAKS?
OBJECTIVE
3
6?
4. Which line has a slope of ⫺__
5
y
F
1. What is the slope of the line whose
equation is 2y ⫽ ⫺3(x ⫺ 5)?
10
A ⫺3
C
2
⫺__
D
15
___
8
6
3
4
2
B
3
⫺__
2
–10 –8 –6 –4 –2
2
–2
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
–4
–6
–8
equation is 3y ⫹ 2x ⫺ y ⫽ 6 ⫹ 2y?
F
–10
y
G
0
10
8
6
4
1
G __
2
2
–10 –8 –6 –4 –2
–2
–4
–6
H 3
–8
–10
J
undefined slope
y
H
10
8
6
graph is shown?
4
2
–10 –8 –6 –4 –2
y
–2
–4
–6
–8
10
–10
8
y
J
6
10
8
6
4
4
2
2
–10 –8
–6
–4
(4, 0)
–2
2
4
–2
6
–10 –8 –6 –4 –2
8
10
x
–4
–6
–8
–10
–4
–6
5. Line a passes through each of the points
in the table. What is the slope of line a?
–8
–10
2
C ⫺__
5
2
__
5
⫺__
5
(0, –10)
5
A __
2
B
–2
D
x
4
10
16
y
⫺2
2
11
A 6
2
C __
3
B 4
2
D ⫺__
3
2
17
4/14/06 9:49:26 AM
Name
OBJECTIVE
3
Date
Class
Ready for TAKS?
1. According to the graph, which statement
best describes the relationship between
x and y ?
4. What is the equation of the line that
contains point (4, ⫺5) and is parallel to
the graph of 3x ⫺ 2y ⫽ 7.
F
3x ⫺ 2y ⫽ 7
3x ⫺ __
7
G y ⫽ __
2
2
H 2x ⫺ 3y ⫽ 23
J
3x ⫺ 2y ⫽ 22
A As x increases, y remains constant.
5. The table shows the price of purchasing
certain numbers of concert tickets.
B As y increases, x remains constant.
D As x increases, y decreases.
2. Which of the following pairs of equations
describes a pair of parallel lines?
F
y ⫽ 2x ⫹ 4 and y ⫽ ⫺2x ⫹ 4
G
1x ⫹5
y ⫽ 3x ⫺ 1 and y ⫽ ⫺__
3
x ⫹ 2y ⫽ 6 and 2x ⫺ y ⫽ 5
3. Which graph could represent the money
in Jack’s bank account if the money
increased for a few months, then
increased by a greater amount, then
increased by an even greater amount?
A
C
B
D
Cost ($)
4
108
8
216
12
324
16
432
If the linear function that represents this
data were graphed with the number of
tickets on the horizontal axis and the
cost on the vertical axis, which would be
the best interpretation of the slope of the
line?
H x ⫹ 3y ⫽ 9 and 2x ⫹ 6y ⫽ 7
J
Number of Tickets
A The cost of buying 4 tickets is $108.
B The cost of buying 0 tickets is $0.
C Each ticket costs $27.
D The cost per ticket increases as
more tickets are purchased.
18
4/14/06 9:49:26 AM
Name
OBJECTIVE
3
Date
Ready for TAKS?
1. The graphs of line ᐉ and line m are
shown.
Line ᐉ
10
8
8
6
6
4
4
–2
A It will reflect the graph across the
x-axis.
y
10
2
–10 –8 –6 –4 –2
3. The function y ⫽ 3.4x ⫺ 6.9 is changed
to y ⫽ 3.4x ⫹ 6.9. What will be the effect
on the graph of the function?
Line m
y
B It will reflect the graph across the
y-axis.
2
2
4
6
8
10
x
–10 –8 –6 –4 –2
–2
–4
–4
–6
–6
–8
–8
–10
–10
2
4
6
8
10
x
C It will translate the graph 13.8 units
right.
D It will translate the graph 13.8 units
up.
3 and
4. Line a has equation y ⫽ ⫺2x ⫹ __
2
Line b has the same slope as Line a,
How does the graph of line ᐉ compare to
the graph of line m?
A The slope of ᐉ is less, but the
y-intercept is greater.
B The slope of ᐉ is less and the
y-intercept is less.
but has a y-intercept of 5. Which
C The slope of ᐉ is greater and the
related to Line a?
statement describes how Line b is
F
D The slope of ᐉ is greater, but the
H Line b is a reflection of Line a across
the x-axis.
y
J
10
8
6
4
–2
2
4
6
8
10
x
–4
–6
–8
–10
A y ⫽ 3x ⫺ 2
If the y-intercept is decreased by 5 units,
what would be the equation of the new
function?
F
5
1x ⫹ __
f (x) ⫽ __
2
2
15
1x ⫺ ___
G f (x) ⫽ __
2
2
B y ⫽ ⫺6x ⫹ 1
C y ⫽ ⫺4x ⫹ 9
D 3y ⫽ ⫺2x ⫹ 1
9x ⫺ __
5
H f (x) ⫽ ⫺__
2
2
J
Line b is a reflection of Line a across
the y-axis.
5. A line has equation y ⫽ ⫺2x ⫹ 3. If the
slope of the line is multiplied by 3 and
⫺2 is added to the y-intercept, what will
be the equation of the new line?
2
–10 –8 –6 –4 –2
Line b is a translation of Line a 3.5
unit up.
G Line b is a translation of Line a 3.5
units down.
5
1x ⫺ __
2. The graph of the function f (x) ⫽ __
2
2
is shown.
Class
5x ⫺ __
5
f (x) ⫽ ⫺__
2
2
19
4/14/06 9:49:27 AM
Name
OBJECTIVE
3
Date
Class
Ready for TAKS?
3, what
4. If the slope of the line shown is __
2
is the x-coordinate of the x-intercept?
1. Which equation describes a line that
passes through the point (⫺2, 1) and
1?
has a slope of ⫺__
4
1
1x ⫺ __
A y ⫽ ⫺__
4
2
y
1x ⫹ __
1
B y ⫽ ⫺__
4
2
C
x
–4
1x ⫹ 3
y ⫽ ⫺__
4
3
1x ⫺ __
D y ⫽ ⫺__
4
2
contains the points (1, 2) and (2, ⫺1)?
F
F
3x ⫹ y ⫽ 5
5
G __
2
G 3x ⫺ y ⫽ 5
8
H __
3
H 3x ⫹ y ⫽ ⫺5
J
⫺4
3x ⫺ y ⫽ ⫺5
J
3. Which equation describes the line with
x-intercept ⫺4 and y-intercept 3?
6
5. Which could be the equation of the line
whose graph is shown?
A 4y ⫺ 3x ⫽ 12
B 3y ⫺ 4x ⫽ 9
y
C 4y ⫹ 3x ⫽ 12
D 3y ⫺ 4x ⫽ 0
x
4x ⫹ 2
A y ⫽ __
5
4x ⫺ 2
B y ⫽ __
5
4x ⫹ 2
C y ⫽ ⫺__
5
4x ⫺ 2
D y ⫽ ⫺__
5
20
4/14/06 9:49:27 AM
Name
Date
OBJECTIVE
3
Ready for TAKS?
Benchmark Pre-Test (A.6)(E)
1. If the line 5x ⫺ 3y ⫽ ⫺12 were graphed,
what would be the x-intercept?
on a line. What would be the x-intercept
of this line if it were graphed?
12
B ⫺___
5
A ⫺4
C
Class
12
___
D 4
5
2. If the line 5x ⫺ 7y ⫽ ⫺24 were graphed,
what would be the y-intercept?
F
24
G ___
7
24
___
5
24
H ⫺___
7
F
⫺2
6
⫺3
8
⫺4
10
2
H 0
3. An equation of the line graphed is
2(x ⫺ y) ⫽ c ⫺ x. What is the value of c?
J
⫺5
5. A refrigerator company is testing a new
refrigerator. The temperature, in °F, is
recorded every hour, h, from the time
the refrigerator is turned on. The table
shows that the temperature decreases
according to a linear relationship.
y
10
8
6
y
G 1
24
⫺___
5
J
x
(0, 6)
4
2
(–4, 0)
–10 –8
–6
–4
–2
2
4
–2
6
8
10
x
–4
–6
–8
h
Temperature (°F)
0
72
1
56
2
40
If the pattern continues and the linear
relationship was graphed with h on
the horizontal axis, what would be the
x-intercept of the line?
–10
A ⫺12
B ⫺4
3
C __
2
D 12
A 3
B 3.5
C 4
D 4.5
21
4/14/06 9:49:27 AM
Name
OBJECTIVE
3
Date
Class
Ready for TAKS?
Benchmark Pre-Test (A.6)(F)
1. The graph of a line is shown. If the
y-intercept is doubled and the slope is
tripled, which equation represents the
new line?
Use the information and the graph to
answer questions 3–5.
A plumber charges a flat fee of $80 to make
a house call. The graph shows the total
cost for a visit based on the flat fee and the
number of hours to complete the visit.
y
10
8
6
Cost ($)
4
2
–10 –8
–6
–4
–2
2
4
6
8
10
–2
x
(2, 130)
80
–4
(1, 105)
–6
–8
1
2
Number of Hours
–10
3x ⫹ 12
A y ⫽ __
2
C y ⫽ 6x ⫹ 12
B y ⫽ 3x ⫹ 12
D 3y ⫽ x ⫹ 6
3. If the plumber increased his flat fee by
$20 but kept his hourly rate the same,
what would be the total charge for a visit
that took 2 hours?
2. Two start-up companies’ profits over a
six month period of time are represented
by the graphs.
Company A
B $150
D $100
F
Company B
$165
G $140
H $110
J
$80
5. If the plumber increased his flat fee by
$20 and increased his hourly rate by $5,
what would be the total charge for a visit
that took 2 hours?
The two companies’ profits grew at
the same rate.
G Company B’s profits grew faster
since the y-intercept is greater.
H Company A’s profits grew at the
same rate that company B’s profits
declined.
J
C $125
4. If the plumber left his flat fee at $80 but
increased his hourly rate by $5, what
would be the total charge for a visit that
took 2 hours?
Which statement best compares the two
companies’ profits?
F
A $175
A $230
C $160
B $165
D $130
Company B’s profits grew faster
since the slope of the line is greater.
22
4/14/06 9:49:28 AM
Name
OBJECTIVE
3
Date
Ready for TAKS?
Benchmark Pre-Test (A.6)(G)
1. A truck’s value decreases according to
the age of the vehicle. The table shows
the value of the truck depending on its
age.
Age (years)
Value (dollars)
0
18,000
1
15,000
3
9,000
4. The Canadian bobsled team is practicing
for the Winter Olympics. The coach
recorded the following data during
practice. All distances are measured
from the top of the course but because
of repairs on the course the bobsled
started 20 m down from the top of the
course.
Time (seconds)
Distance (meters)
3.50
80
7.00
140
8.75
170
If the value of the truck continues to
decrease at the rate shown in the table,
how old will the truck be when it is worth
nothing?
A 4 yrs
C 6 yrs
B 5 yrs
D 7 yrs
If the bobsled team continues to sled at
the rate shown in the table, what is the
approximate distance they will move in
20 seconds?
2. The force that must be applied to lift
an object using a certain pulley system
varies directly with the weight of the
object. If a force of 0.225 pounds is
required to lift an object that weighs 17
pounds, approximately how much force
is required to lift an 80-pound desk?
F
F
H 457 m
J
514 m
5. The time it takes to hear thunder varies
directly with a person’s distance from
the lightning that precedes the thunder.
The table shows the number of seconds
between seeing lighting and hearing
thunder for several times and distances.
0.000165 lbs
H 0.944 lbs
Time (seconds)
Distance (miles)
10
2
8
1.6
5
1
1.059 lbs
3. Based on the given exchange rate for
Aruban florin on a certain day at the
airport, Ms. Marvel purchased a purse
that was marked 400 florin for 225 U.S.
dollars. At this same rate, approximately
what would a 45 florin bag cost in U.S.
dollars?
A $25.31
C $130
Based on the data in the table, how
many seconds does it take a person to
hear the thunder if the lightning is 6.5
miles away?
B $80
D $220
A 0.77
C 32.5
B 1.3
D 35.6
343 m
G 400 m
G 0.048 lbs
J
Class
23
4/14/06 9:49:28 AM
Name
OBJECTIVE
4
Date
Ready for TAKS?
1. Marsha is exercising using a specific
program in which the number of hours
she runs each week, r, is twice the
number of hours she does aerobics, a.
Which equation represents the number
of hours she runs each week?
4. Ms. Jackson is doing a study on the
weight of turkeys compared to the
number of handfuls of corn the turkeys
eat each day. She feeds 100 turkeys
a certain number of handfuls each day
and then after one year, counts to see
how many turkeys weigh more than
40 pounds. The results are given in
the table.
A r⫽a⫺2
B r⫽a⫹2
C a ⫽ 2r
D r ⫽ 2a
2. Michael has allotted a maximum of
2 hours each day to work on SAT
practice problems. Each math question,
m, takes Michael approximately
3 minutes to complete. Each verbal
question, v, takes Michael approximately
2 minutes to complete. Which inequality
best represents the time Michael can
spend practicing a combination of math
and verbal questions?
F
Number of Turkeys
over 40 lbs
Handfuls of Corn
Fed to each Turkey
1
4
2
6
3
8
4
10
relationship between h, the number of
handfuls of corn, and t, the number of
turkeys?
F
m⫹v<2
h ⫽ 4t
G h⫽t⫹3
H h ⫽ 2t ⫹ 2
G 5(m ⫹ v) < 2
J
h ⫽ 3t ⫹ 1
5. Bobby has $40 to spend at an
amusement park. The table shows the
price of each item he wants to spend
money on.
H 2m ⫹ 3v < 120
J
Class
3m ⫹ 2v < 120
3. A toy rocket is launched straight down
from a platform that is 100 feet tall. If the
rocket falls at a constant rate of 15 feet
per second for the first minute, which
equation could be used to determine t,
the time in seconds it will take the toy
rocket to hit the ground?
Items
Price
Hot Dogs
$3.5 each
Cans of Juice
$2 each
Ride Tickets
$2.50 each
If he buys one hot dog and one can of
juice, which inequality best describes the
total number of ride tickets, r that he can
purchase?
A 100 ⫽ 15t
B 0 ⫽ 15t
C 0 ⫽ 15t ⫹ 100
A r ⱕ 40
D 100 ⫽ 15 ⫹ t
B 2.5r ⱕ 40
C r ⱕ 40 ⫺ (3.5 ⫹ 2)
D 2.5r ⱕ 40 ⫺ (3.5 ⫹ 2)
24
4/14/06 9:49:37 AM
Name
OBJECTIVE
4
Date
Ready for TAKS?
4. The table shows several solutions (x, y )
to the equation 2x ⫺ 3y ⫽ 14.
1. A student is solving the equation
7 ⫹ x ⫺ 2 ⫽ 4x ⫹ 3x ⫺ 5 . Which of the
following strategies would be the BEST
way to start this problem?
x
B Add 7 and 2.
C Add 4x and 3x.
x
⫺3
What is the missing value of x ?
D Subtract 4x from both sides.
F
2. What is the value of x if (x, 5) is a
2 x ⫹ 10?
solution to the equation y ⫽ __
3
2
⫺__
5
1
G __
2
42
___
H 1
5
G 10
J
10
H ⫺___
3
J
7
y
14
⫺ ___
3
0
0
A Divide both sides of the equation by
7.
F
Class
5
__
2
5. What is the solution to the statement
“the product of 5 and the quantity x
decreased by 10, is 40?”
15
⫺___
2
A 6
3. Each of the points on the line is a
solution to the equation ⫺6x ⫹ 3y ⫽ 3.
B 10
C 18
y
D 45
(2, y )
(0, 1)
x
(–4, –7)
What is the missing value of y ?
A 3.5
B 4
C 4.5
D 5
25
4/14/06 9:49:38 AM
Name
OBJECTIVE
4
Date
Class
Ready for TAKS?
1. The cost of renting a circular saw at
a hardware store is described by the
function f (x ) ⫽ 25x ⫺ 10 in which f (x )
is the cost and x is the time in days. If
Mr. Lewis has $200 to spend, what is the
maximum number of days that he can
rent a saw if tax is not considered?
4. The graph of the linear inequality
5x ⫺ 3y ⬍ 4 is shown.
y
8
6
4
2
–8
A 5 days
–6
–4
–2
2
4
6
8
–2
B 6 days
x
–4
–6
C 7 days
–8
D 8 days
Which point is in the solution set to the
inequality 5x ⫺ 3y ⬍ 4?
2. The dance committee at a high school
is trying to raise money for homecoming
by holding car washes throughout the
fall. They decide to charge $17 per
wash, inside and out. If the committee
wants to raise at least $2,500, what is
a reasonable number of cars they must
wash?
F
F
G (⫺2, ⫺5)
H (0, 5)
100 cars
J
G 150 cars
H 200 cars
J
(3, 1)
1, 3__1 5. The graph of the linear inequality
4 x ⫹ 1 is shown.
y ⱖ __
5
250 cars
3. Matt purchased x baseball cards at
75¢ each and y boxes of raisins at
$1.25 each. He spent less than $20,
not including tax. The number of items
he purchased can be described by the
linear inequality 0.75x ⫹ 1.25y ⬍ 20. If
Matt purchased 9 baseball cards, what is
the maximum number of boxes of raisins
he could have purchased?
y
8
6
4
2
–8
–6
–4
–2
2
4
6
8
–2
x
–4
–6
–8
A 10 boxes
B 11 boxes
Which point is NOT in the solution set
4 x ⫹ 1?
of y ⱖ __
5
C 12 boxes
D 13 boxes
26
A (1, 5)
B (3, 2)
C (⫺4, 2)
D (⫺1, ⫺4)
4/14/06 9:49:38 AM
Name
OBJECTIVE
4
Date
Ready for TAKS?
1. Meg has 25 pictures of her friends
and her favorite singers on her wall.
The number of pictures of singers is 5
less than the number of pictures of her
friends. Which system of equations can
be used to find the number of friend
pictures, f, and the number of singer
pictures, s, on her wall?
A f ⫽ s ⫺ 25
s⫽f⫺5
B f ⫽ 25 ⫺ s
s⫽5⫺f
C f ⫽ 25 ⫺ s
s⫽f⫺5
D f ⫽ s ⫺ 25
s⫽f⫹5
4. The diagram shows a right triangle. The
measure of angle y is 10 degrees less
than three times the measure of angle x.
Which system of equations can be used
to find the measure of each angle?
x
y
F
2. Mrs. Crews is decorating her house. She
bought a total of 18 lamps and vases.
She bought twice as many lamps as
vases. Which system of equations can
be used to find the number of lamps, ᐉ,
and the number of vases, v, she bought?
F
Class
ᐉ ⫹ v ⫽ 18
ᐉ ⫽ 2v
H ᐉ ⫹ v ⫽ 18
v ⫽ 2ᐉ
3. The length of a rectangle is 7 more
than 3 times the width. Which system
of equations can be used to find the
dimensions of the rectangle if the
perimeter is 80 inches?
B 2(ᐉ ⫹ w ) ⫽ 80
ᐉ ⫽ 7 ⫹ 3w
C ᐉ ⫹ w ⫽ 80
w ⫽ 7 ⫹ 3ᐉ
D 2w ⫽ 80 ⫺ 2ᐉ
ᐉ ⫽ 3 ⫹ 7w
J
x ⫽ 90 ⫺ y
y ⫽ 3x ⫺ 10
5. The table shows the number of pizza
slices and bags of popcorn sold at a
movie theater before and after the show.
18 ⫺ v ⫽ ᐉ
v⫽2⫹ᐉ
A 2ᐉ ⫹ 2w ⫽ 80
w ⫽ 3 ⫹ 7ᐉ
G x ⫹ y ⫽ 90
y ⫺ 10 ⫽ 3x
H x ⫹ y ⫽ 90
y ⫽ 10 ⫺ 3x
G 18 ⫺ ᐉ ⫽ v
ᐉ⫽2⫹v
J
x ⫹ y ⫽ 90
x ⫽ 3y ⫺ 10
Before the
Show
After the
Show
Pizza Slices
18
15
Popcorn Bags
25
29
$181.75
$190.25
Total Sales
If the price of a slice of pizza is
represented by z and the price of a bag
of popcorn is represented by c, which
system of equations can be used to
determine the price of each?
A z ⫹ c ⫽ 43
18z ⫹ 25c ⫽ 181.75
B z ⫹ c ⫽ 44
15z ⫹ 29c ⫽ 190.25
C z ⫹ c ⫽ 87
z ⫹ c ⫽ 372
D 18z ⫹ 25c ⫽ 181.75
15z ⫹ 29c ⫽ 190.25
27
4/14/06 9:49:38 AM
Name
OBJECTIVE
4
Date
Class
Ready for TAKS?
4. The graph shows the solution to which
system of equations?
1. Ellen has 20 coins in nickels and dimes.
She has 6 more dimes than nickels. The
system of equations
y
x ⫹ y ⫽ 20
y⫽x⫹6
8
6
4
represents this situation if x is the
number of nickels and y is the number
of dimes. What is the solution to the
system?
2
–8
–6
–4
2
–2
4
6
8
–2
x
–4
–6
A (7, 13)
–8
B (13, 7)
F
C (8, 12)
D (6, 12)
3x ⫺ 4y ⫽ 0
G 3x ⫺ 4y ⫽ 0
⫺3x ⫹ 4y ⫽ 24
3x ⫹ 4y ⫽ 24
H 3x ⫹ 4y ⫽ 0
3x ⫺ 4y ⫽ 24
2. Jamie has 25 coins in dimes and
quarters. The coins are worth $4.15. The
system of equations
5. The graph of the system of equations
is shown. What is the solution to the
system?
d ⫹ q ⫽ 25
0.1d ⫹ 0.25q ⫽ 4.15
y
represents this situation. If q represents
the number of quarters Jamie has, what
is the value of q ?
F
8
6
4
2
11
–8
G 12
–6
–4
–2
2
–2
4
6
8
x
–4
H 14
J
3x ⫹ 4y ⫽ 0
⫺3x ⫹ 4y ⫽ 24
J
–6
–8
15
3. What is the y-coordinate of the solution
to the system of equations
A (2, 2)
B (2, 3)
6x ⫺ 3y ⫽ 6
2x ⫹ 3y ⫽ ⫺22 ?
C (3, 2)
A ⫺2
D (2, 4)
B ⫺3
C ⫺4
D ⫺6
28
4/14/06 9:49:39 AM
Name
OBJECTIVE
4
Date
Ready for TAKS?
1. Ariel knits hats and scarves. She
charges $15 per hat and $18 per scarf.
One month she sold a total of 25 hats
and scarves and earned $387. The
system of equations
4. Gary wrote down a system of equations
to solve, but part of the second equation
got wet. The remaining part read
2x ⫹ y ⫽ 12
7x ⫺ ?y ⫽ ?
x ⫹ y ⫽ 25
15x ⫹ 18y ⫽ 387
Which of the following is NOT a possible
solution to the system regardless of what
the missing numbers are?
represents this situation. If the solution
to the system is (9, 14), what does 14
represent?
F
H (4, 4)
B the price per scarf
J
C the number of hats Ariel sold
2. Esther incorrectly solved the system of
equations
aebec
3x ⫹ y ⫽ 1
⫺3x ⫺ y ⫽ 1
Her solution was (⫺1, 4). Why is this
solution incorrect?
f ⫹ t ⫽ 17
5f ⫹ 20t ⫽ 185
because 3(4) ⫹ (⫺1) ⫽ 1
Solve the system to determine which
reason best describes why at least one
of Aaron’s totals must be wrong.
G because ⫺3(4) ⫺ (⫺1) ⫽ 1
H because 3(⫺1) ⫹ 4 ⫽ 1
A When you solve the system you get
a negative number of $5 bills.
because ⫺3(⫺1) ⫺ 4 ⫽ 1
3. Garth solved a system of equations
1, 3 .
and found the solution to be __
2
Which of the following could NOT have
B When you solve the system you get
a negative number of $20 bills.
been the system Garth solved?
C When you solve the system you get
a fraction for both types of bills which
is not possible.
A 2x ⫺ y ⫽ ⫺2
4x ⫹ 2y ⫽ 8
B 4x ⫹ y ⫽ 5
y ⫺ 2x ⫽ 2
D There is no way to get a total of $185
using only $5 and $20 bills.
C 6x ⫹ y ⫽ 6
y ⫽ 8x ⫺ 1
D y ⫽ 4x ⫹ 1
y ⫽ 2x ⫺ 4
(10, ⫺8)
5. Aaron has a wallet full of 5- and 20dollar bills. He counted the number of
each and found that he had a total of
17 bills. He then counted the total value
of the bills and found that he had $185.
The system of equations represents this
situation.
D the price per hat
J
(⫺2, 16)
G (⫺6, 0)
A the number of scarves Ariel sold
F
Class
29
4/14/06 9:49:39 AM
Name
OBJECTIVE
5
Date
Class
Ready for TAKS?
4. The graphs of two parabolas, P1 and P2,
are shown.
1. What is the effect on the graph of the
2
equation y ⫽ ⫺4x when the equation is
2
changed to y ⫽ 4x ?
y
A The graph of y ⫽ 4x2 is translated 8
units up from the original graph.
P1
P2
B The graph of y ⫽ 4x2 is translated 8
units down from the original graph.
C The graph of y ⫽ 4x2 is a reflection of
the original graph across the x-axis.
x
D The graph of y ⫽ 4x2 is a reflection of
the original graph across the y-axis.
are shown.
The coefficient of x2 in P1 is 1. Which of
the following could be the coefficient of
2
x in P2?
y
P1
F
5
__
4
H 1.1
4
G __
5
x
P2
兹2
J
5. The graph of the function y ⫽ 2x2 is
given.
If the equation of P1 is y ⫽ ax 2, what
best describes the change to “a ” from P1
to P2?
y
8
6
F
the value of a becomes negative
G
1
a changes to __
4
2
a
–8
–6
–4
–2
2
4
6
8
–2
1
__
H a changes to ⫺a
x
–4
–6
J
the value of a remains the same
–8
3. If the coefficient of x2 in the equation
2
y ⫽ ⫺3x is changed to ⫺6, what is the
effect on the graph of y?
B The graph will be narrower.
If the graph is reflected across the y-axis
and made wider, which of the following
could be the equation of the new
parabola?
C The graph will be wider.
A y ⫽ ⫺2x
D The graph will be shifted left.
1x2
B y ⫽ __
2
A The graph will be shifted up.
30
2
C y ⫽ ⫺x2
D y ⫽ ⫺4x2
4/14/06 9:48:23 AM
Name
OBJECTIVE
5
Date
Class
Ready for TAKS?
1. How do the graphs of the functions
2
2
f (x) ⫽ x ⫺ 9 and g(x) ⫽ x ⫹ 2 relate to
each other?
4. The point (⫺2, 3) is the vertex of the
parabola whose equation is f (x) ⫽ x2 ⫹
4x ⫹ 7. What is the vertex of a parabola
that has been shifted down 6 units?
A The graph of f(x) is 7 units above the
graph of g(x).
F
(⫺6, 3)
G (⫺2, ⫺3)
B The graph of f (x) is 11 units below
the graph of g(x).
H (⫺2, ⫺6)
C The graph of f (x) is 7 units to the
right of the graph of g(x).
J
(⫺8, 3)
5. When graphed, which function would
appear to be the graph of f (x) ⫽ x2 ⫺ 2
shifted left 4 units?
D The graph of f(x) is 11 units to the
2
2. If the graph of f (x) ⫽ x ⫹ 1 is translated
down 6 units, which function represents
the new graph?
F
f(x) ⫽ (x ⫹ 6)
y
8
2
6
G f (x) ⫽ (x ⫺ 6)2
4
H f (x) ⫽ x2 ⫺ 5
2
J
–8
f(x) ⫽ x2 ⫹ 6
–6
–4
–2
2
–2
3. The graph shows the function
2
f (x) ⫽ x ⫺ 4.
4
6
8
x
–4
–6
y
–8
8
6
A f (x) ⫽ (x ⫺ 4)2 ⫺ 2
4
B f (x) ⫽ x2 ⫹ 2
2
–8
–6
–4
–2
2
4
6
8
–2
C f (x) ⫽ (x ⫹ 4)2 ⫺ 2
x
D f (x) ⫽ x2 ⫺ 6
–4
–6
–8
Which statement describes the
translation of the parabola if the
y-intercept is moved to y ⫽ 3?
A 7 units down
C 1 unit up
B 1 unit down
D 7 units up
31
4/14/06 9:48:24 AM
Name
OBJECTIVE
5
Date
Class
Ready for TAKS?
1. Deb’s dirt bike speed is shown below.
H The ball’s height increased for
approximately 2 seconds.
y
J
8
6
3. A company’s weekly profit is given by the
2
function P(x) ⫽ ⫺80x ⫹ 800x ⫹ 15,000,
where x is the number of machines
produced. The graph of P(x) is shown.
4
2
–8
–6
–4
–2
2
4
6
x
8
–2
The height of the baseball was 6 feet
when it was thrown.
y
Profit ($)
18000
Which best describes Deb’s speed?
A Went down a hill and then back up.
16000
14000
12000
1
B Speed increased, reached a peak,
and then decreased.
5
6
7
8
x
9
A The maximum weekly profit is
approximately $17,000.
B The profit continues to increase
regardless of machine produced.
2. The graph shows the height, h, in feet of
a baseball versus the time, t, in seconds,
after the ball is thrown.
C The company can produce at most
5 machines and still make a profit.
D Maximum profit comes by producing
approximately 19 machines.
y
22
20
4. The graph shows the number of
teenagers, T (in thousands) in a city that
bought a portable music player x years
after 2000.
18
16
14
12
10
y
8
Number of
Players
Height (in feet)
4
What conclusion can be made?
D Slowed down, came to a stop, and
then sped up.
6
4
2
1
2
3
4
5
6
7
8
9
x
150
100
50
2
3
4
5
6
7
8
x
Time (in years)
How many thousands of teenagers
bought a portable music player in 2004?
The ball reached its maximum height
after 20 seconds.
F
G The ball was in flight for 3 seconds.
200
1
Time (in seconds)
3
Number of Machines
C Slowed down and then went
backwards.
F
2
4
G 7
32
H 61
J
83
4/14/06 9:48:25 AM
Name
Date
Ready for TAKS?
OBJECTIVE
5
4. If a rock is dropped from the top of a
building that is 150 feet high, the height
of the rock above the ground t seconds
later (neglecting air resistance) is given
2
by the equation h ⫽ 150 ⫺ 16t where h
is the height in feet. What is the height of
the rock after 2.5 seconds?
1. The factored form of a quadratic
equation is (9x ⫺ 3)(2x ⫹ 4). What are
the solutions of the quadratic equation?
A x ⫽ 3 and x ⫽ ⫺4
B x ⫽ 3 and x ⫽ ⫺2
C
Class
F
1 and x ⫽ ⫺2
x ⫽ __
3 ft
G 50 ft
3
H 70 ft
1 and x ⫽ ⫺__
1
D x ⫽ __
3
2
J
110 ft
2
2. Solve. 3x ⫽ 20x ⫺ 12
F
5. Sketch the graph of the equation in
question 4 on the grid provided and find
the approximate number of seconds it
takes the object to hit the ground.
4 and ⫺3
⫺__
3
2 and 6
G ⫺__
3
y
2 and 6
H __
3
J
8
6
4 and 3
__
4
3
2
3. Which of the following are solutions to
2
the equation 3x ⫹ 2x ⫽ 5 ⫺ x?
–8
–6
2
4
6
8
x
–4
–6
5
B x ⫽ ⫺1 and x ⫽ __
3
–8
⫹ i兹51and x ⫽ ⫺3
⫺ i兹51
__________
__________
C x ⫽ ⫺3
6
6
–2
–2
1
A x ⫽ 5 and x ⫽ ⫺__
3
–4
A 2 sec
⫹ 兹69and x ⫽ ⫺3
⫺ 兹69
_________
_________
D x ⫽ ⫺3
6
6
B 2.5 sec
C 3 sec
D 3.5 sec
33
4/14/06 9:48:25 AM
Name
OBJECTIVE
5
Date
Class
Ready for TAKS?
4. One of the factors of the quadratic
equation 0 ⫽ 3x2 ⫺ 11x ⫹ 10 is (x ⫺ 2)
which produces a root of 2. What is the
other root of the equation?
1. What are the roots of the quadratic
2
equation 2x ⫺ 16x ⫺ 96 ⫽ 0?
A ⫺4 and 12
B ⫺4 and ⫺12
F
C 4 and 12
D 4 and ⫺12
⫺2
5
G ⫺__
3
2. What are the roots of the function
graphed?
5
H __
3
y
J
18
2
16
14
5. The graph shows the roots of a
quadratic equation.
12
10
8
y
6
4
2
–14–12 –10 –8 –6 –4 –2
–2
2
4
6
8 10 12 14
x
–4
–6
–4
–8
2
x
–10
–12
–14
–16
–18
F
Which of the following could NOT be the
equation?
(1, ⫺16) and (0, ⫺15)
G (⫺3, 0) and (5, 0)
A x2 ⫹ 4x ⫺ 5 ⫽ 0
H (0, ⫺3) and (0, 5)
J
B ⫺2x2 ⫺ 8x ⫹ 10 ⫽ 0
(3, 0) and (⫺5, 0)
C 3x2 ⫹ 12x ⫺ 15 ⫽ 0
3. If x ⫽ ⫺2 is a root of the equation
ax2 ⫹ 2x ⫹ ax ⫺ 6 ⫽ 0, what is the
value of a?
D 4x2 ⫹ 8x ⫺ 32 ⫽ 0
A 5
B ⫺2
C ⫺3
D ⫺10
34
4/14/06 9:48:25 AM
Name
Date
OBJECTIVE
5
Class
Ready for TAKS?
4. The area of the rectangle shown is
52m9n3 square units. If the length of the
3 4
rectangle is 8m n units, how many units
wide is the rectangle? (m ⫽ 0 and n ⫽ 0)
1. Which expression represents the area of
the triangle shown?
5xy 8
6x 5 y 4
2x 2y
3x 4y 6
A 3x6y7
8m 3n 4
7 5
B 6x y
6
F
9 10
C 9x y
D 15x6y12
13m
_____
2n
G 44m6n
2. Which expression is equivalent
2 ⫺3 ⫺1
13m6n
H ______
2
28x y z
to _________
?
5 7
24x y
3
F
7x3y4
_____
6z
G
4z
____
J
13m
_____
2n
5. The table shows several values of r
and s.
x3y10
4
H _____
3 10
xy z
7
______
J
s
2x
8x4
2
27x
3x
3 10
6x y z
3
r
4x3
7
64x10
3
4x ⫺ 3x
________
Which of these best describes the
relationship between r and s?
7
(2x )(3x)?
1
A ___
6x5
C x5
A s ⫽ 4xr
x5
B __
6
⫺ x2
______
D 2
x4
B s ⫽ r4
C s ⫽ xr3
D s ⫽ 2r2
35
4/14/06 9:48:26 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
Benchmark Pre-Test (G.4)(A)
1. Which expression can be used
to determine the total area of the
composite figure shown?
4. What is the point of intersection of the
diagonals of the parallelogram whose
vertices are A(3, 6), B(4, 3), C(⫺2, 0),
and D(⫺3, 3)?
ᐉ
y
6
w
4
2
w2
A ᐍw ⫹ __
4
–6
–4
F
G
2. The measure of one interior angle in an
isosceles triangle is 90°. What are the
measures of all three interior angles?
x
2__1, 2__3 2__1, 3 H (1, 3)
90°, 90°, and 90°
J
G 90°, 90°, and 180°
3, 2__1 5. A quarter of a circle is inscribed in a
square with sides of length s as shown.
H 30°, 60°, and 90°
45°, 45°, and 90°
3. Mr. Smith had a square garden with
sides of length 12 feet. He redesigned
his garden in the shape of a circle
and used all the fencing from the old
garden to make the new garden. What
is the approximate diameter of the new
garden?
s
Which expression represents the area of
the shaded region?
A 3.8 ft
B 7.6 ft
3s2
A ___
4
C 15.3 ft
B s2 1 ⫺ __
4
D 37.7 ft
6
–6
D 2ᐍ ⫹ w
4
–4
C ᐍw ⫹ w2
J
2
–2
w2
B ᐍw ⫹ __
2
F
–2
36
C s2(1 ⫺ )
s
D s2 ⫺ __
4
4/14/06 9:48:37 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
1. If the measure of angle ABC in the figure
is n°, which of the following expressions
represents the measure of angle BCD in
degrees?
A
4. The regular polygons shown form a
pattern.
B
P = 3 cm
C
E
P = 8 cm
P = 15 cm
P = 24 cm
If P represents the perimeter of the
figure, what is the value of P for the sixth
figure in this pattern?
D
A n
F
B 90 ⫺ n
G 42 cm
C 180 ⫺ n
H 48 cm
D 270 ⫺ n
J
2. A square is inscribed inside a circle with
radius r. Which expression represents
the area of the square?
35 cm
56 cm
5. David starts at the center of town
and travels due north for w miles. He
then travels due east for x miles. After
resting for a few minutes, he travels
due north again for y miles and finally
due east again for z miles. The diagram
represents David’s path.
r
z
F
r2
y
2
G 2r
H 4r2
J
x
8r2
3. If the length of the hypotenuse of a 30°,
60°, 90° triangle is 4x, which expression
represents the perimeter of the triangle?
w
A 2x
Which expression represents the number
of miles David is from his starting point?
B 2 3 x
C 6x ⫹ 23 x
2
A w⫹x⫹y⫹z
D 8 ⫹ 2 3 x
B w 2 ⫹ x2 ⫹ y2 ⫹ z2
C
D
37
w2 ⫹ x2 ⫹ y2 ⫹ z2
w2 ⫹ x2 ⫹ y2 ⫹ z2
4/14/06 9:48:37 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
Benchmark Pre-Test (G.5)(B)
4. The measure of one angle of a right
trapezoid is 70°. Which of the following
could be the measure of one of the other
angles?
1. In the figure shown, line l is parallel to
line m.
ᐉ
x
140°
m
What is the value of x?
F
A 30°
80°
G 100°
B 40°
H 110°
C 50°
J
D 60°
cannot be determined
5. The diagonals of parallelogram ABCD
intersect at point P.
2. The figure shows the first three stages of
a fractal.
C
B
P
A
How many unshaded triangles will the
nth stage of this fractal contain?
F
Which statement is NOT correct?
3n⫺1
_
_
_
_
_
_
_
_
A BP PD
G 3n ⫺ 1
B BC AD
H 3n ⫺ 1
J
D
C AP PC
3(n ⫺ 1)
D BP AP
3. What is the measure of each exterior
angle of a regular decagon?
A 36°
B 144°
C 360°
D 1440°
38
4/14/06 9:48:38 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
Benchmark Pre-Test (G.5)(C)
1. Which of the following shapes CANNOT
be used to generate a tessellation of a
plane surface?
3. A pure tessellation is a tessellation that
consists of congruent copies of one
figure. Which of the following series of
compositions of transformations could
NOT result in a pure tessellation given
the right figure?
A
A multiple rotations followed by multiple
glide reflections
B multiple rotations followed by multiple
translations
B
C multiple rotations followed by multiple
dilations
D multiple glide reflections followed by
multiple translations
4. Which of the following compositions of
transformations would move the triangle
completely into quadrant IV?
C
y
10
D
8
(0, 9)
6
4
2
(–3, 1)
–10 –8 –6 –4 –2
2. Which of the following statements is
true?
F
8
10
x
–8
–10
a reflection across the x-axis followed
by a reflection across the y-axis
1
G a reduction by a scale factor of __
3
followed by a reflection across
the x-axis
1
H a reduction by a scale factor of __
3
followed by a translation to the
right 2 units
1
J a reduction by a scale factor of __
3
right 2 units and then a reflection
across the x-axis.
F
H Neither reflections nor rotations
result in congruent figures.
6
–6
Both reflections and dilations result
in congruent figures.
Only dilations do not result in
congruent figures.
4
–4
G Neither reflections nor dilations result
J
–2
(6, 1)
2
39
4/14/06 9:48:38 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
Benchmark Pre-Test (G.5)(D)
4. A skateboarding ramp rises from the
ground at a 30° angle. If the ramp covers
20 feet on the ground, how long is the
inclined surface of the ramp?
1. Which is the best approximation of the
perimeter of a right isosceles triangle if
its hypotenuse is 12 units long?
A 8.5 units
B 20.5 units
C 24 units
D 29 units
2. Find the area of triangle ABC.
30°
20 ft
F
10 ft
203 ft
G _____
3
45°
F
J
40 ft
5. Mark is flying a kite. The angle of
elevation from Mark’s hand, which is
4 feet off the ground, to the kite is 60°.
If the kite is 44 feet off the ground,
approximately how many feet of string
has Mark let out?
25 ft2
G 30 ft2
H 50 ft2
J
403 ft
H _____
3
10 3 ft
100 ft2
3. The area of square ABCD is 400 units.
B
C
A
D
60°
_
What is the approximate length of AC ?
4
A 20 units
B 28 units
A 20 ft
C 50 ft
C 40 units
B 46 ft
D 80 ft
D 100 units
40
4/14/06 9:48:38 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
1. Figure EFGH is shown on the coordinate
plane.
3. Triangle A⬘B⬘C⬘ is the result of performing
a transformation on triangle ABC. Which
could NOT be the transformation if the
two triangles are congruent?
y
10
A a reflection
8
6
4
2
–10 –8 –6 –4 –2
E
F
G
H
2
–2
4
6
8
B a translation
C a rotation
10
x
D a dilation
–4
4. What are the coordinates of the image of
M if triangle MNP is translated up 3 units
and then reflected across the x-axis?
–6
–8
–10
y
Which transformation creates an image
with a vertex of (⫺2, ⫺1)?
10
8
6
A Rotate the figure 90° around vertex E
4
2
B Reflect the figure across the x-axis
and then across the y-axis.
–10 –8 –6 –4 –2
C Reflect across the line x ⫽ 1.
F
6
2
4
6
8
10
H (⫺1, 5)
J
(1, 5)
second dilation by a factor of 2
x
B a reflection across the line x ⫽ 2 and
1
then a dilation by a factor of __
2
2 and then a
C a dilation by a factor of __
3
3
second dilation by a factor of __
2
–6
–8
–10
(0, 3), (6, 3), and (6, 8)
D a translation up 2 units and then a
1
dilation by a factor of __
2
G (0, 3), (0, ⫺3), and (6, ⫺3)
H (3, 0), (8, 0), and (8, 5)
(3, 0), (3, ⫺5), and (9, 0)
x
A a dilation by a factor of 2 and then a
2
–4
J
10
5. Which of the following compositions
would result in congruent figures?
4
F
(1, ⫺5)
G (⫺5, 1)
8
–2
8
–8
y
–10 –8 –6 –4 –2
6
–10
10
M
4
P
–6
2. Which coordinates are the vertices of a
triangle congruent to triangle LMN?
L
2
–4
D Translate the figure to the left 4 units
and then down 1 unit.
N
–2
N
M
41
4/14/06 9:48:39 AM
Name
OBJECTIVE
7
Date
Class
Ready for TAKS?
1. What three-dimensional figure does the
net represent?
3. If the net shown is folded into a cube,
what letter is on the face of the cube
opposite the face labeled D?
F
C
B
A
C
A
D
D
E
B
A A
E
B B
C C
D F
A cone
4. Which of the following is a true
statement about the net of the cube
shown?
B triangular pyramid
C triangular prism
D square pyramid
J
2. Which of the following nets could NOT
be used to form a cube?
K
M
N
O
L
F
F
Faces O and N are parallel.
G Faces O and K are parallel.
G
H Faces N and K are perpendicular.
J
Faces M and K are perpendicular.
5. The net of a cylinder is composed of
which of the following?
H
A two congruent rectangles and a
circle
J
B two congruent circles and a
rectangle
C two congruent circles and an
equilateral triangle
D two congruent circles and a right
triangle
42
4/14/06 9:48:49 AM
Name
Date
OBJECTIVE
7
Class
Ready for TAKS?
4. What is the volume of a threedimensional object whose different views
are shown?
Use the net to answer questions 1⫺3.
The top, side, and front views of an object
built with cubes are shown.
Side View
4 ft
Top View
3 ft
7 ft
7 ft
Side View
4 ft
7 ft
Front View
4 ft
Front View
7 ft
1. What is the maximum number of cubes
in any one row or column?
A 3
Top View
B 4
F
84 ft3
C 8
G 196 ft3
D 12
H 280 ft3
2. How many cubes are needed to
construct this object?
F
J
434 ft3
5. Which of the following is the right view of
the three-dimensional solid shown?
7
G 11
H 13
J
17
3. If the length of each side of each cube is
2 centimeters, what is the total volume of
the object?
Front
A 56 cm3
B 88 cm3
Right
A
B
C
D
C 104 cm3
D 136 cm3
43
4/14/06 9:48:49 AM
Name
Date
Class
Ready for TAKS?
OBJECTIVE
7
3. Point P has coordinates (2, 5). If Point
P is translated down 3 units and to the
left 4 units, and then reflected across the
x-axis, what are the coordinates of the
new point?
1. Which ordered pair could represent the
fourth vertex of a trapezoid if the other
three vertices are (4, ⫺1), (⫺1, 1), and
(⫺2, ⫺3)?
y
y
x
x
A (0, ⫺1)
A (⫺2, ⫺2)
B (2, 2)
B (⫺2, 2)
C (1, 5)
C (2, ⫺2)
D (3, 1)
D (2, 2)
2. If quadrilateral ABCD is rotated 270°
counterclockwise around the origin, in
which quadrant will point A appear?
4. A hexagon is graphed on the grid.
y
y
D
A
x
x
C
F
B
What is the equation of the line of
symmetry that passes through (⫺4, 1)?
I
x ⫽ ⫺4
G II
F
H III
G x⫽1
IV
H y⫽1
J
J
44
y ⫽ ⫺4
4/14/06 9:48:50 AM
Name
OBJECTIVE
7
Date
Class
Ready for TAKS?
4. Line
ᐉ is the perpendicular bisector
_
of AB . What is the slope of line ᐉ?
1. Which two lines are parallel?
A 3x ⫹ 5y ⫽ 7 and 5x ⫹ 3y ⫽ ⫺2
y
B 3x ⫹ 2y ⫽ 9 and 6x ⫹ 4y ⫽ ⫺2
C 2x ⫹ 7y ⫽ 8 and ⫺2x ⫹ 7y ⫽ ⫺11
8
D 5x ⫹ 4y ⫽ 12 and 10x ⫺ 8y ⫽ 20
6
A
4
2. Which equation describes a line parallel
to the line graphed?
2
B
–8
y
–6
–4
–2
2
–2
8
–4
6
–6
4
–8
4
6
8
x
2
–8
–6
–4
–2
2
–2
4
6
8
x
F
–4
5
G ⫺__
4
–6
–8
F
4
H __
5
3x ⫺ 3
y ⫽ ⫺__
2
J
5
__
4
5. Segments of the lines y ⫽ 3x ⫺ 4 and
y ⫽ mx ⫹ 1 form opposite sides of a
parallelogram. What is the value of m in
the second equation?
2x ⫺ 5
G y ⫽ ⫺__
3
2x ⫹ 1
H y ⫽ __
3
J
4
⫺__
5
A ⫺3
3x ⫹ 4
y ⫽ __
2
B 3
3. Which of the following best describes
the graphs of the lines y ⫽ 5 ⫺ 3x and
6y ⫽ 2x ⫹ 5?
1
C ⫺__
3
A The lines have the same x-intercept.
1
D __
3
B The lines have the same y-intercept.
C The lines are parallel to each other.
D The lines are perpendicular to each
other.
45
4/14/06 9:48:50 AM
Name
OBJECTIVE
7
Date
Class
Ready for TAKS?
_
1. What is the approximate length of AB
shown?
_
3. PQ is a diameter of the circle shown.
What are the exact coordinates of the
center of the circle?
y
y
8
6
P
B
4
2
–8
–6
–4
–2
2
4
6
8
–2
A
x
x
–4
Q
–6
–8
A (0, 0)
A 4.1 units
B
B 2.2 units
C 12.0 units
C
D 12.2 units
D
2. The parallelogram shown has two
vertices as indicated. The diagonals of
the parallelogram intersect at point X.
0, 2__1 0, ⫺2__1 0, ⫺3__2 4. What is the area of the circle whose
diameter has endpoints (0, ⫺6) and
(8, 0)?
(–3, 2)
F
25 units2
G 36 units2
H 64 units2
X
J
(5, –6)
100 units2
5. What is the distance between (4, 5) and
(⫺2, ⫺3)?
Which of the following are the
coordinates of X ?
A 2 2
(⫺4, 4)
B 10
G (1, ⫺2)
C 14
H (2, ⫺4)
D 100
F
J
(⫺2, 1)
46
4/14/06 9:48:50 AM
Name
OBJECTIVE
7
Date
Class
Ready for TAKS?
4. Which statement is true about the threedimensional figure shown?
1. How many faces, edges, and vertices
does the three-dimensional figure shown
have?
F
A 4 faces, 6 edges, and 4 vertices
B 5 faces, 8 edges, and 5 vertices
The figure has more faces than
vertices.
G The figure has the same number of
faces as vertices.
C 5 faces, 9 edges, and 6 vertices
D 6 faces, 12 edges, and 8 vertices
H The figure has more edges than
vertices.
2. What is the sum of the number of faces
of the two three-dimensional figures
shown?
J
The figure has the same number of
edges as vertices.
5. What is the sum of the number of
faces, edges, and vertices of the threedimensional figure shown if the base of
the figure is a rhombus?
F
11
G 14
H 18
J
A 14
21
B 18
3. Which of the following three-dimensional
figures has twice as many edges as it
has faces?
C 20
D 26
A a square pyramid
B a triangular pyramid
C a triangular prism
D a rectangular prism
47
4/14/06 9:48:51 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
1. What is the area of a square that has
one of its sides with endpoints at (⫺2, 3)
and (0, 5)?
4. Which best represents the approximate
area of the composite figure shown?
10 ft
A 兹8 units2
B 4兹 8 units2
4 ft
C 8 units2
D 16 units2
45°
2. The figure shown is a regular octagon.
Which expression shows the area of
the figure?
F
60°
52.0 ft2
G 52.6 ft2
H 56.0 ft2
5
J
61.9 ft2
5. If the two shaded triangles are
congruent, what is the area of the
portion of the rectangle that is NOT
shaded?
x⫹2
12 cm
F
20x ⫹ 40
G 5x ⫹ 10
15 cm
H 40x ⫹ 80
J
8x ⫹ 80
30 cm
3. A circle with a diameter of 8 centimeters
is inscribed in a square. What is the area
of the square?
A 540 cm2
B 450 cm2
A 64 ⫺ 16 cm2
C 270 cm2
B 32 cm2
D 180 cm2
2
C 16 cm
D 64 cm2
48
4/14/06 9:50:10 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
4. What is the approximate length of
arc ABC?
Use the diagram to answer questions 1
and 2.
A portion of a circular playground is to be
fenced off for pets.
A
Area to be fenced
for pets
25 ft
12
100°
C
135°
B
F
20.9 units
G 54.5 units
1. What is the approximate area of the
portion of the playground to be used
for pets?
H 75.4 units
J
A 29 ft2
326.7 units
5. The area of the shaded section in the
circle shown is 18. What is the value
of x ?
B 736 ft2
C 1,277 ft2
D 1,963 ft2
2. If a 6-foot chain-link fence is to be put
around the entire portion of the park that
is to be used for pets, about how many
feet of fence is needed?
F
18
x°
59 ft
G 69 ft
H 109 ft
J
A 20°
185 ft
B 25°
3. A grandfather clock has a circular face
whose diameter is 18 inches. The face
is divided into 12 congruent sections,
which have alternating colors. What is
the approximate area of each section?
C 30°
D 35°
A 0.8 in2
B 8.5 in2
C 21 in2
D 85 in2
49
4/14/06 9:50:11 AM
Name
Date
OBJECTIVE
8
Ready for TAKS?
4. A door is 3 feet wide and the diagonal
length across the door is 7 feet. If Mr.
Peterson is buying a special type of
weather stripping to go around the four
edges of the door, about how many feet
of the stripping does he need?
1. Jake’s house is 5 miles due north of
Sarah’s house and 8 miles due west of
Mary’s house. What is the approximate
straight line distance from Sarah’s house
to Mary’s house?
A 6.2 mi
F
B 8.0 mi
6.3 ft
G 9.3 ft
C 9.4 mi
H 18.6 ft
D 13.0 mi
J
2. What is the area of the triangle that has
vertices at the points (2, ⫺5), (2, 3), and
(5, 3)?
F
Class
12 units2
5. A rectangle is inscribed in a circle as
shown.
G 15 units2
H 24 units2
J
20.0 ft
If the length and width of the rectangle
are 5 and 11 inches respectively, what
is the approximate circumference of
the circle?
30 units2
3. A mailman travels from his home to the
Post Office and then to the Government
Building as shown in the figure.
Home
25 mi
Government
Building
9 mi
A 50 in.
Post
Office
B 38 in.
C 25 in.
If he travels straight back home from the
Government Building, about how much
shorter is this trip than the one from his
home to the Government Building via the
Post Office?
D 12 in.
A The distances are the same.
B 2 mi
C 11 mi
D 23 mi
50
4/14/06 9:50:12 AM
Name
Date
OBJECTIVE
8
Class
Ready for TAKS?
1. In the rectangular prism, AB ⫽ 6 cm,
1BC.
BC ⫽ 12 cm, and DC ⫽ __
3
3. If the edge of a cube is 10 inches and
the edge of a smaller cube is 8 inches,
what is the difference in the surface
areas of the two cubes?
D
A 600 in2
B 488 in2
C
C 384 in2
D 216 in2
A
B
4. A balloon for a parade is being sewn
from a special form of spandex. If the
balloon will be in the shape of a sphere
with a diameter of 15 feet, about how
much spandex is required to make the
balloon?
What is the volume of the prism?
A 288 cm3
B 215 cm3
C 144 cm3
F
D 24 cm3
177 ft2
G 707 ft2
2. The figure is a rectangular prism topped
by a pyramid. What is the approximate
volume of the figure?
H 1,767 ft2
J
2,827 ft2
5. Approximately how much grain can the
conical grain bin hold?
8
2m
6
2
F
4
5m
7 units3
G 20 units3
A 50 m3
H 112 units3
J
B 21 m3
240 units3
C 10 m3
D 5.4 m3
51
4/14/06 9:50:12 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
1. If 䉭ABC is similar to 䉭XYZ, which
proportion is NOT true?
4. There are two pentagons, ABCDE and
FGHIJ. If the ratios given are true, which
is the correct way to write the similarity
between the two pentagons?
BC ⫽ ___
AC
A ___
YZ
XZ
AC ⫽ ___
DE and ___
EB
AB ⫽ ___
___
AB ⫽ ___
XY
B ___
YZ
BC
IH
F
AC ⫽ ___
YZ
C ___
XZ
BC
FG
IJ
HG
ABCDE ⬃ FGHIJ
G ABCDE ⬃ HIJFG
H ABCDE ⬃ IGJFH
AC ⫽ ___
AB
D ___
XZ
XY
J
2. A rectangular prism is shown. If a
second prism is similar to the one
shown, which of the following could be
the dimensions of the second prism?
ABCDE ⬃ IHJFG
5. The two photos shown are similar
rectangles. The perimeter of the smaller
photo is 14 centimeters and its area is
10 square centimeters. If the perimeter
of the larger photo is 42 cm, what is the
area of the larger photo?
9 ft
3 ft
F
12 ft
1 ft by 3 ft by 4 ft
G 2 ft by 8 ft by 11 ft
A 3 cm2
H 6 in. by 18 in. by 22 in.
B 30 cm2
6 ft by 12 ft by 15 ft
C 38 cm2
J
D 90 cm2
3. Which of the following would prove
that quadrilateral ABCD is similar to
quadrilateral WXYZ ?
A The sum of the angles of both
quadrilaterals is 360°.
B Each angle in both quadrilaterals has
a measure of 90°.
C The ratio of AB to CD is the same as
the ratio of WX to YZ.
D None of these.
52
4/14/06 9:50:12 AM
Name
Date
OBJECTIVE
8
Class
Ready for TAKS?
_
_
4. Use the diagram to find the value of x if
both triangles are right triangles and the
top angles of the two triangles are equal.
1. If AB is parallel to CD in the diagram,
_
what is the approximate length of OD ?
C
A
5
6
B
O
8
x
7
6
8
40
D
30
A 6.7 units
F
B 7.0 units
G 32
C 9.0 units
H 38
D 9.3 units
J
53.3
_
_
F
_
5. BE is_
parallel to CD . The length of AB
is 4, CB is 16, and the perimeter of
triangle ABE is 20.
2. A triangle has a base of length 20 units
and a perimeter of 66 units. If a similar
triangle has a base of 15 units, what is
its perimeter?
A
49.5 units
G 51 units
B
H 56 units
J
61 units
3. Triangle ABC with vertices A(2, 3),
B(2, 6), and C(4, 6) is similar to triangle
DEF with vertices D(6, 9), E(6, 24), and
F. Which of the following could be the
coordinates of F ?
C
A 24 units
B 36 units
B (12, 18)
C (⫺6, ⫺24)
C 80 units
D (⫺4, ⫺18)
D 100 units
D
What is the perimeter of triangle ACD ?
A (⫺4, 24)
E
53
4/14/06 9:50:12 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
4. Which of the ratios is equivalent to
tan A?
1. Use the diagram to find the value of x.
A
6
5
2
4
x
A 6
C
B 8
C 9
兹 21
____
F
D 10
2
3
2
2
G ____
21
兹
2. Which theorem justifies the statement
that the two triangles shown are similar?
F
B
2
H __
5
4
5
__
2
J
5. Use a trigonometric ratio to find the
value of x in the triangle. (Round to the
nearest tenth.)
6
SSS
G SSA
H SAS
J
x
AAA
42°
3. Which set of three integers could be a
Pythagorean Triple?
5
A a ⫽ 3, b ⫽ 5, and c ⫽ 8
A 0.2
B a ⫽ 4, b ⫽ 5, and c ⫽ 8.6
B 3.3
C a ⫽ 8, b ⫽ 15, and c ⫽ 22
C 3.7
D a ⫽ 20, b ⫽ 48, and c ⫽ 52
D 4.5
54
4/14/06 9:50:13 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
4. The two cylinders shown are similar. The
lateral areas of the cylinders are 196
square centimeters and 324 square
centimeters.
1. Rebecca’s old rectangular suitcase is
12 inches wide, 20 inches long, and
6 inches tall. Her new suitcase has
dimensions that are double her old one.
By how much did the volume of her
suitcase increase when she bought the
new one?
A twice
B 4 times
C 6 times
D 8 times
The volume of the smaller cylinder is
686 cubic centimeters. What is the
volume of the larger cylinder?
2. The circumference of a circle is 3 times
the circumference of a smaller circle. If
the area of the larger circle is 1,350
square inches, what is the area of the
smaller circle?
F
50 in
F
G 882 cm3
2
H 1,134 cm3
2
G 150 in
J
2
H 450 in
J
814 cm3
1,458 cm3
5. A glass paperweight shaped like a
pyramid has a volume of 4 cubic
centimeters. What is the volume of a
similarly shaped paperweight if each
dimension is three times as large as the
smaller paperweight?
1,350 in2
3. The figures shown represent the faces of
two cubes. If Pete knows the volume of
the cube on the left how can he get the
volume of the cube on the right?
A 108 cm3
B 64 cm3
C 36 cm3
x
3x
D 12 cm3
A Multiply the volume by 3.
B Multiply the volume by 9.
C Multiply the volume by 27.
D Cube the volume.
55
4/14/06 9:50:13 AM
Name
OBJECTIVE
9
Date
Class
Ready for TAKS?
Benchmark Pre-Test (8.3)(B)
4. The circle graph shows the distribution of
the ages of 250 people at an art exhibit.
1. There are 218 seniors and 182 juniors at
a local high school. Only 65% of those
students signed up to go to the prom.
How many of the juniors and seniors did
NOT sign up to go to prom?
30%
Under 25
A 400
B 260
70%
Over 25
C 140
D 35
2. A cylindrical grain bin is being filled. The
height of the grain bin is 20 feet and the
diameter of its base is 10 feet. After the
first 10 minutes, the height of the grain in
the bin is 1 foot. At this rate, what will be
the volume of the grain in the bin after
one half hour?
Of the people under the age of 25, 20%
are younger than 16. How many people
at the art exhibit are younger than 16?
F
6
G 15
H 50
10⬘
J
75
5. The number of cars entering a car wash
between certain times is shown in the
bar graph. About what percent of the
total number of cars entered the park
after 4 PM?
20⬘
100
75 ft
Number of Cars
F
3
3
G 50␲ ft
H 75␲ ft3
J
300␲ ft3
3. Elena answered 82% of the questions on
her history test correctly. If she missed
9 questions, how many questions were
there on the test?
75
50
25
0
8AM to
Noon
12 to
4PM
4 to
8PM
8 to
Midnight
A 0%
A 18
B 25%
B 41
C 50%
C 50
D 75%
D 91
56
4/14/06 9:51:27 AM
Name
OBJECTIVE
9
Date
Class
Ready for TAKS?
Benchmark Pre-Test (8.11)(A)
1. A new toy store is giving away 20 model
airplanes: 9 are red, 6 are white, and
5 are blue. An airplane is selected at
random and given to a customer. If the
airplane is red, what is the probability
that the next airplane, selected at
random, is also red?
4. Each of the smaller squares inside the
larger square shown is the same size.
If the diagram represents a dart board,
what is the probability of hitting a shaded
square, assuming the board is hit?
8
A ___
20
8
B ___
19
9
C ___
20
D
F
9
___
G 0.52
19
H 0.56
2. If 2 balls are drawn simultaneously at
random from a box containing 5 red
balls, 3 white balls, and 4 blue balls,
what is the probability that both balls
are white?
F
J
J
0.92
5. A multiple-choice test has five choices
for each answer. There are twenty
questions. If a student guesses on
the first two questions, what is the
probability that the student will get both
questions correct?
1
___
11
1
G ___
16
H
0.48
1
A ___
25
1
___
22
1
B __
5
19
___
44
2
C __
5
3. At the end of a conference, 80 teachers
enter a prize drawing by placing their
name tags in a hat. After 6 name tags
have been selected and removed from
the hat, Mrs. Jones has not yet won
a prize. What is the probability that
Mrs. Jones will win the next prize?
16
D ___
25
A 0.0125
B 0.014
C 0.075
D 0.167
57
4/14/06 9:51:27 AM
Name
Date
OBJECTIVE
9
Ready for TAKS?
3. David bought 5 packs of yogurt covered
raisins and recorded the number of
orange raisins in each pack. Each pack
contains 40 raisins.
Jason conducted an experiment by rolling
a standard number cube 400 times. The
results of Jason’s experiment are shown in
the bar graph. Use the bar graph to answer
questions 1 and 2.
400 Tosses of a Number Cube
Number of Times Tossed
80
70
Class
75
75
65
60
70
63
52
50
40
Pack
Number of Orange
Yogurt Covered Raisins
1
11
2
7
3
8
4
13
5
9
30
According to David’s sample data,
what is the probability that a randomly
selected raisin from one of these packs
is orange if all the packs are poured out
together?
20
10
0
1
2
3
4
5
6
Digit
A 0.229
1. According to the data, what is the
experimental probability of rolling a 3 on
the next roll of the number cube?
A
B 0.240
C 0.275
3
____
D 0.833
400
4. The editor of a community newspaper
polled 100 residents of a neighborhood
to determine how they were going to
vote on the proposal to add a new
stoplight at a certain intersection. The
results of the poll are shown in the table.
1
B ___
75
3
C ___
75
3
D ___
16
2. What is the approximate difference
between the experimental probability
and the theoretical probability of rolling a
3 on the next roll?
F
H 0.153
0.159
F
45
H 216
Frequency
Yes
45
No
55
Based on these experimental results,
and assuming that all 480 residents
in the neighborhood vote, how many
people could be expected to vote “Yes”
for the new stoplight?
0.021
G 0.127
J
Vote
58
G 55
J
264
4/14/06 9:51:28 AM
Name
OBJECTIVE
9
Date
Class
Ready for TAKS?
1. During Eric’s first four months of
lifeguarding, he saved a total of 25
swimmers. His saves per month were 5,
4, 7, and 9. Which measure of the data
would be the most impressive to report
to his parents and friends?
4. Sandy’s scores on her first five chemistry
quizzes were recorded in the table.
Sandy’s Scores
Quiz 1
80
Quiz 2
82
A range
Quiz 3
88
B mean
Quiz 4
100
Quiz 5
98
C median
Which measure of the data would NOT
change if Sandy had actually scored two
points less on Quiz 1 and Quiz 4?
D mode
2. Debbie earned the following grades on
her philosophy papers: 86, 92, 86, and
89. Which measure of the data will give
her the highest overall score?
F
F
G mean
range
H median
G mean
J
H median
J
range
mode
5. A company that sells notebooks is
analyzing a frequency table to identify
the number of notebooks they sold last
year. Which measure of data describes
the most popular color of notebook sold?
mode
3. A set of data has 10 values, no two of
which are the same. If the smallest data
value is removed from the set, which of
the following statements MUST be true?
A mean
B median
A The range of the first data set is
larger than the range of the second
data set.
C mode
D range
B The mode of the first data set is
greater than the mode of the second
data set.
C The medians of the two data sets are
the same.
D The mean of the first data set is less
than the mean of the second data
set.
59
4/14/06 9:51:28 AM
Name
Date
OBJECTIVE
9
Ready for TAKS?
Benchmark Pre-Test (8.12)(C)
1. A travel agency surveyed visitors to
Virginia to find out how many historical
sites they visited. The survey results are
shown in the bar graph.
4. Margie gathered information about the
ages of people living in her community.
She used the information to create the
histogram and the circle graph shown.
The histogram accurately reflects the
information gathered, but two sections
of the circle graph were switched.
Virginia Survey Results
70
Frequency
Class
60
50
Age Groups
40
30
Under 20
18%
20
20–39
25%
10
0
0
1
2
3
Numbers of Sites Visited
80 and
Over
12%
4 or
more
60–79
15%
Approximately how many people visited
fewer than 2 historical sites?
B 100
C 170
D 230
Age Group Survey Results
30
Frequency
A 70
2. Of the 800 people at Shopmart,
200 people are alone, 318 people are
with a friend, 160 are with a spouse, and
the rest are with a family member who’s
not a spouse. If a circle graph were
constructed, which of the following is
the approximate percentage needed to
represent the category for the number of
people with a family member who’s not a
spouse?
F
5%
H 25%
C 78
D 80
15
10
5
F
Under
20
20–39
40–59
60–79
80–99
Age Group
60–79 and 80 and Over
G under 20 and 80 and Over
H under 20 and 60–79
3. The students at a local school chose
among 3 candidates for Best Dressed.
A total of 240 students voted and
Maylene received 27.5% of the votes,
and she came in last. If a bar graph
is constructed, and the vertical axis
represents the number of votes received,
which of the following could NOT be the
height of the bar for one of the other
candidates?
B 75
20
According to the information in the
histogram, which two sections of the
circle graph were switched?
122%
A 60
25
0
G 15%
J
40–59
30%
J
60
under 20 and 20–39
4/14/06 9:51:28 AM
Name
Date
OBJECTIVE
9
Class
Ready for TAKS?
Use the circle graph to answer questions
1 and 2.
Use the bar graph to answer questions 3
and 4.
The circle graph shows the percent of
sales for each color of a particular model of
refrigerator sold at an appliance store last
month.
The bar graph shows the number of students
enrolled in different math classes at a local
high school.
Student Enrollment: Mathematics
Black
10%
Pre-Calc
Cream
15%
Algebra 2
Stainless
Steel
40%
Geometry
White
35%
Algebra 1
0
100
200
300
400
Number of Students
Refrigerator Sales by Color
3. Which statement is true?
1. Which statement is true?
A The color of refrigerator sold the
least was cream.
A There are more students enrolled in
Algebra 1 than in any other class at
the high school.
B The color of refrigerator sold the
most was white.
B Pre-Calculus has the greatest
number of students enrolled.
C More than three times as many white
refrigerators were sold as cream.
C There are more than twice as many
students enrolled in Algebra 1 as
there are in Algebra 2.
D Four times as many stainless steel
refrigerators were sold as black.
D There are slightly more than half
as many students enrolled in PreCalculus as there are in Algebra 2.
2. Which is a reasonable conclusion from
the information provided in the graph?
F
Most people don’t believe black
refrigerators will keep their food cold.
F
G Most people prefer the appearance
of stainless steel refrigerators.
G Students cannot take Pre-Calculus
unless they get a C or better in
Algebra 2.
H Sales of black refrigerators are
declining.
J
None of these.
H The school needs larger rooms for
the Algebra 1 classes because the
class size is bigger.
J
Almost all of the students in the
school are enrolled in Algebra 1.
61
More teachers are needed for
Algebra 1 than for Algebra 2.
4/14/06 9:51:28 AM
Name
OBJECTIVE
10
Date
Class
Ready for TAKS?
1. A pickle company reported that the
average price of cucumbers in the U.S.
increased by 2% per year from 1979
to 1984. What additional information is
needed to calculate the average price of
cucumbers in 1984?
Use the Venn diagram to answer
questions 4 and 5.
The Venn diagram represents all
700 students at a school. The circle on the
left represents the students that have taken
Mr. White for English, and the circle on the
right represents the students that have taken
Ms. Red for math.
A the amount of cucumbers sold
between 1979 and 1984
B the average price of cucumbers in
1985
Mr. White
Ms. Red
C the difference in prices of cucumbers
between 1979 and 1984
Z
D the average price of cucumbers
in1979
2. Ken’s father’s age is 5 years less than
three times Ken’s. If Ken is 15 years
old, which equation can be used to
determine his father’s age?
F
X
W
4. What does the section labeled with an X
represent?
3(15) ⫹ 5 ⫽ x
G 3(15) ⫺ 5 ⫽ x
F
H 3(15 ⫺ 5) ⫽ x
J
Y
3(15) ⫽ x ⫺ 5
Students who have taken Ms. Red
for math but have not taken Mr. White
for English.
G Students who have taken both
Ms. Red for math and Mr. White for
English.
3. Erin bought a pair of shoes for 60% off
the original price. If the sale price is x,
which equation could Erin use to find the
original price, p, of the shoes?
H Students who have not taken
Mr. White for English.
3
A p ⫽ x ⫺ __
5
J
3x
B p ⫽ x ⫹ __
5
All students who have taken Ms. Red
for math.
5. Which of the labeled sections represents
the students who have NOT taken either
Mr. White for English or Ms. Red for
math?
3x
C p ⫽ x ⫺ __
5
3p ⫽ x
D p ⫺ __
5
A W
B X
C Y
D Z
62
4/14/06 9:51:37 AM
Name
OBJECTIVE
10
Date
Ready for TAKS?
4. The value of a $250,000 home in a
certain area increases by approximately
$12,500 per year. After how many years
will the home be worth approximately
$300,000?
1. A full cylindrical hot tub with a height
of 4 feet and a radius of 3 feet is
being emptied at a rate of 5 ft3 every
2 minutes. How many minutes would it
take to completely empty the tub at that
rate?
F
A 2.5 min
2 yrs
G 3 yrs
B 23 min
H 4 yrs
C 45 min
J
D 113 min
5 yrs
5. A farmer is plowing the rectangular
field shown. If the farmer can plow
approximately 500 square feet per
minute, about how many hours will it
take him to plow the whole field?
2. Jamie bought a comforter that was on
sale for 30% off and a bedspread for
20% off. The original cost of each was
$150.00. If the tax rate is 6.25% and
Jamie gives the salesclerk five $50.00
bills, how much change should she get
back?
F
Class
700 feet
$10.94
400 feet
G $25.00
H $90.63
J
$130.37
3. The trapezoid shows the shape of
Miguel’s yard. Miguel would like to put
grass seed on the entire yard. What
does Miguel FIRST need to find in order
to calculate the number of bags of seed
to buy?
A 9 hr
B 10 hr
C 11 hr
D 12 hr
70 ft
35 ft
40 ft
50 ft
A the cost of one bag of seed
B the perimeter of the yard
C the area of the yard
D the volume of the yard
63
4/14/06 9:51:38 AM
Name
OBJECTIVE
10
Date
Ready for TAKS?
Benchmark Pre-Test (8.14)(C)
4. The volume of a large box is 9,000 ft3.
If the height of the box is 15 ft, which
of the following could be the length and
width of the box?
1. A car dealership has 20 rows of cars.
The first row has 25 cars; the second
row has 30 cars; and the third row has
35 cars. If this pattern continues, how
many cars will there be in the last row?
F
A 120 cars
10 ft by 90 ft
G 20 ft by 45 ft
B 125 cars
H 20 ft by 30 ft
C 130 cars
J
D 135 cars
30 ft by 30 ft
5. The point (2, 3) is reflected across the
x-axis and then across the y-axis. The
resulting point is (⫺2, ⫺3). The new
point is again reflected across the x-axis
and then the y-axis. The resulting point
is (2, 3). If this pattern continues, what
will be the resulting x-coordinate for the
point after three pairs of reflections?
2. The bottom of a pool is a circle that
covers 300 square feet. What is the best
first step to determine the length of the
pool’s diameter?
F
Class
Square 300.
G Take the square root of 300.
H Divide 300 by 2.
J
y
Divide 300 by .
10
3. Which of the equations could represent
the step before Step 2 in the solution to
an algebra problem?
8
6
4
Step 1.
2
Step 2. 18x ⫺ 48 ⫹ 2 ⫽ ⫺10
–10 –8
Step 3. 18x ⫺ 46 ⫽ ⫺10
–6
–4
–2
2
–2
4
6
8
10
x
–4
Step 4. 18x ⫽ 36
–6
Step 5. x ⫽ 2
–8
A 6(3x) ⫺ 8 ⫹ 2 ⫽ ⫺10
–10
B 3(6x ⫺ 8) ⫹ 2 ⫽ ⫺10
C 6(3x ⫺ 8) ⫹ 2 ⫽ ⫺10
A ⫺3
D 6(3x) ⫺ 8 ⫹ 40 ⫹ 2 ⫽ ⫺10
B ⫺2
C 2
D 3
64
4/14/06 9:51:38 AM
Name
OBJECTIVE
10
Date
Class
Ready for TAKS?
4. A newspaper editor has been given four
articles to print in the paper. The circle
graph shown belongs to one of the
articles. Which list of data goes with the
circle graph?
Use the figure to answer questions 1
and 2.
1. If the figure is an ice cream cone, the
amount of dough needed to make the
cone best represents the cone’s—
A lateral area
B circumference
C radius
F
D volume
2. If the figure is a drinking cup, the amount
of water that the cup can hold best
represents the cup’s—
F
circumference
G lateral area
H surface area
G The election results were as follows:
40% for Jones, 24% for Mack, 22%
for Vito, and 14% for Ellis.
volume
J
3. Which transformation describes how to
get from point A to point B ?
H The school budget is allocated
accordingly: 40% for building, 35%
for salaries, 20% for books, 5% for
other.
y
10
8
6
J
4
A
2
–10 –8 –6 –4 –2
–2
–4
2
4
6
8
10
x
B
–6
–8
–10
B a 270° clockwise rotation
C a reflection over the line with
equation y ⫽ x
D a reflection across the x-axis and
then the y-axis
The town census reported the
following for the ages of residents:
4% were over 75 years old, 11%
were between 50 and 75 years old,
60% were between 25 and 50 years
old, and 25% under 25 years of age.
5. If the product of the quantities 8 ft,
ft, and 5 s is found, what units of
17 s__
measure will be in the answer?
A a 90° clockwise rotation
A survey of citizens had the following
results: 23% supported totally
financing the new stadium, 10%
supported partially financing the
new stadium, 34% did not support
financing the stadium, and 33% were
undecided.
65
ft
A s__
B ft ⴢ s
C ft2
D There will be
no units of
measure.
4/14/06 9:51:38 AM
Name
Date
OBJECTIVE
10
Class
Ready for TAKS?
3. What is the missing term in the pattern?
1. Use the examples and non-examples
provided to determine which of the
following is a tergon.
Tergons
4 2
2, ____
4 , ____
2 , ______, ____
___
xy
x2y3
x 4y 7 x 5y 9
3
A ____
3 5
x y
Not Tergons
3
B ____
x 3y 5
22
C ____
x 3y 5
22
D ____
x 4y 4
4. For which of the following sets of points
is a linear model NOT reasonable?
A
F
B
{(3, ⫺3), (4, ⫺2), (5, ⫺1), (6, 0)}
G {(⫺5, 0), (⫺1, 2), (3, 4), (7, 6)}
H {(⫺2, 2), (1, 0), (4, ⫺2), (7, ⫺4)}
C
J
D
5. Mabel made the conjecture that the
domain of the function f (x ) ⫽ x is all
real numbers. Which of the following
values of x is a counterexample to
Mabel’s conjecture?
2. The table lists several powers of the
number 3.
Powers of 3
Resulting Value
3
1
3
3
2
9
3
3
27
3
4
81
3
5
243
3
6
729
3
7
2,187
3
8
6,561
{(6, 1), (4, 4), (0, 2), (5, 8)}
A (⫺2)2
B 2
1
C __
2
D ⫺2
Given that the digit in the ones place will
continue to repeat in the pattern above,
what will be the digit in the ones place in
96?
F
3
H 7
G 9
J
1
66
4/14/06 9:51:39 AM
Name
OBJECTIVE
10
Date
Class
Ready for TAKS?
1. If the variables x and y both represent
real numbers, which statement is NOT
true?
4. Which statement about the quadrilaterals
shown is true?
B
A If x ⬎ y, then x ⬎ y .
C
B If x ⬎ y, then ⫺y ⬎ ⫺x.
C If x ⬎ y, then x 3 ⬎ y 3.
D If x ⬎ y, then x 2 could be equal to
y 2.
2. If the variables x and y both represent
negative real numbers and are related
so that x 2 ⬎ y 2, which statement must
be true?
F
D
E
F
x is greater than y
G y is greater than x
F
2
H y is a positive integer
J
A
H
G
_
_
If AB is perpendicular to AD , then
exactly one of the quadrilaterals is a
rectangle.
_
_ _
_ _
_
EF_
, CD FG , DA GH ,
G If BC_
and AB HE , then both
quadrilaterals have the same area.
⫺1 ⬍ 1
___
x
3. Which of the following statements is true
for triangle ABC ?
H If ⬔A ⬔C, then both quadrilaterals
are rectangles.
B
J
If quadrilateral ABCD is a
parallelogram and the measure of
⬔C ⫽ 90°, then both quadrilaterals
are rectangles.
true?
A
A All rectangles are squares.
C
B All quadrilaterals are rectangles.
A If ⬔A ⬔B, then the triangle is an
equilateral triangle.
C All squares are rhombuses.
D All trapezoids are parallelograms.
B If the measure of ⬔C is twice the
measures of both ⬔A and ⬔B, then
triangle ABC is a right triangle.
C If ⬔A ⬔B, then the triangle must
be a right triangle.
_
_
D If ⬔A ⬔B, then AB BC .
67
4/14/06 9:51:39 AM
Name
OBJECTIVE
1
Date
Class
Ready for TAKS?
Benchmark Post-Test (A.1)(A)
1. The total amount c charged by a storage
warehouse for one month of rent is given
by the equation c 75 1.5s , where
s represents the number of square feet
rented. Which of the following is the best
interpretation of what the independent
variable represents?
4. When a weight is attached to the spring
shown, the length of the spring is
determined by the equation given.
ᐉ = 0.4g 12
A the number of square feet rented
B the total amount charged by the
storage warehouse
C the number of months for which the
storage is kept
In this equation, what might the
independent variable represent?
D a $75 flat fee charged by the
warehouse to rent space
F
2. A furniture store marks its furniture up
125% from the wholesale price. Which
statement best represents the functional
relationship between the retail price (the
price at which the store sells the item)
and the wholesale price at this store?
F
G the original length of the spring
H the maximum length of the spring
J
the length of the spring when g
grams of weight are attached
5. The graph shows a function in which
the variable y is the dependent variable.
Which statement is the best description
of the functional relation between x
and y ?
The wholesale price and the retail
price are independent of each other.
G The wholesale price is dependent on
the retail price.
H The retail price is dependent on the
wholesale price.
J
the number of grams of weight
attached to the spring
y
It is not possible to determine the
relationship without both prices.
3. Which of the following does not
represent a relation in which the first
quantity depends on the second?
x
A the volume of a sphere; the radius of
the sphere
A As x increases, y decreases at a
variable rate.
B the length of the base of a rectangle;
the perimeter of the rectangle
B As x increases, y increases at a
constant rate.
C the surface area of a cube; the
length of the side of the cube
C As x increases, y increases at a
variable rate.
D the circumference of a circle; the
radius of the circle
D As x increases, y sometimes
decreases and sometimes increases.
68
4/14/06 9:50:39 AM
Name
OBJECTIVE
1
Date
Class
Ready for TAKS?
Benchmark Post-Test (A.1)(B)
3. Which function could be used to
describe the data set shown?
1. Which equation best describes the
relationship between x and y shown in
the table?
{(2, 8), (1, 1), (1, 1), (2, 8)}
A y 4x
x
y
1
4
B y 2(x )2
2
16
C y x 3
5
100
D y (x )3
10
400
4. Which function represents the data set
shown?
A y 4x
Domain
Range
25
16
9
10
8
6
B x 4y
C y 4x 2
D x 4y 2
between two variables, t and h. Which
function represents this relationship?
F
x 2.5y
G x y 15
H y 2
x
t
J
7
y 2x
5. The table shows the number of calories,
c, in an item of food that has f grams of
fat in it. Which equation best describes
the relationship between c and f ?
–5
h
Calories, c
Grams of fat, f
9
1
18
2
5
27
3
7h
H t __
5
36
4
F
7t
h __
5
G
7h 7
t __
J
A c 9f
7h 7
t __
5
B f 9c
C c 9f 2
D f 9c 2
69
4/14/06 9:50:39 AM
Name
OBJECTIVE
1
Date
Ready for TAKS?
Benchmark Post-Test (A.1)(C)
3. A saline solution is described by the
percent of the solution that is salt. A
chemist mixed 20 grams of a 35% saline
solution with x grams of a 20% saline
solution. Which equation describes
S, the amount of salt in the chemist’s
mixture?
1. If Terry’s CarMart doesn’t have the
color car that a customer wants, they
will go get one from another dealership.
They charge $50 to send a driver and
50 cents for each mile the driver has
to travel. The chart shows the cost of
several dealership exchanges.
Number of
miles, m
Cost, c
A S 20(0.35) 0.2x
10
$55
B S 20(0.35) 20x
20
$60
50
$75
100
$100
C S (20 x)(0.55)
4. Mr. Randall invested $7,500 in two
money market accounts. He put part of
the money into an account that earns
4.25% interest per year and the rest
into an account that earns 4.5% per
year. Which equation describes i, the
total amount of interest earned by both
accounts for one year?
A c 50 0.50
B c 50 0.50m
C c 50m 0.50
F
D c 50m 0.50m
H i 3750(0.0425) 3750(0.045)
J
G 36w 10w 2
J
i 7500(0.0425x 0.045x)
5. The Academic Excellence Scholarship
at a certain college requires that eligible
students have at least a B grade point
average, which is equivalent to a GPA
of 3.3. Since the highest GPA that a
student can earn is 4.0, this means the
student’s average must be at least 3.3
but no more than 4.0. If z represents
a student’s GPA, which inequality best
expresses this requirement?
If w represents the width of the pool,
which expression best represents the
area of the portion of the pool that will
be cleaned?
H 36w 5w 2
i 0.0875(7500)
G i 0.0425x 0.045(7500 x)
2. A country club is having the bottom and
sides of their pool pressure cleaned. The
length of the pool is 5 times the width
of the pool and the depth of the pool is
3 feet everywhere. The pool is shown.
21w 10w 2
0.20
__________
D S (20 x) 0.35
2
Which equation best represents the
relationship between the number of
miles driven, m, and the total cost, c, to
go get a vehicle?
F
Class
A 4.0 z 3.3
B 3.3 z 4.0
C 3.3 z 4.0
D 3.3 z 4.0
5(5w 3 w)
70
4/14/06 9:50:40 AM
Name
OBJECTIVE
1
Date
Ready for TAKS?
Benchmark Post-Test (A.1)(D)
3. Which of the following equations does
NOT represent a function?
1. The function
_
f (x ) {(1, 1), (4, 0.5), (9, 0.3), (16, 0.25)}
can be represented in a variety of
different ways. Which of the following is
NOT an accurate representation of f (x)?
A y
1
__
x2
A y x 4
B x2 y 6
with domain {1, 4, 9, 16}
3
x2
________
C y 6x
x
_
B
C
1 with range {0.25, 0.3, 0.5, 1}
x __
y2
D y x 2(x 6)
_
x
0.25
0.3
0.5
1
y
16
9
4
1
D Domain
4. Which of the following best describes the
graph of the inequality 3x y 5 ?
F
Range
1
4
9
16
1
0.5
0.25
0.3
H the area that is shaded above the
dotted line y 3x 5
J
6
4
2
–4
–2
2
–2
4
6
x
A f (x) {(3, 6), (1, 2), (1, 2)}
B y 2x for 5 x 3
–4
–6
C
4x 3y 12
G 4x 3y 12
x
3
1
1
y
6
2
2
y
D
H 3x 4y 12
J
the area that is shaded above the
solid line y 3x 5
5. A function is defined as follows: x is an
odd integer between, but not including,
5 and 3, and y is always twice x.
Which of the following is NOT a correct
representation of the function?
y
–6
the area that is shaded below the
dotted line y 3x 5
G the area that is shaded below the
solid line y 3x 5
2. Which inequality best describes the
graph shown?
F
Class
6
3x 4y 12
4
2
–6
–4
–2
2
4
6
x
–2
–4
–6
71
4/14/06 9:50:40 AM
Name
OBJECTIVE
1
Date
Ready for TAKS?
Benchmark Post-Test (A.1)(E)
4. The net profit, p, that a musical clock
company makes from producing c
clocks is represented by the equation
p 4.5c 13,500. Which is the best
interpretation of this information?
1. Which of the following is true for the
parabola y 1 (x 2)2?
A The vertex is (2, 1).
B The axis of symmetry is x 2.
C The minimum value is at (0, 3).
F
D The maximum value is at (0, 3).
H The company needs to sell more than
3,000 clocks before it makes a profit.
J
Speed
The company has sold more than
13,500 shower heads.
5. A ball is thrown straight up from a flat
roof of a building that is 240 feet tall with
an initial velocity of 32 feet per second.
If there is no air resistance, the height
of the ball at any time t is given by the
function h(t ) 16t 2 32t 240. The
graph of the function is shown.
Time
Which of the following might describe
the same jog?
y
Joe jogs along a flat road. He then
jogs up a hill at the same pace.
260
G Joe jogs at a steady pace along a
flat road . He then jogs up a hill and
his speed decreases.
Height (h)
220
H Joe jogs at a steady pace up a hill.
He then runs down the hill and his
speed increases.
J
The company’s profit is always at
least $13,500.
G The company’s profit last year was
$13,500.
between speed and time during Joe’s
evening jog.
F
Class
100
20
1
2
3
4
5
x
Time (t)
3. If x 1, which is always a correct
conclusion about the quantities in the
function y x1?
Which statement is true about h(t )?
A After one second, the ball fell at a
constant rate.
A The variable y is always less than
the variable x.
B The height of the ball decreased for
all values of t.
B The variable y is always greater than
the variable x.
C After one second, the height of the
D After five seconds, the ball hit the
ground.
D As x increases, y approaches 0.
140
60
Joe jogs along a flat road and then
down a hill.
180
72
4/14/06 9:50:41 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
1. Which of the functions is NOT a linear
function?
3. The graph of which function would pass
through the points (9, 3) and (16, 4)?
A x ⫽ 2y ⫹ 1
A y ⫽ 3x
B (x ⫹ 5)(y ⫺ 3) ⫽ 2
1x
B y ⫽ __
3
C x⫹y⫽6
C y ⫽ x2
1x ⫹ 4y ⫽ 3
D __
2
D y ⫽ x3
1
__
1
__
4. Which statement best describes the
y
graph of x__ ⫽ ⫺1?
F a line with a slope of ⫺1 and a hole
at x ⫽ 0
2. Which is the best representation of the
function y ⫽ ⫺x2 ⫺ 3?
y
F
G a vertical line that passes through
the point (⫺1, 2)
x
–3
H a parabola that passes through
(0, ⫺1)
J
y
G
none of the above
5. Which equation is the parent function of
the graph shown?
y
x
–3
x
y
H
x
A y ⫽ x
–3
J
B y⫽x
C y ⫽ x2
y
D y⫽
x
x
73
4/14/06 9:50:51 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
graphed?
given?
f (x) ⫽ 2⫺ x
y
A x⬍2
B xⱕ2
C x⬎2
D xⱖ2
5
x
2. Identify the range of the function given.
{( ⫺2, 3), ( ⫺ 1, 5), (3, 4), (5, ⫺ 4)}
F
–5
{⫺2, ⫺1, 3, 5}
G {⫺4, 3, 4, 5}
H {⫺4, ⫺2, ⫺1, 3, 4, 5}
J
F
all real numbers
xⱕ0
G ⫺3 ⱕ x ⱕ 0
3. What is a reasonable range for this
function?
H x ⱖ ⫺3
J
all real numbers
5. What is the range, written in interval
notation, of the function graphed?
y
1
1
5
x
–5
A ⫺2 ⬍ y ⬍ 1
B ⫺2 ⬍ y ⬍ 2
A [⫺4, 2]
C ⫺2 ⬍ y ⱕ 2
B (⫺2, 4)
D ⫺1 ⬍ y ⱕ 2
C [⫺2, 4)
D (2, 2)
74
4/14/06 9:50:51 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
1. The graph shows the decrease in value
of a plasma TV over a period of 24
months.
H The bond only lost value between
months 4 and 6.
J
y
Value ($)
2000
The bond hit its lowest value at
month 4.
A quarterback throws a football to a wide
receiver. The points in the figure show the
height of the football, in feet, above the
ground in terms of its distance, in feet, from
the quarterback.
1600
1200
800
400
4
8
12
16
20
24
(35, 14)
x
Time (in months)
What is a reasonable conclusion about
the value of this TV during the time
period shown on the graph?
Height
(ft)
7
A It depreciated $500 every 12 months.
(70, 7)
B It depreciated $500 every 6 months.
Distance from
Quarterback (ft)
C Its value at 24 months was half its
value at 6 months.
D Its value at 12 months was twice its
value at 24 months.
Use the diagram above to answer
questions 3 and 4.
2. The graph shows the value, in dollars,
of a certain E-bond during a period of
several months.
3. Which of the following is a reasonable
conclusion?
A The height of the ball when it leaves
the quarterback’s hand is the same
as the height of the ball when the
receiver catches it.
B The maximum height of the ball is
35 feet.
1
2
3
4
5
6
C The ball travels 7 feet from the
quarterback.
7
Which is a reasonable statement about
the value of the bond during this time
period?
F
D At its maximum height, the ball is 5
times as high as its original height.
4. What is the approximate height of the
football, in feet, when the wide receiver
catches it?
The bond lost value for exactly three
months and then gained value.
G The bond experienced its most rapid
decrease in price between months 1
and 2.
F
70
G 35
75
H 14
J
7
4/14/06 9:50:52 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
1. The scatter plot shows the number of
college students who have purchased a
laptop computer since 1985.
Use the scatter plot to answer questions
3 and 4.
Sports Car Acceleration
70
Speed (mph)
60
Laptop
Purchases
by College
Students
50
40
30
20
10
0
0.5
A The number of students purchasing
a laptop continues to grow rapidly.
B Fewer and fewer students are
purchasing laptops.
A 80 mph
D No conclusion can be drawn
because there is no pattern.
C 90 mph
250
400
300
500
350
600
D 100 mph
4. Which statement accurately describes
the relationship between speed and
time?
F
$325
G $350
As the time increases by 0.5
seconds, the speed triples.
G As the time increases by 0.5
seconds, the speed doubles.
H The speed consistently increases by
10 mph per half second.
J
Use the data to predict the retail price of
a microwave with a wholesale price of
$225.
F
3.0
B 85 mph
2. The table shows the retail price
of microwave ovens based on the
wholesale price.
300
2.5
3. Predict the approximate speed that the
same car can reach in 4 seconds.
C The number of students purchasing
laptops appears to have leveled off.
200
2.0
The scatter plot shows the relationship
between the speed and the number of
seconds that a certain sports car takes to
accelerate from 0 mph to that speed. The
plot also shows the line of best fit for the
data.
What conclusion can be drawn about the
number of college students who have
purchased a laptop since 1985?
Retail ($)
1.5
Time (seconds)
Years Since 1985
Wholesale ($)
1.0
The time does not affect the speed.
H $375
J
$425
76
4/14/06 9:50:52 AM
Name
OBJECTIVE
2
Date
Ready for TAKS?
4. A cook needs to prepare 200 plates
of food in an hour for a banquet. If he
prepares 3 plates per minute for the first
m minutes, which equation shows the
number of plates per minute, p, he must
prepare for the remaining minutes to
finish on time?
1. Sue gave 5% of her regular take-home
pay last week to charity. If she normally
takes home p dollars, which of the
following represents the amount of
money she took home last week?
A p ⫺ 0.05p
B p ⫺ 0.5p
p ⫽ 200 ⫺ 3m
C p ⫺ 0.05
F
D p ⫺ 0.5
⫺ 3m
_________
G p ⫽ 200
3
2. Let m represent the average speed, in
miles per hour that Ray ran in a race. Let
f(t) represent the distance in miles Ray
ran after t hours. The function f (t) is best
represented by
F
m⫹t
⫺ 3m
_________
H p ⫽ 200
60 ⫺ m
J
Number of
Workers
Number of
Toy Cars
3
48
5
80
10
160
50
800
x⫹1
2y
2
3x ⫹ y
5x ⫹ __
3y
A A ⫽ __
6
4
2x2 ⫹ __
2xy ⫹ __
1y2
B A ⫽ __
3
3
2
Which equation can be used to model
this relationship?
A c ⫽ 48w
B c ⫽ 48 ⫹ w
C c ⫽ 16w
16
D c ⫽ ___
w
⫺ 3m
_________
p ⫽ 200
3m
5. Which equation represents the area, A,
of the rectangle shown?
H mt
t
m
__
J m
G __
t
3. The table shows the number of toy cars,
c, that w workers can assemble in one
day.
Class
5x ⫹ __
3y
C A ⫽ __
3
2
10x ⫹ 3y
D A ⫽ ___
3
77
4/14/06 9:50:52 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
4. Eric wants to write an expression that
will always produce an odd integer.
Which of the following will always
produce an odd integer for any given
integer, n?
1. What is the sixth term in this pattern?
3
5
7
x , ___
x , ...
x , ___
x, ___
2y2 3y4 4y6
x9
A ___
5y8
n⫹3
x11
B ____
6y12
F
x11
C ____
6y10
H n2 ⫹ 3
2
G 2n ⫹ 4n ⫹ 3
J
x13
D ____
7y12
3n ⫹ 1
5. The figures show a pattern that relates
the figure number, f, and the number
of blocks, b. Which equation relates the
figure number to the number of blocks?
x- and y-coordinates in the coordinate
pairs given?
Figure 1
{(1, 7), (2, 13), (3, 23), (4, 37)}
F
2
y ⫽ 2x ⫹ 5
G y ⫽ 4x ⫹ 3
Figure 2
2
H y⫽x ⫹6
J
y ⫽ 7x2
terms in the following sequence and
their position, n, in the sequence?
Figure 3
4, 7, 10, 13, …
A b ⫽ 3(f ⫺ 1) ⫹ 1
A 3n
B b⫽f
B n⫹3
C b ⫽ 3f
C 3n ⫹ 1
D b ⫽ f2
D 3n2 ⫹ 1
78
4/14/06 9:50:53 AM
Name
OBJECTIVE
2
Date
Ready for TAKS?
2
⫺ 5x ⫺ 8
1. If f (x) ⫽ x__________
, what is f(⫺1)?
x3
A ⫺14
4. Solve the equation y ⫽ ax ⫺ b for b.
F
B 1
D 16
H b ⫽ y ⫺ ax
2. What is the missing value in the function
table?
x
f(x) ⴝ 7 ⴚ 2x
⫺4
⫺25
⫺3
⫺11
0
7
?
⫺1
J
b ⫽ ax ⫺ y
2
5. Three times a number is 5 more than
twice the same number. The algebraic
equation 3x ⫽ 5 ⫹ 2x represents this
situation. Use the equation to find the
number.
A 5
B 1
3
C 0
G 1
D ⫺5
H ⫺1
J
y
___
b ⫽ ax
y
__
G b⫽a
⫹x
C 2
F
Class
6. The rectangle shown has an area of
2x2 ⫹ 11x ⫺ 21.
⫺2
3. What is the perimeter, in simplest form,
of the regular octagon?
x⫹7
Which expression represents the length
of the rectangle?
F
x 2 ⫹ 4x
x⫹3
G x⫺3
2
A x ⫹ 4x ⫹ 32x
H 2x ⫺ 3
2
B 8x ⫹ 32x
J
2
C 4x ⫹ 16x
2x ⫹ 3
D (x2 ⫹ 4x)8
79
4/14/06 9:50:53 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
5. What is the perimeter of the
quadrilateral?
1. Which real number property is illustrated
2
2
by the equation 2x ⫹ (7x ⫺ 7x ) ⫽ 2x?
A the Associative Property of Addition
x2
B the Commutative Property of
Addition
2x 2 ⫹ 5
C the Distributive Property
D the Additive Identity Property of 0
2x ⫹ 4x 2
(4 ⫺ 3x)(2x) ⫺ (5 ⫺ x)(2 ⫹ 3x)?
F
x⫺3
⫺3x ⫺ 3
G 22x7 ⫺ 10
H ⫺3x2 ⫺ 5x ⫺ 10
J
A 7x6 ⫹ 2x2 ⫹ 2
⫺9x2 ⫹ 21x ⫺ 10
B 7x2 ⫹ 3x ⫹ 2
6x ⫺ 2 ___
21x ⫹ __
7 ?
__
5
10
2
7
A ⫺3x ⫹ __
2
C 9x6 ⫹ 2
D 10x8 ⫹ 2
6. The table shows the factored form and
the simplified form for several products.
26x ⫺ 7
B ___
5
Factored Form
(x ⫹ 5)
C ⫺3x ⫺ 7
7
D ⫺3x ⫹ __
2
2
2
⫺12x y ⫺ 6xy ⫹ x ⫺ 2xy ⫹ 9x2y ⫹ 5x?
F
2
x2 ⫺ 6x ⫺ 9
(x ⫹ 3)(x ⫺ 2)
x2 ⫺ 6
(3x ⫹ 1)(3x ⫺ 1)
9x2 ⫺ 1
Which product is correctly simplified?
⫺3x4y ⫺ 8x2y2 ⫹ 4x2
(x ⫹ 5)2
F
H ⫺3x2y ⫺ 8xy ⫺ 4x
G (x ⫹ 3)(x ⫺ 3)
⫺3x2y ⫺ 8xy ⫹ 6x
H (x ⫹ 3)(x ⫺ 2)
2
J
x2 ⫹ 25
(x ⫹ 3)(x ⫺ 3)
G ⫺3x y ⫺ 8xy ⫹ 4x
J
Simplified Form
80
(3x ⫹ 1)(3x ⫺ 1)
4/14/06 9:50:53 AM
Name
OBJECTIVE
2
Date
Class
Ready for TAKS?
1. Which function notation would
4. The graph of a function is shown.
2
⫹ 7?
quadratic equation y ⫽ x______
3
y
8
2
A f (x) ⫽ 3x ⫹ 7
6
4
2
B f(x) ⫽ 3(x ⫹ 7)
2
–8
C f(x) ⫽ 3x ⫹ 7
–6
–4
–2
x
Identify the function.
F
2
H y ⫽ ⫺(8x ⫹ 3)
y ⫽ ⫺8(x ⫹ 3)
2
x
⫺1
H f (x) ⫽ x ⫺ 1
J
x
f (x)
⫺1
⫺4
0
1
1
4
2
5
f (x) ⫽ x ⫹ 1
5. A biology class monitored the growth
pattern of a weed for several weeks. The
initial height of the weed was 1.2 meters
and the weed grew 0.3 meters each
week. The results can be represented
by the function f(x) ⫽ 1.2 ⫹ 0.3w, where
w is the number of weeks that passed.
Which equation would represent the
height, h, of the weed after w weeks
have passed?
A h ⫽ 0.3(1.2 ⫹ w)
Which equation represents the same
relationship?
B h ⫽ 1.2 ⫹ 0.3w
A y ⫽ 2 ⫹ ⫺x ⫹ 5
0.3w
C h ⫽ ____
1.2
B y ⫽ 5 ⫺ (x ⫺ 2)2
C y ⫽ 5 ⫺ (x2 ⫹ 4)
D h ⫽ 1.2(1 ⫹ 0.3w)
D y ⫽ 5 ⫺ (x2 ⫺ 4)
f (x) ⫽ x ⫺ 1
G f (x) ⫽
3. The table shows several values
generated by the function
2
f (x) ⫽ 5 ⫺ (x ⫺ 2) .
8
–8
y ⫽ ⫺8x ⫹ 3
2
J
6
–6
2. Which quadratic equation would
2
function f (x) ⫽ ⫺8(x ⫹ 3) ?
G y ⫽ 8(x ⫹ 3)
4
–4
2
⫹7
D f (x) ⫽ x______
3
F
2
–2
81
4/14/06 9:50:54 AM
Name
OBJECTIVE
3
Date
Class
Ready for TAKS?
1. Which of the following is NOT a linear
equation?
3. Which set of coordinate points does
NOT represent a linear function?
A y ⫽ 7x(1 ⫹ 5x)
A {(⫺5, 1), (0, 3), (5, 5), (10, 7)}
B y ⫽ 7x ⫺ (5x ⫹ 3)
B {(1, 2), (2, 4), (3, 6), (4, 8)}
C y ⫽ 6 ⫹ 2(x ⫺ 5)
C {(⫺3, 1), (⫺6, 2), (⫺9, 3), (⫺12, 4)}
D 6x ⫹ 3y ⫽ 7x ⫹ 4
D {(⫺2, 4), (⫺1, 1), (1, 1), (2, 4)
2. Which table of values represents a linear
function?
F
G
H
J
x
y
2
5
3
7
4
9
5
13
x
y
⫺3
2
⫺1
3
1
4
3
5
x
y
⫺2
⫺6
0
⫺2
2
4
4
10
x
y
⫺1
2
⫺3
4
⫺5
8
⫺7
10
4. Which situation can be represented by a
linear function?
F
A person’s heart rate while jogging at
a steady pace.
G A cable television bill for a 12-month
period of time.
H The total amount of money saved
if a person deposits $50 for three
months, then $25 for three months,
then $50 for six months.
J
The volume of a rectangular prism
whose width and length are x and
whose height is 2 more than its
length.
5. Which of the following functions would
have a graph that is a line?
A y ⫽ 5x⫺1 ⫺2
B y ⫽ 3兹
x⫹5
3 ⫹2
C y ⫽ ___
5x
1
D y ⫽ 3x ⫹ __
5
82
4/14/06 9:50:24 AM
Name
Date
Class
Ready for TAKS?
OBJECTIVE
3
4. Which linear equation represents the
statement “the product of 3 and y is 5
more than twice x”?
1. What is the equation of the line shown?
y
10
F
8
G 3y ⫽ 5 ⫹ 2x
6
H y ⫽ 3(5 ⫹ 2x)
4
J
2
–10 –8
–6
–4
3y ⫽ 2(5 ⫹ x)
–2
2
4
6
8
10
–2
y ⫽ 3(5 ⫺ 2x)
5. Which is the graph of the equation
2x ⫺ 6y ⫽ 12?
x
y
A
–4
10
8
–6
6
4
–8
2
–10
–10 –8 –6 –4 –2
–2
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
–4
–6
–8
–10
⫺3x ⫹ 6
C y ⫽ ___
4
4x ⫹ 6
A y ⫽ __
3
y
B
10
⫺4x ⫹ 6
D y ⫽ ___
3
3x ⫹ 6
B y ⫽ __
4
8
6
4
2
on a given line. Which of the following
could be the equation of the line?
–10 –8 –6 –4 –2
–2
–4
–6
–8
–10
x
y
⫺3
⫺8
0
0
6
y
C
10
16
8
6
4
F
y ⫽ 2x ⫺ 2
2x ⫺ __y ⫽ 0
G ___
3
6
2
8x ⫹ y ⫽ 0
H ___
3
–10 –8 –6 –4 –2
–4
–6
J
3y ⫽ 8x
–8
–10
3. Which linear equation is equivalent to
5?
1x ⫺ __
the equation y ⫽ ⫺__
3
2
A x ⫺ 6y ⫹ 15 ⫽ 0
10
8
6
4
2
–10 –8 –6 –4 –2
–2
–4
C 2x ⫹ 6y ⫹ 15 ⫽ 0
–6
–8
–10
D 2x ⫺ 6y ⫹ 15 ⫽ 0
y
D
B x ⫺ 3y ⫹ 15 ⫽ 0
–2
83
4/14/06 9:50:24 AM
Name
Date
OBJECTIVE
3
Class
Ready for TAKS?
3?
4. Which line has a slope of ⫺__
7
y
F
equation is ⫺3y ⫽ 5(x ⫹ 3) ⫺ x?
10
A ⫺5
C
4
⫺__
D
3
__
8
6
3
4
2
B ⫺3
–10 –8 –6 –4 –2
4
–2
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
–4
–6
–8
equation is ⫺3y ⫺ 3x ⫽ 2(x ⫹ 4) ⫺ 5?
F
5
⫺__
y
G
3
⫺__
H
3
–10
10
8
5
6
4
G ⫺1
2
2
J
–10 –8 –6 –4 –2
–2
–4
graph is shown?
–6
–8
–10
y
y
H
10
8
10
6
4
8
2
–10 –8 –6 –4 –2
6
–2
–4
–10 –8
–6
–4
4
–6
2
–10
–2
–8
(9, 0)
2
4
–2
6
8
10
x
y
J
10
8
6
–4
–6
4
2
(0, –6)
–10 –8 –6 –4 –2
–2
–8
x
–4
–6
–10
–8
–10
3
A ⫺__
2
2
B __
3
2
C ⫺__
3
3
D __
2
5. Line a passes through each of the points
in the table. What is the slope of line a?
84
x
⫺5
⫺3
3
y
⫺5
⫺2
7
3
A __
2
2
B ⫺__
3
2
C __
3
D undefined
4/14/06 9:50:25 AM
Name
OBJECTIVE
3
Date
Class
Ready for TAKS?
1. According to the graph, which statement
best describes the relationship between
x and y?
4. What is an equation of the line that
passes through (⫺4, 1) and has the
same y-intercept as the graph of
3x ⫺ 2y ⫽ 7
y
y
10
8
6
x
4
2
–10 –8
–6
–4
A As x increases, y remains constant.
F
x ⫹ 2y ⫽ 1 and 2x ⫺ y ⫽ 7
3. Which graph could represent a car’s
speed over time if its speed remained
constant for a few seconds, then
decreased for a few seconds, then
remained constant?
y
3x ⫺ __
7
G y ⫽ ⫺__
2
2
J
9x ⫺ __
7
y ⫽ ⫺__
8
2
Number of Tickets
Cost ($)
4
108
8
216
12
324
16
432
If the linear function that represents this
data were graphed with the number of
tickets on the horizontal axis and the
cost on the vertical axis, which would be
the best interpretation of the y-intercept
of the line?
y
x
D
x
5. The table shows the price of purchasing
certain numbers of concert tickets.
H x ⫹ 4y ⫽ 9 and 2x ⫹ 8y ⫽ 7
C
9x ⫺ __
7
y ⫽ __
2
2
3x ⫺ __
7
H y ⫽ __
2
2
1x ⫹5
G y ⫽ 2x ⫺ 1 and y ⫽ __
2
x
10
–8
y ⫽ 3x ⫹ 4 and y ⫽ ⫺3x ⫹ 4
B
8
–10
2. Which of the following pairs of equations
describes a pair of perpendicular lines?
y
6
–6
D As x decreases, y decreases.
A
4
–4
C As x decreases, y increases.
J
2
–2
B As y increases, x remains constant.
F
–2
A The cost of buying 4 tickets is $108.
y
B The cost of buying 0 tickets is $0.
C Each ticket costs $27.
x
D The cost per ticket increases as
more tickets are purchased.
x
85
4/14/06 9:50:25 AM
Name
OBJECTIVE
3
Date
Class
Ready for TAKS?
3 is changed
2x ⫺ __
3. The function y ⫽ ⫺__
5
4
3. What will be the effect
2x ⫺ __
to y ⫽ __
5
4
on the graph of the function?
1. The graphs of line ᐉ and line m are
shown.
Line ᐉ
Line m
y
y
10
10
8
8
6
6
4
4
2
–10 –8 –6 –4 –2
–2
A It will reflect the graph across the
x-axis.
2
2
4
6
8
10
x
–10 –8 –6 –4 –2
–4
–2
2
4
6
8
10
B It will reflect the graph across the
y-axis.
x
–4
–6
–6
–8
–8
–10
–10
C It will translate the graph 10 units left.
D It will translate the graph 10 units
down.
How does the graph of line ᐉ compare to
the graph of line m?
4. Line A has equation y ⫽ 3x ⫹ 7 and
Line B has a y-intercept of ⫺7 and a
slope of ⫺3. Which statement describes
how Line B is related to Line A?
A The slope of ᐉ is less, but the
B The slope of ᐉ is less and the
F
C The slope of ᐉ is greater and the
G Line B is a reflection of Line A
across the x-axis.
D The slope of ᐉ is greater, but the
H Line B is a reflection of Line A
across the y-axis.
2. The graph of the function
3 is shown.
5x ⫹ __
f(x) ⫽ ⫺__
2
4
J
y
8
6
4
2
–2
2
4
6
8
10
x
A y ⫽ ⫺12x ⫺ 5
–4
–6
–8
B y ⫽ 2x ⫺ 4
–10
C ⫺4y ⫽ 3x ⫺ 5
If the y-intercept is decreased by 4 units,
what would be the equation of the new
function?
F
None of these.
5. A line has equation y ⫽ 3x ⫺ 7. If the
y-intercept of the line is multiplied by
⫺4 and 2 is added to the slope, which
equation represents the new line?
10
–10 –8 –6 –4 –2
Line B is a translation of Line A 1
unit down.
D y ⫽ 5x ⫹ 28
5x ⫹ 3
f(x) ⫽ ⫺__
2
5x ⫺ ___
13
G f(x) ⫽ ⫺__
2
4
5x ⫹ ___
19
H f(x) ⫽ ⫺__
2
4
J
3
f(x) ⫽ ⫺10x ⫹ __
4
86
4/14/06 9:50:26 AM
Name
OBJECTIVE
3
Date
Class
Ready for TAKS?
1, what
4. If the slope of the line shown is ⫺__
2
is the y-coordinate of the y-intercept?
passes through the point (5, ⫺4) and
1?
has a slope of ⫺__
3
17
1x ⫺ ___
A y ⫽ ⫺__
3
3
y
1x ⫹ __
7
B y ⫽ ⫺__
3
3
–6
x
1x ⫹ ___
17
C y ⫽ ⫺__
3
3
1x ⫺ __
7
D y ⫽ ⫺__
3
3
contains the points (1, ⫺1) and (5, 2)?
F
⫺12
3x ⫺ 4y ⫽ 7
G ⫺6
G 3x ⫹ 4y ⫽ 7
H ⫺3
H 4x ⫺ 3y ⫽ 7
J
F
J
4x ⫹ 3y ⫽ 7
6
5. Which could be the equation of the line
whose graph is shown?
3. Which equation describes the line with
1 and y-intercept ⫺__
1?
x-intercept __
2
4
A 2y ⫺ 4x ⫽ 0
y
B 2y ⫹ 4x ⫽ 0
C 2x ⫹ 4y ⫽ 0
D 2x ⫺ 4y ⫽ 1
x
1x ⫹ __
2
A y ⫽ ⫺__
5
3
1x ⫺ __
2
B y ⫽ __
5
3
1x ⫹ __
2
C y ⫽ __
5
3
1x ⫺ __
2
D y ⫽ ⫺__
5
3
87
4/14/06 9:50:26 AM
Name
Date
OBJECTIVE
3
Ready for TAKS?
Benchmark Post-Test (A.6)(E)
1. If the line 4x ⫹ 2y ⫽ ⫺15 were graphed,
what would be the x-intercept?
15
A ⫺___
2
15
C ___
4
15
⫺___
15
___
D
Class
D
4
on a line. What would be the x-intercept
of this line if it were graphed?
2
2. If the line 3y ⫺ 5x ⫽ 8 were graphed,
what would be the y-intercept?
F
8
⫺__
3
H 1
G ⫺1
F
y
⫺2
10
⫺3
8
⫺4
6
⫺8
G ⫺7
8
__
3
J
x
H ⫺5
3. An equation of the line graphed is
x ⫺ y ⫺ 5 ⫽ c. What is the value of c?
J
14
5. A small appliance company is testing
a new oven. The temperature, in °F, is
recorded every minute, m, from the time
the oven is turned on. The table shows
that the temperature increases according
to a linear relationship.
y
10
8
6
4
2
–10 –8
–6
–4
–2
(5, 0)
2
4
–2
–4
–6
6
8
10
x
(0, –5)
–8
m
Temperature (°F)
1
134
3
167
5
200
If the linear relationship were graphed
with m on the horizontal axis, what
would be the y-intercept of the line?
–10
A ⫺5
A ⫺3
B ⫺1
B 101
C 0
C 117.5
D 5
D 120
88
4/14/06 9:50:26 AM
Name
OBJECTIVE
3
Date
Class
Ready for TAKS?
Benchmark Post-Test (A.6)(F)
1. The graph of a line is shown. If the
J
y-intercept is cut in half and the slope
1, which equation
is multiplied by __
3
represents the new line?
The value of the two stocks
decreased at the same rate since the
slopes of the lines are the same.
Use the information and the graph to
answer questions 3–5.
y
A math tutor charges an initial fee of $50
plus an hourly rate to make a house call. The
graph shows the total cost for a job based
on the initial fee and the number of hours to
complete the tutoring session.
10
8
6
4
2
–10 –8
–6
–4
–2
2
4
6
8
10
–2
x
–4
(3, 170)
Cost ($)
–6
–8
–10
(2, 130)
50
2x ⫺ 6
A y ⫽ __
3
4x ⫺ 3
C y ⫽ __
3
B y ⫽ 2x ⫺ 2
4x ⫺ 6
D y ⫽ __
3
1
0
Stock B
The value of Stock A decreased
faster since the slope of the line is
greater.
B $170
D $190
$215
G $185
H $170
J
$95
5. If the tutor increased her initial fee by
$20 and increased her hourly rate by
$15, what would be the total charge for
a session that took 3 hours?
H The value of the two stocks
decreased at different rates since the
y-intercepts of the lines are different.
C $180
F
G The value of Stock B decreased
faster since the slope of the line is
greater.
A $100
4. If the tutor left her initial fee unchanged
but increased her hourly rate by $15,
what would be the total charge for a
session that took 3 hours?
Which statement best compares the
value of the two stocks?
F
3
3. If the tutor increased her initial fee by
$20 but kept her hourly rate the same,
what would be the total charge for a
session that took 3 hours?
50
Stock A
2
Number of Hours
2. The values of two stocks over a short
period of time are represented by the
graphs.
100
(1, 90)
89
A $235
C $170
B $180
D $105
4/14/06 9:50:27 AM
Name
OBJECTIVE
3
Date
Ready for TAKS?
Benchmark Post-Test (A.6)(G)
1. A car’s value decreases according to the
age of the car. The table shows the value
of the car depending on its age.
Age (years)
Value (dollars)
0
25,000
1
22,500
3
17,500
4. A bicyclist is practicing for a race. During
a practice run, he traveled at a constant
speed. His times and distances are
shown in the table.
A 8 yrs
C 10 yrs
B 9 yrs
D 11 yrs
Time (minutes)
Distance (miles)
7.5
3
18.75
7.5
If the bicyclist continues to cycle at the
same rate, approximately how long
would it take him to get 10 miles from
home?
If the value of the car continues to
decrease at the rate shown in the table,
how old will the car be when it is worth
nothing?
F
25 minutes
G 30 minutes
H 33 minutes
2. The force that must be applied to push
an object using a certain trolley varies
directly with the weight of the object.
If a force of 3.00 pounds is required to
push an object that weighs 200 pounds,
how much force is required to push a
45-pound child?
F
J
40 minutes
5. The amount of blood in a person’s body
varies directly with the person’s weight.
The table shows several body weights
and the approximate number of quarts of
blood in that person’s body.
0.075 lbs
G 0.675 lbs
Weight (pounds)
Blood (quarts)
200
6.25
160
5
140
4.375
H 1.481 lbs
J
Class
13.333 lbs
3. Based on the given exchange rate for
Mexican pesos on a certain day at the
airport, Mr. Harmon purchased a leather
hat that was marked 1,080 pesos for 120
U.S. dollars. At this same rate, how many
dollars would a 6.75 peso bag cost?
Based on the data in the table,
approximately how many pounds does a
person with 3.5 quarts of blood weigh?
A 100
A 0.25
B 110
B 0.75
C 112
C 60.75
D 115
D 19200.00
90
4/14/06 9:50:27 AM
Name
OBJECTIVE
4
Date
Ready for TAKS?
4. Mr. Hicks is doing a study on the weight
of pigs compared to the amount of food
they eat each day. He feeds 50 pigs a
certain amount each day and then after
three months, counts to see how many
pigs weigh more than 60 pounds. The
results are given in the table.
1. Joey’s house is on the corner of the
block. Sally’s house is 3 blocks north of
Joey’s house. If Peg lives south of Joey
and the distance from Peg’s house to
Sally’s house is b blocks, which equation
represents the total distance, d, from
Peg’s house to Joey’s house?
A d⫽1⫹3
Number of Pigs Number of Buckets
over 60 lbs
of Slop per Day
B d⫽b⫹3
C d⫽b⫺3
D d ⫽ 3b
2. Laura is on the school dance team.
She has allotted a maximum of 3
hours each week to work on routines
and jump sequence. Each routine, r,
takes approximately 6 minutes. Each
jump sequence, j, takes approximately
4 minutes. Which inequality best
represents the time Laura can spend
each week practicing a combination of
dance routines and jump sequences?
F
2
1
3
4
4
7
5
10
relationship between b, the number of
buckets of slop each pig eats per day,
and p, the number of pigs that weigh
more than 60 pounds?
F
p⫽b⫺1
⫹3
_____
H p⫽b
2
r⫹jⱕ3
G 6r ⫹ 4j ⱕ 3
G p⫽b⫺3
J
⫹5
_____
p⫽b
3
5. Peter has $75 and wants to buy food,
toys, and treats for his dog. The table
shows the price of each item he wants
to buy.
H 4r ⫹ 6j ⱕ 180
J
Class
6r ⫹ 4j ⱕ 180
3. A submarine is hovering at 5,000
feet below sea level. If the submarine
ascends at a constant rate of 200 feet
per minute, which equation could be
used to determine t, the time in minutes
it will take the submarine to reach the
surface?
Items
Price
Food
$10.25 per bag
Toys
$6.75 each
Treats
$1.50 each
If he buys one bag of food and one toy,
which inequality best describes the total
number of treats, t, that he can buy?
A 0 ⫽ 5000 ⫺ 200t
B 5000 ⫽ 200 ⫺ t
A t ⱕ 75
C 5000 ⫽ 60 ⫹ 200t
B t ⱕ 75 ⫺ (10.25 ⫹ 6.75)
D 0 ⫽ 200t
C 1.5t ⱕ 75 ⫺ (10.25 ⫹ 6.75)
D 1.5t ⱕ 75
91
4/14/06 9:51:47 AM
Name
OBJECTIVE
4
Date
Ready for TAKS?
4. The table shows several solutions (x, y)
to the equation 4x ⫹ 3y ⫽ 15.
1. A student is solving the equation
4 ⫺ x ⫹ 5 ⫽ 9x ⫹ x ⫹ 7. Which of the
following strategies would be the BEST
way to start this problem?
A Add x to both sides of the equation.
B Subtract x from both sides of the
equation.
F
D Divide both sides of the equation by
4.
y
0
5
6
⫺3
2
y
7
__
3
9
G __
4
2. What is the value of x if (x, ⫺2) is a
4x ⫺ 9 ?
solution to the equation y ⫽ __
3
3
H ⫺__
7
44
⫺___
3
J
4
⫺__
9
5. What is the solution to the statement
“the product of 6 and the quantity x
increased by 3, is 27?”
33
G ⫺___
4
21
H ___
4
J
x
What is the missing value of y?
C Divide both sides of the equation by
9.
F
Class
1
A __
2
28
___
3
B 1
3. Each of the points on the line is a
solution to the equation 5x ⫺ 3y ⫽ ⫺3.
3
C __
2
y
5
D __
2
(2,
(0, 1)
6. Mr. Roe replaced the gutters on his
house. The carpenter charged him
$1,280 for materials, $60 per hour to
install the gutter, and 10% tax on all the
materials and labor. The total charge
was $1,804. About how long did it take
to install the new gutters?
13
)
3
x
(x, –1)
What is the missing value of x?
3
A ⫺__
2
6
B ⫺__
5
4
⫺__
2
⫺__
C
5
D
F
G 4 hours
H 5 hours
3
J
3 hours
92
6 hours
4/14/06 9:51:48 AM
Name
OBJECTIVE
4
Date
Class
Ready for TAKS?
1. The cost of hiring a painter is described
by the function f (x ) ⫽ 40x ⫹ 50 in
which f (x ) is the cost and x is the time
the painter works. Mr. Ray has already
bought the paint and has $200 left
to paint his living room. What is the
maximum number of hours that he can
hire the painter?
⫺3x ⫺ 2y > 14 is shown.
y
8
6
4
2
–8
–6
–4
–2
2
4
6
8
–2
A 2 hours
x
–4
–6
B 3 hours
–8
C 4 hours
D 5 hours
Which point is in the solution set to the
inequality ⫺3x ⫺ 2y > 14?
2. The student government is trying to raise
money for a set of 2 speakers by holding
several yard sales. They decide to
charge $1.25 for each item in the sale. If
each speaker costs about $68, including
the tax, what is a reasonable number of
items they must sell?
F
F
(3, 1)
G (⫺2, ⫺3)
H (0, ⫺7)
J
(⫺2, ⫺5)
2 x ⫺ 7 is shown.
y ⱕ __
5
40 items
G 80 items
H 120 items
J
y
16
160 items
12
3. Manny purchased x baseball bats at
$105 each and y baseball gloves at
$82 each. He spent less than $2,100,
not including tax. The number of items
he purchased can be described by the
linear inequality 105x ⫹ 82y ⬍ 2100. If
Manny purchased 9 bats, what is the
maximum number of gloves he could
have purchased?
8
4
–16 –12 –8
–4
4
–4
8
12
16
x
–8
–12
–16
Which point is NOT in the solution set
2 x ⫺ 7?
of y ⱕ __
5
A 13 gloves
B 14 gloves
A (1, ⫺7)
C 15 gloves
B (5, ⫺5)
D 16 gloves
C (0, ⫺9)
D (⫺5, ⫺10)
93
4/14/06 9:51:48 AM
Name
OBJECTIVE
4
Date
Ready for TAKS?
1. Rex has a total of 141 action figures.
The number of his bad guys is 15 more
than twice the number of his good guys.
Which system of equations can be used
to find the number of bad guys, b, and
the number of good guys, g, Rex has?
A g ⫽ 15 ⫺ 2b
b ⫹ g ⫽ 141
B b ⫽ 15 ⫹ 2g
b ⫺ g ⫽ 141
C g ⫽ 15 ⫹ 2b
b ⫹ g ⫽ 141
D b ⫽ 15 ⫹ 2g
141 ⫺ b ⫽ g
4. The diagram shows two angles. The
measure of the larger angle, y, is
140 degrees more than five times the
measure of the smaller angle, x. Which
system of equations can be used to find
the measure of each angle?
y°
F
2. Ms. Green bought two kinds of flowers
for her yard. All together, she bought 40
daisies and begonias. She bought three
and a half times as many begonias as
daisies. Which system of equations can
be used to find the number of begonias,
b, and the number of daisies, d, she
bought?
F
Class
b ⫹ d ⫽ 40
1d
d ⫽ 3 ⫹ __
2
H b ⫽ d ⫺ 40
d ⫽ 3.5b
H x ⫹ y ⫽ 360
y ⫽ 5x ⫹ 140
b ⫽ 40 ⫺ d
b ⫽ 3.5d
B 2w ⫽ 92 ⫺ 2ᐉ
w ⫽ 8ᐉ ⫺ 5
C 2(ᐉ ⫹ w) ⫽ 92
ᐉ ⫽ 8w ⫺ 5
D 2(ᐉ ⫹ w) ⫽ 92
w ⫽ 5 ⫺ 8ᐉ
J
x ⫽ 360 ⫺ y
x ⫽ 5y ⫹ 140
Day 1
Day 2
Pretzels
55
42
Smoothies
49
61
Total Sales
$406.05
$432.70
If the price of a pretzel is represented
by p and the price of a smoothie is
represented by s, which system of
equations can be used to determine the
price of each?
3. The length of a rectangle is 5 feet less
than 8 times the width. Which system
of equations can be used to find the
dimensions of the rectangle if the
perimeter is 92 inches?
A ᐉ ⫹ w ⫽ 92
ᐉ ⫽ 5 ⫺ 8w
G x ⫹ y ⫽ 360
x ⫽ 140 ⫹ 5y
5. The table shows the number of pretzels
and smoothies sold at a shop on two
different days.
G b ⫺ d ⫽ 40
1d
b ⫽ 3 ⫹ __
2
J
x ⫹ y ⫽ 360
y ⫹ 140 ⫽ 5x
x°
A p ⫹ s ⫽ 104
55p ⫹ 49s ⫽ 406.05
B p ⫹ s ⫽ 103
42p ⫹ 61s ⫽ 432.7
C 55p ⫹ 49s ⫽ 406.05
42p ⫹ 61s ⫽ 432.7
D p ⫹ s ⫽ 104
p ⫹ s ⫽ 103
94
4/14/06 9:51:49 AM
Name
OBJECTIVE
4
Date
Class
Ready for TAKS?
4. The graph shows the solution to which
system of equations?
1. Barry has 68 coins in pennies and
nickels. He has 10 fewer pennies than
nickels. The system of equations
y
x ⫹ y ⫽ 68
x ⫽ y ⫺ 10
8
6
4
represents this situation if x is the
number of pennies and y is the number
of nickels. What is the solution to the
system?
2
–8
–6
–4
2
–2
4
6
8
–2
x
–4
–6
A (28,30)
–8
B (30, 28)
F
C (29, 39)
D (39, 29)
x ⫺ 3y ⫽ 0
2x ⫺ y ⫽ 10
G x ⫹ 3y ⫽ 0
2x ⫺y ⫽ ⫺10
H x ⫺ 3y ⫽ 0
2x ⫺ y ⫽ ⫺10
2. Manuel has 42 coins in nickels and
dimes. The coins are worth $3.35. The
system of equations
5. The graph of the system of equations
is shown. What is the solution to the
system?
n ⫹ d ⫽ 42
0.05n ⫹ 0.10d ⫽ 3.35
y
represents this situation. If n represents
the number of nickels Manuel has, what
is the value of n?
F
8
6
4
2
17
–8
G 22
–6
–4
–2
2
–2
4
6
8
x
–4
H 25
J
x ⫺ 3y ⫽ 0
⫺2x ⫹ y ⫽ 10
J
–6
–8
29
3. What is the y-coordinate of the solution
to the system of equations ?
A (1, ⫺1)
B (2, ⫺1)
7x ⫺ 4y ⫽ ⫺6
2x ⫹ 4y ⫽ 24 ?
C (⫺1, 2)
A ⫺5
D (⫺1, 1)
B ⫺2
C 2
D 5
95
4/14/06 9:51:49 AM
Name
OBJECTIVE
4
Date
Class
Ready for TAKS?
1. Keith sold some CD’s for $3 and some
DVD’s for $5. He sold a total of 41
items and earned $181. The system of
equations
4. Joseph wrote down a system of
equations to solve, but part of the
second equation got torn. The remaining
part read
x ⫹ y ⫽ 41
3x ⫹ 5y ⫽ 181
4x ⫹ y ⫽ ⫺7
9x ⫹ ?? ⫽ ?
represents this situation. If the solution
to the system is (12, 29), what does 12
represent?
Which of the following is NOT a possible
solution to the system regardless of what
the missing numbers are?
A the number of CD’s Keith sold
F
B the price per CD
G (⫺3, 5)
C the number of DVD’s Keith sold
H (⫺2, ⫺1)
D the price per DVD
J
2. Tiffany incorrectly solved the system of
equations:
aebec
3x ⫹ y ⫽ 3
2x ⫺ y ⫽ 0
q ⫹ d ⫽ 35
0.25q ⫹ 0.10d ⫽ 5.55
because 3(3) ⫺ 6 ⫽ 3
G because 2(3) ⫺ 6 ⫽ 0
Solve the system to determine which
reason best describes why at least one
of LaTonya’s totals must be wrong.
H because 2(3) ⫺ ( ⫺6) ⫽ 0
J
because 2( ⫺6) ⫺ (3) ⫽ 0
3. Lisa solved a system of equations and
found the solution to be (0, ⫺5). Which
of the following could NOT have been
the system Lisa solved?
A When you solve the system you get
a fraction for each coin.
B There is no way to get a total of
$5.55 using only dimes and quarters.
A x⫺y⫽5
B x ⫹ y ⫽ ⫺5
3x ⫹ 2y ⫽ ⫺10
y⫺x⫽5
C 5x ⫹ y ⫽ ⫺5
y⫽x⫺5
(1, ⫺11)
5. LaTonya has a coin purse full of quarters
and dimes. She counted the number
of each and found that she had a total
of 35 coins. She then counted the total
value of the coins and found that she
had $5.55. The system of equations
represents this situation.
Her solution was (3, ⫺6). Why is this
solution incorrect?
F
(2, ⫺15)
C When you solve the system you get
a negative number of dimes.
D y ⫽ 3x ⫺ 5
2y ⫽ x ⫺ 10
D When you solve the system you get
a negative number of quarters.
96
4/14/06 9:51:50 AM
Name
OBJECTIVE
5
Date
Class
Ready for TAKS?
are shown.
1. What is the effect on the graph of the
2
equation y ⫽ 6x when the equation is
2
changed to y ⫽ ⫺6x ?
A The graph of y ⫽ ⫺6x2 is translated
12 units up from the original graph.
B The graph of y ⫽ ⫺6x2 is translated
12 units down from the original graph.
C The graph of y ⫽ ⫺6x2 is a reflection
of the original graph across the
y-axis.
2
D The graph of y ⫽ ⫺6x is a reflection
of the original graph across the
x-axis.
P2
P1
1. Which
The coefficient of x2 in P1 is ⫺__
2
of the following could be the coefficient
are shown.
2
of x in P2?
F
3
H ⫺__
4
⫺0.2
P1
G 1
1
⫺__
3
J
2x2 is
5. The graph of the function y ⫽ ⫺__
3
given.
y
P2
4
2
2
If the equation of P2 is y ⫽ ax , what is
the equation of P1?
F
2
y ⫽ ax ⫺ 1
–8
–6
–4
J
2
4
6
8
–2
x
–4
G y ⫽ ⫺ax2
1x2
__
H y ⫽ ⫺a
–2
–6
1x2
__
y⫽a
–8
2
3. If the coefficient of x in the equation
2
y ⫽ ⫺10x is changed to ⫺5, what is the
effect on the graph of y?
If the graph is reflected across the x-axis
and made wider, which of the following
could be the equation of the new
parabola?
A The graph will be shifted down.
B The graph will be narrower.
A y ⫽ ⫺2x
C The graph will be wider.
D The graph will be shifted right.
2
B y ⫽ 0.7x2
97
C y ⫽ ⫺x2
1x2
D y ⫽ __
2
4/14/06 9:52:00 AM
Name
OBJECTIVE
5
Date
Class
Ready for TAKS?
4. The point (1, 2) is the vertex of
the parabola whose equation is
2
f(x) ⫽ 3x ⫺ 6x ⫹ 5. What is the
vertex of a parabola that has been
translated down 3 units?
1. How do the graphs of the
2
functions f(x) ⫽ x ⫺ 3x ⫹ 2 and
2
g(x) ⫽ x ⫺ 3x ⫺ 5 relate to each other?
A The graph of f(x) is 7 units to the left
of the graph of g(x).
F
B The graph of f(x) is 3 units to the
(2, 2)
G (⫺1, 2)
H (1, ⫺1)
C The graph of f(x) is 7 units above the
graph of g(x).
J
D The graph of f(x) is 3 units below the
graph of g(x).
(1, 2)
5. When graphed, which function would
appear to be the graph of f(x) ⫽ x2 ⫺ 1
shifted right 3 units?
2
2. If the graph of f(x) ⫽ x ⫺ 3 is translated
up 2 units, which function represents the
new graph?
y
2
f(x) ⫽ x ⫺ 5
8
G f(x) ⫽ x2 ⫺ 1
6
F
4
H f(x) ⫽ (x ⫺ 2)2 ⫺ 3
J
2
f(x) ⫽ (x ⫹ 3)2 ⫹ 3
–8
–6
–4
–2
3. The graph shows the function
2
f(x) ⫽ x ⫺ 9.
2
–2
4
6
8
x
–4
–6
y
–8
8
6
–8
–6
–4
4
A f(x) ⫽ x2 ⫹ 2
2
B f(x) ⫽ (x ⫺ 3)2 ⫺ 1
–2
2
4
6
8
–2
x
C f(x) ⫽ (x ⫹ 3)2 ⫺ 1
D f(x) ⫽ x2 ⫺ 4
–4
–6
–8
Which statement describes the
translation of the parabola if the
y-intercept is moved to y ⫽ ⫺19?
A 10 units up
C 10 units down
B 8 units up
D 8 units down
98
4/14/06 9:52:00 AM
Name
OBJECTIVE
5
Date
Class
Ready for TAKS?
1. Derek’s dirt bike speed shown below.
F
y
G The ball was in flight for 1 second.
8
H The ball’s height increased for
approximately 15 seconds.
6
4
J
2
–8
–6
–4
The ball reached its maximum height
at approximately 1 second.
–2
2
4
6
x
8
–2
The height of the baseball was 6 feet
when it landed.
3. A company’s weekly profit is given by the
2
function P(x) ⫽ ⫺80x ⫹ 800x ⫹ 15,000,
where x is the number of machines
produced. The graph of P(x) is shown.
–4
–6
–8
Profit ($)
y
Which best describes Derek’s speed?
16000
14000
12000
A Went up a hill and then back down.
1
2
3
4
5
6
7
8
B Increased, reached a peak, and then
decreased.
C Slowed down and then went
backwards.
A The maximum weekly profit is
approximately $5,000.
D Slowed down, came to a stop, and
then sped up.
B The profit decreases always.
C The company must produce 5
machines to maximize their profit.
2. The graph shows the height, h, in feet of
a baseball versus the time, t, in seconds,
after the ball is thrown.
D The minimum profit comes by not
producing any machines.
y
4. The graph shows the number of
teenagers, T in a city that bought a
portable music player x years after 2000.
22
20
18
16
y
14
200
Number of
Players
Height (in feet)
x
9
Number of Machines
12
10
8
6
150
100
50
1
4
2
3
4
5
6
7
8
x
Time (in years)
2
1
2
3
4
5
6
7
8
9
How many thousands of teenagers
bought a portable music player in 2000?
x
Time (in seconds)
F
0
G 7
99
H 61
J
2000
4/14/06 9:52:01 AM
Name
Date
Ready for TAKS?
OBJECTIVE
5
4. If a package is dropped from a helicopter
whose height is 750 feet, the height of
the package above the ground t seconds
later (neglecting air resistance) is given
2
by the equation h ⫽ 750 ⫺ 16t where h
is the height in feet. What is the height of
the object after 4 seconds?
1. The factored form of a quadratic
equation is (3x ⫹ 7)(5x ⫺ 4). What are
the solutions of the quadratic equation?
A x ⫽ ⫺7 and x ⫽ 4
5
3 and x ⫽ __
B x ⫽ ⫺__
7
4
C
Class
F
3 and x ⫽ ⫺__
5
x ⫽ ⫺__
7
7 ft
G 350 ft
4
H 494 ft
7 and x ⫽ __
4
D x ⫽ ⫺__
5
3
J
700 ft
2
2. Solve. 2x ⫽ 5 ⫺ 3x
F
5. Sketch the graph of the equation in
question 4 on the grid provided and find
the approximate number of seconds it
takes the object to hit the ground.
5 and 1
⫺__
2
5 and 1
G __
2
y
5 and ⫺1
H __
2
J
8
6
1 and ⫺5
__
4
2
2
3. Which of the following are solutions to
the equation 8x2 ⫽ 5x ⫹ 7?
–8
–6
⫹ 兹 249and x ⫽ 5
⫹ 兹249
_________
_________
A x⫽5
16
16
–4
–2
2
–2
4
6
8
x
–4
–6
⫹ i兹199and x ⫽ 5
⫺ i兹 199
_________
_________
B x⫽5
16
16
–8
1
7 and x ⫽ ⫺__
C x ⫽ __
2
4
A 5 sec
1 and x ⫽ ⫺__
7
D x ⫽ __
4
2
B 7 sec
C 9 sec
D 12 sec
100
4/14/06 9:52:01 AM
Name
OBJECTIVE
5
Date
Class
Ready for TAKS?
1. What are the roots of the quadratic
2
equation x ⫹ 5x ⫺ 6 ⫽ 0?
4. One of the factors of the quadratic
2
equation y ⫽ 7x ⫺ 25x ⫺ 12 is (x ⫺ 4)
which produces a root of 4. What is the
other root of the equation?
A ⫺3 and ⫺2
B 2 and 3
⫺7
C 1 and ⫺6
F
D 1 and 6
3
G ⫺__
7
2. What are the roots of the function
graphed?
3
H __
7
J
7
5. The graph shows the roots of a
quadratic equation.
y
8
6
4
2
–8
F
(⫺4, ⫺12) and (0, 8)
2
4
6
8
x
–6
–8
–10
(2, 0) and (⫺4, 0)
–12
3. If x ⫽ ⫺3 is a root of the equation
3x2 ⫹ 2x ⫹ ax ⫺ a ⫽ 0, what is the
value of a?
Which of the following could NOT be the
equation?
21
___
4
A x2 ⫹ 2x ⫺ 24 ⫽ 0
4
B ___
21
C
–2
–4
H (⫺8, 0) and (⫺1, 0)
A
–4
–2
G (0, ⫺2) and (0, 4)
J
–6
B ⫺2x2 ⫺ 4x ⫹ 48 ⫽ 0
C 3x2 ⫺ 6x ⫺ 72 ⫽ 0
4
⫺___
21
D 4x2 ⫹ 8x ⫺ 96 ⫽ 0
21
D ⫺___
4
101
4/14/06 9:52:02 AM
Name
Date
OBJECTIVE
5
Class
Ready for TAKS?
4. The area of the rectangle shown is
30m8n2 square units. If the length of the
3 2
rectangle is 9m n units, how many units
wide is the rectangle? (m ⫽ 0 and n ⫽ 0)
1. Which expression represents the area of
the triangle shown?
3x 4y 6
5xy 6
2x 2y
6x 5 y 4
A 3x6y7
9m 3n 2
7 5
B 6x y
5
F
9 10
C 9x y
D 15x6y12
3m
____
H 21m5
10
5
G 21m5n
J
10m
_____
3
3 ⫺3
5. The table shows several values of r
and s.
21x y z
________
?
4 ⫺5 -2
70x y z
2 3
F
10xy z
_______
r
s
3
2x2
4x3
3x3
9x5
4x4
16x7
3
10xz
G _____
3y2
3y2z3
H _____
10x
Which of these best describes the
relationship between r and s?
3
J
3z
_____
10xy2
A s⫽r
4
4
⫺ 5x?
2x
________
12x⫺3
7
⫺x
A ____
4
C ⫺4x7
7
⫺ 5x4
B x_______
6
4
D __
x7
3
B s ⫽ xr
r2
C s ⫽ __
x
3
r
D s ⫽ __
3
x
102
4/14/06 9:52:02 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
Benchmark Post-Test (G.4)(A)
1. Which expression can be used to
determine the total perimeter around the
outside of the composite figure shown?
4. What is the point of intersection of the
diagonals of the parallelogram whose
vertices are P(2, 5), Q(6, 5), R(2, 1), and
S(⫺2, 1)?
ᐉ
y
6
w
4
2
w2
A ᐍw ⫹ __
4
–6
–4
–2
2
4
–2
w2
B ᐍw ⫹ __
2
6
x
–4
–6
C ᐍw ⫹ w2
F
D 2ᐍ ⫹ w
G (5, 4)
H (2, 3)
2. The measure of one interior angle in an
isosceles triangle is 100°. What are the
measures of all three interior angles?
F
(4, 5)
J
(3, 2)
5. A quarter of a circle is inscribed in a
square with sides of length s as shown.
40°, 40°, and 100°
G 30°, 50°, and 100°
H 80°, 80°, and 100°
J
100°, 100°, and 100°
s
3. A farmer had a square sheep pen with
sides of length 30 feet. He redesigned
his pen in the shape of a circle and used
all the fencing from the old pen to make
the new pen. What is the approximate
diameter of the new pen?
Which expression represents the portion
of the area of the circle that is inside the
square?
A 9.5 ft
B 19.1 ft
C 38.2 ft
D 94.2 ft
103
s2
A __
4
C s2
s2
B __
4
3s2
D ___
4
4/14/06 9:51:03 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
4. The regular polygons shown form a
pattern.
1. If the measure of angle DEF in the figure
is n°, which of the following expressions
represents the measure of angle EFG?
D
E
P = 12 cm
P = 20 cm
P = 30 cm
P = 42 cm
A n°
If P represents the perimeter of the
figure, what is the value of P for the next
figure in this pattern?
B 90 ⫺ n°
F
C 180 ⫺ n°
G 52 cm
D 270 ⫺ n°
H 56 cm
G
F
J
2. A square is inscribed inside a circle with
radius r. Which expression represents
the perimeter of the square?
48 cm
72 cm
5. Josh starts at the center of town and
travels due north for w miles. He then
travels due east for twice as many miles.
After resting for a few minutes, he travels
due north again for x miles and finally
due east again for y miles. The diagram
represents Josh’s path.
r
y
F
r2
G r兹 2
x
2 H r 兹2
J
2w
4r兹 2
3. If the length of the hypotenuse of a 30°,
60°, 90° triangle is 4x, which expression
represents the area of the triangle?
w
A 2x2
B 2兹 3x
of miles Josh is from his starting point?
C 2x兹3
D 2x2兹3
A
B
兹5w2 ⫹ 兹x2 ⫹ y2
兹5w2 ⫹ x2 ⫹ y2
C 3w2 ⫹ x2 ⫹ y2
D 3w ⫹ x ⫹ y
104
4/14/06 9:51:03 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
Benchmark Post-Test (G.5)(B)
1. In the figure shown, line ᐉ is parallel to
line m.
4. The measure of one angle of a right
trapezoid is 60°. Which of the following
could be the measure of one of the other
angles?
ᐉ
42°
x°
m
What is the value of x ?
F
A 42°
60°
G 120°
B 48°
H 150°
C 90°
J
D 132°
cannot be determined
5. The diagonals of parallelogram ABCD
intersect at point P.
2. The figure shows the first three stages of
a fractal.
C
B
P
A
of unshaded triangles in the next stage
of the fractal?
F
Which statement is NOT correct?
A m⬔BAP ⬵ m⬔DAP
33⫺1
B m⬔DPC ⬵ m⬔APB
G 3(3) ⫺ 1
C m⬔BPC ⬵ m⬔CPD
H 33 ⫺ 1
J
D
D m⬔BCP ⬵ m⬔PAD
33
3. What is the measure of each interior
angle of a regular decagon?
A 36°
B 144°
C 360°
D 1440°
105
4/14/06 9:51:04 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
Benchmark Post-Test (G.5)(C)
1. Which of the following shapes CANNOT
be used to generate a tessellation of a
plane surface?
3. A pure tessellation is a tessellation that
consists of congruent copies of one
figure. Which of the following series of
compositions of transformations would
most likely result in a pure tessellation
given the right figure?
A
A multiple rotations followed by multiple
dilations
B multiple reflections followed by
multiple dilations
B
C multiple translations followed by
multiple dilations
D multiple translations followed by
multiple rotations
C
4. Which of the following compositions of
transformations would move the triangle
shown completely into quadrant I?
y
D
10
8
(0, 9)
6
4
2
(–3, 1)
–10 –8 –6 –4 –2
NOT true?
–2
(6, 1)
2
4
6
8
10
x
–4
–6
–8
F
Both reflections and translations
–10
G Neither reductions nor enlargements
a reflection across the x-axis followed
by a reflection across the y-axis
1
G a reduction by a scale factor of __
3
followed by a reflection across
the x-axis
1
H a reduction by a scale factor of __
3
right 2 units
1
J a reduction by a scale factor of __
3
right 2 units and then a reflection
across the x-axis.
F
H Only reflections and translations
J
Both reflections and rotations result
106
4/14/06 9:51:04 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
Benchmark Post-Test (G.5)(D)
4. A ramp rises from the ground at a 30°
angle. If the inclined surface of the ramp
is 20 feet long, how many feet on the
ground does the ramp cover?
1. Which is the best approximation of the
perimeter of a right isosceles triangle if
its leg is 8 units long?
A 11 units
B 19 units
C 27 units
20 ft
D 32 units
2. Find the area of triangle ABC.
30°
F
16 cm
G 10兹 3 ft
45°
F
J
20兹3 ft
5. A hot air balloon is staked to the ground
and the wind is blowing. The angle of
elevation from the stake to the balloon
is 60°. If the balloon is 110 feet off the
ground, approximately how long is the
rope holding the balloon?
2
32 cm
G 64 cm2
H 128 cm2
J
10兹 3 ft
H _____
3
10 ft
256 cm2
3. The area of square ABCD is 225 units.
B
C
A
D
60°
_
What is the approximate length of AC ?
A 55 ft
C 127 ft
A 19 units
B 95 ft
D 191 ft
B 21 units
C 23 units
D 30 units
107
4/14/06 9:51:04 AM
Name
OBJECTIVE
6
Date
Class
Ready for TAKS?
1. Figure EFGH is shown on the coordinate
plane.
3. Triangle A⬘B⬘C⬘ is the result of performing
a translation on triangle ABC. Which
statement is true?
y
A ABC could be congruent to A⬘B⬘C⬘
10
8
B ABC must be congruent to A⬘B⬘C⬘
6
4
2
–10 –8 –6 –4 –2
E
G
H
2
–2
C ABC could not be congruent to A⬘B⬘C⬘
F
4
6
8
10
D ABC is not congruent to A⬘B⬘C⬘
x
4. What are the coordinates of the image of
P if triangle MNP is translated up 3 units
and then reflected across the y-axis?
–4
–6
–8
–10
y
10
Which transformation creates an image
with a vertex of (0, 4)?
8
A Rotate the figure 90° around vertex E
2
6
4
B Reflect the figure across the x-axis
and then across the y-axis.
–10 –8 –6 –4 –2
F
6
2
2
4
6
8
10
x
J
(⫺3, ⫺1)
then a rotation 270° clockwise
–6
2 and then a
C a dilation by a factor of __
3
3
2
–8
–10
(0, 3), (4, 3), and (4, 7)
D a translation up 2 units, then a
G (0, 3), (0, ⫺3), and (5, ⫺3)
reflection through the origin, then a
1
dilation by a factor of __
2
H (4, 0), (8, 0), and (8, 3)
J
H (⫺3, 1)
B a reflection across the line x ⫽ 2 and
–4
F
x
A a dilation by a factor of 3 and then a
1
3
4
–2
10
5. Which of the following compositions
would NOT result in congruent figures?
8
–2
(3, 1)
G (3, ⫺1)
y
M
8
–8
10
–6
6
–10
2. Which coordinates are the vertices of a
triangle congruent to triangle LMN?
L
4
P
–6
D Translate the figure to the left 4 units
and then down 1 unit.
–10
2
–4
C Reflect across the line x ⫽ 1.
N
–2
N
M
(4, 1), (4, ⫺4), and (0, 4)
108
4/14/06 9:51:05 AM
Name
OBJECTIVE
7
Date
Class
Ready for TAKS?
1. What three-dimensional figure does the
net represent?
3. If the net shown is folded into a cube,
what letter is on the face of the cube
opposite the face labeled C?
F
C
A
D
E
B
A A
A cone
B B
B triangular pyramid
C C
C triangular prism
D E
D square pyramid
4. Which of the following is a true
statement about the net of the cube
shown?
2. Which of the following nets could be
used to form a cube?
F
J
K
G
M
N
O
L
F
Faces N and K are parallel.
G Faces M and N are parallel.
H
H Faces O and K are parallel.
J
J
Faces J and L are perpendicular.
5. The net of a triangular prism is
composed of which of the following?
A three rectangles that may or may not
be congruent and two triangles that
may or may not be congruent
B three rectangles that must be
congruent and two equilateral
triangles
C three rectangles that may or may
not be congruent and two equilateral
triangles
D three rectangles that may or may
not be congruent and two congruent
triangles
109
4/14/06 9:51:15 AM
Name
OBJECTIVE
7
Date
Class
Ready for TAKS?
4. What is the volume of a threedimensional object whose different views
are shown?
Use the net to answer questions 1⫺3.
The top, side, and front views of an object
built with cubes are shown.
Side View
4 ft
Top View
6 ft
Side View
4 ft
6 ft
6 ft
Front View
4 ft
Front View
1. What is the maximum number of cubes
in any one row or column?
6 ft
A 1
B 2
Top View
C 3
F
D 6
G 96 ft3
2. How many cubes are needed to
construct this object?
F
H 192 ft3
J
4
216 ft3
5. Which of the following is the top view of
the three-dimensional solid shown?
G 5
H 6
J
48 ft3
7
3. If the length of each side of each cube is
3 centimeters, what is the total volume of
the object?
A 108 cm3
Front
B 135 cm3
C 162 cm3
Right
A
B
C
D
D 189 cm3
110
4/14/06 9:51:16 AM
Name
Date
Class
Ready for TAKS?
OBJECTIVE
7
3. Point P has coordinates (2, 5). If Point
P is translated down 3 units and to the
left 4 units, and then reflected across the
y-axis, what are the coordinates of the
new point?
1. Which ordered pair could represent the
fourth vertex of a parallelogram if the
other three vertices are (5, ⫺1), (⫺3, 1),
and (⫺1, ⫺2)?
y
y
x
x
A (3, 2)
A (⫺2, ⫺2)
B (2, 3)
B (⫺2, 2)
C (3, 3)
C (2, ⫺2)
D (2, 1)
D (2, 2)
2. If quadrilateral ABCD is rotated 540°
clockwise around the origin, in which
quadrant will point A appear?
4. A hexagon is graphed on the grid.
y
y
D
A
x
x
C
F
B
What is the equation of the line of
symmetry that passes through (⫺1, 3)?
I
x ⫽ ⫺1
G II
F
H III
G x⫽3
IV
H y⫽3
J
J
111
y ⫽ ⫺1
4/14/06 9:51:16 AM
Name
OBJECTIVE
7
Date
Class
Ready for TAKS?
1. Which two lines are perpendicular?
4. Line m is parallel to segment AB. What
is the slope of line m?
A 3x ⫹ 5y ⫽ 8 and 5x ⫹ 3y ⫽ ⫺2
y
B 3x ⫹ 2y ⫽ 9 and 6x ⫹ 4y ⫽ ⫺5
C 2x ⫹ 7y ⫽ ⫺3 and ⫺7x ⫹ 2y ⫽ ⫺11
8
D 5x ⫹ 4y ⫽ ⫺20 and 8x ⫹ 10y ⫽ 20
6
4
2. Which equation describes a line parallel
to the line graphed?
A
2
B
–8
y
–6
–4
–2
2
–2
8
–4
6
–6
4
–8
4
6
8
x
2
–8
–6
–4
–2
2
4
6
8
10
–2
x
F
–4
5
G ⫺__
4
–6
–8
F
4
H __
5
2x ⫹ 7
y ⫽ ⫺__
3
J
5
__
4
5. Segments of the lines y ⫽ 5x ⫺ 4 and
y ⫽ mx ⫹ 1 form consecutive sides of a
rectangle. What is the value of m in the
second equation?
3x ⫺ 4
G y ⫽ ⫺__
2
2x ⫹ 1
H y ⫽ __
3
J
4
⫺__
5
A 5
3x ⫹ 4
y ⫽ __
2
B ⫺5
3. Which of the following best describes
the graphs of the lines 2y ⫽ 3x ⫹ 2 and
4y ⫽ 6x ⫹ 1?
1
C __
5
A The lines have the same x-intercept.
1
D ⫺__
5
B The lines have the same y-intercept.
C The lines are parallel to each other.
D The lines are perpendicular to each
other.
112
4/14/06 9:51:17 AM
Name
OBJECTIVE
7
Date
Class
Ready for TAKS?
_
1. What is the approximate length of CD
shown?
_
3. PQ is a diameter of the circle shown.
What is the approximate area of the
circle shown?
y
y
8
P (–3, 4)
D
6
4
2
–8
–6
–4
–2
x
2
4
–2
C
6
8
x
Q (1, –5)
–4
–6
A 20.25 units2
–8
B 24.25 units2
C 48.5 units2
A 4.5 units
D 97 units2
B 8.2 units
4. What is the center of the circle whose
diameter has endpoints (⫺2, 5) and
(4, 6)?
C 8.9 units
D 12.0 units
2. The parallelogram shown has two
vertices as indicated. The diagonals of
the parallelogram intersect at point X.
F
G
(6, 1)
H
X
J
(–2, –3)
5. What is the distance between (⫺2, 7)
and (⫺8, ⫺1)?
Which of the following are the
coordinates of X ?
F
1, 2__1 3, 2__1 11
1, ___
2 11
3, ___
2 A 100
(2, ⫺1)
B 14
G (⫺1, 2)
C 136
H (4, 2)
D 10
J
(2, 4)
113
4/14/06 9:51:17 AM
Name
OBJECTIVE
7
Date
Ready for TAKS?
4. Which statement is NOT true about the
three-dimensional figure shown?
1. How many faces, edges, and vertices
does the three-dimensional figure shown
have?
F
A 4 faces, 6 edges, and 4 vertices
The figure has fewer faces than
vertices.
G The figure has the same number of
edges as vertices.
B 5 faces, 8 edges, and 5 vertices
C 5 faces, 9 edges, and 6 vertices
H The figure has more edges than
vertices.
D 6 faces, 12 edges, and 8 vertices
J
2. What is the sum of the number of edges
of the two three-dimensional figures
shown?
F
Class
The figure has twice as many edges
as faces.
5. What is the sum of the number of
faces, edges, and vertices of the threedimensional figure shown?
11
G 14
H 18
J
A 14
21
B 18
3. Which of the following three-dimensional
figures has only two more edges than
faces?
C 20
D 26
A a square pyramid
B a triangular pyramid
C a triangular prism
D a rectangular prism
114
4/14/06 9:51:17 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
4. Which best represents the approximate
area of the composite figure shown if the
rectangle is topped by a semicircle?
1. What is the area of a square that has
one of its sides with endpoints at (⫺1, 5)
and (4, 7)?
A 兹29 units2
B 13 units2
C 4兹29 units2
D 29 units2
2. The figure shown is a regular hexagon.
Which expression shows the area of
the figure?
7 units
12
16 units
F
125 units2
G 189 units2
x⫹1
H 212 units2
F
6(x ⫹ 12)
J
G 12x ⫹ 12
5. If the two shaded triangles are congruent
right triangles, what is the area of the
portion of the rectangle that is NOT
shaded?
H 36x ⫹ 36
J
301 units2
72x ⫹ 72
3. A circle with a diameter of 12 inches
is inscribed in a square. What is the
perimeter of the square?
10 cm
A 144 ⫺ 12 in.
6 cm
B 48 in.
C 48 in.
3 cm
D 144 in.
A 18 cm2
B 42 cm2
C 51 cm2
D 60 cm2
115
4/14/06 9:58:02 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
4. What is the approximate length of
arc ABC?
Use the diagram to answer questions 1
and 2.
A section of a circular flower bed is to be
used only for herbs.
A
Area to be used
only for herbs
10
125°
12 ft
100°
B
F
C
21.8 units
G 32.6 units
1. What is the approximate area of the
section of the flower bed that is for herbs
only?
H 41.0 units
J
62.8 units
5. The area of the shaded section in the
circle shown is 12. What is the value
of x ?
A 452 ft2
B 327 ft2
C 126 ft2
D 10 ft2
12
2. If a small fence is to be put around the
entire section of the garden to be used
for herbs, about how many feet of fence
is needed?
F
x°
21 ft
G 33 ft
A 20°
H 45 ft
J
B 25°
75 ft
C 30°
3. A circular stained glass window is to
have a diameter of 20 inches. The
window is divided into 10 congruent
sectors, which will have alternating
colors. What is the approximate area of
each sector?
A 31 in2
B 40 in2
C 62 in2
D 126 in2
D 35°
116
4/14/06 9:58:02 AM
Name
OBJECTIVE
8
Date
Ready for TAKS?
1. Pete’s house is 9 miles due south of
Ann’s house and 4 miles due east of
Dana’s house. What is the approximate
straight line distance from Ann’s house
to Dana’s house?
4. A door is 3 feet wide and the diagonal
length across the door is 7 feet. If
Mr. Davis wants to cover the entire door
with plastic, about how many square feet
of plastic does he need?
6 ft2
A 5.0 mi
F
B 8.1 mi
G 13 ft2
C 9.8 mi
H 19 ft2
D 13.0 mi
J
21 ft2
5. A rectangle is inscribed in a circle as
shown.
2. What is the area of the triangle that has
vertices at the points (3, ⫺4), (3, 1), and
(11, 1)?
F
Class
14 units2
G 20 units2
H 24 units2
J
40 units2
3. A courier travels from his home office
to deliver a package to Company A and
then to deliver a package to Company B
as shown in the figure.
Home Office
If the length and width of the rectangle
are 6 and 13 inches respectively, what
is the approximate circumference of
the circle?
A 14 in.
7 mi
B 45 in.
C 47 in.
Company B
4 mi
Company A
D 90 in.
If he travels straight back home from
Company B, about how much shorter
is this trip than the one from his home
office to Company B via Company A?
A 1.3 mi
B 3.0 mi
C 5.3 mi
D 5.7 mi
117
4/14/06 9:58:02 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
1. In the rectangular prism, AB ⫽ 9 cm,
1BC.
BC ⫽ 15 cm, and DC ⫽ __
3
3. If the edge of a cube is 6 inches and the
edge of a smaller cube is 4 inches, what
is the difference in the volumes of the
two cubes?
D
A 216 in3
B 152 in3
C
C 120 in3
D 64 in3
A
B
4. A balloon that is in the shape of a
sphere will be used in a parade. What is
the approximate volume of the balloon, if
the diameter of the balloon is 15 feet?
What is the volume of the prism?
A 27 cm3
B 87 cm3
F
C 405 cm3
G 707 ft3
D 675 cm3
H 1,325 ft3
2. The figure is a rectangular prism topped
by a pyramid. What is the approximate
volume of the figure?
J
236 ft3
1,766 ft3
5. Approximately how much grain can the
cylindrical grain bin hold?
2m
4
Golden
Grain
3
5m
4
2
F
A 21 m3
4 units3
G 13 units3
B 63 m3
H 32 units3
C 100 m3
48 units3
D 157 m3
J
118
4/14/06 9:58:03 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
1. If 䉭ABC is similar to 䉭XYZ, which
proportion is true?
4. There are two pentagons, ABCDE and
FGHIJ. If the ratios given are true, which
is the correct way to write the similarity
between the two pentagons?
BC ⫽ ___
AC
A ___
YZ
XY
AC ⫽ ___
CD and ___
AB ⫽ ___
BD
___
AB ⫽ ___
XY
B ___
YZ
BC
GJ
F
AC ⫽ ___
YZ
C ___
XZ
BC
HI
GH
JI
ABCDE ⬃ FGHIJ
G ABCDE ⬃ HIJFG
H ABCDE ⬃ IGJFH
AC ⫽ ___
AB
D ___
XZ
YZ
J
2. A rectangular prism is shown. If a
second prism is similar to the one
shown, which of the following could be
the dimensions of the second prism?
ABCDE ⬃ GJHIF
5. The two rectangles shown are similar.
The perimeter of the smaller rectangle is
20 centimeters and its area is 24 square
centimeters. If the area of the larger
rectangle is 96 square centimeters, what
is the perimeter of the larger rectangle?
18 in
4 in
F
9 in
3 in. by 8 in. by 17 in.
G 0.75 ft by 3 ft by 6 ft
A 4 cm
H 12 in. by 18 in. by 27 in.
B 40 cm
2 ft by 4.5 ft by 9 ft
C 80 cm
J
D 92 cm
3. Which of the following would prove that
triangle ABC is similar to triangle WXY ?
A The sum of the angles of both
triangles is 180°.
B Each angle in both triangles has a
measure of 60°.
C The ratio of AB to AC is the same as
the ratio of WX to XY.
D BC has the same length as XY.
119
4/14/06 9:58:03 AM
Name
Date
OBJECTIVE
8
Class
Ready for TAKS?
_
_
4. Use the diagram to find the value of x if
both triangles are right triangles and the
top angles of the two triangles are equal.
1. If AB is parallel to CD in the diagram,
_
what is the approximate length of OD ?
C
A
4
7
B
O
13
x
5
6
7.5
45
D
36
A 7.4 units
F
B 9.3 units
G 37.5
C 10.0 units
H 43.5
D 11.0 units
J
56.25
_
_
F
_
5. BE_
is parallel to CD . The length of AB is
2, CB is 7, and the perimeter of triangle
ABE is 8.
2. A triangle has a height of 15 units and a
perimeter of 40 units. If a similar triangle
has a height of 9 units, what is its
perimeter?
A
34 units
G 32 units
B
H 26 units
J
E
24 units
3. Triangle ABC with vertices A(2, 4),
B(5, 4), and C(5, 10) is similar to triangle
DEF with vertices D(2, ⫺2), E(14, ⫺2),
and F. Which of the following could be
the coordinates of F ?
C
What is the perimeter of triangle ACD ?
A (⫺4, 24)
A 10 units
B (12, 18)
B 15 units
C (⫺6, ⫺18)
C 30 units
D (14, 22)
D 36 units
D
120
4/14/06 9:58:03 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
4. Which of the ratios is equivalent to
cos B ?
1. Use the diagram to find the value of x ?
A
8
13
x
5
32
A 2
B 4
C
C 6
5
___
12
F
D 8
B
5
G ___
13
2. Which theorem justifies the statement
that the two triangles shown are similar?
12
H ___
13
12
___
J
F
5
5. Use a trigonometric ratio to find the
value of x in the triangle. (Round to the
nearest tenth.)
SSS
G SSA
A
H SAS
J
AAA
17
3. Which set of three integers could be a
Pythagorean Triple?
x
A a ⫽ 5, b ⫽ 9, and c ⫽ 14
42°
B a ⫽ 7, b ⫽ 14, and c ⫽ 19
C a ⫽ 7, b ⫽ 24, and c ⫽ 25
C
D a ⫽ 12, b ⫽ 13, and c ⫽ 25
A 0.1
B
B 11.4
C 12.6
D 15.3
121
4/14/06 9:58:03 AM
Name
OBJECTIVE
8
Date
Class
Ready for TAKS?
4. The two cylinders shown are similar. The
lateral areas of the cylinders are 324
square centimeters and 576 square
centimeters.
1. Maggie’s old rectangular fish tank is
12 inches wide, 24 inches long, and
13 inches tall. Her new fish tank has
dimensions that are double her old one.
By how much did the volume of her fish
tank increase when she bought the new
one?
A 8 times
B 6 times
C 4 times
D 2 times
The volume of the smaller cylinder is
1,242 cubic centimeters. What is the
volume of the larger cylinder?
2. The circumference of a circle is 3 times
the circumference of a smaller circle.
If the area of the larger circle is 486
square inches, what is the area of the
smaller circle?
F
18 in
F
G 2,208 cm3
2
H 2,944 cm3
2
G 54 in
J
2
H 81 in
J
1,656 cm3
3,726 cm3
5. A glass paperweight shaped like a
hemisphere has a volume of 5 cubic
inches. What is the volume of a similarly
shaped paperweight if each dimension
is four times as large as the smaller
paperweight?
163 in2
3. The figures shown represent the faces of
two cubes. If Matt knows the volume of
the cube on the left how can he get the
volume of the cube on the right?
A 20 in3
B 80 in3
C 320 in3
m
D 1,280 in3
7m
A Multiply the volume by 7.
B Multiply the volume by 49.
C Multiply the volume by 343.
D Cube the volume.
122
4/14/06 9:58:04 AM
Name
OBJECTIVE
9
Date
Class
Ready for TAKS?
Benchmark Post-Test (8.3)(B)
4. The circle graph shows the distribution
of the ages of 200 people at a job fair.
1. There are 176 freshmen and 194
sophomores at a local high school. Only
60% of those students signed up to go
to the homecoming dance. How many of
the freshmen and sophomores did NOT
sign up to go to the dance?
30%
Over 25
A 40
70%
Under 25
B 148
C 222
D 370
2. A cylindrical grain bin is being filled. The
height of the grain bin is 15 feet and the
diameter of its base is 8 feet. After the
first 15 minutes, the height of the grain in
the bin is 1 foot. At this rate, what will be
the volume of the grain in the bin after
one hour?
Of the people over the age of 25, 15%
are older than 50. How many people at
the job fair are older than 50?
F
5
G 9
H 21
8⬘
J
30
5. The number of cars entering a car wash
between certain times is shown in the
bar graph. About what percent of the
total number of cars entered the park
before 8 PM?
15⬘
F
Number of Cars
100
16␲ ft3
G 64␲ ft3
3
H 96␲ ft
J
256␲ ft3
75
50
25
0
3. Jim answered 25% of the questions
on his history test incorrectly. If he
answered 33 questions correctly, how
many questions were there on the test?
8 AM to
Noon
12 to
4 PM
4 to
8 PM
8 to
Midnight
A 0%
A 25
B 42.5%
B 30
C 75%
C 40
D 87.5%
D 44
123
4/14/06 9:53:36 AM
Name
OBJECTIVE
9
Date
Class
Ready for TAKS?
Benchmark Post-Test (8.11)(A)
1. A new toy store is giving away 20 toy
rings: 9 are red, 6 are white, and 5 are
blue. A ring is selected at random and
given to a customer. If the ring is red,
what is the probability that the next ring,
selected at random, is NOT red?
4. Each of the smaller squares inside the
larger square shown is the same size.
If the diagram represents a dart board,
what is the probability of hitting a shaded
square, assuming the board is hit?
9
A ___
20
9
B ___
19
11
C ___
20
11
D ___
19
F
G 0.52
2. If 2 marbles are drawn simultaneously
at random from a box containing 6 red
marbles, 4 white marbles, and 4 blue
marbles, what is the probability that
neither of the marbles is white?
F
0.48
H 0.56
J
0.92
5. A multiple-choice test has five choices
for each answer. There are twenty
questions. If a student guesses on
the first two questions, what is the
probability that the student will get both
questions wrong?
6
___
91
6
G ___
49
45
H ___
91
1
A ___
25
45
___
49
16
B ___
25
J
3. At the end of a conference, 75 attorneys
enter a prize drawing by placing their
name tags in a box. After 8 name tags
have been selected and removed from
the box, Mrs. Jacobs has not yet won
a prize. What is the probability that
Mrs. Jacobs will win the next prize?
Round to the hundredth place.
4
C __
5
8
D __
5
A 0.01
B 0.02
C 0.11
D 0.13
124
4/14/06 9:53:37 AM
Name
OBJECTIVE
9
Date
Ready for TAKS?
3. Mavis bought 4 packs of yogurt covered
raisins and recorded the number of
purple raisins in each. Each pack
contains 40 raisins.
Jake conducted an experiment by rolling
a standard number cube 300 times. The
results of Jake’s experiment are shown in
the bar graph. Use the bar graph to answer
questions 1 and 2.
300 Tosses of a Number Cube
70
Number of Times Tossed
Class
60
60
55
50
46
40
55
43
42
30
20
1
2
3
4
5
6
Digit
1. According to the data, what is the
experimental probability of rolling a 4 on
the next roll of the number cube?
12
2
6
3
8
4
10
B 0.300
C 0.333
D 0.900
1
B ___
15
4. A local newspaper polled 50 residents of
a small town to determine how they were
going to vote on the proposal to tear
down the community center. The results
of the poll are shown in the table.
1
C ___
60
1
D ___
75
2. What is the approximate difference
between the experimental probability
and the theoretical probability of rolling
a 4 on the next roll?
Vote
Frequency
Yes
30
No
20
Based on these experimental results,
and assuming that all 320 residents in
the town vote, how many people could
be expected to vote “Yes” to tear down
the center?
0.033
G 0.100
H 0.150
J
1
A 0.225
1
A __
5
F
Number of Purple Yogurt
Covered Raisins
According to Mavis’s sample data,
what is the probability that a randomly
selected raisin from one of these packs
is purple if all the packs are poured out
together?
10
0
Pack
0.153
F
20
G 30
H 128
J
125
192
4/14/06 9:53:37 AM
Name
OBJECTIVE
9
Date
Class
Ready for TAKS?
1. During the first four days of a new pizza
place’s opening, they sold a total of
143 pizzas. The sales per day were 26,
35, 53, and 29. Which measure of the
data would be the most impressive to
report to the public?
4. The number of patients treated at an
emergency room each day for a week
was recorded in the table.
Patients Treated
A range
B mean
C median
Monday
62
Tuesday
52
Wednesday
51
Thursday
50
Friday
44
D mode
Which measure of the data would NOT
change if the number of patients treated
on Monday was actually 8 less than
recorded and on Friday was 8 more?
2. Egbert earned the following grades on
his biology tests: 79, 84, 95, 84, 89, and
92. Which measure of the data will give
him the highest overall score?
F
F
range
G mean
G mean
H median
H median
J
range
J
mode
mode
5. A pet store is analyzing a frequency
table to identify the number of fish they
sold last year. Which measure of data
describes the most popular kind of fish
sold?
3. A set of data has 10 values, no two of
which are the same. If the largest data
value is removed from the set, which of
the following statements MUST be true?
A The range of the first data set is
greater than the range of the second
data set.
A range
B mode
C median
B The mode of the first data set is
greater than the mode of the second
data set.
D mean
C The medians of the two data sets are
the same.
D The mean of the first data set is less
than the mean of the second data
set.
126
4/14/06 9:53:37 AM
Name
OBJECTIVE
9
Date
Ready for TAKS?
Benchmark Post-Test (8.12)(C)
1. The census bureau surveyed families in
a certain geographic region to find out
how many children lived in the home.
The survey results are shown in the bar
graph.
4. Zack gathered information about the
approximate price range of cars parked
at the mall. He used the information
to create the bar graph and the circle
graph shown. The circle graph accurately
reflects the information gathered, but two
of the columns in the bar graph were
switched.
Census Bureau Survey Results
70
60
Frequency
Class
50
Price Range of Cars
40
35
20
30
Frequency
30
10
0
0
1
2
3
Numbers of Children
4 or
more
25
20
15
10
5
0
Approximately how many of the families
surveyed had children living at home?
A 45
B 70
C 185
D 230
19%
H 32%
C 119
D 109
Over 50
Under $15
33%
$35–$50
14%
$25–$35
15%
$15–$25
28%
According to the information in the circle
graph, which two columns of the bar
graph were switched?
F
3. The students at a local high school
recorded the number of votes that each
of three teachers received for “Favorite
Teacher.” A total of 280 students voted.
Mr. Bradley received 42.5% of the votes
and came in first place. If a bar graph
is constructed, and the vertical axis
represents the number of votes received,
which of the following could be the height
of the bar for one of the other teachers?
B 120
35–50
Over $50
10%
105%
A 125
25–35
Price Range
(in thousands of dollars)
G 25%
J
15–25
Price (in thousands of dollars)
2. Of the 420 people at a concert, 80
people are attending alone, 105 people
are with a friend, 135 are with a
spouse, and the rest are with another
member of their family. If a circle graph
is constructed, which of the following
is the approximate percentage needed
to represent the number of people
attending the concert with a friend?
F
Under
15
Under $15 and $15–$25
G Under $15 and Over $50
H $25–$35 and Over $50
J
127
$25–$35 and $35-$50
4/14/06 9:53:38 AM
Name
OBJECTIVE
9
Date
Class
Ready for TAKS?
Use the circle graph to answer questions
1 and 2.
Use the bar graph to answer questions 3
and 4.
The circle graph shows how a company’s
budget was distributed last year.
The bar graph shows the number of
moviegoers who prefer certain types of
movies.
Janitorial
6%
Moviegoer Preferences
Romance
Operating
Expenses
33%
Salaries
46%
Horror
Action
Drama
Supplies Employee Benefits
9%
6%
Comedy
0
Budget Distribution
100
200
300
400
Number of Moviegoers
1. Which statement is NOT true?
3. Which statement is NOT true?
A Salaries made up slightly less than
half the budget.
A Horror movies are preferred the
least.
B Salaries and Employee Benefits
together made up more of the
budget than all the other categories
combined.
B More than twice as many moviegoers
prefer Drama to Romance.
C Action movies are preferred by more
moviegoers than Comedy movies.
C Operating expenses made up more
than one-third of the budget.
D Drama movies are preferred the
most.
D Janitorial services and Employee
Benefits made up equal parts of the
budget.
F
F
G There’s a larger potential audience
for dramas than other types of
movies.
The company needs to cut down on
its salaries.
G The company needs to increase its
budget for operating expenses.
H Horror movies do not make a profit.
J
H The company budgets approximately
1/8 of the amount of Salaries for
Employee Benefits.
J
There are too many drama movies
produced.
Moviegoers prefer Horror movies the
least because they are rated “R.”
The company does not spend any
money on medical insurance.
128
4/14/06 9:53:38 AM
Name
OBJECTIVE
10
Date
Class
Ready for TAKS?
1. An ice cream company reported that
the average price of vanilla increased
by 0.4% per year from 1949 to 1965.
What additional information is needed to
calculate the average price of vanilla in
1965?
Use the Venn diagram to answer
questions 4 and 5.
The Venn diagram shown represents all
840 students at a school. The circle on the
left represents the students who have taken
Mr. Jones for history, and the circle on the
right represents the students who have taken
Ms. Smith for science.
A the average price of vanilla in 1900
B the average price of vanilla in 1949
C the average price of vanilla in 1970
Mr. Jones
Ms. Smith
D the range of vanilla prices from 1949
to 1965
2. Holly’s mother’s age is 10 years more
than 4 times Holly’s age. If Holly’s
mother is 32 years old, which equation
can be used to determine Holly’s age?
F
Z
X
W
4x ⫽ 32
G 4(x ⫹ 10) ⫽ 32
4. What does the section labeled with a Y
represent?
H 10 ⫹ 4x ⫽ 32
J
Y
F
4x ⫺ 10 ⫽ 32
3. Sarah bought a pair of pants on sale for
40% off the original price. If the original
price was x, which equation could Sarah
use to find the sale price, s, of the
pants?
Students who have taken Ms. Smith
for science but have not taken
Mr. Jones for history.
G Students who have taken both Ms.
Smith for science and Mr. Jones for
history.
2x
A s ⫽ x ⫺ __
5
H Students who have not taken
Mr. Jones for history.
2s⫽ x
B s ⫺ __
5
J
All students who have taken
Ms. Smith for history.
5. Which of the labeled sections represents
the students who have taken Mr. Jones
for history but not taken Ms. Smith for
science?
2x
C s ⫽ x ⫹ __
5
2
D s ⫽ x ⫺ __
5
A W
B X
C Y
D Z
129
4/14/06 9:53:57 AM
Name
OBJECTIVE
10
Date
Ready for TAKS?
4. The value of a $250,000 home in a
certain area increases by approximately
$12,000 per year. After how many years
will the home be worth approximately
$310,000?
1. A full swimming pool that is 6 feet
deep by 35 feet long by 15 feet wide is
being emptied at a rate of 60 ft3 every
10 minutes. How many minutes would it
take to empty the pool at that rate?
2 yr
A 5 min
F
B 53 min
G 3 yr
C 525 min
H 4 yr
D 3,150 min
J
5 yr
5. A farmer is plowing the circular
field shown. If the farmer can plow
approximately 500 square feet per
minute, about how many hours will it
take him to plow the whole field?
2. Jeff bought a tie that was on sale for
35% off and a hammer for 55% off.
The original cost of each was $25.00. If
the tax rate is 7.5% and Jeff gives the
salesclerk two $20.00 bills, how much
change should he get back?
F
Class
$10.44
G $17.50
H $22.50
J
400 feet
$29.56
3. A cylindrical barrel is to be filled with oil.
What additional information is needed to
determine how much oil the barrel will
hold?
A 4 hr
B 5 hr
4 ft
C 200 hr
D 251 hr
A the lateral area of the barrel
B the radius of the barrel
C the surface area of the barrel
D the weight of the barrel
130
4/14/06 9:53:58 AM
Name
OBJECTIVE
10
Date
Ready for TAKS?
Benchmark Post-Test (8.14)(C)
4. The volume of a cylinder is 13,500 ft3.
Which of the following could be the
height and radius of the cylinder in feet?
1. A small theatre has 30 rows of seats.
The first row has 100 seats; the second
row has 98 seats; and the third row has
96 seats. If this pattern continues, how
many seats will there be in the last row?
F
10 ft and 90 ft
G 20 ft and 45 ft
A 38 seats
H 20 ft and 35 ft
B 40 seats
J
C 42 seats
15 ft and 30 ft
5. The point (⫺3, 2) is reflected across the
line with equation y ⫽ x. The resulting
point is (3, ⫺2). The new point is again
reflected across the line with equation
y ⫽ x. The resulting point is (⫺3, 2). If
this pattern continues, what will be the
resulting x-coordinate for the point after
2 pairs of reflections?
D 44 seats
2. The surface area of a cube is 300
square feet. What is the best first step to
determine the length of one of the sides
of the cube?
F
Class
Take the cube root of 300.
G Take the square root of 300.
y
H Divide 300 by 4.
J
10
Divide 300 by 6.
8
3. Which of the equations could represent
the step before Step 2 in the solution to
an algebra problem?
6
4
2
Step 1.
–10 –8
Step 2. 12 ⫺ 6x ⫹ 15 ⫽ ⫺15
–6
–4
–2
2
–2
Step 3. 27 ⫺ 6x ⫽ ⫺15
–4
Step 4. ⫺6x ⫽ ⫺42
–6
4
6
8
10
x
–8
Step 5. x ⫽ 7
–10
A ⫺2 (6 ⫹ 3x) ⫹ 15 ⫽ ⫺15
B 2(6 ⫹ 3x) ⫹ 15 ⫽ ⫺15
A ⫺3
C 12 ⫺ 3(2x ⫹ 5) ⫽ ⫺15
B ⫺2
D 12 ⫺ 3(2x ⫺ 5) ⫽ ⫺15
C 2
D 3
131
4/14/06 9:53:58 AM
Name
OBJECTIVE
10
Date
Class
Ready for TAKS?
4. A newspaper editor has been given four
articles to print in the paper. The circle
graph shown belongs to one of the
articles. Which list of data goes with the
circle graph?
Use the figure to answer questions 1
and 2.
1. If the figure is a solid billiard ball, the
amount of ceramic needed to make the
ball best represents the ball’s—
A diameter
B circumference
C surface area
D volume
F
2. If the figure is a world globe, the straight
line distance through the globe from
the north pole to the south pole best
represents the globe’s—
F
diameter
G The election results were as follows:
40% for Barry, 24% for Andrews,
22% for Jones, and 14% for
Hawthorne.
G circumference
H surface area
volume
J
3. Which of the following transformations
describes how to get from point A to
point B ?
H The school budget is allocated
accordingly: 40% for building, 35%
for salaries, 20% for books, 5% for
other.
y
10
8
J
6
4
A
2
–10 –8 –6 –4 –2
–2
–4
2
4
6
8
10
A survey of citizens had the following
results: 23% supported totally
financing the new library, 10%
supported partially financing the new
library, 34% did not support financing
the library, and 33% were undecided.
x
B
The town census reported the
following for the ages of residents:
4% were over 75 years old, 11%
were between 50 and 75 years old,
60% were between 25 and 50 years
old, and 25% under 25 years of age.
–6
5. If the product of the quantities 8 ft,
ft , and 5 s is found, what units of
17 __
s2
measure will be in the answer?
–8
–10
A a 90° counter clockwise rotation
ft
A s__
ft2
C __
s
B a 180° rotation
C a reflection over the line with
equation y ⫽ ⫺x
D a reflection across the x-axis
132
B ft ⴢ s
D There will be
no units of
measure.
4/14/06 9:53:58 AM
Name
Date
OBJECTIVE
10
Class
Ready for TAKS?
3. What is the missing term in the pattern?
1. Use the examples and non-examples
provided to determine which of the
following is NOT a tergon.
Tergons
⫺5, ______, ____
8
⫺7 , ____
___
y3
x 2y 7 x 3y 9
6
A ___
xy 5
Not Tergons
⫺6
B ___
xy 5
6
C __
y5
⫺6
D ___
y5
4. For which of the following sets of points
is a linear model reasonable?
A
B
F
{(3, ⫺5), (4, ⫺2), (5, 3), (6, 0)}
G {(⫺5, 0), (⫺1, ⫺2), (3, 4), (7, ⫺6)}
C
H {(⫺2, 2), (1, 0), (4, ⫺2), (7, ⫺4)}
D
J
5. Gertrude made the conjecture that the
1 is all
domain of the function f (x ) ⫽ x__
real numbers. Which of the following
2. The table lists several powers of the
number 7.
Powers of 7
7
7
7
2
49
7
3
343
7
4
2,401
7
5
16,807
7
6
117,649
77
823,543
7
values of x is a counterexample to
Gertrude’s conjecture?
Resulting Value
1
8
{(6, 1), (4, 4), (0, 2), (5, 8)}
A (⫺2)2
B 2
C 0
1
D ⫺__
2
5,764,801
Given that the digit in the ones place will
continue to repeat in the pattern above,
what will be the digit in the ones place in
495?
F
7
H 3
G 9
J
1
133
4/14/06 9:53:58 AM
Name
OBJECTIVE
10
Date
Class
Ready for TAKS?
4. Which statement about the quadrilaterals
shown is NOT true?
1. If the variables x and y represent real
numbers, which statement is NOT
always true?
B
C
A If x ⬎ y, then ⫺x ⬍ ⫺y.
B If x ⬎ y, then x ⫹ y ⬎ 0.
C If x ⬎ y, then 2x ⬎ 2y.
D
A
y
D If x ⬎ y, then __x ⬎ __.
2 2
E
F
H
G
2. If the variables x and y represent real
numbers and x ⬎ y , which statement
must be true?
F
x⬎y
G y⬎x
F
H 2x ⬎ 2y
J
x2 ⬎ y2
G If ⬔B ⬔D and ⬔A ⬔C,
then both quadrilaterals are
parallelograms.
3. The value of A in the triangle shown
CANNOT equal which of the following
quantities?
H If ⬔B ⬔A and ⬔D ⬔C,
then both quadrilaterals are
parallelograms.
B°
_
J
A°
The sum of the measures of the
angles of both quadrilaterals is 720°.
C°
_ _
_ _
_
EF_
, CD FG , DA GH ,
If BC_
and AB HE , then both
quadrilaterals have the same
perimeter.
NOT true?
A 90 ⫺ C
A The diagonals of a rectangle are
always congruent.
B 180 ⫺ C
C 180 ⫺ 2C
B The diagonals of a square are
always congruent.
D 90 ⫺ B
C The diagonals of a trapezoid are
sometimes congruent.
D The diagonals of a rhombus are
never congruent.
134
4/14/06 9:53:59 AM

Benchmark Post-Test (8.11)

Transcription

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