Find the opposite and the reciprocal of the
number.
HONORS ALG. 2 CH. 1 TEST REVIEW
Multiple Choice
Identify the choice that best completes the statement or
answers the question.
____
9. 3
a. 3, 3
b.
To which sets of numbers does the number
belong?
____
1.
a.
b.
c.
d.
____
____
2
15
a. integers, rational numbers, real numbers
b. rational numbers, real numbers
c. irrational numbers, real numbers
d. rational numbers, irrational numbers, real
numbers
3. An irrational number can ________ be
expressed as a quotient of integers.
a. always
b. sometimes
c. never
c.

1
3
50
, –1.74
87
d.
50
1.74, 
87
, c.
 d.
,
a.
b.
c.
d.
Associative Property of Multiplication
Distributive Property
Commutative Property of Addition
Associative Property of Addition
____ 13.
–5 –4 –3 –2 –1 0 1 2 –53 –44 –35 –2 –1 0 ____
1 2
d
.
–5 –4 –3 –2 –1 0 1 2 –53 –44 –35 –2 –1 0 1 2
____
a. Associative Property of Multiplication
b. Commutative Property of Addition
c. Commutative Property of Multiplication
d. Closure Property
3
4
5  0 = –2.5
14. –2.5
a. Inverse Property of Multiplication
b. Identity Property of Addition
3 4 5
c. Inverse Property of Addition
d. Identity Property of Multiplication
15. Simplify
.
a. 14
b. 8
c. –8
d. –14
5.
a. =
b. >
Evaluate the expression for the given value of
the variable(s).
c. <
6.
____ 16.
a. >
b. <
c. =
;
a. –55
,
b. 55
c. 5
d. –5
a. 32
b. 48
c. 48
d. 30
a. 3
; x = –3
b. –1
c. 11
d. –17
____ 17.
7.
a. >
____
3,
____ 12.
c
.
Insert <, >, or = to make the sentence true.
____
d.
1
3
Name the property of real numbers
illustrated by the equation.
4.
b
.
____
3, 
2. 
a
.
____
1
3
____ 10. –1.74
a. 50 87
 ,
87 50
irrational numbers, real numbers
b.
87
integers, rational numbers, real numbers
1.74, 
50
rational numbers, irrational numbers
whole numbers, integers, rational numbers, ____ 11.
a.
, b.
real numbers
Graph the number on a number line.
____
3,
c.
b. =
c. <
____ 18.
8.
a. <
b. >
c. =
____ 19.
; x = –3
a. –76
b. 62
c. 32
d. 30
Solve the equation or formula for the
indicated variable.
Simplify by combining like terms.
____ 28.
____ 20.
a
.
b
.
c
.
, for t
b
.
a
.
d
.
c
.
____ 29. The formula for the time a traffic light remains
____ 21.
yellow is
a.
b.
c.
d
.
d.
, where t is the time in
seconds and s is the speed limit in miles per
hour.
a. Solve the equation for s.
b. What is the speed limit at a traffic light that
remains yellow for 4.5 seconds?
____ 22. Find the perimeter of the figure. Simplify the
answer.
x+y
a.
; s = 28
c.
; s = 35
mi/h
2x
4x
b.
; s = 36 mi/h d.
; s = 28
mi/h
y
Solve for x. State any restrictions on the
variables.
2x
x
____ 30.
a.
c.
;
;
a. 9x + 2y b. 10x + y c. 10x + 2y d. 9x + 3y
b.
Solve the equation.
;
d.
;
____ 23.
a.

1
17
a.

1
2
2
3
c. 23
d. 17
1
2
c. 2
d.
b. –2
c. 0.5
d. 2
b.
7
____ 24.
b.
2

2
5
____ 25.
a. –0.5
____ 26.
a.
x = 2 or x = 1
b. x = 2 or x = 4
1
3
c. x = 2 or x = 2
d.
1
x = 1 or x = 2
3
____ 27.
a.
8
2
or x = 
9
9
b.
2
x = 0 or x = 2
3
x=
c.
8
2
or x = 2
9
3
d.
8
x = or x = 0
9
x=
____ 31. A rectangle is 3 times as long as it is wide. The
perimeter is 60 cm. Find the dimensions of the
rectangle. Round to the nearest tenth if
necessary.
a. 7.5 cm by 22.5 cm c. 20 cm by 60 cm
b. 7.5 cm by 52.5 cm d. 15 cm by 22.5 cm
____ 32. The sides of a triangle are in the ratio 3 : 4 : 5.
What is the length of each side if the perimeter
of the triangle is 90 cm?
a. 10.5 cm, 11.5 cm, c. 7.5 cm, 11.5 cm,
and 12.5 cm
and 32.1 cm
b. 22.5 cm, 30 cm, and d. 19.3 cm, 25.7 cm,
37.5 cm
and 32.1 cm
____ 33. Two cars leave Denver at the same time and
travel in opposite directions. One car travels 10
mi/h faster than the other car. The cars are 500
mi apart in 5 h. How fast is each car traveling?
a. 35 mi/h and 45 mi/h c. 45 mi/h and 55 mi/h
b. 55 mi/h and 35 mi/h d. 55 mi/h and 65 mi/h
____ 34. An inequality ____ has a real number solution.
a. always
b. sometimes
c. never
Solve the inequality. Graph the solution set.
____ 35. 2 + 2k  8
a k3
.
–8 –6 –4 –2
0
2
4–8 6–6 8–4 –2
0
2
4
____ 36. 2r – 9  –6
a
1
. r  12
2
4–8 6–6 8–4 –2
0
2
4
8 –8 –6 –4 –2
6
dk5
.
0
0
____ 40. 26 + 6b  2(3b + 4)
a all real numbers
.
c k3
.
b k5
.
–8 –6 –4 –2
–8 –6 –4 –2
6
0
6
8
2
4 6 8
–8 –6 –4 –2
0
2
4
0
2
4
0
2
4
4–8 6–6 8–4 –2
0
2
4
4–8 6–6 8–4 –2
0
2
4
4–8 6–6 8–4 –2
0
2
4
d no solutions
.
8
–8 –6 –4 –2
4
c
1
. b  12
b
1
. b  12
c
1
. r  12
2
0
2
–8 –6 –4 –2
4 6 8
Solve the problem by writing an inequality.
–8 –6 –4 –2
0
b
1
7
. r 2
–8 –6 –4 –2
4–8 6–6 8–4 –2
0
d
1
7
. r 2
0
____ 37. –4k + 5  21
a k  –4
.
–8 –6 –4 –2
2
2
4–8 6–6 8–4 –2
0
b
1
6
. k 2
2
4–8 6–6 8–4 –2
2
4
6
8
Solve the compound inequality. Graph the
solution set.
c k  –4
.
0
2 4 6 8
____
41. If the perimeter of a rectangular picture frame
must be less than 200 in., and the width is 36 in.,
what must the height h of the frame be?
a. h < 64 b. h > 128 c. h > 64 d. h < 128
in.
in.
in.
in.
0
d
1
6
. k 2
____ 42. 5x + 10  10 and 7x – 7  14
2 4 6 8
a x  4 or x  1
c x  4 or x  3
.
.
–8 –6 –4 –2
0
b x  0 and x  1
–8 –6 –4 –2
0
2
4–8 6–6 8–4 –2
0
____ 38.
b
5

. y 8
4
6 . 8
–8 –6 –4 –2
4–8 6–6 8–4 –2
d x  0 and x  3
.
0
2
____ 43.
2(4y – 5)  –10
a y0
.
–8 –6 –4 –2
2
2
a
.
c y0
.
0
2
4–8 6–6 8–4 –2
0
2
4
6
d
5

. y 8
b
.
–8 –6 –4 –2
c
.
0
8
2
d
.
–8 –6 –4 –2
0
2
____ 44. The perimeter of a square garden is to be at least
–8 –6 –4 –2 0 2 4–8 6–6 8–4 –2 0 2 4 6 228 feet but not more than 36 feet. Find all
possible values for the length of its sides.
____ 39. 4(3b – 5) < –31 + 12b
a.
c.
a no solutions
c
11
b.
d.

.
. b > 24
____ 45. An absolute value equation ____ has an
–8 –6 –4 –2 0 2 4 6 8
extraneous solution.
b. sometimes
c. never
–8 –6 –4 –2 0 2 4 6 a. 8 always
b
11

. b < 24
d all real numbers
.
–8 –6 –4 –2
Solve the equation. Check for extraneous
solutions.
0
2
4
6
8
____ 46.
a.
c.
b.
d.
52.
53. An engineer predicts that a machine will
manufacture good parts 80% of the time. Use a
simulation of twelve trials and the random
number chart below to find the probability that
the machine will make good parts on all of the
next four attempts.
9295
6742
7980
5522
Solve the inequality. Graph the solution.
____ 47.
a
.
c
.
–40 –30 –20 –10 0
b
.
10 20
–20 30
–15 40
–10 –5
3376
2187
6217
8811
4500
4665
2860
0
5
10 15 201243
0
5
10 15 20
d
.
–20 –15 –10 –5
0
5
10
–20 15
–15 20
–10 –5
____ 48.
a 3
3
4 < x < 4
.
8
8
–6
–4
c
3
3
4
4
. x < 8 or x > 8
–2
b 3
1
4 < x < 4
.
4
4
–6
–4
2 –6 4 –4 6 –2
0
0
2
4
6
0
2
4
6
d
3
1
4
4
. x < 4 or x > 4
–2
0
2 –6 4 –4 6 –2
Short Answer
49. In the following expression: the number of
people p required to paint n square feet of wall
in 24 hours, which set of numbers best describes
the values for each variable?
50. Name the property used in each step of
simplification.
Simplify the expression.
51.
Solve the equation. Check for extraneous
solutions.
45.
46.
47.
48.
HONORS ALG. 2 CH. 1 TEST REVIEW
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
ANS:
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A
B
C
D
B
B
C
B
D
D
A
B
C
B
B
A
B
B
C
B
B
C
D
B
D
D
B
D
A
D
A
B
C
B
C
C
A
C
A
A
A
D
B
C
ANS:
ANS:
ANS:
ANS:
B
C
C
B
SHORT ANSWER
49. ANS:
The number of people p is a natural number, and
the number of square feet n is a rational number.
50. ANS:
Distributive
Property
Commutative
Property of
Addition
Associative
Property of
Addition
Distributive
Property
Definition of
Addition
Commutative
Property of
Multiplication
Commutative
Property of
Addition
KEY: absolute value
51. ANS:
–13
52. ANS:
x = 3 or 2
53. ANS:
Answers may vary. Sample: The digits 0 and 1
will represent failures. In the table, 5 of the 12
groups of four represent four good parts made in
a row. The experimental probability of
manufacturing four good parts in a row is
, or 42%.