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HONORS ALG. 2 CH. 1 TEST REVIEW
Multiple Choice
Identify the choice that best completes the statement or answers the question.
To which sets of numbers does the number belong?
____
1.
a.
b.
c.
d.
____
____
irrational numbers, real numbers
integers, rational numbers, real numbers
rational numbers, irrational numbers
whole numbers, integers, rational numbers, real numbers
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
2. 
Graph the number on a number line.
____
4.
a.
c.
–5 –4 –3 –2 –1 0 1 2 3 4 5
b.
–5 –4 –3 –2 –1 0 1 2 3 4 5
d.
–5 –4 –3 –2 –1 0 1 2 3 4 5
–5 –4 –3 –2 –1 0 1 2 3 4 5
Insert <, >, or = to make the sentence true.
____
____
____
____
5.
a. =
b. >
c. <
a. >
b. <
c. =
a. >
b. =
c. <
a. <
b. >
c. =
6.
7.
8.
Find the opposite and the reciprocal of the number.
____
9. 3
a. 3, 3
c.
3, 
b.
d.
3,
c.

3,
1
3
____ 10. –1.74
a.
50 87
 ,
87 50
b.
87
1.74, 
50
____ 11.
a.
,
1
3
1
3
50
, –1.74
87
d.
50
1.74, 
87
b.
,
c.

d.
Name the property of real numbers illustrated by the equation.
____ 12.
a.
b.
c.
d.
Associative Property of Multiplication
Distributive Property
Commutative Property of Addition
Associative Property of Addition
____ 13.
a. Associative Property of Multiplication
b. Commutative Property of Addition
c. Commutative Property of Multiplication
d. Closure Property
____ 14. –2.5  0 = –2.5
a. Inverse Property of Multiplication
b. Identity Property of Addition
c. Inverse Property of Addition
d. Identity Property of Multiplication
____ 15. Simplify
.
a. 14
b. 8
c. –8
d. –14
Evaluate the expression for the given value of the variable(s).
____ 16.
;
,
a. –55
b. 55
c. 5
d. –5
a. 32
b. 48
c. 48
d. 30
b. –1
c. 11
d. –17
; x = –3
b. 62
c. 32
d. 30
c.
d.
____ 17.
; x = –3
____ 18.
a. 3
____ 19.
a. –76
Simplify by combining like terms.
____ 20.
a.
b.
,
____ 21.
a.
b.
c.
d.
____ 22. Find the perimeter of the figure. Simplify the answer.
x+y
2x
4x
y
2x
x
a. 9x + 2y
b. 10x + y
c. 10x + 2y
d. 9x + 3y
c. 23
d. 17
c. 2
d.
c. 0.5
d. 2
Solve the equation.
____ 23.
a.

1
17
b.
a.

1
2
b.
7
2
3
____ 24.
2
1
2

2
5
____ 25.
a. –0.5
b. –2
____ 26.
a.
x = 2 or x = 1
b. x = 2 or x = 4
c. x = 2 or x = 2
1
3
d.
1
x = 1 or x = 2
3
____ 27.
a.
c.
8
2
or x = 
9
9
b.
2
x = 0 or x = 2
3
8
2
or x = 2
9
3
d.
8
x = or x = 0
9
x=
x=
Solve the equation or formula for the indicated variable.
____ 28.
, for t
a.
b.
c.
____ 29. The formula for the time a traffic light remains yellow is
the speed limit in miles per hour.
a. Solve the equation for s.
d.
, where t is the time in seconds and s is
b.
What is the speed limit at a traffic light that remains yellow for 4.5 seconds?
a.
b.
; s = 28 mi/h
; s = 36 mi/h
c.
d.
; s = 35
; s = 28 mi/h
Solve for x. State any restrictions on the variables.
____ 30.
a.
c.
;
b.
;
d.
;
;
____ 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, and 12.5 cm
c. 7.5 cm, 11.5 cm, and 32.1 cm
b. 22.5 cm, 30 cm, and 37.5 cm
d. 19.3 cm, 25.7 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
c. k  3
–8 –6 –4 –2
0
2
4
6
b. k  5
0
2
4
6
–8 –6 –4 –2
c.
0
2
4
6
d.
____ 37. –4k + 5  21
a. k  –4
0
2
4
6
8
r1
2
4
6
8
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
1
2
–8 –6 –4 –2
8
1
2
–8 –6 –4 –2
–8 –6 –4 –2
8
____ 36. 2r – 9  –6
a.
1
r1
2
r  7
0
d. k  5
–8 –6 –4 –2
b.
–8 –6 –4 –2
8
r  7
1
2
–8 –6 –4 –2
c. k  –4
–8 –6 –4 –2
b.
k  6
2
4
6
d.
0
2
4
6
b.
–8 –6 –4 –2
0
2
4
6
d.
b <
0
2
4
6
–8 –6 –4 –2
8
c.
0
2
4
6
b>
0
2
4
6
c.
0
2
4
6
4
6
8
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
b1
0
2
4
6
8
0
2
4
6
8
1
2
8
d. no solutions
1
2
–8 –6 –4 –2
–8 –6 –4 –2
2
8
–8 –6 –4 –2
b1
0
d. all real numbers
____ 40. 26 + 6b  2(3b + 4)
a. all real numbers
b.
8
11
24
–8 –6 –4 –2
–8 –6 –4 –2
6
8
11
24
–8 –6 –4 –2
4
5
8
y
–8 –6 –4 –2
b.
2
1
2
–8 –6 –4 –2
8
____ 39. 4(3b – 5) < –31 + 12b
a. no solutions
–8 –6 –4 –2
0
c. y  0
5
8
y
k  6
–8 –6 –4 –2
8
2(4y – 5)  –10
a. y  0
–8 –6 –4 –2
–8 –6 –4 –2
8
1
2
–8 –6 –4 –2
____ 38.
0
0
2
4
6
8
Solve the problem by writing an inequality.
____ 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 in.
b. h > 128 in.
c. h > 64 in.
d. h < 128 in.
Solve the compound inequality. Graph the solution set.
____ 42. 5x + 10  10 and 7x – 7  14
a. x  4 or x  1
c. x  4 or x  3
–8 –6 –4 –2
0
2
4
6
–8 –6 –4 –2
8
b. x  0 and x  1
–8 –6 –4 –2
0
2
4
6
8
0
2
4
6
8
d. x  0 and x  3
0
2
4
6
–8 –6 –4 –2
8
____ 43.
a.
c.
–8 –6 –4 –2
0
2
4
6
8
b.
–8 –6 –4 –2
0
2
4
6
8
–8 –6 –4 –2
0
2
4
6
8
d.
–8 –6 –4 –2
0
2
4
6
8
____ 44. The perimeter of a square garden is to be at least 22 feet but not more than 36 feet. Find all possible values for
the length of its sides.
a.
c.
b.
d.
____ 45. An absolute value equation ____ has an extraneous solution.
a. always
b. sometimes
c. never
Solve the equation. Check for extraneous solutions.
____ 46.
a.
c.
b.
d.
Solve the inequality. Graph the solution.
____ 47.
a.
c.
–40 –30 –20 –10 0
10 20 30 40
b.
–20 –15 –10 –5
0
5
10 15 20
–20 –15 –10 –5
0
5
10 15 20
d.
–20 –15 –10 –5
0
5
10 15 20
____ 48.
a.
–6
b.
c.
3
3
4 < x < 4
8
8
–4
–2
0
2
4
–6
–4
–6
6
d.
3
1
4 < x < 4
4
4
–2
0
2
4
6
3
3
x < 4 or x > 4
8
8
–4
–2
0
2
4
6
0
2
4
6
3
1
x < 4 or x > 4
4
4
–6
–4
–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.
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
3376
2187
6217
8811
1243
4500
4665
2860
HONORS ALG. 2 CH. 1 TEST REVIEW
Answer Section
MULTIPLE CHOICE
1.
2.
3.
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6.
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29.
30.
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32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
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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
KEY: absolute value
45.
46.
47.
48.
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
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%.