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Math 9
Review for January Exam #2
Answer Sheet
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Math 9
Review for January Exam
Handout #2
Name ___________
1. Arrange from least to greatest
a) 12, -2, 7, -5, 0, 1
b) -6, 15, -1, 4, 11, -19, -24
2. What integer is suggested?
a) 200m above sea level
b) a debt of $5
c) 2 strokes under par
d) 30C below freezing
3.
a) Which integer corresponds to B? b) Which letter corresponds to +2?
c) Which is the opposite integer of the integer at A?
4. Find the next two integers in the sequence.
a) 4, 2, 0, -2, ____, ____ b) -4, -1, 2, 5, ____ , ____
c) -1, 2, -4, 8, ____, ____
d) -2, -3, -5, -9, ____, ____
5. Add.
a) -126 + 28
b) -212 + (-48) c) 72 + (-40) d) -5 + (-11) + 24
e) -17 + 25 + (-3)
f) 18 + (-12) + 11
6. Subtract.
a) 94 – 96
b) -34 – (-25)
e) 72 – (-6) – (-4) – 22
c) -942 – 42
d) 87 – (-13)
f) 19 – 25 – (-5)
7. Multiply.
a) 25 x (-4)
b) -16 x (-5)
e) -3 x (-3)
f) -5 x 12 x (-2)
c) -18 x 4
d) 5 x 6 x (-3)
8. Divide.
a) 48  (-16)
b) -500  (-25)
c) -552  24
e) -24  (-2)  (-2)
f) 96  6  (-4)
d) -2298  (-6)
9. Find the result.
a) -6 + 5 – 12
b) 22 – (-5) + (-8) c) 9 – 11 + 8
e) 15 – (-15) + 9 – 14
d) 24 + (-11) + (-24) – 2
f) 12 – 5 + 14 – 11 – 20
10. Evaluate
a) 6 + (-8) x 5 (-3)
b) 248  8 + 7 x (-3) c) 12 + 18  3 – 24  (-6)
d) [ (-24 – 12  2) + 8  (-4) ] – 16
e) (-4)2 x 2 – 8  22
f)
24  8  2  5
3  (4)  3  (7)
2
11. Express as integers and solve.
a) What is the difference in the golf scores? Janice: 14 over par, Heather: 5
under par
b) At noon the temperature was -4oC. In four hours, it had risen 9oC. What
was the temperature at 4:00 pm.
12. Evaluate when a = 2, b = -2, and c = 1
a) 4a + 3b
b) a – 2b
e) (c – b)2 + (b – c)2
c) a + b2 – c
d)
abc
a2
f) 3b  (b + c)
13. Use integers to represent the situation. Then solve.
a) A football team starts on its 10 yard line. They gain 17 yards, lose 6
yards, gain 9 yards, and are penalized 5 yards on successive plays. At
what yard line is the team now?
b) Air temperature drops by about 6oC/km as you go upward from sea level.
What is the temperature at the top of Mount Everest (8848 m) if it is – 8oC
at sea level?
c) Mr. Whitney deposited $300/week for two weeks into his new account.
The next week he made five withdrawals, each for $45, and two more for
$190 and $170. How much did he then have in the account?
14. What can you say about two integers with:
a) a positive product?
b) a negative product?
c) zero as the product?
15. Which shows the numbers arranged in order from least to greatest?
a) 0, 1, -2, -5, 7, 12
b) -2, -5, 0, 1, 7, 12
c) -5, -2, 0, 1, 7, 12
d) 0, -5, -2, 1, 7, 12
16. Use >,<, = to make the statement true.
a) -4, -7
b) 4, 7
c) -6, -3,
d) – 6, 0
17. What integer is suggested by a discount of $10?
a) +10
b) +$10
c) – 10
d) n – 10
18. Which letter corresponds to -2?
a) A
b) B
c) C
d) D
19. Which would be the next two integers in the sequence? 1, -2, 4, -8, ….
a) -16, 32
b) 16, -32
c) -14, 22
d) 16, -24
c) 38
d) 106
20. Solve: -24 + (-48) + 34
a) -106
b) -38
21. Which describes the sum of two or more positive integers?
a) always positive
b) sometimes positive
c) always negative
d) sometimes zero
22. Solve: (+17) – (-9)
a) -8
b) +8
c) -26
d) + 26
23. Which describes the result when a positive integer is subtracted from a negative
integer?
a) always positive
b) sometimes positive
c) always negative
d) sometimes zero
24. Solve: -24 – 6
a) -18
b) -30
c) 18
d) 30
c) -14
d) 8
c) 36
d) 0
25. Solve: -8 + 5 – 11
a) -24
b) -2
26. Solve: 16 – (-16) + 5 – 9
a) -4
b) 28
27. Solve: -24 + 6 – (-6) + 24 – 6 + (-6)
a) -12
b) 12
c) -6
d) 0
28. Which expression gives a result of zero?
a) -6 + (-6)
b) 24 – (-24)
c) -18 + 18
29. Solve: -5 x 9
a) 4
b) 14
c) 45
d) -45
c) 48
d) -2
30. Solve: -8 x (-6)
a) -48
b) -14
31. Solve: -2 x (-2) x (-2) x (-2) x (-2) x (-2)
a) -12
b) 64
c) -64
d) 12
32. Which is the value of mn2 if m = -2 and n = 3?
a) 36
b) -18
c) 18
d) -36
d) – 9 – 9
33. If two integers a and b are both negative, which is true for a  b?
a) always positive
b) sometimes positive
c) always negative
d) sometimes zero.
34. Solve: -48  12
a) -4
b) -3
c) -36
d) 4
35. Which quotient is the largest?
a) -12  (-3)
b) 24  (-6)
c) 14  7
d) -36  3
36. Which is the value of 2m2 + 3n if m = -2 and n = -3?
a) 7
b) 16
c) -1
d) 17
37. Evaluate: 24 – 8  (-2) + 4 x 5
a) 48
b) -20
38. Evaluate:
a) 1
c) 40
d) 12
c) 9
d) 45
 9  12  (3)
24  (8)  3
b) 5
39. On a test, marks are given as follows:
4 correct answer
-2 for an incorrect answer
- 1 for a question not answered
Of the 50 questions, John got 38 correct and he left 2 blank. How many marks
did John get on the test?
a) 150
b) 130
c) 170
d) 140
40. Which does not give a result of zero?
a) -6 – (-6)
b) – 8 + 8
c) -9 x 0
d) -11  (-11)
41. Evaluate:
6
a) 10
3
10
b) (-5)
c) (-1)
2
d)  
5
2
42. Write as a power. Do not use 0 or 1 as the exponent.
a) 49
b) -8
c) -7 cubed
d) 64
43. Express as a single power.
a) 33 x 32 x 38
b) (-2)3 x (-2)5 x (-2)7
c) (22)4
d) (22 x 3)5
44. Evaluate when m = 3 and n = 4.
a) m2n
b) mn2
c) nm
45. Which statements are not correct?
a) 23 x 24 = 27
b) 53 + 52 = 57
c) 23 x 32 = 65
e) 54 x 5 x 52 = 56
f) (-1)10 x (-1)6 = 1
d) (23)2 = 26
46. Rewrite each incorrect statement in exercise 45 to make it correct.
47. Express as a single power.
a)
35
32
b)
( 5) 7
5
c) 415  45
d) (-2)10  (-2)10
48. Which is the larger in the pair?
a) 23, 32
b) 53, 102
c) (-2)4, 42
d)
85 36
,
83 32
49. Express as a single power.
a)
2 2  25
24
b) (54 x 56)  58
c) (23)2 (22)2
d)
(3.1)10
(3.1)( 3.1) 8
50. Express with a positive exponent.
a) 4-2
b) (-2)-3
1
c)  
6
3
2
d)  
3
2
51. Evaluate each result in exercise 50.
52. Express as a single power with a positive exponent.
a) 25 x 2-4 x 2
c) 45  4-3
b) 50 x 4-2
d)
7 3  7 4
7 5
53. Express in scientific notation.
a) 47 500 000 000
b) 0.000 000 142
54. Express in standard form.
a) 3.7 x 108
b) 9.02 x 10-9
55. Evaluate. Write your result in scientific notation.
a) (4.8 x 1016)  (1.2 x 1011) b) (3.2 x 10-8) x (2 x 1012)
c)
72000000  0.00025
1200
56. Find the principal square root without using your calculator.
a) 1 000 000 b) 169
c) 4900
d) 0.0064
e) 3721
f)
36
121
57. Evaluate.
a)
72  8
b)
64  36
c) 2 144  3 16
d)
 25    9 
2
2
58. A square picture with area 169 cm2 is displayed in a square-shaped frame. The
area of the frame and picture together is 225 cm2. How wide is the frame?
59. Choose the best estimate.
a) 250
b) 110
c) 3800
d) 20
15.8
10.2
61
4.1
16
10.5
65
4.3
15.5
10.8
68
4.5
60. Is the number rational or irrational?
a) 144
b) 18
c)
5
d) 3 49
61. Divide each of the following:
p4q2
a) 2 2
p q
25 x 2 y 3
c)
5 x 4 y 2
18st
b)
 9 st
62. Find the quotient.
a)
3a  2b 4c 
b)
12abc
4m 4n  4 p 
2n 2 p 
63. Solve (-6)4
a) -24
b) 24
c) 1296
d) -1296
64. Which shows 64 written as a power?
a) 26
b) 43
c) 82
d) all of these
65. Which shows 52 x 5 x 57 expressed as a single power?
a) 59
b) 510
c) 514
d) 515
66. Evaluate x2y3 when x = 3 and y = -2.
a) -36
b) 36
c) 72
d) -72
67. Which statement is NOT correct?
a) 23 + 33 = 53
b) 45 x 43 = 48
c) (54)2 = 58
d) (-2)3 x (-2) x (-2)5 = (-2)9
68. Which should have 2 as the exponent?
1
b) (-3) =
9
?
?
a) 5 = 125
?
1
1
c)   
4
2
69. Express as a single power. (-5)10  (-5)2
a) (-5)8
b) (-5)5
70. Which shows
c) 18
d) 15
98  9 2
expressed as a single power?
95
d) (0.5)? = 1
a) 92
b) 911
c) 95
d) 99
71. Which has the greatest value?
a) 43
b) 34
c) 2 x 62
b) -16
c)
d) 5 x 24
72. Solve 4-2
a) -8
1
8
d)
1
16
73. Which statement is NOT correct?
1
a) (-4) =  
4
3
-3
1
b) 5 =  
5
3
-3
2
c)  
3
5
74. Express as a single power with a positive exponent.
1
b)  
4
-3
a) 4
3
 
2
5
1
d)  
3
2
 32
4 5  4 2
4 
2 3
3
c) 43
d) 42
c) -5
d) -1
75. Solve (-5)0
a) 1
b) 0
76. Which shows 0.000 000 000 267 is scientific notation?
a) 2.67 x 10-9 b) 2.67 x 10-10
c) 2.67 x 109
d) -2.67 x 1010
c) 2 x 108
d) 1.4 x 108
77. Solve: (2.8 x 1016)  (1.4 x 108)
a) 2 x 102
b) 2 x 1024
78. Which is the same as 8.02 x 10-8?
a) 0.000 00 008 02
b) 802 000 000 c) 0.000 000 080 2 d) 80 200 000 000
79. If 1296 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3, what is 1296 equal to?
a) 24 x 34
80. Find
b) 2 x 2 x 2 x 2
92 to the nearest tenth.
c) 3 x 3 x 3 x 3
d) 22 x 32
a) 9.592
81. Find
b) 9.5
c) 9.6
d) 9.59
9000 to the nearest tenth.
a) 94.9
b) 94.8
c) 948.7
d) 95
82. The small square in the middle of the target has an area of 16cm2. If the
background square has an area of 324 cm2, how far is the side of the small
square form the edge of the target?
a) 4 cm
b) 7 cm
c) 14 cm
83. Between which two whole numbers does
a) 10 and 11
b) 12 and 13 c) 13 and 14
84. Which is the best estimate for
a) 15
b) 5.2
d) 18 cm
205 lie?
d) 14 and 15
30 ?
c) 5.5
d) 5.7
85. A rectangle has dimensions of 2n metres by 3n metres. If the rectangle has an
area of 150 m2, what is the length of the longer side?
a) 5 m
b) 6 m
c) 10 m
d) 15 m
86. Choose a variable and write an expression for phrase.
a) Twenty-five decrease by a number
b) The product of a number and eight increased by five
c) Seven added to a number, halved
87. List the variables in the expression.
a) 6a – 9b – 12
b) 3xyz
c) 3x2 + 2
88. List the terms in the expression.
a) 8z2 + 5w
b) 7x + 9y – 13
c) 5x2 – 3x + 6
89. Identify the numerical coefficient and the literal coefficient in the term. Then
write a like term.
a) 5m
b)
1 2
x
2
c) a3b4
90. Add: 2a2b + 4ab and 3a2b – 2ab
91. Subtract: x2 – 3x from 4x2 – 9x
92. Classify the polynomial. ( monomial, binomial, trinomial)
a) 4x
b) x2 + 5x + 6
e) x – y2
f) b(3b)(b3)
c) 3
d) b3 – 3
93. Simplify:
a) (4x + 5) – (x – 3) + (5x – 2)
b) (3x2 + 6x) – (x2 + 2x) – (-7x2 + x + 3)
94. Write an expression for the perimeter.
95. Multiply: Is the product positive or negative?
1
a) (3x)(2x2)( x 3 )
2
b) (-5ab)(-2a2b)(-a2b2)
96. Write an expression for the area of the shaded region.
97. Multiply:
a) -3x(2x – 5)
b) 5x(x2 – 3y + 2)
98. Write a simplified expression for the area of the rectangular picture frame.
99. Divide. Is the quotient positive or negative?
a) 10st2  2t2
100.
b)
45a 2 b  21ab 2  18ab
 3ab
Find the length.
101.
The volume of the rectangular prism is 40k2 + 30k. What is the missing
side if the other sides are 2k and k.
102.
Find the product.
a) (2d – 1)(d + 5)
b) (xy + z)(2y – 3)
c) (3p – 2q)2
103.
Express the area as a product of binomials. Then expand the product.
104.
Factor.
a) 4t3 + 8t
105.
b) 15m3n + 25m2n2 – 20mn
Factor the trinomial.
a) x2 + 2xy + y2
b) m2 + 10m – 24
106.
Write the trinomial for the area of the rectangle. Express in factored form.
Then write the length and the width.
107.
Which equation means “five less than twice a number is four”?
a) 5 – 2x – 4
108.
b) 4
c) 2
c) -3y2
b) -3x
d) 5, 3, -6, x
d) 3
d) -3
Find the sum of 3a2b and -5a2b.
b) 2a2b
c) 8a4b2
d) -2a2b
Which expression is a binomial?
a) x2 + 3x + 7y
114.
c) 5x2, 3x, -6
Which is alike term for -3x2?
a) -2
113.
b) 5, x2, 3, x , 6
b) 1
a) 5x2
112.
d) -3
Which is the numerical coefficient of 3x2y?
a) 3x2
111.
c) 2
Find all the terms in the expression 5x2 + 3x - 6.
a) x2, x , 6
110.
d) 2(x – 5) = 4
How many terms are there in the expression 5x2 – xy + 7y2 – 3?
a) 9
109.
b) 2x – 5 – 4 c) 5 < 2x + 4
b) 5(k + 6x + 3)
c) x + y
Which expression gives the perimeter of the figure?
a) 4x + 5
b) 8x + 10
c) 6x + 8
d) 6x + 14
d) 5x
115.
Brass is made from copper and zinc. In a piece of brass with mass
(33x – 25)g, there is (28x – 20)g of copper. How much zinc is there?
a) (5x – 5)g
116.
b) (61x – 5) g
b) -12x3y5
b) 45x2y
b) 48x2 + 16x
a) -33
121.
a) 54ab
c) 60x2y
d) 60xy
c) 18x2 + 3x
d) 18x2 – 18x + 4
c) 14xy + 21xz
d) 14x2y + 21xz
Expand: 7x(2xy + 3z)
a) 42x2yz
120.
d) –x3y5
Which expression gives the area of the figure?
a) 30x2 – 19x
119.
c) -12x2y2
Solve : 5x(-3y)(-4x)
a) 12x2y
118.
d) (61x – 45) g
Solve: 3xy3(-4x2y2)
a) -12x2y5
117.
c) (5x + 5) g
Solve :
b) 14x2y + 3z
12 x 3
 4x
b) -3x2
c) 8x2
d) 8x3
Which expression gives the unknown side of the rectangle?
b) 3a2b
c) 9a
d) 3ab
122.
Find the base of the triangle.
a) 2x + 3
123.
b) t – 3
b) 5x + 3
b) x2
d) 6x2 + 5x + 2
c) x4
d) x6
c)  (r  2r )
d) 3r 3
Which binomial is a factor of x2 + 20x + 96?
b) x + 16
c) x + 8
d) x + 4
Factor: x2 – 7x - 30
a) (x – 6)(x + 5)
129.
c) 6x2 + 7x + 2
b) r (r 2  2 )
a) x + 24
128.
d) 6t
Factor: r 2  2mr
a) r (r  2)
127.
c) 2t + 6
Which is the GCF of the terms in x6 – x4?
a) x
126.
d) 6x2 + 12x
Expand: (3x + 2)(2x + 1)
a) 6x + 2
125.
c) 6x2 + 6x
Find the length of the prism.
a) t + 3
124.
b) 4x + 6
b) ( x + 10)(x – 3)
4 2 
Given R = 8  1 and S =
0 3 
a) R + S
b) R – S
c) (x + 6)(x – 5) d) (x – 10)(x + 3)
 1  5
 3 5  , calculate the following.


 4  3
c) -3(S)
d) 2(R)