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Math 9
Review for January Exam #2
Answer Sheet
Name SOLUTIONS
1a. -5,-2,0,1,7,12
1b. -24,-19,-6,-1,4,11,15 2a.____+200____
2b.___-5_____
2c.____-2______
2d. ____-3______
3a. ____-3______
3b. _____E____
3c. ___+4______
4a. ____-4,-6___
4b. ___8,11_____
4c. ___-16 , +32_
4d. __-11, -13__
5a. _____-98___
5b. __-260____
5c. ___32_____
5d. ___8______
5e. ___5______
5f. ___17_____
6a. ___-2_____
6b. ___-9_____
6c. ___-984____
6d. ___100____
6e. __60______
6f. ____-1____
7a. ___-100___
7b. ____80____
7c. ___-72____
7d. ___-90____
7e. ___9______
7f. ___120____
8a. __-3______
8b. ___20_____
8c. ___-23____
8d. ___383____
8e. ___-6_____
8f. ___-4_____
9a. ___-13_____
9b. ___19_____
9c. ___6______
9d. ___-13____
9e. ___25_____
9f. ____-10____
10a. __126____
10b. ___10____
10c. __22_____
10d. ___-48____
10e. __30_____
11b. ___5_____
12a. ___2_____
10f. ___
25
1
 6 __ 11a. ____19___
4
4
12b. ___6____
12c. ____5____
12d. ___-1____
12e. ___18____
12f. ___6_____
13a. ____25___
13b. __-53096_
13c. __5______
14a. _Both are + or - 14b. _+, - _____
14c. 1 is zero__
15. ____C_____
16a. ____>____
16b. ____<____
16c. ____<____
16d. ___<_____
17. ____C_____
18. ____B_____
19. _____B____
20. ____B______
21. ____A_____
22. ____D_____
23. _____C____
24. _____B_____
25. ____C_____
26. ____B______
27. _____D_____
28. _____C____
29. _____D____
30. ____C_____
31. _____B____
32. ____B_____
33. ____A_____
34. ____A_____
35. ____A_____
36. ____C_____
37. ____A_____
38. ____B_____
39. ____B_____
40. ____D______
41a. _100 000_
41b. __-125___
41c. ____1____
41d. __
42a. __72_____
42b. __(-2)3___
42c. ___(-7)3___
42d. _26 or 43 or 82
43a. ___313____
43b. ___(-2)15__
43c. ____28____
43d. ___125____
44a. ___36____
44b. ____48___
44c. ____64____
45. ____B______
45. ____C_____
45. _____E____
46. _will vary__
46. __will vary__
46. __will vary_
47a. ____33___
47b. __(-5)6___
47c. ____410___
47d. ___(-2)0__
48a. ___32____
48b. ____53___
48c. ____equal__
36
__
32
49a. ___23____
49b. ___52____
49c. ____23____
 1
50b. ___   _
 2 
50c. ___63____
48d. ____
2
49d. __(-3.1)1__
1
50a. ___   __
4
2
3
50d. ___   __
2
51a. ___
1
___
16
4
_____
25
3
51b. ___
1
___
8
51c. ___216____
2
52a. ____2 ___
1
52b. ____   _
4
52c. ____48____
53a. _4.75 x 1010_
53b. _1.42 x 10-7_
54a. 370 000 000
54b. 0.00000000902 55a. __4.0 x 105_
55b. _6.4 x 104_
55c. _1.5 x 101_
56a. _1000
56b. ____13___
56c. ___70____
56d. ___0.08___
9
51d. ___ ____
4
52d. ___74____
___
2
56e. __61_____
56f. ___
6
____
11
57a. ___8_____
57b. ___10_____
57c. ___12____
57d. ___34____
58. ____1 cm__
59a. ____15.8___
59b. __10.5____
59c. ___61____
59d. ____4.5___
60a. ___Rational__
60b. ___Irrational_
60c. _Irrational__
60d. __Rational_
61a. __13 cm___
61b. _18 cm___
62. ___200 cm_
63. ____C____
64. ____D______
65. ____B_____
66. _____D____
67. _____A____
68. ____C______
69. _____A____
70. ____C_____
71. _____B____
72. ____D______
73. _____A____
74. _____B____
75. _____A____
76. ____B______
77. _____C____
78. _____C____
79. _____D____
80. ____C______
81. _____A____
82. _____B____
83. _____D____
84. _____C_____
85. _____B____
86. _____D____
87. _____A____
88. _____D_____
89a. _25 – N __
89b. _8n + 5___
89c. _
90b. _x , y , z__
90c. ____x_____
91a. _8z2, 5w__
91c. _5x2, -3x, 6_
92a. _5, m_____
92b. _
93. _5a2b + 2ab_
94. _3x2 – 6x___
95a. _monomial_
95b. _Trinomial_
95c. _Monomial_
95d. _Binomial_
95e. _Binomial_
95f. _Monomial_
96a. _8x – 6____
96b. _9x2 – 3x – 3_
97. _6x2 – 2x - 6_
98a. ___3x6____
98b. __-10a5b4__
99. __80x2 – 16xy_
100a. _-6x2 + 10_
100b. 5x3-15xy+10x
101. _2xy+3x2_
102a. ___5s____
102b. _-15a-7b+6_
103. __3w - 4__
105a. _2d2+9d-5_
105b.2xy2-3xy+2yz-3z 105c. 9p2-12pq+4p2
104. _ 20 
15
_
k
n7
__
2
1
_, x2__
2
106. (2m+4n)(3m-n) 106. 6m2+10mn-4n2 107a. _4t(t2+2)_
90a. ___a, b____
91b. _7x, 9y, -13
92c. _a3, b4____
107b. 5mn(3n2+5mn-4)
108a. (x+y)(x+y)
108b. (m+12)(m-2)
109. _x2+5x+4_
109. _(x+4)(x+1)_
110. ____B_____
111. ____B_____
112. ____C_____
113. ____D____
114. ____A_____
115. ____D_____
116. ____C_____
117. ____B_____
118. ____A_____
119. ____B_____
120. ____C_____
121. ____B____
122. ____A_____
123. ____D_____
124. ____B_____
125. ____D____
126. ____B_____
127. ____D_____
128. ____C_____
129. ___B_____
130. ____C_____
131. ____C_____
132. ____A_____
133. ____C____
134. ____D_____
135. ____C_____
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:
 9  12  (3)
24  (8)  3
a) 1
b) 5
c) 40
d) 12
c) 9
d) 45
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. Find the unknown length of the side.
62. Amanda can normally hit a golf ball 180 m from the tee (including roll) Should
she aim for the flag on the hole or take the longer route around the water?
Explain.
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?
?
a) 5 = 125
1
b) (-3) =
9
?
?
1
1
c)   
4
2
d) (0.5)? = 1
69. Express as a single power. (-5)10  (-5)2
a) (-5)8
70. Which shows
b) (-5)5
c) 18
d) 15
98  9 2
expressed as a single power?
95
a) 92
b) 911
c) 95
d) 99
b) 34
c) 2 x 62
d) 5 x 24
b) -16
c)
71. Which has the greatest value?
a) 43
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
74. Express as a single power with a positive exponent.
a) 4-3
1
b)  
4
5
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
c) 3 x 3 x 3 x 3
d) 22 x 32
92 to the nearest tenth.
a) 9.592
81. Find
b) 2 x 2 x 2 x 2
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. Which is the measure of the unknown side of the triangle?
a) 17.5 cm
b) 12cm
c) 13cm
d) 6cm
86. Which set of numbers is a Pythagorean triple?
a) 5, 8, 13
b) 9, 12, 16
c) 40, 41, 57 d) 10, 24, 26
87. Which is the distance, to the nearest metre, from A to B?
a) 25 m
b) 43 m
c) 20 m
d) 32 m
88. 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
89. 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
90. List the variables in the expression.
a) 6a – 9b – 12
b) 3xyz
c) 3x2 + 2
91. List the terms in the expression.
b) 7x + 9y – 13
a) 8z2 + 5w
c) 5x2 – 3x + 6
92. 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
93. Add: 2a2b + 4ab and 3a2b – 2ab
94. Subtract: x2 – 3x from 4x2 – 9x
95. Classify the polynomial. ( monomial, binomial, trinomial)
a) 4x
b) x2 + 5x + 6
e) x – y2
f) b(3b)(b3)
c) 3
d) b3 – 3
96. Simplify:
a) (4x + 5) – (x – 3) + (5x – 2)
b) (3x2 + 6x) – (x2 + 2x) – (-7x2 + x + 3)
97. Write an expression for the perimeter.
98. Multiply: Is the product positive or negative?
1
a) (3x)(2x2)( x 3 )
2
b) (-5ab)(-2a2b)(-a2b2)
99. Write an expression for the area of the shaded region.
100.
Multiply:
a) -3x(2x – 5)
b) 5x(x2 – 3y + 2)
101.
Write a simplified expression for the area of the rectangular picture frame.
102.
Divide. Is the quotient positive or negative?
a) 10st  2t
2
2
45a 2 b  21ab 2  18ab
b)
 3ab
103.
Find the length.
104.
The volume of the rectangular prism is 40k2 + 30k. What is the missing
side if the other sides are 2k and k.
105.
Find the product.
a) (2d – 1)(d + 5)
b) (xy + z)(2y – 3)
c) (3p – 2q)2
106.
Express the area as a product of binomials. Then expand the product.
107.
Factor.
b) 15m3n + 25m2n2 – 20mn
a) 4t3 + 8t
108.
Factor the trinomial.
a) x2 + 2xy + y2
b) m2 + 10m – 24
109.
Write the trinomial for the area of the rectangle. Express in factored form.
Then write the length and the width.
110.
Which equation means “five less than twice a number is four”?
a) 5 – 2x – 4
111.
a) 9
b) 2x – 5 – 4 c) 5 < 2x + 4
d) 2(x – 5) = 4
How many terms are there in the expression 5x2 – xy + 7y2 – 3?
b) 4
c) 2
d) -3
112.
Find all the terms in the expression 5x2 + 3x - 6.
a) x2, x , 6
113.
b) 1
d) 3
c) -3y2
d) -3
Find the sum of 3a2b and -5a2b.
b) 2a2b
c) 8a4b2
d) -2a2b
Which expression is a binomial?
a) x2 + 3x + 7y
117.
c) 2
b) -3x
a) -2
116.
d) 5, 3, -6, x
Which is alike term for -3x2?
a) 5x2
115.
c) 5x2, 3x, -6
Which is the numerical coefficient of 3x2y?
a) 3x2
114.
b) 5, x2, 3, x , 6
b) 5(k + 6x + 3)
c) x + y
d) 5x
Which expression gives the perimeter of the figure?
a) 4x + 5
b) 8x + 10
c) 6x + 8
d) 6x + 14
118.
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
119.
c) (5x + 5) g
d) (61x – 45) g
c) -12x2y2
d) –x3y5
c) 60x2y
d) 60xy
Solve: 3xy3(-4x2y2)
a) -12x2y5
120.
b) (61x – 5) g
b) -12x3y5
Solve : 5x(-3y)(-4x)
a) 12x2y
b) 45x2y
121.
Which product is shown by the diagram?
a) mn x mn
122.
b) 2m x 3n
Which expression gives the area of the figure?
a) 30x2 – 19x
123.
b) 48x2 + 16x
Solve :
a) -33
125.
b) 14x2y + 3z
d) 18x2 – 18x + 4
c) 14xy + 21xz
d) 14x2y + 21xz
12 x 3
 4x
b) -3x2
c) 8x2
d) 8x3
Which expression gives the unknown side of the rectangle?
b) 3a2b
a) 54ab
126.
c) 18x2 + 3x
Expand: 7x(2xy + 3z)
a) 42x2yz
124.
d) (mn)6
c) m x n x 3
c) 9a
d) 3ab
Find the base of the triangle.
a) 2x + 3
b) 4x + 6
c) 6x2 + 6x
d) 6x2 + 12x
127.
Find the length of the rectangular model.
a) 12w2 – 6wv + 6wz
b) 4w + 2v + 2z
c) 12w2 + 6wv + 6wz
d) 4w – 2v + 2z
128.
Find the length of the prism.
b) t – 3
a) t + 3
129.
a) x
b) x2 + 2x – 8
c) x2 – 8
d) x2 + 2x – 4x – 8
Expand: (3x + 2)(2x + 1)
a) 6x + 2
131.
d) 6t
Find the area of the rectangle.
a) x2 + 2x
130.
c) 2t + 6
b) 5x + 3
c) 6x2 + 7x + 2
d) 6x2 + 5x + 2
Which is the GCF of the terms in x6 – x4?
b) x2
c) x4
d) x6
132.
Factor: r 2  2mr
a) r (r  2)
133.
b) r (r 2  2 )
b) x + 16
c) x + 8
d) x + 4
Factor: x2 – 7x - 30
a) (x – 6)(x + 5)
135.
d) 3r 3
Which binomial is a factor of x2 + 20x + 96?
a) x + 24
134.
c)  (r  2r )
b) ( x + 10)(x – 3)
c) (x + 6)(x – 5) d) (x – 10)(x + 3)
Which product of binomials is described by the rectangular model?
a) (x + 3)(x – 3)
b) (x + 1)(x – 1)
c) x – 3)(x – 3)
d) (x – 1)(x – 3)