# 10C Final Review Key

```Mathematics 10C
McGraw-Hill Ryerson Version
Chapter 1 – Measurement Systems
1.1
SI Measurement
1.
2.
3a.
3b.
4.
5a.
5b.
5c.
42 mm; 4.2 cm
8 mm; 0.8 cm
3 cm
25.5 cm
0.426 m
152 cm
1.5 m
1.2
Imperial Measurement
6.
11
A = 1' ''
16
1' 2
8.
9a.
9b.
10.
110 yards
46'
6
13.6 feet
1.3
Converting Between SI and
Imperial Systems
11.
12.
13.
14.
15.
16a.
16b.
17.
18.
19.
7.239 m; 723.9 cm
320 mi
2201.4 feet
10 213 m
0.0002
1
B = 1' 1 ''
4
1
D = 1' 3 ''
16
9
''
16
7.
C=
2067&quot;
52&quot;
4 ' 4&quot;
one mile is further by 109 m
156.2 mi / h
620.1 m
74&quot;
Chapter 2 – Surface Area and Volume
2.1
Units of Area and Volume
20.
21a.
21b.
The private shop has the better price
66 000 m2
710 400 ft 2
22.
23.
24.
483 096 m2
52.6 in3
2.2
Surface Area
25a.
346 cm2
5906 m2
25b.
25c.
25d.
26.
940.88 m2
3848.5 m2
2965.7 dm2
756 cm2
27.
1975.32 m2
28.
18.4 m2
29.
The square-based prism has the
greater surface area by 799.4 cm2
30a. SA = 113.1 cm2
30b. SA = 19.6 cm2
2.8 m
31.
32.
33.
124.7 mm2
4.8 cm
2.3
Volume
34a.
34b.
34c.
117.3 m3
7833.9 cm3
1.51 cm3
35.
36.
37.
38a.
38b.
39.
40.
2834.9 m3
2281.5 m3
108.0 m3
1150.3 cm3
73.6 cm3
8785 m3
7420.7 cm3
Chapter 3 – Right Triangle Trigonometry\
3.1
The Tangent Ratio
41a.
41b.
41c.
41d.
41e.
41f.
42a.
42b.
42c.
42d.
42e.
43a.
43b.
43c.
43d.
44.
45.
0.3640
0.7536
1.0000
1.9626
2.9042
14.3007
35
44
65
74
27
33.7
18.4
12.4 m
0.7 cm
5.9 m
27 and 63
3.2
The Sine and Cosine Ratios
46a.
46b.
46c.
46d.
46e.
46f.
0.8660
0.2079
0.2079
0.9455
0.5299
0.3090
47a.
47b.
47c.
47d.
47e.
48a.
48b.
48c.
48d.
48e.
48f.
49a.
49b.
50.
51.
52.
38
45
13
40
29
7.3 cm
23.8 cm
7.1 cm
28.0 m
48.2
60.1
AB = 21.4 m ; BC = 12.9 m
AB = 24.5 m ; BC = 5.2 m
5
98.4 m
1.4 m
3.3
Solving Right Triangles
53.
54.
55.
56.
57.
58.
380.1 m
117.6 m
YZ = 24.3 m
EF = 332.3 m
UV = 38.6 m
125.8 m
Chapter 4 – Exponents and Radicals
4.1
Square Roots and Cube Roots
59a.
59b.
59c.
59d.
60a.
60b.
60c.
60d.
61.
62.
63a.
63b.
64.
65a.
65b.
65c.
65d.
66.
67a.
67b.
67c.
67d.
67e.
67f.
67g.
67h.
67i.
68a.
68b.
68c.
68d.
68e.
68f.
69a.
69b.
2
4
70a.
5
70b.
12
4.24
5.74
9.75
7.81
49
70c.
70d.
4.36 m
8.9 m
35.6 m
1406.8 cm
2
70e.
3
10
0.1
70i.
x 24
x10
2a 9b8
14x11 y13
x6 y9 z 6
215
14a12b7
2x13 y9
3x 2 y 6 z13
a 3bc 2
a8
a 6b 4
6a
9a 2b 2
6a 3b3
42 or 16
102 or 100
 2 
69d.
7
70h.
70j.
11.7 cm
69c.
70f.
70g.
9
or  512
70k.
70l.
71a.
71b.
71c.
71d.
71e.
1
24
1
53
34
1
 3 
2
1
32
4 or 22
3
1
3
42 or 24
1
83
2
22
a4
b
1
x2
y
x5 y 5
1
3 5
x y
72.
73.
74.
y4
x5
m  500 kg
d  300 m
P  1500 kPa
4.3
Rational Exponents
75a.
58
75b.
34
71f.
7
3
75c.
75d.
75e.
10
6
25
79c.
23
12
79d.
a
1
27
6
x
4
3

4
5
79e.
 2b 
79f.
80a.
80b.
80c.
80d.
27 n
18
 48
675
288
80e.
80f.
3
m3
1
8
n
524 cycles per second
76.
77.
10 702 days
4.4
Irrational Numbers
78a.
78b.
78c.
78d.
3
2
x
1
7
1
7
or 2 b
1
1
75f.
1
3
1
3 3
81a.
81b.
81c.
81d.
81e.
81f.
82.
83.
x3
3x
78e.
78f.
3 x
79a.
72
79b.
 11 3
1
24
432
4 2
4 3
9 3
30 6
43 2
93 5
4
4 3, 5 2, 3 6, 2 15
625
1
Chapter 5 – Polynomials
5.1
Multiplying Polynomials
84a.
84b.
84c.
84d.
84e.
84f.
85a.
85b.
85c.
85d.
85e.
86a.
a 2  3a  2
n 2  5n  6
x 2  16 x  63
a 2  4a  4
2 x2  7 x  6
6a 2  5a  6
5n3  n 2  4n
k 3  5k 2  k
a3  8
15 p3  8 p 2  6 p  4
10 x  17 x  5 x  16 x  12
x 2  x  11
4
3
2
86b.
86c.
86d.
87.
18a 2  51ab  2b 2
12a 2  15ab  20b 2
8 x3  9 x 2  14 x  40
88.
58n 2
5.2
Common Factors
89a.
89b.
89c.
90a.
7x
y4
 x  2
4a 2b
3
5  y  2
 x3  6 x 2  12 x  8
90d.
x  3 x  5 x 2  1
93h.
3 y  2 2 y  5
12m  5 m  2
 2x 1 x  5
90e.
8xy  x  4 y  2 xy 
94a.
94b.
b  8 or  16
b  0;  5;  9;  16 or  35
90b.
90c.
91a.
91b.
91c.
91d.
92a.
92b.
92c.
92d.
92e.
92f.
92g.
92h.
93a.
93b.
3xy 17 x  13 y  24
7 z 2 5  2 z 4 
 2x  3 y  2
 a  b a  2
 2  p  p  q 
 a  6 a  7
 x  10 x  4
 g 11 g  7
 x 12 x  2
 k  15 k  6
 p  20 p  3
 x  5 x  3
2  y  2 y 1
6  m  4 m 1
 2 x  1 x  1
3 y  1 y 1
93c.
4  3m  4m  1
93d.
 4x  7
2
2
8x  3 x  4
4  3x  2 or 12 x  8
93e.
Chapter 6 – Linear Relations and Functions
6.1
Graphs of Relations
102.
103a.
103b.
104.
105a.
105b.
106.
93f.
93g.
96a.
 5x  2 x  3
 2a  2 a  5
96b.
12 m  36 m or 24 m  18 m
5.4
Factoring Special Trinomials
95.
97a.
97b.
97c.
97d.
98a.
98b.
98c.
98d.
99a.
99b.
99c.
100.
101.
or  a 1 2a  10 
 x  9 x  9
 2 x  5 2 x  5
5x 115x 11
Not Possible
2
 x  9
 x  7
2
5  x  1
2
 x  8
2
600
1400
6400
a  5; b  2 or a  11; b  10
x
y
ordered
pair
1
2
3
4
17
43
2
4
6
8
34
86
(1, 2)
(2, 4)
(3, 6)
(4, 8)
(17, 34)
(43, 86)
107a. x is a member of the Real Number System
 ,  
x | x  
y is a less than or equal to -1 and y is a member of the Real Number System
 , 1
 y | y  1, y  
107b. x is greater than -2 and x a member of the Real Number System
 2, 
x | x  2, x  
y is a less than 1 and y is a member of the Real Number System
 ,1
 y | y  1, y  
107c. x is a member of the Real Number System
 ,  
x | x  
y is a member of the Real Number System
 ,  
y | y  
107d. x is greater than or equal to -2 but is less than or equal to 4 and x a member of the
Real Number System
 2, 4
x | 2  x  4, x  
y is greater than or equal to -1 but is less than or equal to 5 and y a member of the
Real Number System
1, 5
 y | 1  x  5, y  
108a.
108b.
108c.
109a.
109b.
109c.
109d.
110a.
110b.
110c.
110d.
111a.
111b.
111c.
111d.
112a.
112b.
113.
yes
no
yes
yes
yes
yes
no
15
9
5
3995
6
14
12
8.2
1
9
c 8  9.6 mg
114.
H  34  164.98 cm
A  6  15.6 in2
3
116a. m  
4
115.
5
3
6
116c. m 
5
116d. m  1
3
116e. m 
4
117. 9 m
118a. m  2
118b. m  1
119a. m  2; b  5
119b. m  0.5; b  2.25
119c. m  0; b  7
120a. y   x  5
120b. y   x  7
3
120c. y  2 x 
2
3
120d. y   x  3
2
1
120e. y  x  3
3
121a. y  2 x  3
116b. m 
121b. y  3 x  2
1
121c. y  x  1
2
2
121d. y   x  2
3
122a. b  5
122b. b  1
123a. 8 x  y  3  0
123b. 5 x  2 y  7  0
123c. 2 x  6 y  3  0
124a.
124b.
124c.
125a.
125b.
126a.
126b.
127a.
5, 0
 6, 0
and  0,  5
and  0,  8
 6
and  0, 
 5
5 x  y  14  0
x  4y  2  0
x  6 y  17  0
x  y 1  0
4
A
3
 3, 0 
127b. B  3
127c. C  10
7.3
Slope-Point Form
128a.
y  0.5  x  4
128b. y  2  3  x  5
129.
1
1
 x  2  or y  7    x  6 
2
2
perpendicular
parallel
neither
perpendicular
y 5  
130a.
130b.
130c.
130d.
131a. m  2
1
131b. m 
3
131c. m  0
132. m  15
133. k  2.5
3
134. y   x  11
2
135. neither
3
13
136. y   x 
2
2
Chapter 8 and 9– Solving Systems of Linear Equations Graphically
8.1
Systems of Linear Equations and
Graphs
137a.  3,  1
137b.
137c.
137d.
138a.
138b.
138c.
139.
140.
otters
 1, 6
 4, 1
infinite solutions
yes
no
yes
Austria = 9; Germany = 16
south sea otters = 5000; north sea
= 125 000
8.2
Modelling and Solving Linear
Systems
141a. 3 f  s  155
2 f  3s  220
141b. 2 x  y  60
3 x  2 y  104
141c. 3c  2t  72
c  3t  52
141d. i  6m  220
i  12m  340
141e. x  y  350
5 x  8 y  2050
8.3 Number of Solutions for Systems of
Linear Equations
142a. no solutions
142b. infinite solutions
142c. one solution
143a. no
143b. yes
143c. no
143d. no
Chapter 9 – Solving Systems of Linear
Equations Algebraically
9.1
Solving Systems of Linear
Equations by Substitution
144a.
144b.
144c.
144d.
144e.
10,12
1, 3
 1, 1
 4, 1
 2,  3
145.
f  4663m
b  832m
146.
147.
289 and 463
s  21
h  11
9.2
Solving Systems of Linear
Equations by Elimination
148a.
148b.
148c.
148d.
1, 2
 1, 3
1, 1
 3,1
 14 12 
148e.   , 
 11 11 
149. hamburger = \$1.75; Coke = \$1.25