Answers
Chapter 1
SkillCheck
2
3
1 a 25y
2 a 5x þ 10
d 10 2y
3 81, 25, 100, 16, 64
4 a m 2 þ 10m þ 21
c n 2 5n þ 6
e 4 17p 15p 2
g x 2 þ 8m þ 16
i 4k 2 þ 4k þ 1
k t 2 49
2
b 64m
b 4y 12
e 10a 15
b
d
f
h
j
l
c 9x
c 3 þ 6w
f k þ 2k 2
y 2 3y 4
6d 2 þ 11d þ 3
3a 2 þ 17af þ 10f 2
y 2 6y þ 9
a 2 25
9m 2 16
pffiffiffiffiffi pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffiffiffiffi
1 C
2 B
3 32; 125; 4:9; 52; 288
4 a R
b I
c R
d R
e R
f R
g R
h R
i I
j R
k I
l I
pffiffiffi
pffiffiffiffiffi
5 a 1 47 ; p2 ; 2
b 2 79 ; 3 20; 2:6_
6 a 1.8
b 0.7
c 0.4
d 3.5
e 2.5
f 2.6
g 1.6
h 1.9
– 3 15
–4
–3
–1
–2
4
5
4
11 74%
–1
0
1
π
5
5 187% 2
9
2
3
7 1.41
pffiffiffiffiffi
pffiffiffiffiffi
pffiffiffi
8 Teacher to check, 5 2:24; 10 3:16; 17 4:12
Exercise 1-02
1 a
e
2 a
f
k
p
3 a
e
i
m
4 B
6 a
2
0.09
pffiffiffi
5 2
pffiffiffi
3 5
pffiffiffi
12 2
pffiffiffi
11 2
pffiffiffi
6 5
pffiffiffi
3
pffiffi
b 5
c 27
d
f 28
g 45
h
pffiffiffi
pffiffiffi
pffiffiffi
b 2 3
c 2 7
d 5 6
e
pffiffiffi
pffiffiffi
pffiffiffi
g 4 3
h 10 2
i 4 6
j
pffiffiffi
pffiffiffi
pffiffiffi
l 6 3
m 5 3
n 7 3
o
pffiffiffi
pffiffiffi
pffiffiffi
q 9 2
r 7 5
s 5 5
t
pffiffiffi
pffiffiffi
b p
16ffiffi 2
c 48 2
d
pffiffiffi
f 37
g 6 6
h
pffiffiffi
pffiffiffi
5 5
j
3
2
k
3
3
l
2 pffiffiffi
pffiffiffiffi
pffiffiffiffiffi
15 3
n 14 17
o 313
5 B
false b false c true d true e true
250
50
pffiffiffi
10 7
pffiffiffi
3 7
pffiffiffi
4 2
pffiffiffi
16 2
pffiffiffiffiffi
10
pffiffiffiffiffi
18 17
pffiffiffiffiffi
40 10
f false
Exercise 1-03
1 a
e
i
2 a
d
g
j
608
pffiffiffi
pffiffiffi
pffiffiffi
11 3
b 3 2
c 4 6
pffiffiffiffiffi
pffiffiffiffiffi
10
0
f
g 8 15
pffiffiffiffiffi
pffiffiffi
pffiffiffi
2 3
j 10 5
k 6 10
pffiffiffiffiffi
pffiffiffi
pffiffiffi
7 39
b 7 10 7 2
pffiffiffi
pffiffiffi
pffiffiffiffiffi
pffiffiffi
7 15 þ 8 2
e 2 5 3 7
pffiffiffiffiffi pffiffiffi
pffiffiffi
pffiffiffiffiffi
13 11 3
h 11 7 6 13
pffiffiffi
3 5
b
b
f
j
n
r
v
z
A
pffiffiffi
3 3
pffiffiffi
7 5
pffiffiffi
8 3
pffiffiffi
5
pffiffiffi
41 2
0
pffiffiffi
4 6
b
f
j
n
r
v
b
f
j
n
r
pffiffiffiffiffi
66
144
pffiffiffi
30 2
pffiffiffi
24 6
pffiffiffi
160 5
pffiffiffiffiffi
60 10
pffiffiffi
6
21
pffiffiffi
5 p2ffiffi
42
pffiffiffi
21 2
c
g
k
o
s
w
pffiffiffi
2 5
pffiffiffiffiffi
10
pffiffiffi
3 2
pffiffiffi
6 3
pffiffiffi
5 6
pffiffiffi pffiffiffi
6 2þ2 3
pffiffiffi
7
pffiffiffiffiffi
8 11
pffiffiffi
9 2
pffiffiffi
30 3
pffiffiffi
29 2
pffiffiffi pffiffiffi
12 3 þ 3 6
d
h
l
p
t
x
Exercise 1-04
Exercise 1-01
– 12
3 a D
pffiffiffi
4 a 6 2
pffiffiffi
e 5 6
pffiffiffi
i 6 2
pffiffiffi
m 11 3
pffiffiffi
q 5 7
pffiffiffi
u 15 3
pffiffiffi pffiffiffi
y 3 2 6 5
pffiffiffi
d 4 5
pffiffiffi
h 6
pffiffiffi
l 5 3
pffiffiffi
pffiffiffi
c 5 29 3
pffiffiffi
pffiffiffi
f 2 68 3
pffiffiffi
i 6 7
1 a
e
i
m
q
u
2 a
e
i
m
q
u
3 a
4 C
6 a
pffiffiffiffiffi
30
5
140
112
396
pffiffiffi
36 5
pffiffiffi
3pffiffi
27
pffiffiffi
5 3
pffiffiffiffiffi
2 14
4
pffiffiffi
2 10
pffiffiffiffiffi
15 30
36
80
pffiffiffi
216 2
pffiffiffi
252 3
pffiffiffi
8 7
1
pffiffiffi
4 3
1
12
c
g
k
o
s
w
c
g
k
o
s
d
h
l
p
t
x
d
h
l
p
t
2
3
6
b 7
2
pffiffiffi
b 4 6
c 6
5 A
pffiffiffiffiffi
c 30
d 15y
2
45
d
6
pffiffiffiffiffi
10 21
pffiffiffi
60 2
pffiffiffi
90 6
pffiffiffi
96 6
144
pffiffiffi
2 2
8
pffiffiffi
2 6
10
2
e x
pffiffiffi
f a a
pffiffiffi
e 14 3
f 2
Mental skills 1
2 a
f
k
p
11
6
40
135
b 40
g 43
l 65
c 7
h 80
m 11
d 24
i 18
n 14
e 23
j 15
o 12
Exercise 1-05
1 a
d
g
2 C
3 a
c
e
g
4 C
5 a
d
g
6 a
e
7 C
8 a
d
pffiffiffiffiffi pffiffiffiffiffi
15 þ 10
pffiffiffiffiffi
3 10 5
pffiffiffi
42 8 7
pffiffiffi pffiffiffi
b 2 3 6
pffiffiffi
e 6þ6 6
pffiffiffi
h 5 5 þ 75
pffiffiffi
pffiffiffiffiffi
pffiffiffi
10 þ 10 6 5 3 2
pffiffiffi
pffiffiffi
pffiffiffi
28 6 þ 21 þ 8 2 þ 2 3
pffiffiffiffiffi
109 þ 10 77
pffiffiffiffiffi
16 10 þ 54
b
d
f
h
pffiffiffi pffiffiffiffiffi
c
6 þ 14
pffiffiffiffiffi
pffiffiffiffiffi
f
55 4 11
pffiffiffi
i 24 þ 3 6
pffiffiffi pffiffiffiffiffi
pffiffiffi
7 þ 2 7 21 2 3
pffiffiffiffiffi
20 þ 10
pffiffiffi
72 23 6
pffiffiffiffiffi
16 35
pffiffiffiffiffi
pffiffiffiffiffi
8 2 15
b 9 þ 2 14
pffiffiffi
pffiffiffiffiffi
19 þ 6 10
e 77 þ 30 6
pffiffiffiffiffi
pffiffiffiffiffi
38 þ 12 10
h 23 þ 4 15
1
b 22
c 8
1
f 166
g 13
pffiffiffi
88 30 7
pffiffiffi
73 þ 40 3
pffiffiffi
b 21 2 10
e 29
pffiffiffi
c 9 4 5
pffiffiffi
f 179 20 7
d 2
h 43
pffiffiffiffiffi
c 5 35 þ 29
pffiffiffi
f 92 12 5
9780170194662
Answers
Exercise 1-06
1 B
2 a
g
3 A
5 a
6 a
pffiffi
2
2
pffiffi
3
6
b
h
pffiffi
2 2
2
pffiffi pffiffi
2 7þ7 2
14
pffiffi
7
7
pffiffi
7
28
c
pffiffi
3
3
pffiffi
7 5
15
i
4
D
pffiffi
55
5
pffiffiffiffi pffiffi
10þ5 3
5
b
b
d
j
c
c
pffiffi
3 2
2
pffiffiffiffi
10
15
e
k
pffiffi pffiffi
5 2þ 6
4
pffiffi pffiffi
3 2
2
pffiffi
2 7
7
pffiffi
3
2
d
f
l
pffiffi
2
6
pffiffiffiffi
15
4
pffiffi pffiffi
2 33 2
18
Power plus
pffiffi
1 a Yes, because you are multiplying by 1.
b 37 2
pffiffiffi
pffiffiffi
pffiffiffi
pffiffiffi pffiffiffi
2 a 52 3
b 2þ 3
c
d
51
7þ 3
pffiffiffiffi pffiffi
pffiffi pffiffi
pffiffi
pffiffiffi
7þ 3
104 3
3 a 2þ 3
b 104 2
c
d
4
13
pffiffi
pffiffi
pffiffiffi
4 s ¼ 33D
5 22
6 ð2 þ 2 3Þ mm
Chapter 1 revision
1 A
2 a I
b R
e R
f R
pffiffiffi
pffiffiffi
3 a 6 2
b 7 2
pffiffiffi
pffiffiffi
f 14pffiffi 7
g 48 2
pffiffiffi
50 5
k 3
l 2 2
pffiffiffi
4 a 13 2
b
pffiffiffi
pffiffiffi
d 32 5 9 7
e
pffiffiffiffiffi
pffiffiffiffiffi
21
5 a
b 2 10
pffiffiffi
pffiffiffiffiffi
6
e
f 7pffiffi 14
i 53
j 322
pffiffiffi
6 a 9 2 12
b
pffiffiffi
d 23 8 7
e
g 103
h
pffiffiffiffi
pffiffi
10
3 2
7 a 10
b 2
c
c R
d
g R
h
pffiffiffiffiffi
c 5 11
d
pffiffiffi
h 15 5
i
pffiffiffiffiffi
m 4 11
n
pffiffiffi
pffiffiffi
5 27 5
pffiffiffi
pffiffiffi
38 2 24 3
pffiffiffi
c 4 3
d
pffiffiffi
g 4 6
h
k 23
l
pffiffiffiffiffi
pffiffiffi
10 10 5
pffiffiffi
77 þ 10 6
pffiffiffi
70 þ 38 5
pffiffi
pffiffi
7
d 43
35
I
I
pffiffiffi
pffiffiffi
8 2
e 15 6
pffiffiffi
pffiffiffi
6
28 3
j
pffiffiffi
6
o 6 2
pffiffiffi
pffiffiffi
c 14 2 þ 17 3
pffiffiffiffiffi
f 8 11
pffiffiffiffiffi
55
125
7
5
e
pffiffiffiffiffi
c 7 35 27
f 43
pffiffi
5 6
6
f
pffiffi
2 2þ1
3
Chapter 2
SkillCheck
1 a
e
2 a
3 a
4 a
5 a
d
6 a
7 a
0.04
0.095
$72
$7350
36
52
4
1152
$5962.59
b
f
b
b
b
b
e
b
b
0.22
0.0675
$116.25
$4034.10
24
26
12
50
$33 433.46
c
g
c
c
c
c
f
c
c
0.183
d 0.047
0.1525
h 0.2
$4494
$8737.60
60
365
8 years 4 months
0.06
$18 481.63 d $64 937.10
Exercise 2-01
1 a $874
b $938.80
2 Greta earns more per week by $27.48.
9780170194662
c $367.20
3
4
5
10
14
15
a $3461.86
b $6923.73
c $15 053.33
Job 1: $1104.64; Job 2: $1160; Job 2 by $55.36
$1096.10 6 $735.23 7 $761.24 8 A 9 $13 312.50
$1394.40 11 $2115 12 54
13 $63.95
a $427
b $700
c $956.87
d $625.55
a $972.12
b $680.48
c $4568.96
Exercise 2-02
1
2
3
4
7
9
10
11
12
13
a $45 697
b $6398.53
a $114 719
b $30 393.03
a $90 904
b $21 581.48
C
5 $19 924.99
6 $45 456.10
$696.42
8 $623.52
a $452
b $1711.10
c 25.0%
a $458
b $1747.65
c 24.0%
a $2296
b $456
c $1646.73
a $2297.59
b $456
c $1550.39
Gross weekly income ¼ $816.90; Total deductions ¼ $369.10;
Net income ¼ $447.80
Exercise 2-03
1 a $5040
d $96.95
2 a $87.50
d $820
3 A
4 a $11 200
5 a $1440
7 a $6750
9 2 years
12 C
15 a $18.90
b
e
b
e
$2953.50
$71.92
$5925.15
$279
c
f
c
f
$102.50
$451.20
$391 000
$723.04
b $1569
c $9392.50
d $11 331.25
b $7440
6 4.5%
b 18.75%
8 9.75% p.a.
10 26 weeks
11 137 days
13 2.5 years
14 2.6% p.a.
b $1063.90
Exercise 2-04
1 a Check with your teacher. Investment after 1st yr ¼ $24 150;
Investment after 2nd yr ¼ $25 357.50
b Compound interest ¼ $2357.50
2 a $16 153.36
b $1153.36
3 a $38 459.48
b $4359.48
4 a $5408, $408
b $30 245.29, $2445.29
c $11 113.20, $1513.20
d $41 905.55, $2405.55
e $19 337.39, $937.39
5 a $4791.80
b $1642.38
c $308.93
d $3913.84
e $6834.42
Mental skills 2
2 a
e
i
4 a
e
18
$7.50
$240
10
37.5
b
f
j
b
f
$126
10.8
$3.30
166
$5.80
c
g
k
c
g
39
$27
900
$50
135
d
h
l
d
h
$30.30
60
$52.50
$22
$22.60
609
Answers
6 a
e
i
8 a
e
500
81
$195
160
$67.50
b
f
j
b
f
$20
$35
$425
$1.50
$31.25
c
g
k
c
g
4.5
16.5
$31.50
7.5
38
d
h
l
d
h
$6.25
74.5
290
$32.50
170
Exercise 2-05
1 $14 332.50
2 a i $9754.75
ii $3254.75
b i $13 858.59
ii $3858.59
c i $12 634.81
ii $394.81
d i $43 949.46
ii $9349.46
e i $8427.39
ii $427.39
3 D
4 $1 301 018.83
5 B
6 a i $13 488.50
ii $3488.50
b i $52 751.13
ii $17 251.13
c i $9448.23
ii $548.23
d i 53 366.91
ii $11 366.91
e i $19 473.44
ii $2973.44
f i $5177.03
ii $277.03
7 C
8 a $600
b $615
c Tegan by $15.
9 a $10 510.31
b $1969.48 less
10 a i $7554.45
ii $7688.85
iii $7758.33
iv $7805.54
b Monthly, because it earns the most interest.
Exercise 2-06
1 a
d
2 a
d
3 a
4 a
5 a
d
6 a
7 a
8 a
9 a
$175.50
$1907.64
$1275
$34 641.75
$1379
$3420
$2080
$4880
$32.90
$1073.40
$2599
$262.50
b
e
b
e
b
b
b
e
b
b
b
b
$1579.50
$105.98
$24 225
$577.36
$2316.72
$720
$8320
58.7%
$437.42
$273.40
$3576
7.4%
c
f
c
f
c
c
c
$328.14
$2083.14
$10 416.75
$35 916.75
$217.58
$1500
d 48%
$13 200
c $ 108.42
c 34.2%
c $677
8 Yes, it will lose approximately 52% after 7 years.
9 a $1800
b 5 years
c $798.67
d Yes, in the 30th year.
e No
Power plus
1 4 years and 61 days
2 $4444.44
3 $12 838.71
4 $63 367.49
5 $2276.87
6 790 000
7 a 18 years.
b 18 years.
c No. The size of the interest rate and the number of
compounding periods determine how quickly the principal
takes to double in value.
Chapter 2 revision
1
3
4
5
6
7
9
12
$13 045.75
a $797.45
a $1052.51
a $67 725
a $2400
a $5955.08
$15 374.72
a $487.50
d $6296.06
13 a $8851.45
c $78.75
d $621.37
8 $36 282.78
11 $45 815.75
c $1908.56
f $6783.56
c 59%
SkillCheck
1 a (6, 1)
b (5, 4)
e AC ¼ BC ¼ 4.5
f isosceles
2 a
x
0
1
2
3
y
3
2
1
0
c 6
g 13
d 6
h 23
y
4
2
d 10.4%
–4
Exercise 2-07
610
c $4946.80
Chapter 3
d 36.62%
1 $933.89
2 a $20 429.69
b $29 560.31
3 a i $659.66
ii 60%
b i $2459.54 ii 45.2%
c i $5073.42
ii 60%
d i $778.24
ii 41%
e i $14 020.37 ii 51%
f i $851.35
ii 37%
g i $403.03
ii 46.3% h i $1097.20 ii 68.6%
4 a i 90%
ii 73%
iii 53%
iv 48%
b By trial and error, in approx 6.6 years.
5 a i $10 000
ii $8000 iii $4096
b 32.8%
6 a $11 138.51
b $4661.49
7 a $6472.88
b $3441
c 8 years and 9 months.
d 23.2%
2 $1349.18
b $1011.40
b $736.76
b $13 557.63
b $392.50
b $955.08
10 $852.91
b $4387.50
e $174.89
b $6138.55
–2 0
–2
2
x
4
–4
b
x
y
2
4
0
2
1
1
1
5
y
4
2
–4
–2 0
–2
2
4
x
–4
9780170194662
Answers
c
0
1
1
3
x
y
1
1
12 a
e
13 a
e
2
3
y
4
2
–4
2
x
4
–4
3 a 2
b 8
c 5
e 14
d 4
pffiffiffiffiffi
f 2 17
Exercise 3-01
1 B
4 a 13
5 a i 2.2
b i 10.8
c i 7.1
d i 7.6
e i 10.2
f i 5.7
pffiffiffiffiffi
6 a
89
7 k: m ¼ 15; l: m ¼ 12
y
9 a
4
2 C
b 2
ii (6, 2.5)
ii (3.5, 3)
ii (2.5, 0.5)
ii (0.5, 7.5)
ii (6, 3)
ii (5, 0)
pffiffiffiffiffiffiffiffi
b
194
8 B
–2
A(–1, –1)
–2
3 A
c 73
iii 12
iii 23
iii 1
iii 37
iii 5
iii 1
pffiffiffiffiffi
82
c
27
37
0.40
1
1 a
d
2 a
3 a
4 D
7 a
b
8 a
c
g
c
g
neither
neither
4
1
b perpendicular
e parallel
b 2
b 16
5 B
mAB ¼ 43, mCD ¼ 43; [ AB || CD
mPQ ¼ 34, mCD ¼ 43; [ PQ ’ CD
1
b 3
3
45
174
0.90
0.05
d
h
d
h
68
146
14.30
0
1 a i
1
3
d 0.2
d 25
ii 1
y
4
2
–4
–2 0
–2
4x
2
–4
ii 5
y
10
C(3, 1)
2
c parallel
f neither
c 13
c 23
6 A
Exercise 3-03
b i 2.5
B(1, 3)
2
–4
b
f
b
f
Exercise 3-02
1
2
–2 0
–2
72
117
1.73
0.14
4x
5
–4
pffiffiffi
pffiffiffi
b AB ¼ AC ¼ 2 5, BC ¼ 2 2
d isosceles
y
10 a
10
pffiffiffi
c AB ¼ AC ¼ 2 5
e 11.8
–6 –4 –2 0
b
d
e
f
g
11 a
b
c
L(7, 2)
P(–3, 0)
square
c mKL ¼ 23, mPM ¼ 23
3
3
x
m–10
mLM ¼ 2
KP ¼ 2,–5
5
10
the gradients are equal, they are parallel
pffiffiffiffiffi
–5
M(3,
KL ¼ LM ¼ PM ¼ KP
¼ –4)
2 13
28.8
h 52 sq. units
–10
P(2, 1), Q(1, 3)
PQ ¼ 3.6, AC ¼ 7.2, AC ¼ 2 3 PQ
mPQ ¼ 23, mAC ¼ 23; the gradients are equal.
4
6
8x
–5
K(1, 6)
5
2
c i 4
ii 4
y
4
2
–4
–2 0
–2
2
4
x
–4
d i 1
ii 2
4
y
2
–4
–2
0
–2
2
4x
–4
9780170194662
611
Answers
y
y
4
2
0
–2
0
–4 –2–2
–4
–6
–8
–10
e i 0
ii 0
4
d
2
–4
–2
4x
2
–4
f
i
ii 3
6
4
e
4
y
–4
0
2
4
–2
x
6
8
10
x
y
0
–2
2
4
x
–4
–4
y
4
f
2 a
4
2
2
–10 –8 –6 –4 –2
–2
2
2
y
4
–4 –2 0
–2
2
–4
–2
0
–2
2
4
x
4
g
–2
x
10
8
y
y
2
0
–2
6
4
2
–4
4
–4
–4
b
2
2
4
–4
x
–2
0
–2
2
4
x
–4
–4
h
c
y
10
8
6
4
2
0
–10 –8 –6 –4 –2–2
–4
612
2
4x
y
10
8
6
4
2
–4 –2–2
2
4
6
8
10
x
9780170194662
Answers
y
10
i
b
y
x=6
10
5
–4 –2 0
2
4
6
5
8 10 x
y=1
–5
–10
–10
0
–5
y
j
–5
10
–10
5
0
–5
5
10
15
x
–5
–10
k
6
4
2
–4
–2
0
2
–2
4
x
1 a
d
g
j
2 a
d
3 a
m ¼ 3, b ¼ 2
m ¼ 1, b ¼ 9
m ¼ 12, b ¼ 11
m ¼ 2, b ¼ 6
y ¼ 2x þ 1
y ¼ 25 x þ 3
m ¼ 2, b ¼ 1
y
4
–6
2
–4
–10
l
d y ¼ 2
h x ¼ 1
b y-axis
m ¼ 2, b ¼ 7
m ¼ 34, b ¼ 6
m ¼ 23, b ¼ 6
m ¼ 3, b ¼ 11
y ¼ 34 x þ 2
y ¼ 2x 3
c
f
i
l
c
f
m ¼ 1, b ¼ 4
m ¼ 1, b ¼ 0
m ¼ 13, b ¼ 8
m ¼ 1, b ¼ 72
y ¼ 7x þ 5
y ¼ 3x þ 12
y = 2x + 1
1
0
–2
2
4
x
b m ¼ 3, b ¼ 2
0
2
–2
4
y
4
x
y = 3x – 2
2
–4
a no
b yes
c yes
d yes
e no
f no
C
a x ¼ 4
b x¼1
c y¼5
d y ¼ 3
a
y
x = 2.5
10
–4
–2
0
–2
y
–5
10 x
y = –3
x
y = 2x
4
5
4
c m ¼ 2, b ¼ 0
2
y=1
0
2
–4
5
–5
c x ¼ 1
g y¼6
10 a x-axis
–4
2
–2
–2
y
4
–10
b
e
h
k
b
e
–4
–8
–4
x = –0.5
b x¼4
f x ¼ 1
9 C
7 a y¼2
e y¼3
8 A
Exercise 3-04
y
10
8
3
4
5
6
10 x
y = –2
5
–4
–2
0
–2
2
4
x
–4
–10
9780170194662
613
Answers
d m ¼ 12, b ¼ 1
Mental skills 3
y
4
y=x –1
2
–4
–2
2
x
4
2
–2
8 h 30 mins
8 h 15 mins
5 h 10 mins
7 h 40 mins
b 5 h 40 mins
e 11 h 25 mins
h 5 h 45 mins
c 3 h 25 mins
f 1 h 40 mins
i 7 h 55 mins
Exercise 3-05
–4
e m ¼ 2, b ¼ 3
y
4
2
–4
2 a
d
g
j
–2 –2
2
x
4
1 a
c
e
g
i
2 a
c
e
3 B
xyþ2¼0
5x y þ 8 ¼ 0
x 2y 6 ¼ 0
6x y 3 ¼ 0
3x 5y þ 10 ¼ 0
m ¼ 2, b ¼ 6
m ¼ 32, b ¼ 2
m ¼ 2, b ¼ 5
b
d
f
h
3x y 1 ¼ 0
x þ 2y 3 ¼ 0
8x y þ 2 ¼ 0
x 2y 6 ¼ 0
b
d
f
4
m ¼ 4, b ¼ 5
m ¼ 2, b ¼ 1
m ¼ 43, b ¼ 4
B
–4
y = –2x + 3
f m¼
34,
Exercise 3-06
b¼0
y
4
2
–4
–2
2
–2
x
4
1 a 2x y þ 1 ¼ 0
c 4x y 20 ¼ 0
e x þ 5y þ 38 ¼ 0
g 4x þ y þ 1 ¼ 0
i 2x þ y þ 10 ¼ 0
2 a and b
b
d
f
h
y
–4
xþyþ2¼0
2x 3y 4 ¼ 0
3x þ y 4 ¼ 0
3x 4y þ 10 ¼ 0
4x + y – 10 = 0
y = –3x
x–y–5=0
a
4
g m ¼ 52, b ¼ 1
x + 3y + 3 = 0
y
4
0
2
–4
–2
–2
–4
x
P
2
x – 5y – 13 = 0
x
4
d
(3, –2)
b
y = –5x +1
2
c
h m ¼ 35, b ¼ 4
y
4
2
y = 3x – 4
5
–2–2
2
4
6
8
x
–4
–6
4 y ¼ 2x
5 a C
b B, D c B
6 a y ¼ 4x þ 3, y ¼ 4x 6
614
d C, D e A, B f D
b 3x y þ 7 ¼ 0, y ¼ 3x 2
3 a xy4¼0
b 4x 5y þ 18 ¼ 0
c 5x 6y þ 23 ¼ 0
d 8x þ 3y 10 ¼ 0
e 3x þ 2y 6 ¼ 0
f 5x 3y 1 ¼ 0
g 6x þ 11y þ 38 ¼ 0
h xþy3¼0
i 4x 3y 11 ¼ 0
4 k: x þ 2y 7 ¼ 0, l: 3x y þ 7 ¼ 0
5 4x þ y 20 ¼ 0
6 5x 7y þ 42 ¼ 0
7 2x 3y þ 18 ¼ 0
8 3x þ 5y 30 ¼ 0
9 a 2x y þ 1 ¼ 0
b same
9780170194662
Answers
y2 y1
x2 x1
y y1 ¼ mðx x1 Þ
y2 y1
ðx x1 Þ
y y1 ¼
x2 x1
y y1 y2 y1
¼
)
x x1 x2 x1
b xy4¼0
10 a
m¼
6
c same
7
Exercise 3-07
1 a
d
2 a
d
g
y ¼ 2x þ 5
y ¼ x þ 3
y¼ xþ2
y ¼ 12 x þ 4
y ¼ 3x 10
b
e
b
e
h
y ¼ 34 x þ 3
y ¼ 12 x þ 3
y ¼ 34 x
y ¼ 3x 3
y ¼ 25 x þ 2
c
f
c
f
i
y ¼ 3x þ 6
y ¼ 3x 3
y ¼ 13 x þ 6
y ¼ x 2
y ¼ 2x 3
9
10
Exercise 3-08
1 a
d
2 a
d
3 a
4 a
5 a
d
y ¼ 2x þ 4
b y ¼ 3x þ 6
y ¼ 2x 12
e y ¼ 5x 13
y ¼ 2x 2
b y ¼ 15 x 15
y ¼ 3x 3
e y¼xþ6
m¼2
b M(0, 2)
c 12
1
y ¼ 3x þ 1
b 3
y ¼ 45 x þ 8
b A(10, 0)
y ¼ 54 x 25
e (0, 12.5)
2
8
y ¼ 12 x þ 11
2
y ¼ 12 x 10
y ¼ 13 x þ 43
y ¼ 13 x 31
3
d y ¼ 12 x þ 2
c y ¼ 3x þ 11
c 54
c
f
c
f
11
12
Exercise 3-09
1 a i 5x þ 2y 18 ¼ 0
ii 3x 4y 16 ¼ 0
iii (0, 9)
iv (0, 4)
v 26 units2
b i x 5y þ 20 ¼ 0
ii x þ 2y þ 6 ¼ 0
iii (0, 4)
iv (0, 3)
v 35 units2
c i 3x y 46 ¼ 0
ii 7x þ 15y þ 66 ¼ 0
2
iii ð15 13, 0Þ
iv ð9 37, 0Þ
v 123 17
21 units
2 a 5x 2y 25 ¼ 0
b 5x þ 7y 25 ¼ 0
c w¼5
d t ¼ 10 25
3 a DE ¼ EF ¼ FG ¼ DG ¼ 5 units
b For DE and GF, m ¼ 0
For DG and EF, m ¼ 43
c Diagonal DF, m ¼ 12
Diagonal EG, m ¼ 2
Since 12 3 2 ¼ 1 it is true that DF ’ EG.
d Midpoint of DF ¼ (0, 0)
Midpoint of EG ¼ (0, 0)
The diagonals bisect each other because their midpoints
are the same.
e Opposite sides are equal and parallel, adjacent sides are
equal, diagonals bisect each other at right angles.
pffiffiffi
4 b 6 5 units
c (1, 1)
d No, since mPR 3 mQS 6¼ 1
e Rectangle, diagonals are equal and bisect each other but
not at right angles.
pffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffi
5 b CE ¼ 130 units, DF ¼ 130 units
1 1
1 1
c 2, 2 and 2, 2
9780170194662
13
14
15
16
3
d mCE ¼ 11
3 , mPR ¼ 11
3
[ CE ’ DF because 11
3 3 11 ¼ 1
e Square, diagonals are equal and bisect each other at right
angles.
pffiffiffiffiffi
pffiffiffiffiffi
a BC ¼ DE ¼ 61 units, CD ¼ BE ¼ 65 units
b mBC ¼ 56, mCD ¼ 47, mDE ¼ 56, mBE ¼ 47
c Midpoint of BD ¼ 1 12, 2 12 ; Midpoint of CE ¼ 1 12, 2 12
d Parallelogram, opposite sides are parallel and equal.
pffiffiffiffiffiffiffiffi
a AC ¼ BD ¼ 104 units
b Midpoint of AC ¼ (1, 2), midpoint of BD ¼ (1, 2)
mAC ¼ 5, mBD ¼ 15, [ AC ’ BD
c The diagonals are equal and bisect each other at right
angles.
Midpoint of KM ¼ Midpoint of LN ¼ 2 12, 12
mKM 3 mLN ¼ 1 3( 1) ¼ 1
Teacher to check.
a mJK ¼ 13, mLM ¼ 13, mKL ¼ 52, mJM ¼ 52
b Parallelogram because opposite sides are parallel.
a X 3, 12 ; Y 1 12, 3 12
b mXY ¼ 23, mCB ¼ 23
[ XY || CB
pffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffi
c XY ¼ 12 117, CB ¼ 117
[ CB || 2XY
a mWN ¼ 1 and mCT ¼ 1
mWN 3 mCT ¼ 1
[ WN ’ CT
MWN (1.5, 0.5) and MCT (1.5, 0.5)
[ Diagonals bisect at right angles.
b rhombus
Trapezium
pffiffiffiffiffi
ST ¼ WX ¼ 37 units
pffiffiffiffiffi
TW ¼ SX ¼ 2 37 units
XS ’ ST because mXS ¼ 16, mST ¼ 6
[ STWX is a rectangle because opposite sides are equal and
angles are right angles.
a Midpoint of TU ¼ A(4, 1)
Midpoint of UV ¼ B(0, 3)
Midpoint of SV ¼ C(5, 1)
Midpoint of ST ¼ D(1, 5)
b Gradient of AB ¼ 1 ¼ gradient of CD
Gradient of AD ¼ 45 ¼ gradient of BC
pffiffiffiffiffi
AC ¼ 9 units, BD ¼ 65 units
[ ABCD is a parallelogram.
a mLM ¼ 13, mLN ¼ 13, mMN ¼ 13
b L, M and N are collinear points.
Power plus
1
2
5
6
a 23
b y ¼ 23 x 2
c y¼4
k¼5
3 B(2, 1)
4 X(2, 3)
a 32
b 3x þ 2y þ 2 ¼ 0 or y ¼ 3x
2 1
D(3, 5) or (7, 9) or (1, 3)
615
Answers
Chapter 3 revision
Chapter 4
1 a 12.6
b M(1, 4)
pffiffiffiffiffi
2 a HJ ¼ JK ¼ KL ¼ HL ¼ 58
3
7
b mHJ ¼ 7, mJK ¼ 3, mKL ¼ 37, mHL ¼ 73
pffiffiffi
pffiffiffi
c HK ¼ 10 2, JL ¼ 4 2
d rhombus
3 a 72
b 51
c 135
4 a 12
b 2
5 a
y
c
SkillCheck
1
3
1 a 182 cm2
2 a 1.51 m2
d 146
2
−4
−2
0
2
4 x
−2
b
1 a 200.81 m2 b 3573.56 mm2 c 206.47 cm2 d 15.83 m2
2 a 35 m2
b 3478 cm2
2
3 a 1009 m
b 2160 m2
c 4 m2
d 1895 m2
2
2
2
e 7m
f 14 m
g 1131 m
h 95 m2
2
4 a 41.6 m
b 5L
5 The triangular prism tent by 1.2 m2.
y
8
x + 2y = 16
4
282 m2
b 298 cm2
c 2720 mm2
2
2
204 m
e 1288 mm
f 165 m2
cube, 1944 m2
b rectangular prism, 538 m2
triangular prism, 9720 m2 d open trapezoidal prism, 6378 m2
80 m3, $8400
b 171.4 m2
2
1036 cm
b 1020 mm2
c 204 m2
390 cm2
e 672 cm2
f 5672 mm2
32.91 m2
b 74.56 m2
Exercise 4-02
y = –5x –1
−4
c 680 cm2
c 8.73 m2
Exercise 4-01
1 a
d
2 a
c
3 a
4 a
d
5 a
4
b 770 cm2
b 5.59 m2
Exercise 4-03
−8
−4
0
4
8
12
16
x
−4
−8
c
y
4
2
−4
−2
0
3x + 4y – 12 = 0
2
4
x
−2
−4
616
6 C
7 D
8 a m ¼ 2, b ¼ 10
b m ¼ 4, b ¼ 3
c m ¼ 38, b ¼ 12
9 a 3x y þ 5 ¼ 0
b 2x 5y 50 ¼ 0
c x 3y 6 ¼ 0
10 a m ¼ 1, b ¼ 2
b m ¼ 14, b ¼ 1
c m ¼ 3, b ¼ 9
11 a 3x þ y 20 ¼ 0
b 2x 3y þ 26 ¼ 0
12 a 3x 5y 20 ¼ 0
b xþyþ3¼0
13 a 2x y þ 3 ¼ 0
b x þ 2y þ 8 ¼ 0
14 a 3x y 6 ¼ 0
b 2x þ y ¼ 0
15 8x þ 3y 95 ¼ 0
pffiffiffiffiffi
16 PN ¼ LM ¼ PN ¼ PL ¼ 34 units
3
5
MPN ¼ 5, MPL ¼ 3 [ PN ’ PL
[ LMNP is a square because all sides are equal and it has a
right angle.
1
2
3
4
5
6
7
a 275 m2
a 166.4 m2
a 843 cm2
a 432 cm2
85 854 m2
a 1344 mm2
a 42 m
b
b
b
b
564 mm2
3456 mm2
1592 cm2
2150 cm2
c
c
c
c
b 180 cm2
b A ¼ 735 m2
c 35 m
87.4 cm2
743.1 cm2
3116 cm2
173 cm2
c 343.4 m2
d 28 m
Exercise 4-04
1
2
3
4
5
6
7
9
10
11
a 101 cm2
b 628 cm2
2
a 392.7 mm
b 62.8 m2
2
a 90p m
b 224p mm2
2
a 2827.43 mm
b 380.13 m2
a 432p m2
b 192p m2
2
a 314 m
b 628 m2
c 628 m2
8
2
5.1 3 10 km
8 5525 cm2
a 30.16 cm
b 4.80 cm
c 8 cm
a 21.9 mm
b 25.2 mm
a 6.9 cm
b 85.3 cm
c
c
c
c
c
d
2419 cm2
192.4 cm2
450p cm2
366.44 cm2
768p m2
402 m2
d 193.02 cm2
c 30.9 mm
c 85 cm
Mental skills 4
Exact answers shown
2 a 331
b 157
f 203
g 413
k 276
l 72 37
4 a 28.231 b 14.187
f 5.0237 g 21.75
c 1587
h 734
d 255
i 6723
e 421
j 15 744
c 177.4967 d 416.752 e 2.4156
h 3.69
i 5.81
j 23.9121
9780170194662
Answers
Exercise 4-05
1 a 446.96 cm2
2 a 352 cm2
3 a 9721.7 cm2
d 2858.8 cm2
4 a 26.14 m2
6 1028.32 cm2
7 a 857.7 cm2
d 5969.0 cm2
g 282.7 cm2
j 3769.9 cm2
m 6615.4 cm2
b
b
b
e
b
49 270 cm2
76 cm2
14 031.4 cm2
2793.5 cm2
19 m2
c 864 cm2
b
e
h
k
n
412.3 cm2
250.6 cm2
652.9 cm2
1148.8 cm2
3908.4 cm2
c
f
i
l
o
1042.0 cm2
628.3 cm2
501.6 cm2
3017.7 cm2
328 cm2
c
f
i
c
5
c
f
i
l
7.4 m3
216.9 m3
146.3 m3
21.5%
63 L
1989.38 cm3
3084.96 cm3
167.33 cm3
794.12 cm3
c 14 778.1 cm2
f 394.7 cm2
5 2953 cm2
Exercise 4-09
Exercise 4-06
1 a 9.7 m3
d 135.7 m3
g 42.3 m3
2 a 251.3 cm3
3 500 kL
6 a 4825.49 cm3
d 6375.00 cm3
g 536.19 cm3
j 12 900 cm3
7 a 182.83 m3
b
e
h
b
4
b
e
h
k
b
94 247.8 m3
5026.5 m3
107.5 m3
320 cm3
13 666 cm3
5026.55 cm3
5301.44 cm3
1884.96 cm3
167.55 cm3
$21.94 per day
1 a 192 cm3
b 200 cm3
d 336 m3
e 1200 cm3
2 a i 12 cm ii 1296 cm3
b i 40 m
c i 24 mm ii 1568 mm3 d i 60 mm
e i 7.7 m ii 133.1 m3
f i 84 cm
3 a 151 m3
b 314 cm3
d 616 cm3
e 393 cm3
4 a i 6.3 cm
ii 59.6 cm3
b i 3.9 m
ii 19.9 m3
c i 9.2 cm
ii 153.6 cm3
d i 3.5 m
ii 2.3 m3
e i 244.6 m
ii 296 103.1 m3
f i 71.9 cm
ii 129 674.2 cm3
5 a i 14 137 cm3
ii 14 137 mL
b i 697 m3
ii 697 kL
c i 660 cm3
ii 660 mL
d i 3619 m3
ii 3619 kL
e i 1072 cm3
ii 1072 mL
f i 8579 mm3
ii 9 mL
6 1.1 3 1012 km3
7 a 33.75 m3
8 22.5 m
9 14.1 cm
11 2.8 cm
12 26.9 mm
c
f
ii
ii
ii
c
f
80 cm3
80 m3
14 400 m3
28 160 mm3
564 480 cm3
1780 mm3
2545 mm3
b 19 t
10 5.7 m
Exercise 4-08
9780170194662
1
2
3
4
8
9
10
11
a 9:1
b 9 : 25
c 81 : 25
a 3:5
b 1 : 10
c 8:5
a 3.5 cm
b 18
c 48
54 cm2
5 44.1 cm2
6 7.5 cm
The area is quadrupled (3 4).
The sides are decreased by a factor of 3.
The area has increased by a factor of 6.25.
1
The sides have decreased by a factor of 10
.
d
d
d
7
4:9
4:9
36.75
154 cm
Exercise 4-10
b i 4:9
ii 8 : 27
1 a i 9 : 25
ii 27 : 125
c i 16 : 25 ii 64 : 125
d i 4 : 25
ii 8 : 125
2 a 9 : 10
b 729 : 1000
3 a 5:7
b 25 : 49
4 76 800 mm3
5 75.6 mL
6 2531.25 g or 2.531 kg
7 78 L
8 a 2.25
b 3.375
9 There has been a 27
64 decrease in the volume.
Power plus
Exercise 4-07
1 a 59 m3
2 a 343 cm3
d 6100 cm3
3 a i 31 416 cm3 ii 31.416 L b i 616 cm3 ii 0.616 L
c i 264 cm3
ii 0.264 L
4 28.27 kL
5 a 12 balls
b 60 balls
c 31 416 cm3
d 48%
3
3
6 a 1963 cm
b 0.55 cm /s
7 a 250 m3
b 210 kL
c $415.80
b 59 kL
b 240 cm3
e 6048 cm3
c 1152 cm3
f 2500 cm3
Teacher to check.
Chapter 4 revision
1 a
d
2 a
d
3 a
4 a
d
5 a
d
6 a
7 a
d
8 a
d
9 a
1.08 m2
277.6 m2
7389.0 m2
14 294.2 cm2
960 cm2
704 m2
452 m2
3180 cm2
3318 cm2
36 816 m3
322.67 m3
1340.41 cm3
360 498 mm3
60.75 m3
234.375 cm2
b 3150 mm2
e 216 cm2
b 1437.3 m2
e 5871.2 cm2
b 7776 cm2
b 4524 m2
e 681 m2
b 1268 cm2
e 1728 cm2
b 20 160 m3
b 540 cm3
e 10 262.54 mm3
b 145 125 mm3
e 3054 cm3
3
b 6 14 10 a 250 cm
c
f
c
f
c
c
f
c
f
c
c
f
c
f
5236 cm2
482 mm2
104.3 m2
4427.8 cm2
1370 cm2
2488 m2
5890 m2
395 cm2
3436 cm2
10 016 m3
1568 mm3
904.78 m3
455 cm3
18 096 m3
b 36 : 49
Mixed revision 1
1
2
3
4
5
a 12 124 cm2
143
a $1 001.72
a $425
a 32
b 290 m2
c 1568 mm2
b $701.20
b $860.63
b 23
c $4 708.08
c $1 105
617
Answers
6 a 5629.7 m2
b 135.4 m2
pffiffiffi
pffiffiffiffiffi
7 a 13 2
b 4 11
8 a $47 210
b $6890.25
y y = 3x – 2
9
6
c 21 205.8 cm2
pffiffiffi
pffiffiffi
c 6 66 3
(1, 1)
0
–4 –2
–2
–4
–6
10
12
13
14
16
17
18
21
22
23
24
25
2
4 x
y = –2x + 3
13 824 cm2
11 B
a 565 m2
b 817 m2
c 804 m2
a $4764.06
b $4782.47
c $4786.73
3x 4y þ 24 ¼ 0
15 gradient 5, y-intercept 3
a $768
b $6912
c $3317.76
d $10 229.76
e $213.12
f $10 997.76
a $19 676.44
b $10 313.56
c 65.6%
x þpyffiffiffiffi 2 ¼ 0
19 43
m3
20 5x 2yp
pffiffi
ffiffi 30 ¼ 0
5þ5
a 1010
b 566
c 4 15
pffiffiffiffiffi
Show that all sides have length 34 and two sides are
perpendicular with gradients 35 and 53. Teacher to check.
a 1408.33 mm3
b 39 810.26 cm3
c 11.49 m3
1000 cm2
pffiffiffi
a 218
b 55 14 6
SkillCheck
g9
h 10
6e 7
v 5w 5
b r6
f m4
j 3n 4
3
n wv 3
c d 15
g a
k 1000w 9
o 1y
d k2
h 1
l 25
p y12
2 a 19a
b p6
c 53
d 7yx
20
2
3 a 18m þ 66m
b 15g þ 40
4 a 4(x þ 6)
b 5(4 3a)
c q(q þ 1)
d 6a(3a 2)
e 2(y þ 15)
f 6(3w 4)
5 a 3 and 6
b 2 and 4
c 4 and 5
d 8 and 2
Exercise 5-01
1 a
e
i
2 a
6p 7
30n16t 5
100y 20
l 18m 50
e 1
i
3 a
g
m
4 a
618
n
b
3
k
g
m3n
p2
h
4a 2
5b
7 a
243
1024
c m 30
g 5e 10g 4
2 4
k 3pq2 r
c 7
d 9q 6
h 9a 10b 5
l 54u 4v 3w 8
10
d wt 15
f 64k 2y 10
g 15
h
12
125d 9y 15 j 27k
1000
1
b 1
625
h 128
25
n 10 1000
1
1
b
25
32
c 7
i 1
o 1
1
c 20
k 9
d 1
j 64
p 1
1
d 1000
16b 4
81d 4
l 81p 8q12r 16
e 8
f 9
1
k 64
l 1
b
3
1
x3
e
p
n7
2k 4
c
1
16h 2
d m2
16
81
f
k
1
25b 2
p3
q5
l
5
b2
m
w3
e
3g 3
5
f
3t
2r
d 125
343
6
9
k2
e
2
15
9g
16
i
25t
4d 2
j mh10
8x 36
y6
c
r2
4q 12
d
1
12q 7 r
e
g 32h11
h
8
p 12 h 7
i 64p 10h 20
g
256
a8
k
9p8
25d 6
l
64a6
27c9
8 a 5000x 28y 6
b
a
256x 16
o
10f 3
e
c
d
h
x
27
f
j
1
1331t 3
256
625
f
4
i
1
y
11
t3
c
4
h2
256x 16
a4
Exercise 5-02
1 a 8
g 0.1
pffiffiffiffiffi
10
2 a
pffiffiffiffiffi
8r
e
b 3
h 2
g
f q3
b 27
h
i
b
f
b
f
b
e 243r 5
i
c 64
1
3
6.69
7.62
2
n5
5
a3
8x 3
g ðxyÞ
1
100
j
f 64h 6
1
25n 4
d 400 5
1
7
d 25
14.66
0.05
5
d2
3
5
a
2
4y 3
f 0.2
l 5
pffiffiffiffi
d 4m
pffiffiffiffiffiffiffiffiffiffi
h 9 90ab
1
1
c 20 4
1
1
1
2
d 10
e 2
j 9
k 2
pffiffiffi
g
c
pffiffiffiffiffiffi
g 5 5j8
b 100 3
e a2
4 a 32
c 25
i 2
pffiffiffiffiffi
b 3 12
pffiffiffiffiffi
f 6 6h
1
1
3 a 52
1
32
1
h ð36wÞ6
e
1
2
k
1
8000
1
4
1
25
f
l
c
g
c
g
c
5.24
132.96
p3
3
x4
27d 6
d
h
d
h
d
3.98
0.30
m4
4
x3
512m 12
g
1
16s 8
h
1
16p 6
1
100x 2 y 4
j
1
3
125t 2
k 343a 6b 15
b
17c
10
5y
16
u
4g
3
4h
c
l
Exercise 5-03
1 a
e
i
m
2 a
b 5w 6
f 4x 5y 4
j 64p 3
3
b n8
h
1
35
a
b
b
2r 6
y5
5 a
e
6 a
e
7 a
Chapter 5
1 a
e
i
m
m
8
u3v4
6 a
4
2
g
1
87
1
ab
5 a
e
i
3 a
e
i
5n
14
13t
9
pþ3
z
5rþ3t
rt
f
j
n
5m8n
40
13c
10
21þ8a
28
b
f
j
9mþ2
20
2mþ8
15
14mþ49
36
b
f
j
g
k
o
17t
20
6d11r
33
5e
24
c
g
k
8xþ10
15
3kþ31
70
1712m
35
c
g
k
15r
14
13t
36
1
3f
29
12b
d
4aþ9h
30
9hþ10a
15
7m2n
14
d
7y5
12
k3
6
337k
6
d
h
l
p
h
l
h
l
19y
24
17a
30
2e
5
9p4n
3np
3d2r
48
25þ24w
30
17k
30
9x13
20
23x41
20
1413x
6
Exercise 5-04
1 a
g
3m
20
3x
4y
b
h
kw
12
2
3
c
i
28
pt
d
g
d
j
6
5qy
d2
12
e
k
3d
e
2
3
f
l
8
v
12a 2
k2
9780170194662
Answers
2 a
g
3 a
g
5x
2y
16
27
5x
z
50p 2 t
7
b
h
b
h
t
6r
15
2
c
3b
1
6h 2
c 4
d
i
12
j
c
5
4
2s
35
i
d
j
h2
k2
9
b2
25b
3
2
3n
3d
10
e
f
k 6p
l
4t
27
27ac
w
e
k
1
3
3g
20y
f 25y 2
l
uy
Mental skills 5
2 a
e
i
m
176
682
152
288
b
f
j
n
363
707
540
693
c
g
k
o
261
1818
2142
3939
d
h
l
p
405
3564
588
852
Exercise 5-05
1 a
d
g
j
2 C
3 a
4 a
d
g
j
5 a
d
g
j
m
6 B
7 a
c
e
g
i
4h þ 24
4a þ 20z
6y þ 42y 2
12ab 2 21a 2b
b
e
h
k
3r 30
2 þ t 2
12x 2y 2 4xy
6h 2 þ 18h 3
c
f
i
l
7x 63y
20e 2 30e
16rt 2 8r 2t
25x 3 20xy
Yes
15m 2 þ 21m
49x 3 10x 4
6x 3 þ 35x 2 þ 8
9y 2 36y þ 35
6(4x þ 5)
10y(3 2y)
(a 3)(a þ 6)
q(q þ 36)
hn(n h)
b
b
e
h
k
b
e
h
k
n
No
15e 2 9e
t 2 þ 7t þ 12
6 þ 3v 2v 2
16m 3 þ 2m 2
9(4 3a)
12d(3d þ 2)
(8 þ t)(t 3)
2t(3 5t)
2e(10e þ 11)
c
c
f
i
l
c
f
i
l
o
Yes
3w 3 15w
12 11h 2h2
w 2 8w þ 3
20xy þ 20x 60y
x(x þ 1)
4r(4r 3)
(3b þ 5)(b 2)
3y(y þ 2x)
9m(5m 6)
4xy(3x 4)
36mn(m 3n)
16vw(3v þ 4w)
p(1 8p 4p 2)
8pg(4p 2 þ g 1)
b
d
f
h
j
2pr(9p þ 8)
36bc(ab 4)
25gh(3g 2h 5)
3mn(2n þ 1 þ 16m)
3a 2(6a 3 4 þ 5a 2)
Exercise 5-06
1 a
d
g
j
2 D
3 a
c
e
g
i
k
4 a
e
5 a
c
m 2 þ 7m þ 12
a 2 5a 24
15 þ 14k k 2
t2 þ t 2
b
e
h
k
w 2 þ 10w þ 25
b 2 þ 7b 18
r 2 18r þ 77
x 2 þ 6x 40
2x 2 þ 11x þ 15
3p 2 þ 7p 10
6f 2 þ 4f 10
6 þ 13h 5h 2
10m 2 þ 23m 12
25y 2 25
8y
b w2
18k
f þ80f
h 2 þ 14h þ 49
x 2 2x þ 1
9780170194662
c
f
i
l
y 2 144
u 2 15u þ 56
c 2 9c þ 18
99 2n n 2
9e 2 þ 42e þ 49
49d 2 28d þ 4
12m 2 þ 5m 25
16p 2 40p þ 25
12t 2 4t 1
49a 2 þ 84a 36
c m2
d 14u
g 4d 2 þ 12d
h 36a 2, 1
b k 2 10k þ 25
d q 2 þ 20q þ 100
b
d
f
h
j
l
e
g
i
k
m
o
q
6 a
d
g
j
m
7 a
d
g
8 a
d
g
25 10h þ h 2
x 2 2xw þ w2
4m 2 12m þ 9
81a 2 þ 36a þ 4
16 40p þ 25p 2
64a 2 48ay þ 9y 2
t2 2 þ t12
k2 9
b
49 m 2
e
25r 2 16
h
4 81m 2
k
t 2 t12
n
9t 2 6td þ d 2
b
p 2 þ 4p 4
e
6x2 3y2 7xy
h
3x 2 þ 7x þ 2
b
y 2 þ 18
e
x2
h
f 49 þ 14k þ k 2
h a 2 þ 2ag þ g 2
j 25x 2 60x þ 36
l 25 þ 70b þ 49b 2
n 121d 2 44cd þ 4c 2
p 1 þ 2y þ y12
r w92 þ 6 þ w 2
y 2 64
c w 2 121
2
81 k
f 9d 2 25
2
16p 49
i 9 64k 2
2
2
81k 16l
l 49n 2 64m 2
w2
4
o 1 r12
9
4e 2 1
c 25a 2 16
2
100 36y
f h 2 6hg þ 9g 2
2
2
49a 16b
i u 2 u12
16k 2 48
c 5xy 6x þ 3y þ 9
8m2 þ 2n2
f 12h þ 18
1 2b 2
Exercise 5-07
1 a
c
e
g
i
k
m
o
2 a
c
e
g
i
k
m
o
q
s
u
w
3 a
c
(x þ y)(3p þ 2q)
(3k þ 4g)(5m þ 2n)
(2k 5f)(a þ 4)
4(m þ t)(a þ e)
(3m þ p)(n 2)
( f 10)(g h)
(2 p)(p c)
(a þ y)(x þ 1 k)
(d þ 4)(d 4)
(p þ 11)(p 11)
(5 þ t)(5 t)
(2r þ 3d )(2r 3d )
(12 þ 7m)(12 7m)
(1 þ 9d)(1 9d)
(y þ z)(y z)
(b þ 11d)(b 11d)
(4 þ 9h)(4 9h)
(10 þ 7n)(10 7n)
1
þ 5c 12 5c
2
5h þ 32 5h 32
4(m þ 2p)(m 2p)
y(y þ 5)(y 5)
b
d
f
h
j
l
n
p
b
d
f
h
j
l
n
p
r
t
v
x
b
d
(h þ k)(2w 3u)
(x 2a)(4y þ 7a)
(d þ y)(c h)
3(k 2b)(y þ 4)
(9 þ q)(p 2 3)
3(l þ n)(3k 4m)
(l 3)(l 2 þ m 2)
(a b þ 3q)(p 2q)
(x þ 5)(x 5)
(y þ 9)(y 9)
(10 þ k)(10 k)
(5g þ 2e)(5g 2e)
(9y þ 4k)(9y 4k)
(m þ 2n)(m 2n)
(7 þ 4m)(7 4m)
(6c þ 5k)(6c 5k)
(5a þ 8m)(5a 8m)
(11p þ 12q)(11p 12q)
2t þ 13 2t 13
(1 þ mn)(1 mn)
3(d þ 3)(d 3)
2(3 þ 5g)(3 5g)
e k(1 þ 4k)(1 4k)
f 2(5q þ 1)(5q 1)
g 3(d þ 2v)(d 2v)
i 2(ab þ 1)(ab 1)
h 5t 3(t þ 5)(t 5)
j x 2(y þ w)(y w)
k 12(4f þ 3g)(4f 3g)
l 5 3d þ 12 3d 12 or 54 ð6d þ 1Þð6d 1Þ
m 2(x þ 2a)(x 2a)
n 25(2 þ w)(2 w)
o 5 12 þ 4e 12 4e or 54 ð1 þ 8eÞð1 8eÞ
p 3c þ 2 12 3c 2 12 or 14 ð6c þ 5Þð6c 5Þ
619
Answers
c þ 14 c 14
w 3uw 3u
c 5þ 4 5 4
5b 4a
5b
e 4a
7 þ 2
7 2
4 a
b
m
n
4 þ3
2
m
4
n3
d (k þ 5)(k2 5)
f (t þ 3)(t 3)(t 2 þ 9)
2
g (10 þ n)(10 n)(100 þ n )
i (p þ 3q)(3p q)
h y(2x þ y)
j 2x þ 6y 2x 6y
k 4ab
Exercise 5-08
1 a 3, 8
b
2 a (x þ 3)(x þ 5)
d (e þ 3)(e þ 2)
g (n 3)(n þ 1)
j (w 9)(w þ 2)
m (x þ 4)(x 1)
p (a þ 2)(a 1)
s (p 6)(p 4)
v (m þ 2)(m þ 2)
5, 2
c 3, 5
b (d þ 7)(d þ 2)
c
e (h þ 2)(h þ 2)
f
h (r 7)(r þ 2)
i
k ( f 9)( f þ 3)
l
n (t þ 8)(t 3)
o
q (k þ 7)(k 2)
r
t (n 2)(n 1)
u
w (p 10)(p 10) x
d 3, 4
(m þ 9)(m þ 3)
(n þ 1)(n þ 10)
(h 4)(h þ 1)
(a 6)(a þ 2)
(m þ 5)(m 2)
(w þ 6)(w 2)
(r 3)(r 3)
(c 5)(c 5)
Exercise 5-09
1 a
c
e
g
i
k
m
o
2 a
c
e
g
i
k
3 a
c
e
g
i
k
m
o
q
4 a
5 a
c
e
g
i
k
6 a
c
e
620
3(m þ 1)(m þ 2)
b 2(y þ 2)(y 1)
5(t 10)(t þ 8)
d 5e 2(e þ 8)(e 3)
x(x 11)(x þ 10)
f 4(b 7)(b þ 6)
4(w þ 4)(w 3)
h 3a(a 4)(a þ 1)
2(e þ 5)(e þ 4)
j (t þ 8)(t 3)
(u 7)(u þ 6)
l (x 7)(x þ 4)
(b þ 4)(b 3)
n (k 3)(k 4)
(x 5)(x 7)
(2d þ 3)(3d þ 5)
b (4m þ 3)(2m þ 1)
(y þ 5)(2y þ 7)
d (d þ 10)(2d þ 7)
(w þ 15)(2w þ 1)
f (e þ 3)(4e þ 3)
(2f þ 3)(4f þ 1)
h (d þ 1)(3d þ 2)
(b þ 1)(2b þ 7)
j ( y þ 1)(5y þ 11)
(4g þ 3)(2g þ 5)
l (3a þ 7)(2a þ 3)
(4k 3)(k 2)
b (2w 5)(3w 1)
(p 3)(5p 4)
d (2g 7)2
(3f 4)(4f 3)
f (2h 9)2
(y þ 1)(5y 11)
h (4d 5)(d þ 1)
(2m þ 3)(m 3)
j (2a þ 1)(4a 3)
(5u 4)(3u þ 1)
l (3c þ 1)(3c 5)
(5m þ 7)(m 1)
n (3g 4)(2g þ 3)
(3p 2)(p þ 2)
p (7w 1)(w þ 1)
(5y 1)(y þ 3)
r (3n 2)(n þ 4)
(9w 10)2
b 4(y þ 1)2
c (5h 4)2
3(m þ 4)(3m 2)
b 2(2y 5)(y þ 1)
5(3k 2)(2k þ 3)
d 4(w 4)(3w þ 1)
4(t þ 2)(3t 1)
f (5q þ 3)(5q 2)
2(2m 1)(3m 2)
h (3h þ 4)(4h 5)
6(2c þ 3)(2c þ 1)
j 3(z þ 1)(2z 5)
2(2d 3)(3d þ 5)
l 2(x 3)(3x 2)
(w 1)(7w 1)
b (h 3)(4h þ 5)
(4x 3)(2x þ 1)
d (r þ 5)(5r þ 1)
(d 7)(2d 1)
f (3n þ 1)(2n 3)
g (3m 2)(3m þ 4)
i (3g þ 2)(5g þ 3)
k (x 2)(3x 7)
h (5c 3)(c þ 1)
j (4q þ 3)(2q 5)
l (3d 4)(d þ 4)
Exercise 5-10
1 a
c
e
g
i
k
m
o
q
s
u
2 a
c
e
g
i
k
m
o
q
s
u
(m þ 8)2
(d þ 3)(3d 5)
(5y þ 8)(5y 8)
q(q þ 3 3p)
4(2b þ 5)(3b 2)
(b 2 þ 1)(b þ 1)
(5d 4)(d þ 1)
2(2 þ v)(2 v)
2(w 6)2
(3r 8t)(5r þ 3t)
9(g þ 2k)(g 2k)
e(e 5)(e þ 2)
7(2x þ 1)(2x 1)
(c 2)2(c þ 2)
(t þ 7)(t 5)
(6a 1)(4a þ 1)
(a 3)(2ab 3)
(5u 1)2
3(4 þ w)(4 w)
(k þ 4)2(k 4)
mn(m þ 2)(m 2)
4(2c 3)(4c þ 1)
b
d
f
h
j
l
n
p
r
t
3(d þ 1)(d 1)
(3 þ h)(k 5)
4(5f þ 4)( 5f 4)
(g 3)(g þ 1)
(5r þ 1)(5r 1)
(2x 5)2
(b 1)2(b þ 1)
m(n þ 3)(n þ p)
(6h þ 1)2
(2d þ 1)2
b
d
f
h
j
l
n
p
r
t
20(2p 3q)(3p 2q)
(a b)(a þ b þ 4)
(3a 1)(2a þ 5)
2(3p þ 2)2
9(x þ 2)(x 3)
2(a þ 3)2
(k 3)(4k þ 7)
3(1 þ 3s)(1 3s)
5y(y 2 2y þ 3)
2(a þ 2)(a 2)
Exercise 5-11
1 a xþy
d 1
d
kþ5
k5
yþ4
2
sþ2
s3
7mþ10
mðmþ1Þðmþ2Þ
k2
k ðkþ1Þðk1Þ
g
425r
4ðrþ6Þðr6Þ
g
j
m
2 a
f
k
3
2ðabÞ
2
3ðx2Þ
l
e
kþ1
kþ4
12c
3c1
2w20
wðwþ3Þðwþ5Þ
5hþ12
4hðhþ1Þ
f
h
d 2 þ3d6
d ðdþ2Þðd2Þ
i
k 2 þ9k5
ðkþ1Þðk1Þðk4Þ
g
l
f
h 3(c 1)
i
n
b
r
5ðrþtÞ
1
33
c
e w4
k
3q1
j ðqþ1
Þðq1Þ
1
3 a 6m
b 1 24
1
2ðtrÞ
bc
a
5
dþt
aþ1
mþn
4aþ5c
ac
aþ4
2ðpþ2Þ
4b7
ðb1Þðbþ2Þðb3Þ
4d1
ðdþ2Þðdþ1Þ
b
c
h
m
1
2
4m
m1
ðdþ1Þðd3Þ
6
o
c
d 6k
e
i
4
p
j
n
f þ3
4ð f 3Þ
o
10
hþ1
3
7
3
f 2
Power plus
1 a x 3 þ 15x 2 þ 55x þ 25
b y 3 6y 2 þ 12y 8
c a 3 þ 3a 2b þ 3ab 2 þ b 3 d 27d 3 þ 270d 2 þ 900d þ 1000
2 a 441 b 2025 c 841 d 3481 e 10 404 f 9604
3 899
4 a 399
b 2499
c 8099
d 6396
5 a 3y 2 þ 12y þ 14 b 3x 2 þ 9 c 34n 2 34 d 4b 2
9780170194662
Answers
(n þ 2m) 2
(5x 4y) 2
(c 2 þ 1) 2
x yx y
4þ5 45
(5c 2 10)(5c 2 þ 10)
4a 5b4a 5b
7 þ 2
7 2
b
d
f
h
j
l
(x y) 2
5(a 3b) 2
(t 1)(t þ 1)(t 2 þ 8)
(x þ 1)(x 1)(x 2 þ 1)
(a þ b þ c)(a þ b c)
4pq
Chapter 5 revision
1 a 6v 5w 7
e 4k1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
i
a
a
a
a
a
a
a
c
e
a
c
e
g
i
a
c
e
a
c
a
c
e
a
c
e
a
c
e
a
c
a
625b 24y 12
100 000
20
64a 6
d
2y þ 12
yðyþ3Þðy3Þ
3t
20
7r20
10
3m 2
10
2
b 8t 7h 6
3
f 8p27
c 25x 2y 4
1
g 16m
2
j 512t 14u 16
64
b 125t
3
b 3
b 243t 15
b 19g
6
b 4wþ9
10
b 34
k
c
c
c
c
c
c
b
d
f
b
d
f
h
56tp 40t 2p
4fg 2 30f 2g
8x 3 þ 7x 4
8ar(2r þ 3)
(5x 1)(2 3x)
6p(t 2 þ 2pt 8p 2)
25x 3y 3(2x 3y)
(n 2 þ 6)(n 1)
b 2 þ 13b þ 30
15t 54 t 2
49y 2 9
n 2 þ 18n þ 81
9y 2 12y þ 4
(r þ t)(3p þ 2q)
(b þ 10)(b 10)
5(2x þ 1)(2x 1)
(y þ 5)(y þ 5)
(n þ 11)(n 3)
(m 12)(m þ 7)
(3w þ 2)(w þ 1)
5(b þ 4)(b 3)
2(3x 1)(2x 7)
5(q 3)(q þ 3)
(t 1)2(t þ 1)
2n þ 3t
b
b
d
f
b
d
b
d
f
b
d
f
b
d
f
b
d 1
h m42
5c 4d 4
l
4d 2
81
1
8
1
16p8
x
16
5pþ20
12
b
2a
6a
5b
d 8
d 25x12 y4
d 4w
3
15h 3 35h 2
93 22n
10y 2 41y þ 21
6(4p 3q)
15xy2(1 2x 2y)
4r 2s 3(8s þ 3r 2)
8p 3q 3(1 6q 3)
d 2 þ d 56
20x 2 þ 13x 21
25p 2 80p þ 64
n 2 81
16n 2 121
(2a þ 3c)(2b 3d)
(5 4y)(5 þ 4y)
3t(t þ 3)(t 3)
(x 20)(x 1)
(a 7)(a 4)
(p þ 9)(p 6)
(2y þ 3)(y 3)
(3p 2)(p þ 4)
(3n 2)(2n 3)
4(5x 3)(x 2)
6ðmþ2Þ
5
c
e 9
f
aþ2
aþ1
3ðbþ2Þ
bðb3Þ
Chapter 6
i 10
i 13
i 7
i6
i 48
i 5
9780170194662
Exercise 6-01
1 a i
ii
b i
ii
c i
ii
d i
ii
e i
ii
f i
ii
g i
ii
h i
ii
2 a
symmetrical
clustering at 9, no outliers
not symmetrical, not skewed
clustering in the 30s and 60s, no outliers
positively skewed
clustering at 1, no outliers
negatively skewed
clustering at 2324, no outliers
positively skewed
clustering at 130–150, no outliers
symmetrical
clustering at 5, no outliers
positively skewed
clustering at 13, 23 is an outlier
symmetrical
clustering at 50s and 100s, 136 is an outlier
Score
66
67
68
69
70
71
72
73
74
75
76
77
9
8
7
6
5
4
3
2
1
0
Frequency
1
2
1
5
3
5
9
5
4
4
0
1
66 67 68 69 70 71 72 73 74 75 76 77
Score
mean
SkillCheck
1 a
b
c
d
e
f
2 a i 31
ii 33.3
iii 62
b 78
c i Median ¼ 30, mean ¼ 28.3, range ¼ 25.
ii The outlier has increased the median (by 1), the mean
(by 5), and the range (by 37).
Frequency
6 a
c
e
g
i
k
ii
ii
ii
ii
ii
ii
16.5
1.8
11.5
43.6
34.3
2.2
iii
iii
iii
iii
iii
iii
15
2.5
11
43
34.5
2
iv
iv
iv
iv
iv
iv
15
3
11
43
24, 35
2
mode, median
b no outliers
c negatively skewed
d The lower the score below par, the fewer the golfers that
achieve that score.
e clustering at 72
f mode ¼ 72, x ¼ 71.6, median ¼ 72
621
Answers
3 a 45
b 19 hours (stem of 0)
c no outliers
d positively skewed
e Most students spend limited time on their computers,
and have other commitments and do activities such as
sport. Only a few students spend many hours on the
computer during the week.
f Mode ¼ 1, x ¼ 14, median ¼ 11
4 a Stem Leaf
b
c
d
e
5 a
d
g
12
3
13
14
2 3
15
0 1 3 3 3 5 5
16
0 0 1 2 2 2 2 3 4 5 5 7 8 9
17
0 0 1 2 3
18
2
Symmetrical
123 is an outlier.
Clustering occurs in the 160s.
mode ¼ 162, median ¼ 162, x ¼ 160.2
slight positive skew
b 13.8 is an outlier
c 18.4
19.5
e 19.5
f 10.5
No, the range has been affected by the outlier 13.8.
Exercise 6-02
1 a 5, 6.5, 8
b 18, 20, 26.5
c 32, 34.5, 38
2 a range ¼ 7, IQR ¼ 3
b range ¼ 22, IQR ¼ 8.5
c range ¼ 16, IQR ¼ 6
3 a 7.5
b 3
4 a 283 mm
b 128 mm
5 a 3 b 2.5
c 17.5
d 19
e 21.5
f 1.5
6 a 34
b 13
c i 68, 72, 72, 75, 77, 78, 79, 80
ii 50%
d 75%
7 a i 28
ii 9.5
b The interquartile range, as it is not affected by the score
of 35.
c 48, 48, 48, 49, 51, 53, 55; 54%
Exercise 6-03
1 a 2.66
b 2.63
c 1.19
d 1.33
e 2.01
2 a 7
b i 2.64
ii 2.28
c Decreases the standard deviation.
3 a C
b A
4 a 1.99
b 13.43
5 a x ¼ 165.89, s ¼ 8.37
b i less than 157 or greater than 175 (to the nearest cm)
ii between 157 and 174 (to the nearest cm)
6 a x ¼ 11.37, s ¼ 0.43
b i less than 10.9, greater than 11.8 (correct to one decimal
place)
ii between 10.9 and 11.8 (correct to one decimal place)
7 C
622
Exercise 6-04
1 a Men: x ¼ 71.40, s ¼ 6.77; Women: x ¼ 77.53, s ¼ 6.96
b Yes, the mean of women’s pulse rates is much higher,
which may be due to stresses involved in shopping (and
looking after children at the same time). The standard
deviation for women is slightly higher.
2 a Dominant hand: x ¼ 0.40, s ¼ 0.11; Non-dominant hand:
x ¼ 0.52, s ¼ 0.51
b Yes, the mean reaction time and standard deviation of the
dominant hand are much lower than the mean and
standard deviation of the non-dominant hand.
c i 0.61 and 0.75
ii x ¼ 0.37, s ¼ 0.05
iii Removing the outliers has reduced the mean 0.40 to
0.37 and more than halved the standard deviation.
d x ¼ 0.40, s ¼ 0.06
e The removal of the outlier from the non-dominant hand
had the greater effect on the mean and standard deviation
as the outlier of 2.60 was a more extreme score than the
outliers for the dominant hand.
3 a Western Tigers: x ¼ 122.92, s ¼ 26.98; Barrington City:
x ¼ 120.92, s ¼ 23.62.
b The Barrington City team is slightly more consistent as the
standard deviation is 23.62 compared with 26.98 for
Western Tigers.
4 a Vatha: x ¼ 13.76, s ¼ 0.55; Ana: x ¼ 14.14, s ¼ 0.66
b Vatha is more consistent as the standard deviation for her
times is significantly lower than the standard deviation for
Ana’s times.
5 B
6 a Maths:
i range ¼ 47 ii IQR ¼ 14 iii s ¼ 10.97
Science:
i range ¼ 45 ii IQR ¼ 19 iii s ¼ 13.16
b Maths: x ¼ 67.82; Science: x ¼ 61.25
c The students performed better in Maths as the mean was
67.82 compared to 61.25 for Science. The marks for maths
were also more consistent as the IQR and standard
deviation are both lower than those of Science.
7 a Roosters:
i range ¼ 48
ii IQR ¼ 20
iii x ¼ 26.67
iv s ¼ 12.55
Dragons:
i range ¼ 32
ii IQR ¼ 8
iii x ¼ 15.88
iv s ¼ 7.36
b The range, IQR and the standard deviation for the Dragons
are significantly lower than those of the Roosters, which show
that the Dragons are more consistent in the number of points
they scored per game. However the mean of the Roosters is
significantly greater than the mean of the Dragons, which
would indicate that they are a better team as they were able
to score many more points per game.
Mental skills 6
2 a
f
k
p
160
900
18
12
b
g
l
q
70
140
34
40
c
h
m
r
240
300
46
8
d
i
n
s
900
180
26
14
e
j
o
t
2600
770
18
24
9780170194662
Answers
2 a
b
c
d
Exercise 6-05
1 a 1, 4.5, 6.5, 10, 18
b
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Number of orders/h
2 a 26
b 1, 2, 5, 13, 50
c
0
4
8 12 16 20 24 28 32 36 40 44 48 52
Amount of snow (cm)
b 5, 21.5, 49.5, 96, 266
3 a 261
c
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280
Monthly Rainfall (mm), Penrith
4 a 27.5 h
b 26 h
5 a 26
b 21
6 a 6, 10, 19, 23, 29
c 30 h
c 14
b 13
d 4h
d i 25%
c i 14
ii 7
7 a 20, 46, 51, 68, 88
iii 7
20
30
40
b 10, 13, 15, 16, 20
10 11 12 13
c 30, 51, 65.5, 75, 95
30
40
8 a 4, 6, 7, 9, 15
e 50%
ii 75%
50
60
iv 21
70
80
90
e
i 33
ii 28
Thunderbirds: 50; Swifts: 49
Thunderbirds: 15.5; Swifts: 9.5
The range for both teams is similar but the IQR of the
Swifts is less than the IQR of the Thunderbirds, indicating
that the Swifts are more consistent in their performance.
The position of the Thunderbirds’ boxplot shows that the
Thunderbirds scored more points in games than the Swifts
and so performed better in the season.
10K: 9; 10N: 10
b 10K: 6.5; 10N: 5.5
10K: 3; 10N: 4
d 10K lower range and IQR.
75%
3 a
c
e
4 C
5 a Brisbane: 26.9, 9.3, 4.7; Sydney: 23.5, 8.5, 4.9;
Melbourne: 21.4, 13, 8.6; Hobart: 18.6, 11.2, 7
b Melbourne – it has the highest range and IQR.
c Brisbane, more than half of the mean monthly
temperatures are higher than most of the mean monthly
temperatures of the other cities.
d Sydney’s median temperature is significantly higher than
Melbourne’s, so Sydney is the warmer city.
e Sydney has the smaller range and IQR of mean monthly
temperatures, so it is more consistent.
6 a Male: 0,1, 2, 4, 7; Female: 2, 4, 5, 7, 10
b
Males
Females
14
50
15
60
16
70
17
80
18
19
90
20
100
0 1 2 3 4 5 6 7 8 9 10
Text messages
c Male: 3; Females: 3
d Males: 7; Females: 8
e Both are positively skewed, the interquartile range is the same,
and the range of females is one more than that of the males.
Females do receive more text messages, as the boxplot shows
that 75% of females receive more messages than 75% of males.
7 a Male: 145, 165, 167, 172.5, 189; Female: 150, 162.5,
165.5, 173.5, 186
Females
4
9 10 11 12 13 14 15
Marks
b Dot plot is positively skewed. The length of the boxplot
from the median to the highest score is greater than the
length from the median to the lowest score.
c 15
d 4, 6, 7, 9, 12
4
5
5
6
6
7
7
8
8
9 10 11 12 13 14 15
Marks
e i The boxplots are the same up to Q3.
ii The whisker from Q3 is reduced without the outlier.
Exercise 6-06
1 a i Year 10: 3.5; Year 8: 8
iii Year 10: 1; Year 8: 2
b i 25% ii 75%
9780170194662
ii Year 10: 7.5; Year 8: 8.5
c
i 10
ii 0
Males
140
150
160
170
180
190
Height of students
b Male:
Range 44 IQR 7.5
Female:
Range 36 IQR 11
c Male students have a greater range (44 compared to 36),
but a smaller interquartile range (7.5 compared to 12).
8 a Low: 64, 73.5, 80, 86, 92; High: 49, 58, 68, 75, 96
High
Low
40
50
60
70
80
90
100
Pulse rate
b Low: 28, 12.5
High: 47, 17
c The range and interquartile range of the High Frequency
group are both greater than that of the Low Frequency group.
d The high frequency group.
623
Answers
9 a Sydney: 17.6, 20.4, 23.45, 25.25, 26.1; Brisbane: 21.1,
23.65, 26.9, 28.45, 30.4
Brisbane
f
Sydney
b
c
10 a
d
f
g
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Average monthly temperature (ºC)
Sydney: 8.5, 4.85
Brisbane: 9.3, 4.8
Sydney average monthly temperatures were slightly more
consistent than Brisbane, since its range was 0.9 less than
Brisbane’s, while Brisbane’s IQR was only 0.05 less than
Sydney’s.
Simone b Simone: 12; Amal: 10 c Amal, smaller range.
Simone: 10; Amal: 9
e Simone: 4; Amal: 5
Not enough information given to make a valid decision.
The interquartile range and range only differ by 1.
25%
Exercise 6-07
1 a Boys: $34.58, Girls: $31.78 b Boys: $33.50, Girls: $28
c Boys: Range ¼ 72, IQR ¼ 25, Girls: Range ¼ 69, IQR ¼ 30.5
d i Boys are positively skewed slightly, girls are positively
skewed.
ii There are no outliers, clustering occurs for the boys in
the 20 30s and for the girls in the 10 20s.
e Boys generally carry more cash they have a higher mean
than the girls and the shape of the data for girls is more
positively skewed.
2 a 21 games
b i 34
ii 51
c Scorpions: x ¼ 1.6 goals; Vale United: x ¼ 2.4
d Scorpions 5, Vale United 6
e The shape of both teams’ results is positively skewed.
Clustering for Scorpions occurs at 1 and 2 and for Vale
United it occurs at 2.
f Vale United performed better as its mean was 2.4 goals/
game compared to Scorpions 1.6 goals/game.
3 a Sydney: x ¼ 26.2, median ¼ 26.5, mode ¼ 28
Perth: x ¼ 34.3, median ¼ 35, mode ¼ 38
b Sydney: Range ¼ 9, IQR ¼ 3
Perth: Range ¼ 16, IQR ¼ 8
c The temperatures for Sydney and Perth are both negatively
skewed, there are no outliers. Sydney’s temperatures are
clustered in the high 20s, while Perth’s are clustered at 34 38.
d Sydney’s temperatures are lower than Perth’s, as evidenced
by the significantly lower mean, median and mode. The range
and interquartile range for Perth are greater than the range
and interquartile range for Sydney, indicating greater spread.
4 a 30
b Quiz 1: x ¼ 5.6, mode ¼ 6; Quiz 2: x ¼ 6.3, mode ¼ 7
c Quiz 1: 6; Quiz 2: 7
d Quiz 1:
i Range ¼ 7
Quiz 2:
i Range ¼ 8
ii IQR ¼ 2
ii IQR ¼ 2
e Quiz 1: Results are symmetrical with clustering at 56, no
outliers.
624
5 a
b
c
e
f
6 a
b
c
d
7 a
b
c
d
e
8 a
b
c
d
e
f
9 a
b
c
d
Quiz 2: Results show negative skewness with clustering at
5 and 78, no outliers.
Scores for Quiz 2 are just better than Quiz 1, as the mean
of Quiz 2 is higher than the mean of Quiz 1. The spread
for both quizzes are similar as there is only a difference of
1 between the ranges and the IQRs are equal.
39
i mode ¼ 2 ii median ¼ 2 iii range ¼ 6 iv IQR ¼ 1.5
positively skewed, no outliers
d 50%
i By the highest columns.
ii By the short length of the box when compared to the
whole length of the boxplot.
i The shape of the distribution, the frequency for each
household size and the mode. The mean can also be
calculated from the histogram.
ii The shape of the distribution, the median and the
quartiles Q1 and Q2.
i 5
ii 16
i mode ¼ 22 ii range ¼ 18 iii IQR ¼ 24 16 ¼ 8
Negatively skewed.
i The tail of the dot plot goes to the left.
ii The length of the boxplot from the lowest score to the
median is longer than from the median to the highest score.
i dot plot
ii boxplot
iii dot plot
iv boxplot
Sunbeam Valley: range ¼ 24, median ¼ 71,
IQR ¼ 75 67 ¼ 8
Bentley’s Beach: range ¼ 30, median ¼ 73,
IQR ¼ 82 67 ¼ 15
Sunbeam Valley: negatively skewed (slight)
Bentley’s Beach: positively skewed
Sunbeam Valley’s speeds are clustered in the 70s.
25%
Bentley’s Beach higher median, positively skewed. 25% of
drivers drive faster than all drivers in Sunbeam Valley. This
may be due to more main roads with higher speed limits.
36
Lamissa: mode 7, median ¼ 7
Anneka: mode ¼ 7, median ¼ 6
Lamissa: range ¼ 8, IQR ¼ 8 6 ¼ 2
Anneka: range ¼ 9, IQR ¼ 7 4 ¼ 3
Lamissa’s distribution of scores is negatively skewed with
clustering at 7. Anneka’s distribution is negatively skewed
with clustering at 6 and 7.
i 30.5%
ii 55.6%
Lamissa is the better archer. Her median score is higher
than Anneka’s, 30.5% of scores are less than 6 compared to
Anneka’s 55.6%. Also, from the boxplot, 50% of Lamissa’s
scores are equal to or better than 75% of Anneka’s.
The range (47) is too large.
Women: 31
Men: 37
Women: Range ¼ 38, IQR ¼ 40 24 ¼ 16
Men: Range ¼ 47, IQR ¼ 46 25 ¼ 21
Distribution for women is positively skewed with
clustering in the 20s. Distribution for men is symmetrical
with clustering in the 30s.
9780170194662
Answers
Exercise 6-08
5 a
700
Points scored against, A
e Men have the greater spread in the number of sit-ups
completed, as the range and IQR are both greater than
those for women.
10 a i 56
ii 38
b i 10 Blue, 10 Yellow ii 10 Green iii 10 Red
c i 10 Green
ii 10 Yellow iii 10 Red, 10 Blue
d 10 Blue. It shares the highest median with 10 Red
but its lowest score is still higher than 25% of 10 Red’s
scores.
600
500
400
300
300
1 a
25
200
24
200
21
20
19
18
17
16
Stride length, L (cm)
140 150 160 170 180 190
Height, H (cm)
b linear c As the heights of students increase, their
handspans tend to increase.
2 a weak negative relationship
b no relationship
c strong positive relationship
3 Weak positive.
4 a Stride length depends on a person’s height; the taller the
person, is, the longer their legs are.
b
80
79
78
77
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62
61
140 150 160 170 180 190
Height, H (cm)
c linear d Students’ stride length increases with height.
e strong positive relationship
f Near 72.5 73 cm
9780170194662
b Yes
6 a
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
300 400 500 600
Points scored for, F
700
c Weak negative relationship
Computer, C (hrs)
22
5 10 15 20 25
Homework, H (hrs)
b no relationship
7 a
190
0
180
Height, H (cm)
Hand span, S (cm)
23
170
160
150
140
130
10 11 12 13 14 15 16 17 18
Age, A (years)
b Age, because as a young person ages, he usually grows in
height.
c weak positive relationship
625
Answers
5 a
Exercise 6-09
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
1 a
Spring stretch, S (cm)
Height, H (cm)
190
180
170
160
150
140
19 20 21 22 23 24 25 26 27 28
Length of radius, r (cm)
b H ¼ 5r þ 48.5
2 a
c 173.5 cm
d 184 cm
5 10 15 20 25 30 35 40 45 50 55 60
Mass, M (g)
14
13
b 22.4 cm
c 56 g
d Yes, because a spring has an elastic limit, which is the
point at which a spring will not return to its original length
as a result of the mass attached to the spring being too
heavy.
6 a
10.1
Shoe size, S
12
11
10
9
8
7
10.0
b S ¼ 0.393H 59
d 12
3 a
Time (seconds)
170 172 174 176 178 180 182 184 186 188
Height, H (cm)
c 8.5
e 13.5
Temperature, T (°C)
20
10
0
–10
1000 2000 3000 4000 5000 6000 7000 8000 900010000
9.7
9.5
–20
1960 1970 1980 1990 2000 2010 2020
Year
–30
–40
b T ¼ 0.0068h þ 16
c 5.8C
4 a
100
90
80
70
60
50
40
30
20
10
0
10 20 30 40 50 60 70 80 90100
Maths results, M
b 80
c 97
Science result, S
9.8
9.6
Height, h (m)
b 9.60
c There is a limit to how fast a person can run.
–50
626
9.9
d 3800 m
Exercise 6-10
1 a i 25
ii 42
iii 15
b December, more customers due to summer and Christmas
holiday season.
c June, fewer customers due to winter, busy end-of-financial
year season.
d Number of people employed peaks in December, then
falls, only to increase in March, April (the Easter
holiday period). It then falls again to a low in June,
July and then slowly the number of people employed
rises to a peak in December. From 2010 to 2012,
the number of people employed is showing a slow
increase.
9780170194662
Answers
2 a
then fell at a rapid rate between 1980 1990 and
continued to fall by about 200/5 years until 2010.
c Improved safety in cars with seat belts being compulsory,
then drink driving laws introduced.
23
22
21
4 a i
20
24
Populations (millions)
19
18
23
Temperature (°C)
17
16
15
14
22
21
13
20
12
11
10
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Year
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
ii
Year
24
b 2005 – 2010
c Australia’s population increased at 1.1–1.2 million every
5 years up to 1975. The population growth then slowed
down for 5 years. From 1980, the population grew at a
steady rate of just over a million people every 5 years but
from in 2005–2010, the rate increased to 1.9 million for
the 5-year period.
d i 2627 million
ii 3234 million, teacher to check
3 a
1400
Temperature (°C)
23
22
21
20
1300
1200
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
1100
Year
1000
b i
900
Fatalities
800
700
600
500
400
300
200
100
1970
1980 1990 2000 2010
Year
b From 1960, road fatalities rose at a steady rate, reaching a
peak of approximately 1300 in 1970 1980. Road fatalities
1950
9780170194662
1960
Starting at 22.3 in 1990, the temperature has seen a
series of increases of less than 1, followed by falls of
less than 1. The increase from 1990 to 2000 is 0.4.
ii Starting at 23.1 in 2001, the temperature falls to 22.7
and then increases to a high of 23.4 for two years
before falling to 22.1. From 2009, the temperature
rose, then remained steady before a slight increase to
22.7 in 2012.
c The temperature from 1990 – 2000 continually increased
and decreased by less than 1. The temperature in 2001 –
2012 started at 23.1, rose to a high of 23.4 in 2004,
before falling for three years. This was followed by a slight
increase. The range of annual temperatures for both
periods is 1.3, but the minimum and maximum
temperatures for 2001 – 2012 are 0.6 higher than for
1990 – 2000.
627
Answers
5 a
560
Annual emissions Mt CO2-e
550
540
530
520
510
500
20022003200420052006 200720082009201020112012
Year
b Carbon emissions increased by 55 Mt.
c Carbon emissions stabilised.
d More environmentally-friendly policies and practices in
Australia.
e i, ii Teacher to check and discuss.
6 a Approximately 4 million.
b 18 million
c 300 000 persons per year
d 26.5 million
7 a Gradual increase in passenger movements with peaks in
October and troughs in February.
b i 3.9–4.0 million
ii 4.25 million
iii 4.2 million
iv 4.5 million
c 15%
Exercise 6-11
1 a Just surveying 300 people between 9 a.m. and 11 p.m. in
shopping centres only targets a narrow group of people in
certain areas.
b The sample needs to be more random and over a large
area, not just in shopping centres. A telephone survey
should produce more accurate feedback.
2 The report does not say what conditions are needed
for the hot water system to work effectively. The
temperature in Queensland is much warmer than
in NSW and Victoria. Consequently, with the cooler
climate in NSW and Victoria, especially in winter,
the heat pump system may not provide the savings that
people in Queensland obtain.
3 a i The price of petrol has shown little increase from
December to February.
ii The price of petrol has shown marked rises and falls
over the period from December to February.
b Both graphs could be improved by starting the vertical
scale at 0 cents/litre.
4 a That there is a marked difference between the fuel
consumption of the different cars.
b i 0.2 L/100 km
ii 1 L/100 km
iii 0.2 L/100 km
c Begin the scale on the vertical axis with 0 and use a scale
of 1 cm ¼ 0.5 L/100 km instead of 1 cm ¼ 0.2 L/100 km.
628
5 Yes, as there is no option for a customer to rate the product
as unsatisfactory or poor.
6 a An example of a biased question could be: Which of these
colours do you prefer red, black, silver, blue?
b Apart from surveying people, they need to look at sales
figures of all cars. This will give information about the
most popular car colour.
7 –8 Teacher to check.
Exercise 6-12
Teacher to check the investigations.
Power plus
1 a 1 and 1
b There is no relationship between the variables.
c i 1
ii 0.2
iii 0.8
2 b, d, f
3 a x ¼ 13.35, median ¼ 14, mode ¼ 14
b Range ¼ 10, IQR ¼ 15 12.5 ¼ 2.5
c The mean, median, and mode will increase by 4, the range
and the interquartile range remain unchanged.
Chapter 6 revision
1 a
b
c
2 a
3 a
b
c
4 a
b
5 a
b
c
i negatively skewed ii clustering at 16 and 17, 10 is an outlier
i positively skewed ii clustering at 40s and 50s, no outliers
i symmetrical ii clustering at 4, no outliers
6.5
b 6
c 2.5
d 12.5
e 2
x ¼ 0.40, s ¼ 0.08
Range ¼ 0.33, IQR ¼ 0.08
The interquartile range is the better measure as the
standard deviation is affected by the outlier 0.62.
Girls: x ¼ 67.73, s ¼ 16.08
Boys: x ¼ 61.67, s ¼ 12.35
The girls performed better than the boys as their mean mark
was about 6 more than the mean mark of the boys. However
the boys’ marks were less spread out than the girls.
Range ¼ 7, IQR ¼ 3 1 ¼ 2
0, 1, 2, 3, 7
0
1
2
3
4
5
Goals scored per game
6
7
6 a Before: 50, 64, 69, 76, 80; After: 82, 89, 95.5, 126, 146
After
Before
50
60
70
80
90
100 110 120 130 140 150
b i Range ¼ 30, IQR ¼ 12
ii Range ¼ 64, IQR ¼ 37
c The pulse rates for after exercise are significantly higher.
In fact, all the rates for after exercise are above all the
rates for before exercise. The median pulse for after
exercise is 95.5 compared to the median pulse of 69 for
before exercise. The range and interquartile range are also
greater for the after exercise pulse rate.
9780170194662
Answers
i Both
ii Stem-and-leaf plot
The range (126 70 ¼ 56) is too large.
i median ¼ 92
ii IQR ¼ 99.5 84 ¼ 15.5
50%
Weeks in storage this determines how many oranges
stay good.
Number of good oranges, N
b
60
50
Mixed revision 2
40
30
20
10
c For the last 10 years, the mean maximum temperatures at
Blacktown, after staying at 30.6, have ranged from a low of
27.4 to a high of 31.7, finishing at a temperature of 30.0
in 2013. This shows there has been little change in
temperature for the month of January over the last 10 years.
11 a That the product is healthy.
b There is no data given on the actual fat content in the
product. This should also be stated in terms of daily
percentage requirement of fat or in mg of fat.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks in storage, W
c linear
d The longer the oranges remain in storage, the fewer good
oranges there are in the box.
e strong negative correlation
9 a
1000
1 a
b
2 a
3 a
4 a
5 a
b
i negatively skewed ii no outliers, clusters at 7 and 8
i positively skewed ii outlier 98, clustering in 40s and 50s
b ¼ 7
b x ¼ 10
81n 4m 8
b 4a 4b 3
c 19
6a20
5xþ36
b 24
c 7r6
15
10
Range ¼ 33; Interquartile range ¼ 7
Interquartile range, because it is not affected by the outlier
of 112.
pffiffiffi
6 a x ¼ 6 3
b n ¼ 0 or 64
c u ¼ 15 or 4
7 a 9d
b 2
c 8pv 2
2
8 a 1, 3.5, 5, 6, 10
b
1
3.5 5 6
10
90
9
10
11
12
13
Weight, W (kg)
80
70
60
50
40
14
15
16
30
130 140 150 160 170 180 190
Height, H (cm)
b W ¼ 0.714 H 51.4
d 65 kg
10 a Year
b
c 70 kg
e i 192 cm
ii 135 cm
Temperature (ºC)
40
30
20
17
18
1 2 3 4 5 6 7 8 9 10 11
a weak negative
b strong negative
c weak positive
1
1
a 4
b 16
c 12
d 1000
y ¼ 5.8
a 53gh 45gh 2
b 7y 4 þ 2y 3
a Girls: mean ¼ 62.7, standard deviation ¼ 16.1
Boys: mean ¼ 66.9, standard deviation ¼ 12.2
b The boys performed better as their mean is higher.
a x 2 þ 14x þ 49
b 25m 2 20m þ 4
c 9n 2 100
20, 21, 22
a i stem-and-leaf plot
ii stem-and-leaf plot
b i median ¼ 42
ii interquartile range ¼ 16
a (y 16)(y 2)
b (n þ 8)(n 6)
c (a 9)(a þ 8)
a The independent variable is W, the weeks in storage. The
number of weeks in storage is set first after which time the
number of good apples is counted.
b
Number of good apples N
7 a
b
c
d
8 a
60
50
40
30
20
10
0
10
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Year
9780170194662
2 4 6 8 10 12 14
Weeks in storage W
c the number of good apples decreases the longer the apples
are in storage.
d there is a strong negative relationship between the
variables W and N
629
Answers
19 a (5n þ 2)(n þ 1)
b (2a þ 3)(a 5)
20 n ¼ 3t 2
21 a
x
–2 –1 0 1 2 3 4
x
b
–2
0
2
4
6
c
x
–10 –8 –6 –4 –2
0
–10 –8 –6 –4 –2
0
d
2
x
22 a n 5
d4
d1
Height, H (cm)
23 a
24 a
c (3x 5)(x þ 2)
b k < 7
c x 1 12
b 16
c
3ðyþ1Þ
yðy3Þ
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
Exercise 7-02
1 a m ¼ 12
b x ¼ 20
c y ¼ 15
d k ¼ 13
e y ¼ 1
f w ¼ 4
g x ¼ 2
h t ¼ 4
i a ¼ 4
j k ¼ 6
k w ¼ 10
l d ¼ 12
m k ¼ 1
n w ¼ 5
o y ¼ 1
p m ¼ 6
q x ¼ 12
r p ¼ 3
s k¼2
t y ¼ 10
pffiffiffi
2 a m ¼ 2
b
a
¼
9
c
m ¼ 2 7
pffiffi
p
ffiffi
ffi
p
ffiffiffiffiffi
d k ¼ 33
e k ¼ 4 6
f k ¼ 3 10
3 a m 1.94
b x 7.58
c y 0.35
d w 7.07
e a 9.24
f y 6.20
4 a x ¼ 2, 1
b y ¼ 4, 1
c y ¼ 4, 12
d x ¼ 4, 3
e x ¼ 3, 1
f x ¼ 8, 5
5 a x ¼ 6, 5
b x¼4
c x ¼ 11, 6
d d ¼ 0, 2
e q ¼ 5, 2
f n ¼ 0, 4
g k ¼ 0, 7
h y ¼ 0, 5
i v ¼ 0, 12
j m ¼ 0, 3
k a ¼ 20, 4
l n ¼ 0, 10
m u ¼ 4, 2
n x ¼ 7, 6
o p ¼ 4, 5
6 You cannot take the square root of a negative number.
7 a, c, f: cannot find square root of negative number.
Exercise 7-03
1 a
e
i
2 a
e
i
3 a
0 10 20 30 40 50 60 70 80 90 100110120
x¼1
b m¼5
pffiffiffiffiffi
y ¼ 9
f n ¼ 3 20
p
ffiffiffiffiffiffiffiffiffi
3
m ¼ 15 j m ¼ 4
w ¼ 2.5
b m ¼ 2.5
x¼3
f x ¼ 5.5
a ¼ 5.5
j a ¼ 0.4
yes b when c is positive
c
g
k
c
g
k
c
a ¼ 11
d u ¼ 2
p
ffiffiffiffiffi
p
ffiffiffiffiffiffiffiffiffi
3
3
11
h¼q
48
ffiffiffiffiffiffi h k ¼ pffiffiffiffiffiffiffiffiffi
3
3 81
x¼
l x ¼ 40
4
m¼6
d t ¼ 3.2
x ¼ 2.4 h x ¼ 0.8
x ¼ 2.3 l t ¼ 4.4
when c is negative d no
Weight, W(kg)
b H ¼1.2W þ 70: other answers possible.
c 48 kg
d 170 cm
25 a 1
b 0
c 3 26 x 3.453
Exercise 7-04
Chapter 7
SkillCheck
1 a a ¼ 12
2 a (k þ 4)(k þ 1)
d (u þ 13)(u 5)
b x¼6
b (y 8)(y 2)
e (w 7)(w 3)
c x¼8
c (m 8)(m þ 7)
f (x 6)(x þ 4)
Exercise 7-01
1 a
e
i
m
2 a
e
i
m
3 a
4 a
e
i
630
y ¼ 15
n ¼ 35
m ¼ 18
n ¼ 14
k ¼ 1 78
y¼3
y ¼ 56
6
a ¼ 11
C
7
x ¼ 15
x ¼ 92
9
w ¼ 11
1
3
6
9
11
13
16
18
100 cm 3 25 cm
child: $21, adult: $48
Anand: 3, Sunjay: 27
Vatha: 22, Chris: 14
x ¼ 35
6
14 x ¼ 15.5
25, 50, 105
8 teachers, 120 students
2 18 mm, 36 mm, 36 mm
4 61, 62, 63
5 94, 96, 98
7 26
8 4
10 213, 214, 215, 216
12 117
15 Scott: 11, Mother: 34
17 72 L when full
Mental skills 7
b
f
j
n
b
f
j
n
b
b
f
j
a¼9
y ¼ 7
x ¼ 29
n ¼ 35
w ¼ 1 13
a ¼ 8 35
w ¼ 10
y ¼ 60
A
p ¼ 109
7
y ¼ 53
5
a ¼ 75
14
c
g
k
o
c
g
k
o
m¼7
x ¼ 31
x ¼ 24
d ¼ 3 34
x ¼ 1 13
p ¼ 9 23
w ¼ 50
a ¼ 1 11
13
d k ¼ 57
h y ¼ 46
l m ¼ 10
c x ¼ 133
7
g a ¼ 41
d x ¼ 76
7
h a ¼ 107
14
d x¼3
h y¼3
l w ¼ 9 35
2 a
e
i
4 a
e
i
3.5
0.8
0.24
66.3
6.63
6630
b
f
j
b
f
j
2.4
0.027
0.012
6630
663
66.3
c
g
k
c
g
k
0.12
0.2
1.8
6.63
0.663
0.663
d
h
l
d
h
l
0.36
8.8
0.028
0.663
663
0.0663
Exercise 7-05
1 a C ¼ 15.1 m b r ¼ 31.8 cm
4 a 36 km/h
b 86.4 km/h
6 a 27C
b 0C
2 w ¼ 17 m 3 30.6 m/s
c 180 km/h 5 43
c 100C
d 39C
9780170194662
Answers
7 a 21.0
9 a 436 km
10 a $97.50
b 105.8 kg
b 7h
b 620 km
8 4.9 m
h w 10
11 h ¼ 13.2 cm
j a3
Exercise 7-06
k a 1
1 a y ¼ 5x
2
c y ¼ P8
k
b y ¼ km
p
d y ¼ 5m
3
l w < 3
y ¼ 4d5
8
e y ¼ KD
M
f
g y ¼ 2cþk
aqffiffiffiffiffiffiffi
i y ¼ w5
x
20m9
h y ¼ 20m
3 3 or y ¼
3
2
j y ¼ kx
d
k y ¼ 5nd
l y ¼ cT 2 k
n or y ¼ 5 n
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Þ
b a ¼ 2ðsut
c a ¼ vu
2 a b ¼ c2 a2
t
t2
qffiffiffiffiffiffiffiffiffiffi
qffiffiffiffiffi
Aþpr2
Apr 2
d r ¼ 3 3V
e
R
¼
f
l
¼
p
pr
4p
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
S
sx
g n ¼ Sþ360
or
þ
2
h
r
¼
i
b
¼
x2 þ 4ac
180
180
xs
j
x ¼ 5y
4
mn
k A ¼ 52m
þY Þ
m a ¼ bðX
Y X
a
l p ¼ aS
–1
0
1
2
–4 –3
–7
–6
–5
–4
–3
–2
–1
–5
–4
–3
–2
–1
0
1
2
3
6
7
–2
3
4
5
b
0
1
2
2
3
5
4
d
4
5
8
9
2
3
4
5
6
7
8
f
–3
–2
–1
0
1
2
3
4
g
–5
–4
–3
–2
–1
1
0
2
3
4
5
h
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
2 a x<4
b x2
c x > 6
d x1
3 B
4 a x1
b x<4
c x>6
d x 1
e x > 6
f x<2
g x 4
h x 25
i x<0
b y4
c m 2
0
1
2
0
1
2
f y > 4
g a 12
9780170194662
3
4
3
5
4
6
5
7
6
8
9 10 11
7
8
–7 –6 –5 –4 –3 –2 –1 0
1
d x 100
e x<5
e p < 6
3
4
5
6
7
8
9 10
–2 –1 0
1
2
3
4
5
6
7
–6 –5 –4 –3 –2 –1 0
–7
b
f
j
1
2
3
–6 –5 –4 –3 –2 –1 0
m6
c y 8
a<4
g m 72
x<6
k y 2
–1 0
1
2
3
4
5
6
4
1
d x5
h m 212
l a 14
5
7
8
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0
–16 –15 –14 –13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0
–5 –4 –3 –2 –1 0
1
2
3
4
5
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1
–9 –8 –7 –6 –5 –4 –3 –2 –1 0
b k 12
f y 2
j p < 4
c t < 2 25
g a>1
k m<4
1
d x 12
h d < 5 12
l x – 27
Exercise 7-09
d log25 5 ¼ 12
c 2
d 4
i 6
j 8
b log4 64 ¼ 3
e 5
f 3
k 6
l 3
c log10 10 000 ¼ 4
1
e log2 16
¼ 4
f log3 19 ¼ 2
pffiffiffi
g log8 4 ¼ 23
h log10 0.01 ¼ 2 i log4 2 ¼ 14
j log16 4 ¼ 12
k log9 27 ¼ 32
l log6 p1ffiffi6 ¼ 12
pffiffiffi 6
3 a 125 ¼ 53
b 10 ¼ 101
c 27 ¼ 3
pffiffiffi
6
3:5
1
d 8 2¼2
e 64 ¼ 2
f 81 ¼ 34
pffiffiffi
1
1
1
3
2 ¼ 86
g 125 ¼ 5
h
i 10 ¼ 100 2
pffiffiffi
3
1
1
1
3
2
j 5 5¼5
k 2¼8
l 100 ¼ 100
4 Because a base raised to any power always gives a positive
number.
Exercise 7-10
Exercise 7-08
1 a x>7
c k > 11
2
1 a 2
b 3
g 3
h 2
2 a log5 25 ¼ 2
10 11
e
1
b y > 8
1
3
c
0
x3
0
5 a x > 3
e w < 1
i w < 11
1 a
1
x1
w > 3
x < 35
f t 4
Exercise 7-07
0
2 a
e
i
3 C
4 a
d m0
uðy1Þ
2a
n x ¼ 52a
5 or 1 5 o b ¼ xay
–5
–14 –13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0
i a5
–102 –101 –100 –99
0
1
2
3
4
5
6
–98
7
8
–8 –7 –6 –5 –4 –3 –2 –1 0
–2 –1 0
1
2
3
4
2
9
1 a
f
k
2 a
d
g
3 a
e
4 a
g
5 a
d
7
2
2
logx 30
logx 2
logx 14
1.2042
0.3979
1
b
3
h
5
b
7
e
b 3
c 2
d
g 4
h 4
i
l 2
m 1
n
b logx 5
c logx 8
e logx 40
f logx 10
h logx 15
i logx 12
b 2.6021
c 3.6021
f 2.2042
g 0.3979
3
c 3
d 2
e
2
i 1
j 4
3
c 1
pffiffiffi 3
0
f 32 loga x or logað xÞ
1
1
2
e 12
j 2
d 0.301 05
h 0.801 05
1
f 0.5
631
Answers
Exercise 7-11
Chapter 8
1 a k¼9
d x ¼ 2.5
g k ¼ 1.5
2 a x ¼ 1.425
d x ¼ 0.943
g x ¼ 7.555
j x ¼ 1.011
3 a x¼2
b
e x ¼ 72
f
4 a x¼8
b
e x¼3
f
ffi
i x ¼ p1ffiffiffi
j
10
m x¼2
n
q x ¼ 16
r
5 11.89 12 years
7 a A ¼ 106 g
b
e
h
b
e
h
k
m¼7
y ¼ 4.5
n ¼ 1.5
x ¼ 2.227
x ¼ 0.428
x ¼ 0.107
y ¼ 0.975
x ¼ 53
c x ¼ 54
x ¼ 13
g x ¼ 54
6
1
x ¼ 1000
c x ¼ 25
1
x¼2
g x ¼ 1000
1
x¼8
k x ¼ 128
x ¼ 15
o x ¼ 12
x¼2
s x ¼ 3.915
6 22.43 23 months
b t ¼ 20 days
c
f
i
c
f
i
l
d ¼ 10
a ¼ 3.5
d ¼ 2.75
x ¼ 2.519
x ¼ 0.661
x ¼ 1.121
k ¼ 2.069
d x ¼ 12
h x ¼ 2
1
d x ¼ 64
pffiffiffi
h x ¼ 16 2
1
l x ¼ 25
p x ¼ 0.1
t x ¼ 23.04
1 a 1
2 a 4
3 a 625
b 29
b 12
b 3125
1
2
3
4
6
a D ¼ 190T
b i
a E ¼ 26.2 h
a I ¼ 16D
425
A
a
h
c
1
$ 7.50
2
$15
3
$22.50
b c ¼ 7.5 h
7 C
9 A
b x ¼ 13
c x ¼ 8
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
c 3
c 85
c 1
d 69
d 3.2
1
d 25
Exercise 8-01
c t ¼ 58 days
Power plus
2
1 a x ¼ 1 25
2 a
–3 –2 –1
b
–3 –2 –1
c
SkillCheck
3.8 km ii 8.55 km c 1 h 5 min
b $183.40
c 5.5 h
b $33.88
c $67.76
5 b ¼ 2.5a
c $45
d 11
8 a F ¼ 0.006m
10 a 22.8 kg
e 7.5. It is the same.
b 15 L/100 km
b 84.1 kg
Exercise 8-02
1 a T ¼ 920
s
3 a i 15C
c
T
b 10 h 13 min
c 92 km/h
2 C
ii 1.8C
b i 562.5 m
ii 200 m
10
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4
3 The solution to D ¼ 12 nðn 3Þ ¼ 100 is not a positive integer.
4 p ¼ 4, q ¼ 3
5 a a¼7
b x ¼ 20
c m¼2
d h¼5
8
6
4
Chapter 7 revision
2
1 a w¼6
d m¼3
2 a m ¼ 25
3
3 a y ¼ 2
d m ¼ 1
g h ¼ 9, 1
4 a u ¼ 1.9
5 Jane: 16, Grace: 13
7 a a ¼ yb
x
8 a x0
b
e
b
b
e
h
b
6
b
35
4
c
f
c
c
f
i
c
y¼
s¼4
y ¼ 57
p ¼ 10
w ¼ 5
u ¼ 7, 11
m ¼ 2.9
120 m
mP 2 ¼ a
a ¼ 3
x ¼ 1 23
m ¼ 32
x ¼ 3
x ¼ 7, 1
k ¼ 0, 5
x ¼ 1.4
c a ¼ 1M
Mþ1
–4
–3
–2
–1
0
1
2
3
4
–2
–1
0
1
2
3
4
5
6
b x<3
c x 2
–6 –5 –4 –3 –2 –1 0
1
2
3
4
5
6
7
d x > 5
–9
9 a
d
10 a
11 a
12 a
13 a
632
y 16
x > 3
63 ¼ 216
1
0.9542
x ¼ 1.490
–8
–7
–6
–5
–4
–3
–2
b y 7 12
e a < 16
1
b 24 ¼ 16
b 0
b 2.4771
c 0.5229
b x ¼ 0.943 c x ¼ 0.236
–1
c
f
c
c
0
a > 5
x 3
pffiffiffi
3
72 ¼ 7 7
3
d 0.9771
d x ¼ 1.420
500
4
7
9
10
1000 1500 2000 2500 3000
4533 people
5 B
a 8 min
b 4 people
a F ¼ 112
b 6 beats/sec
L
1
a y ¼ 16
b x ¼ 114
h
6 14
15
8 a b ¼ 8a
c 25 cm
11 a 2.5 h
b b ¼ 100
a
b 5 friends
Exercise 8-03
1 a
c
2 a
b
c
3 a
b
4 a
d
5 a
e
6 a
b
i £26
ii £57 b i $A28
ii $A92
i approx. £7
ii approx. $A30
i 2 km
ii 20 km
iii 34 km
i 50 furlongs
ii 122 furlongs
iii 180 furlongs
60 km
d 500 furlongs
i ¥16 000
ii ¥63 000
iii ¥78 000
i $A250
ii $A760
iii $A920
18C
b 10C
c 26C
32F
e 14F
f 86F
4.9 ha
b 2 ha
c 10.8 acres
d 12.2 acres
i 32 000 m2 ii 3.2 ha
iii 7.8 acres
i P620
ii P2100
iii P3600
$A12
c $A5
d P4900
9780170194662
Answers
Mental skills 8
b Kate, in 9 minutes
d 680 m
c 1.5 min
e 110 m
f The graph shows the distance they move down the slope
and this increases as more time passes.
3 a The person starts the journey fast (the graph is steep),
then slows down (the graph becomes less steep) before
increasing speed again (the graph becomes steeper).
b The person is travelling or returning towards a specific
place. Initially the person’s speed is fast, then he slows
down and stops (the graph is horizontal).
c The person starts the journey at a high speed and then
gradually slows down to a stop.
4 a H
b D
c AB d F
e E
f C
5
2 a
e
3 a
e
b
f
b
f
3
2, 3, 5, 6
4, 10
none of these
c
g
c
g
2, 3, 6
5
9
9
3, 5
3
10
4, 9, 10
1 a Temperature increases to maximum on first day then
cools down to the initial temperature. Then second day
temperature increases to slightly higher maximum than
first day and then returns to similar minimum temperature
as for previous day.
b This graph could indicate four high tides and four low
tides in a reasonably regular pattern.
c Amount of petrol decreases at constant rate. Petrol tank is
filled, then petrol is used at a constant rate.
d Height of person increases slowly at first then more
quickly (possibly teenage years/ growth spurt indicated by
steeper graph) then slows down as final height reached.
2 a B
b A
c C
d B
e A
3 a
b
100
Time
c
60
40
20
0
Time
Distance from shop
80
d
h
d
h
Exercise 8-05
120
Distance (metres)
2, 5
2
4, 9
4, 9
Height
1 a The cyclist leaves the starting point, travels at a speed of
20 km/h for 1 hour; stops for 1 hour; then continues for
another hour at a speed of 10 km/h. At D, the cyclist stops
for half an hour, then cycles back towards the starting
point at a speed of 30 km/h for 1 hour.
b No, as the gradients of the intervals are all different.
c The cyclist is moving back towards the starting point.
2 a Kate 133 m/min, Colleen 114 m/min
Water level
Exercise 8-04
Time
2
4 a
f
5 a
6 a
7 a
8 a
b
Distance
Distance
6 a
4 6 8 10 12
Time (seconds)
Time
Time
d
Distance
Time
7 a i
b i
i
ii
B
H
E
F
c
h
c
c
c
c
iii
v
B
A
F
B
d
i
d
d
d
d
vi
vii
A
F
D
C
e ix
e C
e A
e A
f B
f D
Exercise 8-06
y = x2
y
10
y = x2 + 2
y = x2 – 1
5
Time
C
ii B
iii A
Is the steepest (has the greatest gradient) and must be
the fastest ( Jade).
ii Is the least steep (the smallest gradient) and must be
the slowest (Cameron).
iii The slope of this graph is between the other two (Kiet).
c Jade stopped to talk to a friend. (Other answers possible.)
d This person speeds up slightly and maintains speed for a
while, slowing down gradually to a stop.
8 a C
b D
c E
d F
e B
f A
9780170194662
b
g
b
b
b
b
1 a
Distance
c
viii
iv
A
B
C
E
2
–4
–2
–1
2
4
x
–5
–10
y = –2x2 y = –x2
b i y ¼ x 2, y ¼ x 2 þ 2, y ¼ x 2 1
ii y ¼ x 2, y ¼ 2x 2
iii y ¼ x 2, y ¼ x 2, y ¼ 2x 2
633
Answers
2 A
3 a F
b I
g B
h L
4 a y ¼ x 2
d y ¼ x 2 9
5 a
Exercise 8-07
c
i
b
e
A
d K
H
j E
y ¼ x2
y ¼ 12 x 2
e
k
c
f
J
f C
G
l D
y ¼ x 2 14
y ¼ x2 þ 9
1 a
y
6
y = 2x2 + 1
y
10
y = (x – 3)2
10
(0, 9)
8
4
2
(3, 0)
8
–2
6
4
0
2
–2
4
6
x
y
10
b
y = (x – 2)2
8
2
6
–2
–1
1
b (0, 1)
6 a
2
x
4
c concave up
d y¼1
2
y
–2
0
–2
2
2
6
4
x
–2
–1
y = (x + 1)2
y
10
c
2x
1
–2
8
–4
6
4
–6
2
–8
b (0, 2)
7 A
8 a B
b G
g A
h K
9 a i narrower
b i wider
c i narrower
d i wider
10 a x ¼ 4
11 a
h
100
–4
y = –3x2 + 2
c x¼0
c
i
ii
ii
ii
ii
b
D
d J
H
j L
up
up
down
down
x ¼ 11
d y¼2
e
k
iii
iii
iii
iii
E
F
3
1
5
12
f I
l C
(0, 1)
0
–2
–2
(–1, 0)
–4
d
4 x
2
y
2
–4 –2 0
–2
(3, 0)
2
4
6
8
10 x
–4
–6
–8
80
(0, –9)
–10
60
e
40
–4
20
y = –(x – 3)2
y
2
(–1, 0)
0 (0, –1)2
–2
–2
4 x
–4
1
b 80 m
12 a x ¼ 9
634
2
3
4
c 35.9 m
d 4.0 s
b x ¼ 14.02
5t
–6
e 3.91 s
–8
–10
y = –(x + 1)2
9780170194662
Answers
f
5
y
b
(5, 0)
–2
–5
2
4
6
8
10
x
c
y
30
y
50
45
25
20
40
–10
15
35
–15
10
30
5
25
–20
–10 –5 0
–5
–25 (0, –25)
y = –(x – 5)2
–30
g
y
60
50
y = 3 (x +
20
5 10 x
15
–10
10
–15
5
–20
4)2
–25
–10 –5 0
–5
y = –x3
5 10 x
–10
–30
(0, 48)
y = 2x3
–15
40
–20
30
–25
–30
20
–35
10
–40
–45
–10
–8
h
–6
y
1
–4
–2
–4
0
–2
2
4
x
d
(1, 0)
0
–1
–50
2
4
x
25
–2
–3
e
y
30
y = x3+3
25
20
20
15
15
10
10
5
–4
–5
–10 –5 0
–5
y = –2(x – 1)2
i
y
2
(–6, 0)
–10
y
30
0
–2
–5
5x
5
0
–10 –5
–5
5 10 x
–10
–10
–15
–15
–20
–20
–25
–25
–30
–30
5 10 x
y = –x3 – 4
–4
f
–6
–8
2 B
3 a D
e B
y = – 1 (x + 6)2
4
c A
g F
d E
h C
35
15
30
25
Exercise 8-08
20
5
0
–10 –5
–5
15
5 10 x
–15
10
y
–25
–30
5
5
5 10 x
–10
–20
y = x3 – 2
10
0
–10 –5
–5
–10
1 a
y = 2x3–3
40
20
10
b G
f H
y
50
45
25
(0, –9)
–10
g
y
30
–15
–20
y=
–x3
+2
–25
–30
–35
–40
–10
–5
0
–2
5
10
x
–45
–50
–55
–5
–10
9780170194662
635
Answers
h
i
y
50
45
10
40
5
35
–10 –5 0
–5
30
25
e
y y = 1 x3 + 4
2
15
f
y
y = –x5 – 2
y = x4
5 10 x
y = (x − 1)4
–10
20
y
y = –x5
0 1
10
5
–10 –5 0
–5
5 10 x
x
3 a Move up 4 units.
c Move left 3 units.
e Move right 3 units.
–10
–15
x
–2
1
15
0
–2
b Move right 5 units.
d Move up 4 units.
f Move left 2 units.
–20
Exercise 8-10
–25
–30
1 a
–35
x
y
–40
–45
3 2 1
23 1 2
0
1
2
2
1
3
2
3
–50
b c
–55
y
10
–60
–65
–70
–75
5
y = –3x3 – 2
–80
(1, 2)
2 a A
b E
f D
g H
3 a y ¼ 2x 3 3
c G
d C
h I
i B
b y ¼ 4x 3 þ 1
e F
c I
h D
b
e G
0
–10
–5
–5
Exercise 8-09
1 a E
f A
2 a
5
y = 2x
x
10
–10
b H
g F
y
d C
i B
y=
y
3x2
+1
d y ¼ x, y ¼ x
2 a
y
10
y = (x − 2) 2
5
4
y = x2
0
c
2
x
0
d
y
–10
1
y = 3x2
y
y = –x3
0
y = –x3 + 2
–2
5
4
y= x
x
10
–5
–10
0
2
0
–5
x
(1, 4)
x
b
y
10
x
5
y = –2x4
y = –2(x + 2)4
–10
–5
0
(1, –2)
5
2
y=– x
x
10
–5
636
–10
9780170194662
Answers
c
b
y
10
y
10
5
5
(1, 3)
–10
3 a
–5
3
y= x
x
10
5
0
–5
–5
–5
–10
–10
t
1 2
3
4
5
6
7
8
9 10
S 1000 500 333 250 200 167 143 125 111 100
b
–10
c
5
10
x
2
y=– x –3
(1, –5)
y
10
s
5
1000
(2, 2)
800
–10
0
–5
y = x –2 1
5
10
x
600
–5
400
–10
200
d
y
10
t
2
4
6
8
10
c The time taken is always positive and it is impossible to
travel with zero time. Also, you cannot divide by zero.
d Yes, when t ¼ 2 h, s ¼ 500 km/h and when t ¼ 4 h,
s ¼ 250 km/h.
4 a k¼3
b y ¼ 3x
5 a
y
10
5
–10
0
–5
y=– 3
x+2
10 x
(1, –1) 5
–5
5
(1, 3)
y = 1x + 2
0
–10
–5
5
–5
–10
9780170194662
10
x
–10
6 a c ¼ 1, k ¼ 6
7 a
L
10 20
W 80 40
b y ¼ 6x þ 1
30
27
40
20
50
16
60
13
70
11
80
10
90 100
9
8
b WL ¼ 800 or W ¼ 800
L
c If the length or width equals zero, the block of land
doesn’t exist.
637
Answers
d
4 a
W
y
10
100
y = 2x
90
5
80
70
(0, 1)
60
50
–5 (0, –1) (0, –1) 5
–10
10
x
40
–5
30
20
10
0
–10
0
10 20 30 40 50 60 70 80 90 100
y= – 2x
L
e As the length increases, the width decreases. The graph
flattens out and gets closer to the horizontal axis, but
never touches it (an asymptote).
f As the length decreases, the width increases. The graph is
steeper and gets closer to the vertical axis, but never
touches it (an asymptote).
8 A
b They are the same graph reflected in the x-axis c y ¼ ax
5
y
10
8
6
4
Exercise 8-11
1 a
2
y = 3x + 1
y = 5x y = 3x
y
y = 2x
10
–10
–8
–6
–2
–4
2
8
–2
6
–4
4
x
Same shape, shifted down 2 units.
y
6 a
y = 2x
4
10
2
(0, 1)
–10
y = 3x – 1
–5
8
5
10
x
6
b 1
c For y ¼ ax where a ¼ 2, 3 or 5, as a increases the graph
increases more rapidly as x becomes larger in the first
quadrant.
2 a
–x y
x
y=4
10
4
2
(0, 1)
y=4
–10
b
8
–5
y = 3–x
6
5
10
10
x
y
8
4
6
2
4
(0, 1)
–10
b i
3 B
638
–5
x
y¼4
5
10
2
x
ii y ¼ a
(0, 1)
x
–10
–5
5
10 x
9780170194662
Answers
y
c
Exercise 8-12
y = –4x
–10
–5
(0, –1)
10 x
5
–2
–4
–6
–8
–10
y
d
–10
–5
(0, –1)
10 x
5
1 a
c
e
2 D
3 a
c
e
g
i
k
4 B
5 a
c
e
6 a
centre (0, 0), r ¼ 2
centre (0, 0), r ¼ 8
centre (0, 0), r ¼ 9
b centre (0, 0), r ¼ 6
d centre (0, 0), r ¼ 10
f centre (0, 0), r ¼ 5
centre (2, 4), r ¼ 7
centre (9, 12), r ¼ 15
pffiffiffiffiffi
centre (6, 1), r ¼ 10
pffiffiffi
centre (0, 0), r ¼ 6 2
centre (2, 0), r ¼ 8
centre (3, 4), r ¼ 9
b
d
f
h
j
l
(x 1)2 þ (y þ 2)2 ¼ 9
(x þ 3)2 þ (y 2)2 ¼ 100
(x þ 6)2 þ (y 2)2 ¼ 5
b (x 10)2 þ (y þ 11)2 ¼ 4
d x 2 þ (y þ 1)2 ¼ 1
f (x þ 1)2 þ (y 5)2 ¼ 8
y
2
–2
1
–4
–3
–6
–2
y = –2 –x –10
y
10
1
–1
x
2
–1
(–1, –1)
–2
–8
e
centre (3, 1), r ¼ 1
centre (0, 3), r ¼ 2
centre (5, 8), r ¼ 4
pffiffiffi
centre (2, 1), r ¼ 5 2
centre (4, 3), r ¼ 2.5
centre (0, 1), r ¼ 13
–3
b
y = 4x + 1
10
y
8
5
6
(0, 4)
4
–10
–5
5
10
x
2
–5
–10
–5
f
10 x
5
y
y
5
c
y = 4x – 1
10
(1, 0)
–5
5
x
8
–5
6
d
y
4
–10
2
–10
–5
–8
–6
–4
(–5, –2)
5
10 x
2x
–2
–2
–4
–2
–6
7 y¼4
x
9780170194662
639
Answers
7 a
e
8 a
d
g
1, 1
b 9, 3
c 16, 4
d 4, 2
49 7
5
f 94, 32
g 14, 12
h 25
4, 2
4, 2
(3, 1), r ¼ 5
b (4, 2), r ¼ 7
c (2, 5), r ¼ 6
(10, 6), r ¼ 1 e (2, 4), r ¼ 5
f (6, 3), r ¼ 4
pffiffiffi
(3, 10), r ¼ 9 h (4, 1), r ¼ 2 3
y
d
x2 + y2 = 49
5
–5
Exercise 8-13
1 a
g
2 a
f
3 a
P
P
G
F
b
h
b
g
L
L
J
C
c
i
c
h
E
P
H
E
d
j
d
i
y
10
y=
L
E
D
B
x2
e
k
e
j
C
P
A
I
(7, 0)
x
5
f L
l C
–5
e
y = 1 x2
2
y
10
–3
8
5
6
(2, 1)
–10
–5
5
10
x
4
2
–5
b
y
10
(2, 2)
y = 5x
–10
–5
f
8
5
10
x
y
10
6
5
4
4
(2, 0)
2
–10
(0, 1)
–10
–5
c
–5
y
4
–10
y = –2x + 4
g
y = 4 – x2
y
12
x2 + y2 = 144
2
10
(2, 0)
–4
–2
x
–5
10 x
5
10
5
2
4
x
5
–2
–4
–12
–10
–5
5
10
12 x
–6
–5
–8
–10
–10
–12
640
9780170194662
Answers
4 a 1
5 a H
e Q
6 a D
e H
7 a i
b i
c i
d i
e i
f i
8 a
b
b
f
b
f
exponential
exponential
exponential
hyperbola
hyperbola
hyperbola
3
C
C
E
B
c
c
g
c
g
ii
ii
ii
ii
ii
ii
6
P
E
C
F
1
2
2
none
23
none
iii
iii
iii
iii
iii
iii
d 1
d H
h H
d A
h G
y¼0
y¼1
y ¼ 3
x ¼ 0, y ¼ 0
x ¼ 3, y ¼ 0
x ¼ 0, y ¼ 2
d
60
40
30
20
10
(5, 0)
2
4
x
6
e
8
10
12
y
10
(1, 6)
5
y=
–10
y = 2(x – 5)2
50
y
10
5
y
5
–5
y=– 1
x+4
6
x
10
–4
–10
x
(–3, –1)
–1
4
5
10
x
–5
–5
–10
–10
b
f
y
10
y
10
y = 3x + 2
8
(–5, 7)
8
6
(–5, 5)
6
4
4
2
(0, 3)
2
–10
–10
–5
5
10
–2
y
10
c
5
–3
9780170194662
–2
–1
y = x3 + 3
–8
–6
–4
Power plus
1
y
10
5
2
3
x
x
3
1
2
–2
y= 1 +2
x–1
(2, 3)
1
x
–10
–5
5
–5
–5
–10
–10
10
x
641
Answers
2 a centre (0, 0) and r ¼ 4
7
y
y
y = 2 (x + 3)2
20 (0, 18)
15
y = 16 – x2
4
10
5
2
(–3, 0)
–8
–2
–4
2
x
4
–6
–4
8
y = x3 + 2
5
2
y
6
–4
2
–2
y = 25 – x2
x
4
–5
4
–10
9
y
2
–2
–4
x
2
y
10
b centre (0, 0) and r ¼ 5
–6
–2
–2
2
4
6
–1
x
1
–2
2
3
5 x
4
(1, –3)
–4
–6
c centre (0, 0) and r ¼ 3
–8
y
–10
4
y = – 3x4 y = –3(x – 2)4
10
y
10
2
5
–6
–4
–2
2
6 x
4
2
–2
–10
y = – 9 – x2
–4
–1
5
–5
–10
Chapter 8 revision
1 H ¼ 310.5
4 d
–5
2
x+1
10 x
y=
(1, 1)
11 a
2 10C
3 a £46
y
10
y = 4x
b $A85
8
6
4
2
(0, 1)
t
5 a B
6 a C
642
b C
b F
c A
c A
d E
e D
f
B
–10
–5
5
10
x
9780170194662
Answers
b
Chapter 9
y = 4–x y
10
SkillCheck
8
1 a 64
2 a 0.8480
d 64.9839
3 a 4548
4 a 64370
6
4
(0, 1)
–5
c
5
y
–10
–5
26
0.7760
13.9884
3311
69410
b
e
h
b
e
b
5
b
b
b
14.2 cm
5.1 cm
59.0 cm
567
6437
5.7 m
114 m
c
c
f
c
c
12
0.1539
13.7044
521
2880
Exercise 9-01
2
–10
b
b
e
b
b
10
x
y = –4x
(0, –1)
5
10 x
1 a
d
g
2 a
d
3 a
4 4
7 a
9 a
10 a
64.7 cm
18.5 cm
48.8 cm
3841
5257
73
5120
11.6 m
49º
c
f
i
c
f
54.5 cm
17.4 cm
17.5 cm
4256
451
6 6.49 m
8 2.6 km
5
4
11.2 m
c
28º
43º
–2
11 127 m
14 180 m
18 47.7 m
–4
–6
1 a 237
f 140
2 a 000
f 125
3 SW
5 a
–10
y
–10
–5
13 177 m
16 79440
20 970 m
17 480 m
Exercise 9-02
–8
d
12 1132 m
15 14290
19 14.5 m
y = –4–x
(0, –1)
5
b
g
b
g
4
295
c
312
h
090
c
330
h
a NNW
N
10 x
T
W
E
42°
–2
046
d
253
i
180
d
225
i
b 337.5
b
W
P
115
065
270
072
e 210
e 038
j 187
N
M
E
80°
P
–4
c
P
S
N
S
N
d
P
–6
10°
W
65°
X
E
W
–8
12 a
c
e
13 a
g
centre (0, 0), r ¼ 10
centre (0, 0), r ¼ 7
centre (10, 0), r ¼ 15
D
b C
c B
L
h G
i I
9780170194662
S
S
–10
b centre (0, 0), r ¼ 6
d centre (5, 6), r ¼ 9
pffiffiffi
f centre (7, 10), r ¼ 4 5
d J
e E
f H
j A
k K
l F
6
7
8
10
12
14
a 22 km
a 37
a 12.2 km
45.7 km
a 2122 km
a 261.08 km
E
K
b 257
b 163 km
b 305
9
11
b 330
13
b 167.82 km
c
a
a
a
323
18.5 km
b NNW
13.509 km b 321
15 km
b 26 km
643
Answers
7 a cos 38
b sin 75
c cos 25
d tan 78
e cos 7.3
f sin 64.5
g cos 4025
h tan 9.2
i sin 5925
j tan 1950
k sin 84.5
l tan 40.5
1
8 a p
b 1pffiffi
c p1ffiffi2
d 12
e p1ffiffi3
2 ffiffi
pffiffiffi
f 23
g 23
h 3
i 1
j p1ffiffi2
9 a, b Teacher to check.
c The tan graph is broken into three sections and repeats
itself after 180. It has asymptotes at 90 and 270.
Exercise 9-03
1
2
3
5
7
9
10
11
pffiffiffiffiffi
a 4 13 cm
b 15.6 cm
c 23
pffiffiffi
pffiffiffiffiffiffiffiffi
800 cm or 20 2 cm b 34.64 cm
a
c 3516
4 34
a 20.40 cm
b 79
a 9.1 cm
b 28
6 a 53 m
b 114 m
37.5 m
8 a 50
b 868 m
a 85 m, 50 m
b 99 m apart
a \WHF ¼ 52 , \WFH ¼ 38 and \HWF ¼ 90
b Tower is 49.1 m.
a 285
b 7
d No
f
Exercise 9-04
1 a 43 b 16 c 87.45 d 34.8 e 5143
2 a 0
b 1
c 1
5
12
3 cos b ¼ 13
, cos a ¼ 12
13, sin b ¼ 13
9
9
4 sin F ¼ 40
41, sin E ¼ 41, cos F ¼ 41
pffiffi
pffiffi
5
2
5 cos Y ¼ 3 , sin Y ¼ 3, sin X ¼ 35
pffiffi
pffiffiffiffi
pffiffiffiffi
6 cos / ¼ 45, sin / ¼ 411, cos u ¼ 411
pffiffiffi
7 a 8
b 12 c 3 2
d 45
e 30
pffiffiffi
8 35 3 m
f 7222
Exercise 9-06
f 30
Mental skills 9
2 a 23
g 56
m 9:7
3 a 17
40
b 34
h 25
n 4:3
b 23
c 57
i 5:9
o 35
c 16
25
d 12
j 5:9
4
p 35
d 14
e 14
f 16
k 9 : 20 l 4 : 5
e
5
24
f
2
25
Exercise 9-05
1 a tan A ¼ 60
b tan Y ¼ 1:
3_
c tan X ¼ 23
91
pffiffiffiffi
9
d tan P ¼ 40
e tan Q ¼ 340
f sin X ¼ 11
61
7
2
g cos X ¼ 25
h sin X ¼ 3
2 a P
b P
c N
d N
e P
f N
g N
h P
3 a 0.89
b 0.19
c 0.77
d 0.11
e 0.51
f 0.58
g 0.05
h 0.42
i 0.78
j 0.87
k 0.18
l 0.28
4 a, b Teacher to check.
c The graph has a wave shape that repeats itself after 360.
Maximum y ¼ 1 at y ¼ 90; Minimum y ¼ 1 and y ¼ 270
d No
e Yes, centre of symmetry at (180, 0).
f
i 0 < y < 180 (1st and 2nd quadrants)
ii 180 < y < 360 (3rd and 4th quadrants)
5 a, b Teacher to check.
c The graph has a wave shape that repeats itself after 360
Maximum y ¼ 1 at y ¼ 0 and y ¼ 360; Minimum y ¼ 1
and y ¼ 180
d Yes, axis of symmetry y ¼ 180
e No
f i 0 < y < 90 and 270 < y < 360 (1st and 4th quadrants)
ii 90 < y < 270(3rd and 4th quadrants)
g Similarities: Both graphs have the same wave shapes that run
between y = 1 and y ¼ 1 and repeat themselves after 360.
Differences: The graphs have different x- and y-intercepts
6 a 10
b 70
c 50
d 83
e 65
f 12
644
e centre of symmetry at (180, 0).
i 0 < y < 90 and 180 < y < 270 (1st and 3rd quadrants).
ii 90 < y < 180 and 270 < y < 360 (2nd and
4th quadrants).
1 a
e
i
2 a
e
i
3 a
d
g
57, 123
7, 173
114
1459
15258
no solution
137
69
45
b
f
j
b
f
j
b
e
h
143
135
33, 147
13157
11551
163180
136
42, 138
60
c
g
k
c
g
k
c
f
i
110
100
105
15926
no solution
126520
61, 119
143
45, 135
d
h
l
d
h
l
130
25, 155
118
17348
126520
154370
Exercise 9-07
1 a 18.4
b 21.1
c 105.0
2 a a ¼ 20.51
b b ¼ 11.91
c c ¼ 12.58
d d ¼ 4.10
e e ¼ 30.85
f f ¼ 3.55
g k ¼ 5.99 cm h w ¼ 29.17 m i p ¼ 8.29 m
3 79 m 4 25 m 5 b 1042 cm 6 a 110 b 131.6 m
7 561 km
8 d 124.7 m
9 b 595 m
Exercise 9-08
1 a 27
2 a 44.5
d 67.3
3 a 1497
d 13533
4 a 46 or 134
5 a 75 or 117
b
b
e
b
e
b
b
37
c 54
46.6
c 32.0
18.8
f 31.8
12900
c 1428
12929
f 16213
39
c 55 or 125
d 44 or 136
41
c 84
Exercise 9-09
1 a 5.6
b 13.1
c 35.8
2 a a ¼ 8.30
b c ¼ 54.52
c e ¼ 88.41
d b ¼ 16.33
e d ¼ 19.44
f f ¼ 40.72
3 0.6 m
4 C
5 a Teacher to check.
b \ XYN ¼ 180 130 ¼ 50 (cointerior angles on
parallel lines) \ XYZ ¼ 50 þ 25 ¼ 75
c 4.4 km
6 47 km
7 a 0
b a2 ¼ b2 þ c2
c With cos 90 ¼ 0, the cosine rule reverts to
Pythagoras’ theorem.
9780170194662
Answers
Exercise 9-10
1 a 70
2 a 112
3 20.8
b 33
c 109 d 131
b 108 c 121 d 23
4 6440
5 99
e 60
f 83
Exercise 9-11
413.4 m2
b 463.1 cm2
2
132.9 mm
e 320.4 cm2
97.4 m2
b 463.6 m2
2
227.6 m
e 93.5 m2
225 m
b 2770 m2
4 a 130
2
418.9 cm
b 173.2 cm2
112
b 37 cm2
1 a
d
2 a
d
3 a
5 a
6 a
c
f
c
f
b
c
c
326.9 mm2
0.1 m2
246.2 m2
152.2 m2
766.07 m2
245.7 cm2
740 cm3
Exercise 9-12
10.2 m
b 16.1 mm
c 17.1 cm
13.1 m
e 3.9 m
f 18.2 m
32
b 142 (or 38)
c 29
55
e 37
f 125
32 þ 23 ¼ 55 (exterior angle of a triangle)
108.50 m
c 89 m
1 b i 15.4
ii 15.4
The results are the same. The sine rule sind90 ¼ sin12:8
56
becomes d ¼ sin12:8
56 (since sin 90 ¼ 1), which is the same
result when using the sine ratio.
5 7.5 km
6 486 km
9
10
11
12
13
14
15
16
a 57
a 1172
a 0.4 m
a 8154 or 986
a 6.8 m
a 96
a 165 cm2
15.5 cm
b
b
b
b
b
b
b
1 a 5
2 a 11
3 a
b 13
b 1
b
y
pffiffiffiffiffiffiffiffiffiffiffi
31
60
120
30, 150
pffiffiffi
2
4
6
y=x+1
4
–4
–2
0
2
4
2
x
–2
30
135
45, 135
45, 135
a 10.9 m
a 64590
13
4 a 320
a 1281 km
a 48
b
b
b
b
b
4.4 m
48590
140
024
pffiffiffi
48 3
y
4
c
–6
–4
–2
y = x– –1
2
d
4
6
2
4
6
x
6
4
2
–6
–4
–2
0
x
–2
y
x+y=4
270°
2
y
e
180°
0
–2
y = cos θ
90°
4x
–4
6 a 33 cm
b 65
pffiffiffi
c p48ffiffi2 ¼ 24 2
0.5
2
–2
c 11.5 cm
c 57120
1.0
0
–2
–4
y=3–x
0
y
2
1
2
c
f
i
5
d 1
d 5 12
6
Chapter 9 revision
8
c 6
c 7
2
b
b
e
h
4
70
272, 15258
136.4 mm
4937
7.6 cm
125
30 m2
SkillCheck
Power plus
pffiffiffi
1 a
31
2 a 45
d 150
g 60, 120
3 Teacher to check.
c
c
c
c
c
c
c
Chapter 10
1 a
d
2 a
d
3 a
b
4 a
c
1
2
3
5
7
87
6533
14.8 cm
7724 or 10236
112.1 mm
56
286 m2
6
4
360° θ
2
–0.5
–4
–1.0
9780170194662
–2
0
2
4
6x
–2
645
Answers
f
c m ¼ 43, b ¼ 5
y
y
6
6
2x – y = 5
4
4
2
2
0
–2
4
y =– – x + 5
3
2
4
6
x
0
–2
–2
2
4
6 x
–2
–4
–6
Exercise 10-01
4 a yes
b no
c no
d yes
e no
5 a For y ¼ 2x þ 1, when x ¼ 2, y ¼ 2 3 2 þ 1 ¼ 5
[ (2, 5) lies on y ¼ 2x þ 1
For x þ y ¼ 7, when x ¼ 2, y ¼ 5, 2 þ 5 ¼ 7
[ (2, 5) lies on x þ y ¼ 7
b (2, 5)
6 a m ¼ 2, b ¼ 3
y
y = –2x + 3
f no
1 a x ¼ 3, y ¼ 1
2 a x ¼ 1, y ¼ 2
b x ¼ 2, y ¼ 1
c x ¼ 1, y ¼ 5
b x ¼ 5, y ¼ 9
c x ¼ 1, y ¼ 2
d x ¼ 12, y ¼ 2 12
e x ¼ 2, y ¼ 9
f x ¼ 5, y ¼ 4
g x ¼ 12, y ¼ 6 12
h x ¼ 3, y ¼ 2
x ¼ 5, y ¼ 1 12
j x ¼ 5, y ¼ 8
i
k x ¼ 1 12, y ¼ 2 12
3 a
l x ¼ 4, y ¼ 0
y
6
6
y = 1 – 2x
4
4
2x + y = 4
2
–4
–2
2
0
2
–6
–4
–2
–2
b m¼
b The lines are parallel.
b ¼ 2
Exercise 10-02
y
y = –5 x – 2
2
4
2
–2
–2
b x ¼ 5, w ¼ 4
c g ¼ 2, h ¼ 25
e q ¼ 5, r ¼ 4
f k ¼ 4 35, x ¼ 5
g c ¼ 1 12, e ¼ 1
2 a d ¼ 14, k ¼ 6
h k ¼ 3, y ¼ 2
b a ¼ 1, c ¼ 1
i a ¼ 2, f ¼ 2
c h ¼ 3, y ¼ 4
d e ¼ 3, x ¼ 13
e q ¼ 3, w ¼ 6 12
f c ¼ 2, p ¼ 3
1 a d ¼ 3, k ¼ 2
6
0
2 x
–2
–4
5
2,
0
2
4
6 x
d n ¼ 3.25, p ¼ 1
g
3 a
d
g
j
23,
m¼
y¼4
q ¼ 3, w ¼ 3
g ¼ 1, n ¼ 3
q ¼ 1, w ¼ 4
a ¼ 2, f ¼ 2
5 12
b
e
h
k
h a ¼ 1, r ¼
i x ¼ 2, w ¼ 2
m ¼ 9, x ¼ 7
c d ¼ 23, h ¼ 7
h ¼ 0, m ¼ 2
f e ¼ 4, y ¼ 3
a ¼ 12, d ¼ 12
i k ¼ 5, p ¼ 2
c ¼ 64, r ¼ 38 l x ¼ 4, y ¼ 3
–4
646
9780170194662
Answers
Exercise 10-03
1 a
d
2 a
c
e
g
i
Chapter 10 revision
x ¼ 2, y ¼ 5
x ¼ 2, y ¼ 2
x ¼ 9, y ¼ 21
x ¼ 14, y ¼ 2
x ¼ 2, y ¼ 2
x ¼ 7, y ¼ 3
x ¼ 2 23, y ¼ 1
b
e
b
d
f
h
j
x ¼ 35, y ¼ 3 45
c x ¼ 7, y ¼ 2
x ¼ 5, y ¼ 1
f x ¼ 4, y ¼ 2
x ¼ 5, y ¼ 3
x ¼ 3, y ¼ 1
x ¼ 7, y ¼ 4
x ¼ 3, y ¼ 2 12
x ¼ 3 15, y ¼ 4 35
1 a x ¼ 2, y ¼ 2
2 a
b x ¼ 4, y ¼ 0
y
6
y = 6 + 2x
Exercise 10-04
1
5
8
9
10
11
12
0
135
50
195
100
255
0
0
50
150
100
300
–6
c
–2
0
(–4, –2)
–2
–4
2
6x
x ¼ 4, y ¼ 2
b
y
6
y = 3 – –x
2
4
y = 2x – 7
$
2
R = 3n
(4, 1)
300
–2
C = 135 + 1.2n
200
4
–4
R ¼ 3n
n
R
4
2
285
2 680
3 b 364
4 12
Aaron 36, Sejuti 12
6 16
7 black 36, colour 24
Pie: $3.60, Sausage roll: $2.70
Supreme 32, Vegetarian 13
Strawberries $3.50; Blueberries $4.99
b 20-cent coins: 154, 50-cent coins: 91
a Teacher to check.
b C ¼ 135 þ 1.2n
n
C
y=x+2
0
2
4
8 x
6
–2
–4
100
–6
0 10 20 30 40 50 60 70 80 90 100
d n ¼ 75
x ¼ 4, y ¼ 1
c
Mental skills 10
2
3
1
4
2 a
e
i 5:9
m 9:7
3 a 17
40
4
5
1
6
5
7
5
6
b
f
j 5:9
n 4:3
b
2
3
c
16
25
c
g
k 9 : 20
o 35
d 14
y
1
2
2
5
d
h
l 4:5
4
p 35
5
e 24
y = 4 – 3x
4
f
2
25
1 a x ¼ 1 12, w ¼ 4 12, y ¼ 5 12
7
3
b a ¼ 1 13
, c ¼ 4 13
, d ¼ 8 11
13
3
4
p ¼ 11 13
, m ¼ 18 11
13, n ¼ 13 13
Teacher to check.
ae bd ¼ 0 and a fraction cannot have denominator 0.
x ¼ 3, y ¼ 1
Teacher to check.
1
x ¼ 2, y ¼ 2
ii x ¼ 28, y ¼ 16
iii x ¼ 11
, y ¼ 2 20
33
9780170194662
y=x
2
Power plus
c
2 a
b
c
d
i
6
(1, 1)
–4
–2
0
2
4 x
–2
–4
x ¼ 1, y ¼ 1
647
Answers
y
d
2 a
d
g
j
3 a
4 a
d
g
y = 2x + 3
8
(2, 7)
6
4
y=9–x
2
0
–2
2
4
6
1 a
d
g
j
m
2 a
d
g
j
m
p
3 a
d
g
j
4 8
x ¼ 2, y ¼ 7
y
8
y = 2x + 1
6
(2, 5)
4
2
–2
–2
x+y=7
0 2 4 6
8
x
x ¼ 2, y ¼ 5
y
6
f
4
y = –1 – x
y = 5 – 2x
2
4
6
x
–4
–6
(6, –7)
3 a
c
e
4 a
d
5 a
c
e
x ¼ 6, y ¼ 7
m ¼ 5, y ¼ 9 12
b x ¼ 2, y ¼ 13
a ¼ 1, d ¼ 1
d x ¼ 6, y ¼ 15
x ¼ 5, y ¼ 2
f d ¼ 3, w ¼ 10
x ¼ 2, y ¼ 11
b m ¼ 1, p ¼ 3
c h ¼ 10, t ¼ 4
a ¼ 3, c ¼ 12
e x ¼ 1, y ¼ 1
f p ¼ 12, q ¼ 4
1600 adults, 900 children b 18 DVDs, 12 CDs
$38
d 28 cheesecakes, 47 mudcakes
120 boys, 93 girls
Chapter 11
SkillCheck
1 a x ¼ 5
d u ¼ 7 or 4
648
m ¼ 7 or 3
k ¼ 0 or 3
w ¼ 0 or 23
x ¼ 13 or 112
c ¼ 13 or 14
y ¼ 2 or 112
t ¼ 215 or 1
y ¼ 34 or 12
c ¼ 1 or 125
g ¼ 212
y ¼ 3 or 4
x ¼ 212 or 3
m ¼ 17 or 1
t ¼ 32 or 5
f ¼ 0 or 12
b
e
h
k
n
b
e
h
k
n
q
b
e
h
k
d ¼ 3 or 7
t ¼ 7 or 0
n ¼ 12 or 3
c ¼ 52
h ¼ 1 or 12
g ¼ 1 or 112
p ¼ 112 or 4
a ¼ 12 or 113
e ¼ 14 or 112
m ¼ 23 or 56
f¼6
t ¼ 212 or 12
p ¼ 4 or 7
d ¼ 73 or 12
w ¼ 16 or 3
c
f
i
l
o
c
f
i
l
o
r
c
f
i
l
y ¼ 5 or 3
p ¼ 0 or 3
a ¼ 12 or 35
f ¼ 12
e ¼ 57 or 1
d ¼ 1 or 23
x ¼ 25 or 112
w ¼ 114 or 3
q ¼ 3 or 123
w ¼ 4 or 113
h ¼34 or 1
u ¼ 18 or 5
e ¼ 1 or 5
h ¼ 5
a ¼ 2 or 13
Exercise 11-02
2
0
–6 –4 –2
–2
2y(7 y)
2(3w 5)(3w þ 5)
(m 8)(m þ 7)
(x 6)(x þ 4)
d y ¼ 10
(2y 5)(3y þ 8)
(2y þ 5)(4y þ 7)
(4d þ 5)2
Exercise 11-01
x
–2
e
(4 m)(4 þ m) b (d 11)(d þ 11) c
5p(2p þ 5)
e 5(x 8)(x þ 8) f
(k þ 4)(k þ 1) h (y 8)(y 2) i
(u þ 13)(u 5) k (w 7)(w 3) l
y ¼ 2
b y ¼ 10
c y¼5
(3a þ 1)(a þ 3) b (5x þ 2)(x 3) c
(3t 1)(5t þ 4) e (5v þ 3)(v 7) f
(3h 4)(5h 1) h (4p 3)(3p þ 5) i
b m ¼ 2
e k ¼ 0 or 3
c x ¼ 2 or 1
f w¼5
1 a x 2 þ 2x þ 1 ¼ (x þ 1)2
b p 2 6p þ 9 ¼ (p 3)2
2
2
c m 8m þ 16 ¼ (m 4)
d k 2 þ 4k þ 4 ¼ (k þ 2)2
2
2
49
7 2
e y þ 7y þ 4 ¼ y þ 2
f w2 3w þ 94 ¼ w 32
2
5 2
g x2 þ x þ 14 ¼ x þ 12
h h2 5h þ 25
4 ¼ h 2
2
7
5 2
i a2 þ 72 a þ 49
j v2 53 v þ 25
16 ¼ a þ 4
36 ¼ v 6
pffiffiffi
pffiffiffi
pffiffiffi
pffiffiffi
2 a d ¼ 3 þ 7, 3 7
b x ¼ 5 þ 5, 5 5
pffiffiffi
pffiffiffi
pffiffiffiffiffi
pffiffiffiffiffi
c p ¼ 1 þ 10, 1 10
d y ¼ 1 þ 2, 1 2
pffiffi
pffiffi
pffiffi
pffiffi
3 23 3
e m ¼ 1þ22 5 , 122 5
f t ¼ 2þ3
,
3
3
pffiffiffiffi
pffiffiffiffi
pffiffiffiffi
pffiffiffiffi
2þ 42 2 42
6þ 82 6 82
g c¼ 2 ,
h w¼ 2 , 2
2
pffiffi
pffiffi
pffiffiffiffi
pffiffiffiffi
i n ¼ 2þ3 7 , 23 7
j e ¼ 3þ2 71 , 32 71
p
pffiffi
ffiffi
pffiffiffi
pffiffiffiffi
k d ¼ 2 þ 5, 2 5
l x ¼ 3þ44 2 , 344 2
pffiffiffi
pffiffiffi
pffiffiffi
3 a h ¼ 1 6
b r ¼1 2
c m ¼ 3 7
pffiffiffiffiffi
pffiffiffiffiffi
d w ¼ 6, 10
e a ¼ 5 30
f y ¼ 4 19
pffiffiffi
pffiffiffiffiffi
g p ¼ 6 41 h h ¼ 2 2
i u ¼ 7, 2
pffiffiffiffi
pffiffiffiffi
pffiffiffiffi
j d ¼ 12 29
k c ¼ 92 73
l e ¼ 52 17
pffiffiffiffi
pffiffi
pffiffiffiffi
m y ¼ 32 41
n b ¼ 12 21
o q ¼ 32 5
pffiffiffiffi
pffiffiffiffi
p g ¼ 74 73
q x ¼ 3 12 , 1
r u ¼ 23 22
4 a x ¼ 11.20 or 0.80
b m ¼ 0.43 or 16.43
c g ¼ 4.65 or 0.65
d h ¼ 1.27 or 2.77
e w ¼ 1.27 or 0.47
f y ¼ 1.14 or 1.47
g p ¼ 2 or 1.33
h e ¼ 1.13 or 0.88
i n ¼ 1 or 2.5
9780170194662
Answers
Exercise 11-03
pffiffiffi
1 a x ¼ 3 7
pffiffiffiffi
d k ¼ 32 29
pffiffiffiffi
g u ¼ 72 61
pffiffi
j c ¼ 13 7
pffiffiffiffi
m d ¼ 2 2 14
b m¼
e
h
k
n
pffiffiffiffi
5 37
2
c w¼4
pffiffiffi
y¼2 5
pffiffiffiffi
a ¼ 34 65
pffiffiffiffi
e ¼ 58 57
pffiffiffiffi
a ¼ 53 31
pffiffiffiffiffi
13
pffiffiffiffi
p ¼ 12 21
q ¼ 15 , 1
pffiffiffiffi
x ¼ 43 10
t ¼ 2 12 , 1
pffiffiffiffiffiffi
n ¼ 5 4 113
pffiffiffiffi
x ¼ 38 41
pffiffi
g ¼ 15 6
pffiffi
p ¼ 23 7
pffiffiffiffi
y ¼ 34 89
f
i
l
o
p y ¼ 23 , 2
pffiffiffiffiffiffi
2 a y ¼ 910141
pffiffiffi
d k ¼ 2 5
pffiffiffiffi
g h ¼ 94 17
pffiffiffiffi
j u ¼ 2 5 14
q k ¼ 56 , 1
3 a k ¼ 8.89, 0.11
d n ¼ 3.19, 0.31
b c ¼ 1.41, 1.41 c m ¼ 2.65, 2.65
e p ¼ 0.85, 2.35 f w ¼ 0.30, 1.13
r
pffiffiffiffi
22
b m ¼ 13
c
pffiffiffiffi
e m ¼ 3 6 21
pffiffi
h w ¼ 13 7
pffiffiffiffi
k a ¼ 26 58
f
i
l
g x ¼ 2.39, 0.28
h h ¼ 3.83, 1.83 i x ¼ 1.62, 0.62
j a ¼ 4, 9
m t ¼ 8.09, 3.09
k v ¼ 1.48, 1.48 l c ¼ 2.31, 0.69
n x ¼ 4.27, 7.73
o d ¼ 3.31, 1.81
Exercise 11-04
d m ¼ 1, 2
e k ¼ 1, 3
pffiffiffi pffiffiffi
c w ¼ 2, 6
pffiffiffi
f w ¼ 2, 3 4
g x ¼ 1, 13
pffiffiffi
j p ¼ 3 5, 1
h y ¼ 45 , 1 25
i a ¼ 1 12 , 12
pffiffiffi
1 a y ¼ 2, 2 2
2 a
d
3 a
d
m 1.2, 2.8
y 1.4, 1.3
w ¼ 5
m ¼ 1.4
b m ¼ 4
k g¼
1
2,
2
l c ¼ 2,
b
e
b
e
x 0.9, 1.4
w 1.2, 1.9
x ¼ 2, 1.3
y ¼ 1.2
b
e
h
k
$1200, $900
$2700, $1800
$600, $1000
$2100, $2800
c
f
c
f
1
5
a 0.9, 1.3
e 0.5
k ¼ 2
v ¼ 2, 1.4
Mental skills 11
2 a
d
g
j
$100, $50
$500, $1500
$3000, $600
$800, $3200
c
f
i
l
$160, $560
$900, $2100
$550, $440
$2000, $1200
Exercise 11-05
1
3
5
7
9
10
12 m by 8 m
2 40 m by 35 m
42 m by 24 m
4 Length 58 m, width 38 m
Length 13 m
6 15 m by 12 m
0.52 s, 3.08 s 8 a 4000 m
b 2000 m
c 24.5 s
a 34 m
b 3.9 s
c i 0.5 s and 1.9 s
ii 3.5 s
8 or 9
11 24, 25 or 24, 25
12 35 or 34
y
6
5
4
3
2
1
0
–4 –3 –2 –1
–1
ii 3 and 1
iii 3
iv x ¼ 3 and 1, same as x-intercepts
b i
x 3 2 1 0
1
2
y
0 3 2 3
12 25
x
y
9780170194662
3 2 1
0 1
0
3
42
y
6
5
y = 2x2+ 7x + 3
4
3
2
1
0
–4 –3 –2 –1
–1
1 2 3 4 x
–2
–3
ii 3 and 12
iii 3
iv x ¼ 3 and 12, same as x-intercepts
c i
x
3 2 1
0
1
y
18
5 4 9 10
2
7
3
0
2
0
3
3
y = 2x2 – 3x – 9
y
6
4
2
–4 –3 –2 –1 0
–2
–4
–6
–8
–10
–12
1 2 3 4 x
ii 112 and 3
iii 9
iv x ¼ 112 and 3, same as x-intercepts
d i
x
3 2 1
0
1
y
15
8
3
0
1
y
8
7
6
5
4
3
2
1
0
1 a i
1 2 3 4 x
–2
–3 –2 –1
–1
Exercise 11-06
y = x2+ 4x + 3
y = x2 – 2x
1 2 3 x
–2
0
3
1
8
2
15
3
24
ii 0 and 2
iii 0
iv x ¼ 0 and 2, same as x-intercepts
2 a 5
b 3
c 0
649
Answers
3 a
y
y
b
4 a i 4, 10
iv (3, 49)
ii 40
v concave up
iii x ¼ 3
y
0
x
4
0
−2
x
−4 0
c
d
y
−40
y
10
–3 0
0
y
e
(3, −49)
b i 0, 3
iv 112, 214
–5 x
–15
10 x
ii 0
v concave up
y
1
2 22
x
0
y
f
3
1
1
(1 2_, −2 _4)
8
−1 − 2_
0
x
−4
3
−2
g
y
h
−2 0
x
c i No x-intercepts
iv 34, 278
4
( − 3_4, 2 7_8 )
0
5 x
0
x
1
13_ x
−20
d i 0.7, 6.7
iv (3, 14)
ii 5
v concave down
y
i
iii x ¼ 34
y
y
−5
x
ii 4
v concave up
5
−1 0
iii x ¼ 112
iii x ¼ 3
(3, 14)
y
5
–0.7 0
0 1
_
−2 2
2
e i 4.2, 1.2
iv ð112, 30Þ
650
x¼3
b x¼0
c x ¼ 212
x ¼ 1
e x ¼ 112
f x¼3
i x¼3
ii (3, 1)
b i x¼5
ii (5, 16)
i x¼1
ii (1, 9)
d i x¼4
ii (4, 25)
i x ¼ 12
ii (12, 2434) f i x ¼ 4 ii (4, 80)
i x¼4
ii (4, 48)
h i x ¼ 14 ii ð14, 114Þ
i x ¼ 16 ii ð16, 114Þ
y ¼ (x þ 2)2 3, (2, 3)
y ¼ ðx þ 52Þ2 1014, 52, 1014
2
y ¼ (x 1) þ6, (1, 6)
y ¼ (x 3)2 9, (3, 9)
y ¼ (x 1)2 þ 1, (1, 1)
y ¼ 2ðx 54Þ2 98, 114, 118
ii 21
v concave down
iii x ¼ 112
y
Exercise 11-07
1 a
d
2 a
c
e
g
i
3 a
b
c
d
e
f
x
6.7
x
(−11_, 30)
2
21
–4.2 0
f
i 0.4, 7.6
iv (4, 13)
1.2
x
ii 3
v concave up
iii x ¼ 4
y
3
0 0.4
7.6 x
(4, −13)
9780170194662
Answers
g i No x-intercepts
iv (0.7, 1.55)
ii 4
v concave up
iii x ¼ 0.7
y
3
4
5
6
7
a
a
a
a
pffiffiffiffi
pffiffiffiffiffiffi
pffiffiffiffiffiffi
m ¼ 52 37
b d ¼ 7 4 137
c k ¼ 1 6 253
x 0.30, 3.30 b h 1.55, 0.80 c w 5.37, 0.37
pffiffiffi
m ¼ 2, 2
b y ¼ 2
c x ¼ 1, 2
32 and 34
b 14 m 3 22 m
y = 2x2 + 5x –7 y
4
–3 _12
(−0.7, 1.55)
h i 0, 4
iv (2, 8)
–4
x
0
ii 0
v concave down
–8
iii x ¼ 2
(2, 8)
y
8 a
x
1
–7
b
y
(–1 1 , 5 1) y
3 3
x
–4 0
0
6
4 x
y = –8x – 3x2
Axis : x = 1
2
y = x – 2x – 24
x
–2 2
3
–24
0 Axis : x = –1 1
3
(1, –25)
i
i 112, 2
iv 134, 18
ii 6
v concave down
y
0
iii x ¼ 134
c
y
(13_4 , 1_8)
11
2
2
y = 5x2 + 3x – 8
x
–1
−6
(3, 9), (2, 4)
(4, 26), (2, 14)
(2, 18), (13, 11)
(7, 39)
(1, 2), (2, 1)
(0, 3), (3, 0)
(1, 7), 125, 5
1 (1, 3), 12, 2
x
1
Axis : x = –0.3
0
–8
(–0.3, –8.45)
9 a (112, 412), (1, 2)
c (0, 4), (4, 0)
Exercise 11-08
1 a
c
e
g
2 a
c
e
g
3
5
b
d
f
h
b
d
f
(0, 0), (4, 32)
(1, 5), 115, 715
(2, 22), (5, 20)
(2, 0), (1, 3)
(0, 1), (1, 0)
(0, 5), (5, 0)
(3, 5), 212, 6
b (5, 13), (1,1)
d (4, 2), (2, 4)
Mixed revision 3
1
y
x+y=6
6
4
(3, 3)
2
Power plus
1 a Teacher to check.
2 Intersects twice
–6
–4
–2 0
pffiffiffiffi
7 37
6
b x ¼ 43, 1,
3 72 cm 3 24 cm
6
x
–4
–6
Chapter 11 revision
9780170194662
4
–2
y = 2x – 3
1 a m ¼ 2, 32
d y ¼ 2, 6
g n ¼ 3, 5
pffiffiffiffiffi
2 a y ¼ 2 11
2
b x ¼ 0, 5
e w ¼ 43, 5
h d ¼ 4 12 , 1 12
pffiffiffiffi
b p ¼ 34 33
c p ¼ 6, 8
f k ¼ 34, 12
i x ¼ 1 12 , 2 12
pffiffi
c w ¼ 15 6
x ¼ 3, y ¼ 3
2 a E17.5
3 a m ¼ 6.8 cm
4 a t ¼ 99:96
S
b AU$86
b k ¼ 22.7 m
b 9.52 m/s
c E98
c d ¼ 3.7 m
c 9.70 s
651
Answers
5 a x¼1
7 a 29
9
b (1, 2)
c 43
b 45
6 f ¼ 3, ypffiffi¼ 3
8 x ¼ 23 7
y
3
y = 2x3 – 2
4
3
2
4
1
–4 –3 –2 –1 0
–1
1
2
3
4
x
–2
–3
5
–4
–5
10
11
12
15
18
2
340 cm
a m ¼ 14 or 1
b y ¼ 45 or 12
c w ¼ 52 or 1
d ¼ 32.5 m
13 b 240 children
14 C
a ¼ 40 30
16 x ¼2 12, y ¼ 5 12
17 52, 128
y
7
8
(–1, 4)
0
x
pffiffi
a p1ffiffi2
b 23
c p1ffiffi3
0
x ¼ 3, 2
21 y ¼ 37 56
a 4w 2 5w 1071 ¼ 0
b 17 m 3 63 m
(4, 1) and (1, 4)
24 a 301 km
b 114 25 C
Chapter 12
SkillCheck
1 C
2 a 3
5
b No, P(10c coin) ¼ 12
, P(20c coin) ¼ 13, P(50c coin) ¼ 14
3 a 13
b 13
c 56
4 a 0
b 1
5 0.4
6 B
7 0.15
Exercise 12-01
1 a
b
c
d
i 0.425
ii 0.14
iii 0.21
i 0.375
ii 0.125
iii 0.25
Yes
Expected frequency ¼ 100. The observed frequency of
red or purple is 115, which is more than the expected
frequency.
33
9
2 a i 15 ¼ 0.2
ii 19
iii 100
¼ 0.33 iv 100
¼ 0.09
50 ¼ 0.38
7
3
1
b i 14 ¼ 0.25 ii 20
¼ 0.35 iii 10
¼ 0.3
iv 10
¼ 0.1
652
v
87
200
¼ 0.435
vi
59
200
¼ 0.295
vii
¼ 0.255
9 a 200
27
b i 200
¼ 0.135
ii
¼ 0.31
iii
80
200
¼ 0.4
21
200
v
62
200
1
200
iv
1
19
20
22
23
6
c Yes
d Expected frequency ¼ 40. The expected frequency
compares very favourably with the observed frequency of 42.
a 50
b Teacher to check.
c i Teacher to check.
ii 12
d Teacher to check.
a 600
b i 281
ii 322
600 ¼ 0.468
600 ¼ 0.537
227
iii 600 ¼ 0.378
iv 522
600 ¼ 0.87
c i 0.5
ii 0.5
iii 0.33
iv 0.83
d The probabilities are similar.
a Teacher to check.
3
7
b i 12 ¼ 0.5
ii 15 ¼ 0.2
iii 10
¼ 0.3
iv 10
¼ 0.7
c Teacher to check.
3
3
1
a i 10
¼ 0.3 ii 25
¼ 0.12 iii 12
iv 10
¼ 0.1
25 ¼ 0.48
b i 0.33
ii 0.17
iii 0.33
iv 0.17
c Yes
d Expected frequency of not yellow is 33. This is more than
the observed frequency of 26.
a 16 0.17
b 16 or 17 times c, d, e Teacher to check.
a 200
4
27
13
b i 200
¼ 0.02
ii 200
¼ 0.135
iii 200
¼ 0.065
iv
86
200
51
200
¼ 0.43
¼ 0.105
¼ 0.005
c Ferry, light rail (tram)
d Teacher to check.
Exercise 12-02
1 a i 11
25
2 a 156
b i 11
52
7
c 31
3 a 135
4 a
ii
4
5
iii
1
5
iv
6
25
v
19
25
b
3
10
ii
7
52
iii
7
78
iv
22
39
v
19
78
vi
1
26
b
56
135
c
1
5
d
17
52
S
11
b
5 a
c
6 a
b
i 1
45
i 19
26
123
P
12
31
ii 11
54
b i
ii 0
1
45
IN
49
iii
ii
31
54
1
3
iv
iii
7
9
1
9
iv
19
45
32
123
iii
27
123
iv
81
123
JA
15
32
d i
49
123
27
c 81
ii
9780170194662
Answers
7 a 200
79
51
77
81
b i 200
ii 100
iii 200
iv 121
v 100
vi
200
c 29
40
d No, because all the people surveyed indicated a day on
which they preferred to shop.
8 a 204
7
23
31
71
b i 204
ii 204
iii 102
iv 102
c i
2
54
First
3 a
H
T
43
54
ii
b
H
T
4
25
i
53
150
ii
iii
28
75
17
32
T
c 63%
2 a 128
b i 68
ii 60
c
d 12
55
3 a 93
b i 21.5%
ii 11.8%
iii 3.2%
c i 15.7%
ii 45%
d The percentage composition of women in the opposition is
three times that of the percentage composition of women
in the government.
4 a 150
b i 0.5
ii 0.04
iii 0.43
iv 0.23
c 22
¼
0.293
75
5 a 160
7
11
9
b i 20
¼ 0.35 ii 160
¼ 0.069
iii 80
¼ 0.113
c 35
¼
0.43
82
6 a 200
b 55%
c
d
7 a
b
i 49.5%
ii 45%
65.5%
878
i 679
ii
878 ¼ 0.773
iii
67
439
¼ 0.153
iv
iii 36%
545
878
21
439
b 8
d i
c i
7
8
b
2 a
First
die
CG
AJ
GE
JR
RC
CJ
AE
GR
EC
RA
1
3
3
8
ii
ii
7
8
¼ 0.048
H
T
5 a
CR
GC
JA
EG
RJ
AC
GA
JG
EJ
RE
1
2
3
4
5
6
b 36
c i 16
9780170194662
3
1, 3
2, 3
3, 3
4, 3
5, 3
6, 3
4
1, 4
2, 4
3, 4
4, 4
5, 4
6, 4
5
1, 5
2, 5
3, 5
4, 5
5, 5
6, 5
6
1, 6
2, 6
3, 6
4, 6
5, 6
6, 6
1st die
1
2
3
4
b 24
c i
1
6
1
4
iii
11
36
iv 14
v
1
2
vi
1st die
5
12
HHT
HTH
T
H
HTT
THH
T
THT
H
TTH
T
TTT
1
8
iv
v
1
2
H2
3
H3
4
5
H4
6
1
H6
T1
2
T2
3
T3
4
5
T4
6
T6
H5
T5
3
1, 3
2, 3
3, 3
4, 3
1
4
iii
ii
4
1, 4
2, 4
3, 4
4, 4
1
2
iv
5
1, 5
2, 5
3, 5
4, 5
3
8
6
1, 6
2, 6
3, 6
4, 6
v 0
2nd die
b i
ii
T
H
2
2
1, 2
2, 2
3, 2
4, 2
6 a
2
1, 2
2, 2
3, 2
4, 2
5, 2
6, 2
HHH
2nd die
1
1, 1
2, 1
3, 1
4, 1
Second die
1
1, 1
2, 1
3, 1
4, 1
5, 1
6, 1
H
1
8
iii
¼ 0.621
CE
AR
JC
EA
RG
Outcomes
e i 75
ii 25
coin die outcomes
1
H1
iv 31.5%
1
6
c
1
8
4
Exercise 12-04
1 a CA
AG
GJ
JE
ER
Third
H
Exercise 12-03
1 a 150
Second
3
50
1
9
v 0
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
ii
vi
1
36
5
12
3
4
5
6
7
8
9
4
5
6
7
8
9
10
iii
vii
1
6
7
12
5
6
7
8
9
10
11
6
7
8
9
10
11
12
iv
viii
1
2
5
12
653
Answers
7 a
1st
coin
2nd
coin
3rd
coin
3 a
4th Sample
coin space
H
H
T
T
H
T
H
H
HH
TH
H
T
HHHH
HHHT
HHTH
b i
4 a
HHTT
1
4
T
HT
TT
ii
1
2
iii
2nd course
H
H
T
H
T
H
T
T
H
T
H
H
H
T
T
T
H
T
T
1
b i 16
15
iv 16
c i 63
ii 14
1
v 16
ii 375
B
CB
FB
YB
HTHH
HTHT
HTTH
1st
course
HTTT
THHH
b i
5 a
THHT
THTH
1
3
THTT
H
T
TTHH
H
T
TTTH
C
F
Y
ii
H
CH
FH
YH
4
15
1st
draw
2nd
draw
3
6
7
4
TTHT
TTTT
iii 38
5
vi 16
iii 937
3
4
b $800
g 250
c 400
h $300
d 700
i $300
e $300
j 500
6
7
6
3
4
7
7
3
4
6
Exercise 12-05
1 a
Girls
Boys
b i
B
C
Ew
W
1
24
2 a i
A
B
C
D
E
ii
A
B
C
D
E
b i
c i
654
ii
Ca
Em
B, Ca B, Em
C, Ca C, Em
Ew, Ca Ew, Em
W, Ca W, Em
1
6
M
B, M
C, M
Ew, M
W, M
iii
B
AB
BB
CB
DB
EB
C
AC
BC
CC
DC
EC
D
AD
BD
CD
DD
ED
E
AE
BE
CE
DE
EE
A
B
AB
C
AC
BC
D
AD
BD
CD
E
AE
BE
CE
DE
CB
DB
EB
ii
ii
DC
EC
4
25
3
5
R
S
B, R B, S
C, R C, S
Ew, R Ew, S
W, R W, S
1st
draw
2nd
draw
R
G
Y
R
G
Y
R
R
ED
iii
iii
12
25
2
5
iv
4
5
S
CS
FS
YS
T
CT
FT
YT
1
15
3rd
Octcomes
draw
346
6
347
7
364
4
367
7
374
4
376
6
436
6
437
7
463
3
467
7
473
3
476
6
634
4
637
7
643
3
647
7
673
3
674
4
734
4
736
6
743
3
746
6
763
3
764
4
i 12
b
ii 34
iii 12
iv 13
6 a Teacher to check. 64 outcomes, beginning with 333, 334,
336, 337, 343, 344, 346, 347, …, 776, 777.
1
1
b i 16
ii 12
iii 12
iv 16
7 a
1
6
A
AA
BA
CA
DA
EA
BA
CA
DA
EA
1
5
1
10
Be
B, Be
C, Be
Ew, Be
W, Be
P
CP
FP
YP
iii
Mental skills 12
2 a $700
f $400
3
4
b i
1
2
ii
G
R
R
Y
Y
R
R
G
1
12
3rd
Octcomes
draw
RRG
G
RRY
Y
RGR
R
RGY
Y
RYR
R
RYG
G
RRG
G
RRY
Y
RGR
R
RGY
Y
RYR
R
RYG
G
GRR
R
GRY
Y
GRR
R
GRY
Y
R
GYR
R
GYR
R
YRR
G
YRG
R
YRR
G
YRG
R
YGR
R
YGR
iii 1
9780170194662
Answers
Second Third Outcomes
child child
First
child
8 a
B
B
G
B
G
G
b i
9 a
1
8
BBB
G
BBG
B
BGB
G
B
BGG
GBB
G
B
GBG
GGB
G
1
8
ii
B
F
R
F
R
R
b i
d i
8 a
3
8
R
iv
1
8
FFF
FRF
R
F
FRR
RFF
R
F
RFR
RRF
R
iii
RRR
1
b i 18
ii 38
8
1
10 a 36
b 36
11 a i 125 outcomes. Teacher to check.
ii 60 outcomes. Teacher to check.
29
18
64
b i 125
ii 125
iii 125
1
3
c i 10
ii 10
iii 0
1
2
9
27
11
36
7
8
ii
10
i
i
3
4
5
6
7
8
9
10
49
1
0
1
2
3
4
5
1
6
1
11
4
5
6
7
8
9
10
5
6
7
8
9
10
11
ii 1
6
ii 27
¼ 29
1
9
9
13 a
b
d
2
3
4
5
6
7
8
¼ 13
1
2
3
4
5
6
iv
c
i
1
40
FFR
F
1
2
3
4
5
6
7
1
2
3
4
5
6
GGG
iii
F
F
7 a
8
9
1
18
4
11
iii
c
e
2
11
1
6
¼ 14
c 6
1
13
11
2
1
0
1
2
3
4
ii
ii
2
8
b
6
7
8
9
10
11
12
12
3
2
1
0
1
2
3
4
3
2
1
0
1
2
1
6
c
e
1
6
5
4
3
2
1
0
1
i
i
1
2
6
18
6
5
4
3
2
1
0
¼ 13
ii 0
ii 1
Power plus
iv
iv
117
125
2
5
1 a 320
7
b i 40
¼ 0.175
57
iii 320
¼ 0.178
c
2 a
Exercise 12-06
16
45
1
1
d Yes, 13314 ¼ 12
e independent
c 12
5 a i 16
ii 12
b independent
b 48 ¼ 12
6 a 59
c Dependent, as the first draw changes the contents of
the bag.
7 a i 58
ii 47
b i 38
ii 57
c i 58
ii 37
d i 38
ii 27
8 12
d
1st
draw
1 a independent
b independent
c dependent
d independent
e dependent
f independent
g dependent
2 Dependent, as the balls are not replaced when drawn.
3 a independent
b 12
1
4 a i 3
ii 14
b 1Y, 2Y, 3Y, 4Y, 5Y, 6Y, 1G, 2G,3G, 4G, 5G, 6G, 1B,
2B, 3B, 4B, 5B, 6B, 1R, 2R, 3R, 4R, 5R, 6R,
3
32 ¼
3
20 ¼
45
107
ii
iv
3
7
R
4
7
B
2
6
4
6
3
6
3
6
1
ii
7
14
7
¼
ii
30
15
4
1
v
20 ¼ 5
2
i 152 ¼ 15
ii
3
2 PðA and
P(B|A) ¼ 7,
PðAÞ
b i
3 a i
iv
b
c
2
7
20
30
4
14
¼ 23
¼ 27
0.094
0.15
2nd Outcomes
draw
R
RR
B
RB
R
BR
B
iii
iii
BB
4
7
4
30
iv
2
¼ 15
6
7
Yes
BÞ
2
¼ 157 ¼ 27
15
Chapter 12 revision
Exercise 12-07
1 a
3 a
4 a
5 13
1
3
4
11
2
11
9780170194662
3
1
6¼2
7
11
b
b
b
4
11
2
c
6
1
6
4
11
2
9
d
5
11
1 a i 0.353
ii 0.427
iii 0.087
iv 0.513
2
b i 13
¼
0.867
ii
¼
0.133
15
15
c Different at least one head occurring excludes zero heads
occurring, which is the same as three tails occurring. The
events are complementary.
655
Answers
2 a 35
2
35
b
ii
1st
card
6
35
3
c i
ii 19
iii 35
35
d They don’t like the types of music mentioned in the
survey.
3 a
B
3
i
9
20
3
20
ii
200
i 0.305
25
110 ¼ 0.227
i 47
69 ¼ 0.681
1
2
3
4
b 16
c i 12
6 a i
1
1, 1
2, 1
3, 1
4, 1
iii
ii 0.11
ii
2
1, 2
2, 2
3, 2
4, 2
ii
2
5
1
4
3
1, 3
2, 3
3, 3
4, 3
iii
1st
card
iv
2nd
card
4
7
2
4
4
7
2
7
4
7
656
iv
3
5
iv 0.425
b
c
7 a
d
8 a
i 23
i 13
independent
independent
b
1
4
4
274
2
7
427
7
2
472
3
4
734
4
3
743
v
1
4
3rd sample
card space
2
222
4
224
7
227
2
242
4
244
7
247
2
272
4
274
7
277
2
4
7
2
4
7
2
4
7
422
424
427
442
444
447
472
474
477
2
4
7
2
4
7
2
4
7
722
724
727
742
744
747
772
774
777
vi
1
2
i
1
3
2
3
ii
ii
1
2
ii 1
iii
iii
1
9
1
3
iv 29
iv 16
c dependent
b dependent
e independent
1
2
3
4
5
1
2
3
4
4
1, 4
2, 4
3, 4
4, 4
2
2
3
20
¼ 0.319
7
16
7
7
iii 0.225
22
69
sample
space
247
4
5
9
b
c
4 a
b
c
d
5 a
3rd
card
7
2
D
3
2nd
card
4
2
3
4
5
6
c
2
7
3
4
5
6
7
d i
1
3
4
5
6
7
8
ii
1
3
e
1
4
Chapter 13
SkillCheck
1 a
d
g
j
2 a
h ¼ 71
b p ¼ 105
c x ¼ 126
m ¼ 68
e a ¼ 24
f w ¼ 36
w ¼ 30, k ¼ 90 h r ¼ 83
i p ¼ 26, r ¼ 98
p ¼ 52
k y ¼ 42
l d ¼ 54
m ¼ 65 (angles on a straight line), n ¼ 65 (alternate angles),
p ¼ 50 (angle sum of n XWY)
b Isosceles triangle (m ¼ n ¼ 65)
Exercise 13-01
1
2
3
4
5
6
7
8
9
a
a
a
a
a
a
a
a
a
1800
b 1440
c
6
b 21
c
16
b 157.5
144
b 135
c
30
b 15
c
72
b 30
c
140
b 162
c
24
b 5
c 18
8
b 10
c 15
1260
13
d 3240
d 30
120
d
45
d
20
d
144
d
d 9
d 180
e 2340
e 9
150
25
60
168
e 72
e 24
f
f
30
12
Exercise 13-02
1 In n ABE and n CBD:
\ABE ¼ \CBD (vertically opposite angles)
AB ¼ CB (given)
EB ¼ DB (given)
[ n ABE ” n CBD (SAS)
9780170194662
Answers
2 In n LMP and n NPM:
LP ¼ NM (given)
LM ¼ NP (given)
MP is common.
[ n LMP ” n NPM (SSS)
3 In n QTW and n PWT:
\QTW ¼ \PWT ¼ 90 (QT ’ WT and PW ’ WT)
QW ¼ PT (given)
WT is common.
[ n QTW ” n PWT (RHS)
4 In n ABY and n CBX:
\BAY ¼ \BCX ¼ 90(equal angles of the square ABCD)
BA ¼ BC (equal sides of the square ABCD)
AY ¼ CX (given)
[ n ABY ” n CBX (SAS)
5 In n CDE and n FED:
\CDE ¼ \FED (given)
\DEC ¼ \EDF (equal angles opposite equal sides of
isosceles n DEY)
DE is common.
[ n CDE ” n FED (AAS)
6 In n XOY and n VOW:
\XOY ¼ \VOW (vertically opposite angles)
OX ¼ OV (equal radii of small circle)
OY ¼ OW (equal radii of large circle)
[ n XOY ” n VOW (SAS)
7 In n KLM and n MNK:
\MKL ¼ \KMN (alternate angles, NM || KL)
\KML ¼ \MKN (alternate angles, KN || LM)
KM is common.
[ n KLM ” n MNK (AAS)
8 In n CDH and n EFG:
\HCD ¼ \GEF (corresponding angles, CH || EG)
\HDC ¼ \GFE (corresponding angles, DH || FG)
CH ¼ EG (given)
[ n CDH ” n EFG (AAS)
9 In n UXY and n WXY:
\UXY ¼ \WXY (YX bisects \UXW)
UX ¼ WX (given)
XY is common.
[ n UXY ” n WXY (SAS)
10 In n ABE and n CBD:
\AEB ¼ \CDB ¼ 90 (AE ’ BC, CD’AB)
\B is common.
BA ¼ BC (given)
[ n ABE ” n CBD (AAS)
11 a In n HEF and n GFE:
\HEF ¼ \GFE (given)
EH ¼ FG (given)
EF is common.
[ n HEF ” n GFE (SAS)
b [ \EHF ¼ \FGE (matching angles of congruent triangles)
12 a In n AOB and n COD:
AB ¼ CD (given)
OA ¼ OC (equal radii)
9780170194662
b
13 a
b
14 a
b
c
15 a
b
16 a
b
OB ¼ OD (equal radii)
[ n AOB ” n COD (SSS)
[ \AOB ¼ \COD (matching angles of congruent triangles)
In n QRX and n QTY:
QR ¼ QT (equal sides of isosceles n QRT)
RX ¼ TY (given)
\R ¼ \T (equal angles of isosceles n QRT)
[ n QRX ” n QTY (SAS)
[ QX ¼ QY (matching sides of congruent triangles)
[ n QXY is isosceles (two sides of the triangle are equal)
In n TAP and n XCP:
\TPA ¼ \XPC (vertically opposite angles)
TP ¼ XP (given)
AP ¼ CP (given)
[ n TAP ” n XCP (SAS)
[ TA ¼ XC (matching sides of congruent triangles)
[ \A ¼ \C (matching angles of congruent triangles)
[ TA || XC (alternate angles are equal)
In n OAM and n OBM:
OA ¼ OB (equal radii)
\OMA ¼ \OMB ¼ 90 (OM ’ AB)
OM is common.
[ n OAM ” n OBM (RHS)
AM ¼ BM (matching sides of congruent triangles)
[ OM bisects AB.
In n GLH and n KLH:
GL ¼ KL (given)
GH ¼ KH (given)
LH is common.
[ n GLH ” n KLH (SSS)
\GLH ¼ \KLH (matching angles of congruent triangles)
[ LH bisects \GLK.
\GHL ¼ \KHL (matching angles of congruent triangles)
[ LH bisects \GHK.
Exercise 13-03
1 \A ¼ \C and \B ¼ \D
Now \A þ \C þ \B þ \D ¼ 360 (angle sum of
a quadrilateral)
[ 2\A þ 2\B ¼ 360 (\C ¼ \A, \D ¼ \B)
[ \A þ \B ¼ 180
[ AD || BC (the pair of co-interior angles have a sum of 180)
Also, from \A þ \C þ \B þ \D ¼ 360 (angle sum of a
quadrilateral)
[ 2\A þ 2\D ¼ 360 (\C ¼ \A, \B ¼\D)
[ \A þ \D ¼ 180
[ AB || DC (the pair of co-interior angles have a sum of 180)
[ ABCD is a parallelogram (opposite sides are parallel).
2 In n LMP and n NPM:
LM ¼ NP (given)
PM is common.
\LMP ¼ \NPM (alternate angles, LM || NP)
[ n LMP ” n NPM (SAS)
\LPM ¼ \NMP (matching angles of congruent triangles)
657
Answers
3
4
5
6
7
8
9
10
658
[ LP || NM (alternate angles proved equal)
[ LMNP is a parallelogram (opposite sides are parallel).
In n DXH and n GXE:
\DXH ¼ \GXE (vertically opposite angles)
HX ¼ EX (given)
DX ¼ GX (given)
[ n DXH ” n GXE (SAS)
\HDX ¼ \EGX (matching angles of congruent triangles)
[ HD || EG (alternate angles proved equal)
Similarly, \GHX ¼ \DEX (matching angles of congruent
triangles HXG and EXD)
[ HG || ED (alternate angles proved equal)
[ DEGH is a parallelogram (opposite sides are parallel).
(Outline of proof only) nFHC ” nFHE ” nDHE ” nDHC (SAS)
[ FC ¼ FE ¼ DE ¼ DC (matching sides of congruent triangles)
Also, \CFH ¼ \EDH and \CDH ¼ \EFH (matching angles
of congruent triangles)
[ CDEF is a rhombus (opposite sides are parallel and all
sides are equal).
(Outline of proof only) Since WY ¼ XV and the diagonals
bisect each other,
TW ¼ TV ¼ TY ¼ TX
[ n TWV ” n TXY (SAS) and n TVY ” n TWX (SAS)
[ \VWT ¼ \XYT and \TVY ¼ \TXW (matching angles of
congruent triangles)
[ VW || YX and VY || XW (alternate angles proved equal)
[ VWXY is a parallelogram.
Also, n YVW ” n XYV ” n VWX ” n YXW (AAS)
[ \V ¼ \W ¼ \X ¼ \Y (matching angles of congruent triangles)
Since the angle sum of VWXY ¼ 360
\V ¼ \W ¼ \X ¼ \Y ¼ 90
[ VWXY is a rectangle.
\B þ \C ¼ 180 and \B þ \E ¼ 180
[ BE || CD and BC || ED (pairs of co-interior angles have
a sum of 180)
[ BCDE is a parallelogram with right angles.
[ BCDE is a rectangle.
Since the sides are equal, TWME is a rhombus (proved in
question 4).
Since \M ¼ 90, TWME is a square (a square is a rhombus
with a right angle).
Since the angles of the quadrilateral are right angles, GHKL is
a rectangle (proved in question 6).
If GL ¼ GH,
GL ¼ GH ¼ LK ¼ KH ( opposite sides of a rectangle are equal)
[ GHKL is a square (all sides are equal, all angles are 90).
The diagonals bisect each other at right angles, so MNPT is a
rhombus (proved in question 4).
[ MN ¼ NP ¼ PT ¼ MT
Also, nMNT ” nNPT ” nPTM ” nMNP (SSS, since TN ¼ PM)
[ \M ¼ \N ¼ \P ¼ \T ¼ 90 (angle sum of a quadrilateral
and matching angles of congruent triangles)
[ MNPT is a square.
a In n ABX and n CDY:
BX ¼ DY (given)
\B ¼ \D (opposite angles of a parallelogram)
AB ¼ CD (opposite sides of a parallelogram)
[ n ABX ” n CDY (SAS)
b AX ¼ CY (matching sides of congruent triangles)
XC ¼ BC BX
¼ AD DY ðBC ¼ AD, opposite sides of
a parallelogram and BX ¼ DY , givenÞ
11
12
13
14
15
16
¼ AY
[ AXCY is a parallelogram as pairs of opposite sides are equal.
a In n DAE and n CEB:
AE ¼ EB (given)
\DAE ¼ \CEB (corresponding angles, AD || EC)
AD ¼ EC (equal sides of a rhombus)
[ n DAE ” n CEB (SAS)
b ED ¼ BC (matching sides of congruent triangles from a)
AE ¼ DC (equal sides of a rhombus) and AE ¼ EB (given)
[ DC ¼ EB
[ BCDE is a parallelogram because its opposite sides are
equal.
a In n APS and n CRQ:
AP ¼ CR (given)
AS ¼ CQ (given)
\A ¼ \C (opposite angles of a parallelogram)
[ n APS ” n CRQ (SAS)
[ PS ¼ QR (matching sides of congruent triangles)
In n PBQ and n RDS:
PB ¼ RD (given AP ¼ CR and opposite sides of a
parallelogram)
\B ¼ \D (opposite angles of a parallelogram)
BQ ¼ DS (given CQ ¼ AS and opposite sides of a parallelogram)
[ n PBQ ” n RDS (SAS)
[ PQ ¼ RS (matching sides of congruent triangles)
b PQRS is a parallelogram because pairs of opposite sides
are equal).
AC and DB are diagonals.
OD ¼ OB (equal radii of small circle)
OA ¼ OC (equal radii of large circle)
[ ABCD is a parallelogram because the diagonals bisect each
other.
SQ and PR are diagonals.
OP ¼ OR (equal radii of small circle)
OS ¼ OQ (equal radii of large circle)
PR ’ SQ (given)
[ PQRS is a rhombus because its diagonals bisect each other
at right angles.
Since WD ¼ WE ¼ GY ¼ YF (W and G are the midpoints of
equal sides DE and GF)
and DZ ¼ ZG ¼ EX ¼ XF (Z and X are the midpoints of
equal sides DG and EF)
[ WZ ¼ WX ¼ YX ¼ ZY (by Pythagoras’ theorem)
[ WZYX is a rhombus (a quadrilateral with all sides equal)
In n APT and n CRQ:
AT ¼ CQ (T and Q are the midpoints of equal sides of a
parallelogram)
9780170194662
Answers
AP ¼ CR (P and R are the midpoints of equal sides of a
parallelogram)
\A ¼ \C (opposite angles of a parallelogram)
[ n APT ” n CRQ (SAS)
[ PT ¼ RQ (matching sides of congruent triangles)
Similarly, proving n DRT and n BPQ congruent (SAS),
TR ¼ QP (matching sides of congruent triangles)
[ PQRT is a parallelogram because its opposite sides are equal.
Exercise 13-04
1 a In n ABD and n ACD:
AB ¼ AC (given)
BD ¼ CD (given)
AD is common.
[ n ABD ” n ACD (SSS)
b \ADB ¼ \ADC (matching angles of congruent triangles)
c \ADB þ \ADC ¼ 180 (angles on a straight line)
[ \ADB ¼ \ADC ¼ 90
[ AD’BC
2 a In n KMP and n KNP:
KM ¼ KN (given)
\KPM ¼ \KPN ¼ 90 (KP’MN)
KP is common.
[ n KMP ” n KNP (RHS)
b MP ¼ NP (matching sides of congruent triangles)
KP’ MN (given)
[ Perpendicular from vertex K to MN bisects MN.
3 a In n ABX and n CDX:
\ABX ¼ \CDX (alternate angles, AB || CD)
\BAX ¼ \DCX (alternate angles, AB || CD)
AB ¼ CD (opposite sides of a rectangle)
[ n ABX ” n CDX (AAS)
b [ AX ¼ CX and BX ¼ DX (matching sides of congruent
triangles)
[ X is the midpoint of diagonals AB and CD.
[ The diagonals of a rectangle bisect each other.
4 a In n DEG and n FGE:
\DEG ¼ \FGE (alternate angles, DE || FG)
\DGE ¼ \FEG (alternate angles, DG || FE)
GE is common.
[ n DEG ” n FGE (AAS)
b In n DGF and n FED:
\DFG ¼ \FDE (alternate angles, FG || DE)
\FDG ¼ \DFE (alternate angles, DG || FE)
DF is common.
[ n DGF ” n FED (AAS)
c \GDE ¼ \EFG (matching angles of congruent triangles
DEG and FGE)
\DGF ¼ \FED (matching angles of congruent triangles
DFG and FED)
[ Opposite angles of a parallelogram are equal.
5 a In n BED and n BCD
BE ¼ BC (given)
DE ¼ DC (given)
9780170194662
b
6 a
b
7 a
b
c
8 a
b
9 a
b
BD is common.
[ n BED ” n BCD (SSS)
\EBD ¼ \CBD (matching angles of congruent triangles)
\EDB ¼ \CDB (matching angles of congruent triangles)
[ Diagonal BD bisects \EBC and\EDC.
In n LXM and n NXP:
\MLX ¼ \PNX (alternate angles, LM || NP)
\LMX ¼ \NPX (alternate angles, LM || NP)
LM ¼ NP (given)
[ n LXM ” n NXP (AAS)
LX ¼ NX and MX ¼ PX (matching sides of congruent
triangles)
[ Diagonals of a parallelogram bisect each other.
In n UAW and n XAW:
UW ¼ XW (equal sides of a rhombus)
AW is common.
\UWA ¼ \XWA (diagonals of a rhombus bisect the angles)
[ n UAW ” n XAW (SAS)
In n UAW and n UAY
UW ¼ UY (given)
AU is common.
\WUA ¼ \YUA (diagonals of a rhombus bisect the angles)
[ n UAW ” n UAY (SAS)
UA ¼ XA (matching sides of congruent triangles UAW
and XAW)
WA ¼ YA (matching sides of congruent triangles UAW
and UAY)
[ Diagonals bisect each other.
\UAW ¼ \XAW (matching angles of congruent triangles
UAW and XAW).
But \UAW þ \XAW ¼ 180
[ \UAW ¼ \XAW ¼ 90
[ WA’UX
[ Diagonals WY and UX are perpendicular.
[ Diagonals bisect each other at right angles.
In n DXF and n EXF:
\D ¼ \E (given)
\DXF ¼ \EXF ¼ 90 (FX ’ DE)
FX is common.
[ n DXF ” n EXF (AAS)
FD ¼ FE (matching sides of congruent triangles)
Also, FD is opposite \E and FE is opposite \D.
[ Sides opposite the equal angles in a triangle are equal.
Join X to B.
In n XBW and n XBY:
XW ¼ XY (equal sides of equilateral n XYW)
WB ¼ YB (B is the midpoint of WY)
XB is common.
[ n XBW ” n XBY (SSS)
Join Y to A.
In n YAX and n YAW:
YX ¼ YW (equal sides of equilateral n XYW)
XA ¼ WA (A is the midpoint of XW)
YA is common.
[ n YAX ” n YAW (SSS)
659
Answers
c \W ¼ \Y (matching angles of congruent triangles XBW
and XBY)
\X ¼ \W (matching angles of congruent triangles YAX
and YAW)
[ \W ¼ \Y ¼ \X
But \W þ \Y þ \X ¼ 180
[ \W ¼ \Y ¼ \X ¼ 60
Mental skills 13
2 a
e
i
4 a
e
i
12:25 p.m.
0610
1100
6:05 p.m.
1245
1545
b
f
j
b
f
j
1:10 a.m.
0010
2305
6:40 a.m.
0355
0400
c
g
k
c
g
10:50 p.m.
9:10 a.m.
12:20 a.m.
12:10 p.m.
10:50 p.m.
d
h
l
d
h
10:55 p.m.
3:15 a.m.
11:35 a.m.
2:50 a.m.
12:15 p.m.
Exercise 13-05
1 \LMK ¼ \LKM ¼ 45 (angle sum of a right-angled
isosceles n KML)
[ \PMN ¼ 135 (angles on a straight line)
[ 2x þ 135 ¼ 180 (angle sum of isosceles n PMN)
[ x ¼ 22.5
2 \ABC ¼ 42 (equal angles of isosceles n ABC)
[ \BCD ¼ \ABC ¼ 42 (alternate angles, CE || AB)
[ \DBC ¼ \BCD ¼ 42 (equal angles of isosceles n BCD)
\ EDB ¼ \ ABD ðalternate angles, CE jj ABÞ
¼ \ ABC þ \ DBC
¼ 42 þ 42
[ m ¼ 84
3 \NKL þ 93 ¼ 147 (exterior angle of n NKL equal to sum
of interior opposite angles)
[ \NKL ¼ 54
[ \NKH ¼ 54 (NK bisects \HKL)
[ \HKL ¼ 108
\NHK þ 108 ¼ 147 (exterior angle of n HKL equal to sum
of interior opposite angles)
[ \NHK ¼ 39
4 \EDC ¼ 180 116 ðco-interior angles, BC jj EDÞ
¼ 64
) x ¼ 6442 ðdiagonals bisect the angles of a rhombusÞ
¼ 32
5 \AED ¼ \ABC (corresponding angles, ED || BC)
\ADE ¼ \ACB (corresponding angles, ED || BC)
But \ABC ¼ \ACB (equal angles of isosceles n ABC)
[ \AED ¼ \ADE
[ n AED is isosceles (two equal angles)
6 Let \XYP ¼ x, \TWP ¼ y
[ \PYW ¼ x (YP bisects \XYW) and \PWY ¼ y (WP
bisects \TWY)
[ 2x þ 2y ¼ 180 (co-interior angles, YX || WT)
[ x þ y ¼ 90
But x þ y þ \YPW ¼ 180 (angle sum of n YWP)
[ 90 þ \YPW ¼ 180
[ \YPW ¼ 90
660
7 a TZ ¼ TY (given)
[ n TZY is isosceles.
[ \TZY ¼ \TYZ (angles opposite equal sides)
TZ ¼ UX (given)
and TZ ¼ WX (equal opposite sides of a parallelogram)
[ UX ¼ WX
[ n XUW is isosceles.
[ \XUW ¼ \XWU (angles opposite equal sides)
But \TZY ¼ \XWU (equal opposite angles of a parallelogram)
[ \TZY ¼ \TYZ ¼ \XUW ¼ \XWU
In n TZY and n XWU:
TZ ¼ XU (given)
\TZY ¼ \XWU (opposite angles of a parallelogram)
\TYZ ¼ \XUW (proven)
[ n TZY ” n XWU (AAS)
b TY ¼ UX (given)
ZY ¼ UW (matching sides of congruent triangles)
TW ¼ ZX (opposite sides of a parallelogram)
) TU ¼ TW UW
¼ ZX ZY
¼ XY
[ TUXY is a parallelogram (opposite sides equal).
8 a In n MNY and n TMW:
MN ¼ MT (equal sides of a square)
MY ¼ TW (Y and W are the midpoints of equal sides
of a square)
\NMY ¼ \MTW ¼ 90 (angles in a square)
[ n MNY ” n MTW (SAS).
b \MNY ¼ \TMW ¼ x (matching angles of congruent
triangles)
[ \NMX ¼ 90 x
) \MXN ¼ 180 x ð90 x Þ
¼ 90
[ MW ’ NY
9 \BCD ¼ \BDC (equal angles of isosceles n BCD)
) \ABD ¼ \BCD þ \BDC ðexterior angle of 4BCD
equal to sum of interior opposite anglesÞ
¼ 2 \BCD
But \ABD ¼ \AED (opposite angles of a parallelogram)
[ \AED ¼ 2\BCD
10 a In n ADB and n ACB:
AD ¼ AC (equal radii of large circle)
BC ¼ BD (equal radii of small circle)
AB is common.
[ n ADB ” n ACB (SSS)
b In n DXB and n CXB:
BX is common.
BD ¼ BC (equal radii)
\DBX ¼ \CBX (matching angles of congruent triangles
proved in a)
[ n DXB ” n CXB (SAS)
DX ¼ CX (matching sides of congruent triangles proved in b)
11 Let \A ¼ \B ¼ x (equal angles of isosceles n ABC)
[ \ACB ¼ 180 2x (angle sum of n ABC)
\DCE ¼ \ACB ¼ 180 2x (vertically opposite angles)
9780170194662
Answers
[ \D ¼ \E ¼ 12[180 (180 2x)] (angle sum of
isosceles n DCE)
[ \D ¼ \E ¼ x
[ \A ¼ \E
[ AB || DE (alternate angles are equal)
12 \YUX ¼ \UYX ¼ \UXY ¼ 60 (angles in equilateral n UXY)
[ \UXW ¼ 120 (angles on a straight line)
\XWU þ \XUW þ 120 ¼ 180 (angle sum of n WXU)
[ \XWU ¼ \XUW ¼ 30 (n WXU is isosceles)
\WUY ¼ \XUW þ \YUX
¼ 30 þ 60
¼ 90
13 \WTP ¼ \P and \YTQ ¼ \Q (alternate angles, WY || PQ)
\WTP þ \PTQ þ \YTQ ¼ 180 ðangles on a straight lineÞ
) angle sum of 4PQT ¼ \P þ \PTQ þ \Q
¼ \WTP þ \PTQ þ \YTQ ðfrom aboveÞ
¼ 180
14 \BAD þ \DAH þ \BAC þ \CAF ¼ 180 (angles on a
straight line)
But \BAD ¼ \DAH (AD bisects \HAB)
and \BAC ¼ \CAF (AC bisects \FAB)
[ 2\BAD þ 2\BAC ¼ 180
[ \BAD þ \BAC ¼ 90
[ \CAD ¼ 90
15 \BAC þ \BCA þ \ABC ¼ 180 (angle sum of n ABC)
[ \ABC ¼ 180 (\BAC þ \BCA)
\CBD þ \ABC ¼ 180 (angles on a straight line)
) \CBD ¼ 180 \ABC
¼ 180 ½180 ð\BAC þ \BCAÞ
¼ \BAC þ \BCA
16 \ABO ¼ x ¼ \BAO and \CBO ¼ y ¼ \BCO (equal angles
of isosceles n ABO and n CBO, equal radii)
[ 2x þ 2y ¼ 180 (angle sum of n ABC)
[ x þ y ¼ 90
[ \ABO þ \CBO ¼ 90 ¼ \ABC
[ \ABC is a right angle.
Exercise 13-06
1 a
2 a
3
4
b 2
c
1
2
d 1.5
3 a i \L and \T, \F and \W, \D and \P, \B and \Y.
ii LF and TW, FD and WP, BD and YP, LB and TY.
iii LFDB ||| TWPY
b i \G and \T, \M and \Q, \Y and \S,
ii MY and QS, GM and TQ, GY and TS.
iii n GYM ||| n TSQ
27
24
18
4 a Yes, (36
12 ¼ 9 ¼ 8 ¼ 6 ¼ 3)
b Yes, all equilateral triangles are similar.
24
19
2
c Yes (28
42 ¼ 36 ¼ 28:5 ¼ 3)
9
3
d Yes (15
¼ 15
25 ¼ 5)
30
6
e Yes, (18
15 ¼ 25 ¼ 5, and the triangle is right-angled)
f Yes, all squares are similar.
Exercise 13-07
1 a w ¼ 22.4
b m ¼ 10
c p ¼ 20, h ¼ 21
d x ¼ 18
e a ¼ 12.8, w ¼ 7.5
f g ¼ 1119, q ¼ 18
2
3
4
g y ¼ 26 3, b ¼ 9 5 or 9.6 h u ¼ 12 5 or 12.8, t ¼ 6 78 or 6.875
2 h ¼ 1357
3 x ¼ 889
4 w ¼ 16 cm
5 h ¼ 12 m
6 B
7 h ¼ 2.408 m
8 D
9 2.24 m
Exercise 13-08
1 a Two pairs of angles are equal (AA).
b All three pairs of matching sides are in the same ratio,
9
11
15:5
1
18 ¼ 22 ¼ 31 ¼ 2 (SSS)
c Two pairs of matching sides are in the same ratio
6
12
3
8 ¼ 16 ¼ 4 and the included angles are equal (SAS).
d Two pairs of angles are equal (AA).
e All three pairs of matching sides are in the same ratio
9
9
14:25
3
12 ¼ 12 ¼ 19 ¼ 4 (SSS)
f In both right-angled triangles, the pairs of hypotenuses
20:8
4
and second sides are in the same ratio 12
15 ¼ 26 ¼ 5 (RHS).
g Two pairs of angles are equal (AA).
h All three pairs of matching sides are in the same ratio
18
27:5
20
5
14:4 ¼ 22 ¼ 16 ¼ 4 (SSS).
i All three pairs of matching sides are in the same ratio
6
8
10
3
8 ¼ 1023 ¼ 1313 ¼ 4 (SSS).
j Two pairs of matching sides are in the same ratio
26
30
10
18:2 ¼ 21 ¼ 7 and the included angles are equal (SAS).
2 a B and C (SAS)
b A and C (SSS)
c B and D (RHS)
3 a n UWY ||| n HEK (SAS)
b n DML ||| n TPA (RHS)
c n ABC ||| n QTP (AA)
d n GHN ||| n WVS (SSS)
Exercise 13-09
1 a In n TCH and n PMB:
TC
18
5
PM ¼ 10:8 ¼ 3
b
9780170194662
5
¼ 25
15 ¼ 3
\C ¼ \M ¼ 90
[ n TCH ||| n PMB (in a right-angled triangle, hypotenuses
and two pairs of matching sides are in proportion or RHS)
b In n VWG and n LQE:
\V ¼ \L ¼ 22
\W ¼ \Q ¼ 123
[ n VWG ||| n LQE (equiangular or AA)
TH
PB
661
Answers
c In n ABC and n TWM:
AB
17
2
TW ¼ 25:5 ¼ 3
c i
AC
12
2
TM ¼ 18 ¼ 3
BC
16
2
WM ¼ 24 ¼ 3
[ n ABC ||| n TWM (three pairs of matching sides in
proportion or SSS)
d In n EVH and n DNL:
EV
21
7
DN ¼ 12 ¼ 4
7
¼ 35
20 ¼ 4
\V ¼ \N ¼ 90
[ n EVH ||| n DNL (two pairs of matching sides in
proportion and the included angles equal or SAS)
2 a In n ADE and n ABC:
AD
1
AB ¼ 2 (D is the midpoint of AB)
d
VH
NL
¼ 12 (E is the midpoint of AC)
\A is common.
[ n ADE ||| n ABC (two pairs of matching sides in
proportion and the included angles equal or SAS)
b In n ABF and n FDE:
\AFB ¼ \FED (corresponding angles, BF || CE)
\FAB ¼ \EFD (corresponding angles, AC || FD)
[ n ABF ||| n FDE (equiangular or AA)
c In n WXY and n TXW:
\WXY ¼ \TXW ¼ 90 (given)
\YWX ¼ 90 \WYX (angle sum of n WXY)
\XTW ¼ 90 \WYX ðangle sum of 4WTY Þ
e
AE
AC
¼ \YWX
[ n WXY ||| n TXW (equiangular or AA)
d In n NDL and n NQR:
ND
8
1
NQ ¼ 16 ¼ 2
1
¼ 10
20 ¼ 2
\N is common.
[ n NDL ||| n NQR (two pairs of matching sides in
proportion and the included angles equal or SAS)
e In n XWH and n YXW:
HW
18
3
WX ¼ 12 ¼ 2
NL
NR
3
¼ 12
8 ¼2
\HWX ¼ \YXW (alternate angles, HW || YX)
[ n XWH ||| n YXW (two pairs of matching sides in
proportion and the included angles equal or SAS)
f In n NML and n KLP:
\NML ¼ \KLP (alternate angles, NM || LK)
\N ¼ \K (opposite angles of a parallelogram)
[ n NML ||| n KLP (equiangular or AA)
3 a i In n FLN and n FDE:
\FLN ¼ \FDE (corresponding angles, LN || DE)
\F is common.
[ n FLN ||| n FDE (equiangular or AA)
ii d ¼ 9
b i In n ACE and n BCD:
\EAC ¼ \DBC ¼ 90 (given)
\C is common.
[ n ACE ||| n BCD (equiangular or AA)
5
ii y ¼ 511
XW
YX
662
f
4 a
b
5 a
b
6 a
b
In n YRT and n WUT:
\YRT ¼ \WUT ¼ 90 (given)
\YTR ¼ \WTU (vertically opposite angles)
[ n YRT ||| n WUT (equiangular or AA)
ii g ¼ 15
i \T þ \PCT ¼ 90 þ 90 ¼ 180
[ TN || CP (co-interior angles are supplementary)
In n NMP and n PCB:
\NMP ¼ \PCB ¼ 90 (given)
\N ¼ \CPB (corresponding angles, TN || CP)
[ n NMP ||| n PCB (equiangular or AA)
ii w ¼ 7.5
i In n TYN and n YNM:
\TYN ¼ \MNY (alternate angles, TY || MN)
\TNY ¼ \YMN (given)
[ n TYN ||| n YNM (equiangular or AA)
ii h ¼ 12
i In n BHU and n XBD:
\BUH ¼ \XDB (given)
\UBH ¼ \DXB (alternate angles, BU || DX)
[ n BHU ||| n XBD (equiangular or AA)
ii y ¼ 18
In n MXG and n KXL:
MG || LH (opposite sides of a rectangle)
\GMX ¼ \LKX (alternate angles, MG || LH)
\MGX ¼ \KLX (alternate angles, MG || LH)
[ n MXG ||| n KXL (equiangular or AA)
x ¼ 16
In n CLW and n LTE:
\CWL ¼ \TEL ¼ 90 (given)
\L is common.
[ n CLW ||| n LTE (equiangular or AA)
x¼2
In n PTU and n KPB:
\PUT ¼ \KPB (alternate angles, PK || TU)
\PTU ¼ \KBP ¼ 90 (given)
[ n BHU ||| n XBD (equiangular or AA)
PB ¼ 4
Power plus
1 a In n ABC and n CBD:
\ACB ¼ 90 (by Pythagoras’ theorem in n ABC)
\CDB ¼ 90 (given)
[ \ACB ¼ \CDB
\B is common.
[ n ABC ||| n CBD (equiangular or AA)
In n ABC and n ACD:
\ACB ¼ 90 (by Pythagoras’ theorem in n ABC)
\CDA ¼ 90 (given)
[ \ABC ¼ \CDA
\A is common.
[ n ABC ||| n ACD (equiangular or AA)
[ n ABC ||| \CDB ||| n ACD
8
b CD ¼ 413
4.62
9780170194662
Answers
2
G
D
C
T
A
H
B
In n DGT and n BHT:
\DGT ¼ \BHT (alternate angles, DC || AB)
\GDT ¼ \HBT (alternate angles, DC || AB)
DT ¼ BT (given)
[ n DGT ” n BHT (AAS)
[ DG ¼ BH (matching sides of congruent triangles)
C
3
Y
P
X
A
W
B
T
(Outline of proof only) X and Y are midpoints of BC and AY.
Medians AX and BY meet at P.
Draw CP to T, so that CP ¼ PT.
Prove that n CYP ||| n CAT (SAS)
[ YP || AT
[ PB || AT
Similarly, prove n CXP ||| n CBT (SAS)
[ PA || BT
[ APBT is a parallelogram (opposite sides are parallel)
W is the midpoint of AB (the diagonals of a parallelogram
bisect each other).
Chapter 13 revision
1 156
2 36
3 a 36
b 15
c 8
d 24
4 B
5 In n WYZ and n XYZ
\W ¼ \X (given)
\WZY ¼ \XZY ¼ 90 (YZ ’ WX)
YZ is common.
[ n WYZ ” n XYZ (AAS)
6 a n BYC is isosceles (BC ¼ BY).
[ \BCY ¼ \C (angles opposite equal sides)
BC ¼ AD (opposite sides of a parallelogram)
[ n ADX is isosceles (AD ¼ XD).
[ \A ¼ \DXA (angles opposite equal sides)
But \A ¼ \BCY (opposite angles of a parallelogram)
[ \A ¼ \DXA ¼ \C ¼\BYC
In n ADX and n CBY
AD ¼ CB (given)
\A ¼ \C (opposite angles of a parallelogram)
\DXA ¼ \BYC (proven)
[ n ADX ” n CBY (AAS)
9780170194662
b AX ¼ CY (matching sides of congruent triangles)
AB ¼ CD (opposite sides of a parallelogram)
) XB ¼ AB AX
¼ CD CY
¼ YD
DX ¼ YB (given)
[ BXDY is a parallelogram (opposite sides equal).
7 a In n PML and n NLM:
LP ¼ MN (opposite sides of a rectangle)
LM is common.
\PLM ¼ \NML ¼ 90 (angles of a rectangle)
[ n PML ” n NLM (SAS).
b [ PM ¼ NL (matching sides of congruent triangles)
c The diagonals of a rectangle are equal.
8 In n NMA and n PQB:
NM ¼ PQ (sides of a square)
AM ¼ BQ (given)
\NMA ¼ \PQB ¼ 90 (angles of a square)
[ n NMA ” n PQB (SAS).
\NAM ¼ \PBQ (matching angles of congruent triangles)
But \NAM ¼ \CAB and \PBQ ¼ \CBA (vertically opposite
angles)
[ \CAB ¼ \CBA
[ n CBA is isosceles (two equal angles).
[ AC ¼ BC (sides opposite the equal angles in isosceles n CBA)
Also, NA ¼ PB (matching sides of congruent triangles)
) NC ¼ NA þ AC
¼ PB þ BC
¼ PC
[ n NPC is isosceles (two sides proved equal).
15
3
9 a Yes, (27
18 ¼ 10 ¼ 2)
22
12
9
4
b Yes, (27:5
¼ 16
20 ¼ 15 ¼ 11:25 ¼ 5 ¼ 0:8)
10 1137
12
11 a SAS
b RHS
c AA
A
X
B
Y
C
In n AXY and n ABC:
AX
1
AB ¼ 2 (X is the midpoint of AB)
AY
1
¼
AC
2 (Y is the midpoint of AC)
\A is common.
[ n AXY ||| n ABC (two pairs of matching sides in proportion
and the included angles equal or SAS)
[ \AXY ¼ \B (matching angles in similar triangles)
[ XY || BC (corresponding angles are equal)
XY
[ BC
¼ AX
AB (matching pairs of sides in proportion)
XY
[ BC
¼ 12
[ XY ¼ 12 3 BC
663
Answers
Mixed revision 4
[ \VXY ¼ 2x ¼ \XVY
) \XTY ¼ \VXT þ \XVY ðexterior angle of 4XVT equal to
1 40
2 a 78
b i 25
ii 14
c 35
39
39
78
3 a 80
9
21
7
b i 13
ii 36
iii 42
iv 56
80
80 ¼ 20
80 ¼ 40
80 ¼ 10
1
_
c 6 ¼ 0:16, which is lower than the experimental probability
of 17
80 ¼ 0:2125
4 a
B
34
10
10
C
10
45
13
P
13
160
5
6
7
8
9
10
11
12
664
38
9
57
b i
ii 19
iii 32
iv 109
v 160
80
160
5
c 27
In n ABC and n CDA:
\BAC ¼ \DCA (alternate angles, AB || CD)
\BCA ¼ \DAC (alternate angles, AD || CB)
AC is common.
[ n ABC ” n CDA (AAS)
9
a i 29
ii 13
iii 50
¼ 0.18
75 ¼ 0.39
30 ¼ 0.43
b i 0.33
ii 0.42
iii 0.25
c The probabilities for drawing a black marble are similar.
d 350
a 36
b 170
40
8
a 135
b 135
¼ 27
67
60
72
8
c i 135
ii 135
¼ 49
iii 135
¼ 15
In n LMP and n LNP:
LM ¼ LN (given)
MP ¼ NP (P is the midpoint of MN)
LP is common.
[ n LMP ” n LNP (SSS)
[ \LPM ¼ \LPN (matching angle of congruent triangles)
But \LPM þ \LPN ¼ 180 (angles on a line)
[ \LPM ¼ \LPN ¼ 90
a In n PRT and n RPQ:
PT ¼ RQ (given)
RT ¼ PQ (given)
PR is common.
[ n PRT ” n RPQ (SSS)
b \PRT ¼ \RPQ (matching angles of congruent triangles)
[ RT || PQ (alternate angles are equal)
\RPT ¼ \PRQ (matching angles of congruent triangles)
[ PT || RQ (alternate angles are equal)
[ PQRT is a parallelogram (opposite sides are parallel)
a 12.86
b 6
Let \VXY ¼ 2x
[ \VXT ¼ \TXY ¼ x (TX bisects \VXY)
Since XY ¼ VY (equal sides of rhombus XYVW),
n XYV is isosceles.
the interior opposite anglesÞ
¼ x þ 2x
¼ 3x
¼ 3 3 \TXY
13 a Teacher to check.
b i 12
ii 14
14 a 2340
b 3240
15 36
16 a SAS
17 10.6
18 a
1
2
1
1
2
2
2
4
3
3
6
4
4
8
5
5
10
6
6
12
b
5
11
c
i1
iii
1
2
iv
3
4
v 14
d 8280
c 1080
b SSS
3
3
6
9
12
15
18
4
4
8
12
16
20
24
ii 0
d
5
5
10
15
20
25
30
1
2
6
6
12
18
24
30
36
e 1
19 a In n YXT and n WVT:
YX ¼ VW and YX jj VW (opposite sides of a rectangle)
\YXT ¼ \WVT (alternate angles, YX jj VW Þ
\YTX ¼ \WTV (vertically opposite angles)
[ n YXT || n WVT (AAS)
b [ YT ¼ TW and XT ¼ TV (matching sides in congruent
triangles)
[ The diagonals of a rectangle bisect each other.
20 a In n ABW and n CDW:
\ABW ¼ \CDW (alternate angles, AB || CD)
\BAW ¼ \DCW (alternate angles, AB || CD)
[ n ABW ||| n CDW (AA)
b CW ¼ 457
21 In n CEO and n DFO:
OC ¼ OD (equal radii)
\CEO ¼ \DFO ¼ 90 (CE ’ AB and DF ’ AB)
\COE ¼ \DOF (vertically opposite angles)
[ n CEO ” n DFO (AAS)
General revision
pffiffiffiffi
pffiffiffi
pffiffiffiffiffi
1 7 2
2 3 1010
3 98 þ 24 10
4 $15 700
4
5 gradient ¼ 5, y-intercept ¼ 2
6 a 6x(x þ 2)
b 25(1 þ 2y)(1 2y)
c (a p10)(a
d 2(2p þ 1)(p 3)
ffiffiffiffi þ 4)
7 x ¼ 72 41
8 x ¼ 50:3, s ¼ 12.2
9 a 360 498 mm3
b 145 125 mm3
10 a 210
b i 16
ii 143
c 31.9%
d 29
210
36
o 0
11 y ¼ 142 49
5
12
12 a 56x
b x4
c 9y12
d mn7
13 a y ¼ 614
b k ¼ 3 37
c x ¼ 3
9780170194662
Answers
14
16
17
18
d ¼ 19.1
15 C
a 1
b 4
a 5
b 1
In n ABC ” n DEF:
AB ¼ DE ¼ 10 cm (given)
CB ¼ FE ¼ 12 cm (given)
\A ¼ \D ¼ 90 (given)
[ n ABC ” n DEF (RHS)
19 a y 1
b x<
30 a F ¼ fine, R ¼ rain
c 12
c 3
Sat
F
F
R
–5 –4 –3 –2 –1
0
1
2
3
4
5
F
712
6
7
8
9
–8 –7 –6 –5 –4 –3 –2 –1
0
1
2
–1
0
1
3
2
4
5
R
10
R
c x < 3
20 2x þ 3y þ 5 ¼ 0
21 x ¼ 2, y ¼ 2
22 x2 þ y2 ¼ 64
23 x-intercepts at 212 and 3, y-intercept at 15, axis of
symmetry x ¼ 14, vertex (14, 1518)
1
8
b i
31 19.2 min
y
10
5
–5
3 5
x
10
–10
(0.25, –15.125)
–20
24 a 7.2 m3
25 $1607.41
pffiffiffiffiffi
26 a i
13, m ¼ 23
pffiffiffiffiffi
iii 13, m ¼ 23
b parallelogram
27 a
b 78.5 cm3
c 5747.0 cm3
pffiffiffiffiffi
ii 2 10, m ¼ 1
3
pffiffiffiffiffi
iv 2 10, m ¼ 1
3
324 km
A
b 40 þ 18 (180 162) ¼ 58
28 a
y
–10
5
C
c 284 km
b
y
y = 3x
d 115
y = 3x
(1, 3)
(1, 3)
–5
5
–5
–10
9780170194662
10 x
1 a 13
b
2 a (x 4)(x þ 4)
b
d 3x(x 3)(x þ 3) e
g (x 2)(2x þ 5) h
3 a x ¼ 52 or x ¼ 2
c x ¼ 0 or x ¼ 35
e x ¼ 10 or x ¼ 12
1 a
d
g
j
2 a
c
e
g
i
3 a
4 a
e
N
40°
29 h ¼ 21, p ¼ 20
F
FFF
R
FFR
F
FRF
R
FRR
F
RFF
R
RFR
F
RRF
R
RRR
3
8
iii
7
8
3
c 12
x(x 4)(x þ 4) c 3(x 3)(x þ 3)
(x 5)(x þ 3)
f (x þ 8)(x 3)
x(x 10)(x þ 7)
b x ¼ 0 or x ¼ 10
d x ¼ 1 or x ¼ 5
f x ¼ 2 or x ¼ 32
Exercise 14-01
B 162°
N 100 km
–10
Outcomes
SkillCheck
–5
–15
ii
Mon
Chapter 14
–2.5
–10
Sun
1
0
x
Yes, not monic
b No
c
Yes, not monic
e No
f
Yes, not monic
h No
i
No
k Yes, monic
l
i 5 ii 9
iii 1
b i 5 ii
i 2 ii 11
iii 10 d i 1 ii
i 5 ii 7
iii 3
f i 0 ii
i 6 ii 1
ii 11 h i 1 ii
i 3 ii 13
iii 0
1
b 17
c 7
d 58
1
b 2
c 14
pffiffiffi
47
f 13 5 3
g 56
64
Yes, monic
Yes, monic
Yes, monic
Yes, not monic
6
iii 3
6
iii 0
9
iii 9
54
iii 22
pffiffiffi
e 7 25
d 3
h 7
Exercise 14-02
1 a
d
f
g
i
2 a
c
3 a
d
4 a
9x3 þ 8x2 þ 6x 2 b x3 þ 4x þ 2 c 4x2 3x 2
5x4 3x3 5x2 þ 4 e x4 x3 þ x2 5x
2x5 þ 10x4 þ 2x3 4x2 þ 4x þ 22
7x6 þ x5 þ x3 þ x2 þ 3x 2 h 8x4 þ 15x2 þ 4x 7
4x4 8x3 þ 5x2 þ x 2
j 6x3 2x2 6x þ 1
x2 þ 11x 1
b x2 3x 5
x2 þ 3x þ 5
d 2x2 þ 26x 5
2x2 15x þ 9
b x2 þ 4x 15
c 3x2 þ 11x þ 6
2
2
x þ 7x þ 3
e 3x 15x þ 3
f 3x2 7x 15
pffiffiffi
x2 7x þ 6
b 24 21 2
c 1, 6
665
Answers
Exercise 14-03
4
c
2
2
3
1 a 3x þ 2x 3x 2x
b 32x þ 80x 22x
c 45x4 13x3 þ 3x2 2x d 18x4 þ 6x3 7x2 11x 6
e 21x7 þ11x6 þ 2x5 3x4 x3 þ 2x2
f 8x5 þ 47x4 þ 41x2 þ 28x 12
2 4x3 þ 25x2 13x 6
3 a 2x4 þ 11x3 þ12x2 66x
b 4x3 þ 9x2 þ24x 54
3
2
c 8x 62x þ 99x
d
y
−1
0
1
j
2 a
c
3 a
c
e
g
x2 þ 7x þ 4 ¼ (x þ 2)(x þ 5) 6
x2 6x þ 2 ¼ (x 3)(x 3) 7
4x2 þ 3x þ 10 ¼ (x 1)(4x þ 7) þ 17
8x2 þ 9x þ 11 ¼ ð2x þ 1Þ 4x þ 212 þ 812
3
2
2
x þ 6x þ 5x 4 ¼ (x 3)(x þ 9x þ 32) þ 92
4x3 þ 2x2 þ x ¼ (x þ 4)(4x2 14x þ 57) 228
2x3 x2 þ 5x þ 3 ¼ (x þ 6)(2x2 13x þ 83) 495
3x3 x2 þ 11 ¼ (x þ 2)(3x2 7x þ 14) 17
x5 x4 þ 8x3 þ 2x2 x 1 ¼
(x þ 1)(x4 2x3 þ 10x2 8x þ 7) 8
x4 x2 10 ¼ (x þ 3)(x3 3x2 þ 8x 24) þ 62
(3x 1), R ¼ 3
b (x þ 7), R ¼ 14
(3x3 þ 14x2 2x þ 21), R ¼ 42
d (4x þ 6), R ¼ 17
(2x 1)(3x þ 2)
b (2x 1)(x2 þ x þ 1)
(2x 1)(4x þ 7)
d (2x 1)(3x2 þ 2x þ 1)
(2x 1)(x3 3x2 4x þ 2) f (2x 1)(x3 x þ 3)
(2x 1)(3x2 þ 1)
h (2x 1)(4 3x x5)
2
3
x
–1
0
1 2 3 4 5 x
–20
e
f
y
6
Exercise 14-04
1 a
b
c
d
e
f
g
h
i
y
3
2
−3 −2 −1
g
0
1
0
x
2
h
y
–3 –2 –1 0
y
1 2 3 4 5
x
y
x
−2
0
–30
i
6
3
1
3 x
−12
y
4
–2
2 x
1
0
Exercise 14-05
1 a
e
2 a
f
5
7
54
174
b
f
b
g
c
g
c
h
181
1709
2
0
d
h
d
i
1
85
14
6
179
29
2
115
e 12
2 B
3 A
4 a x-intercepts are 1, 0, 3 and y-intercept is 0.
Exercise 14-06
y
1 a B, C
b B, C
c A
d A, B, C
e A, B
2 Teacher to check.
3 a x(x þ 2)(x þ 4)
b x(x 2)(x þ 1)
c (x 1)(x þ 1)(x þ 2)
d (x 2)(2x 1)(x þ 4)
e (x 1)(x 2)(x 3)
f (x 2)(x þ 8)(x 5)
g (x 6)(x þ 1)(3x 1)
h (x 2)(3x þ 1)(2x 1)
i x2(2x 1)(x 2)
4 a x ¼ 4, 12, 3
b x ¼ 4
c x ¼ 2, 52, 3
d x ¼ 5
e x ¼ 4, 3, 2
f x ¼ 7, 0, 2
g x ¼ 3, 2, 3
h x ¼ 2, 1, 4
i x ¼ 4, 1, 5
j x ¼ 12, 1, 3
k x ¼ 14, 23, 1
l x¼3
Exercise 14-07
1 a
0
1
2
3
x
y
−1
0
3 x
0
b x-intercepts are 1, 1, 3 and y-intercept is 3.
y
–10
b
y
–3 –2 –1
–1
1
3
x
–3
1
2
x
–12
666
9780170194662
Answers
c x-intercepts are 6, 0, 1 and y-intercept is 0.
e
f
y
y
y
–2
1
–6
0
x
4
1
–2
g
d x-intercepts are 2, 1 and 112 and y-intercept is 6.
h
y
6 x
1
–12
x
0
y
y
6
–2
–3 –2
x
4
1
2
11 x
1
–2
0
3 x
–36
2
2 a
b
y
e x-intercept is 1 and y-intercept is 1.
y
–2
y
3
2x
0
–4
1
x
0
–18
–32
x
–1
c
d
y
–1
f x-intercepts are 2 and 3 and y-intercept is 18.
x
0
y
–2
3
e
x
0
–1
–4
18
y
2
f
y
3
x
y
4
0
–2
1 2
x
0
x
–8
Exercise 14-08
1 a
b
y
–4
–1
1
x
y
9780170194662
4 x
–64
j
y
y
y
1
–3
–2 0
8
–4
x
–4
i
d
y
–1 0
2
0
–2
c
h
y
–1
–2
x
–2
g
y
2
4
x
x
0
1
1
2
2
x
0 0.5
2 x
–64
–3
667
Answers
k
l
y
e
y
f
y
y = –3P(x)
2
2x
1
–2 –1 0
y
y = P(–x)
4
–1
x
–2
–1
x
1
–48
–6
Exercise 14-09
1 a
b
y
(–2, 5)
y = P(x) + 2
y = 2 P(x)
–3 –1
1
(1, 2)
x
x
1
y = P(x)
y
3
(–2, 6) y
x
3
–9
–2
a
b
y
–8
d
y
x
3
y
–3
y = 1 P(x)
2
(–2, 1 1 )
2
y
y = P(–x)
9
1
c
y = –P(x)
–9
x
1
(1, –3)
–2
e
c
y
–7
f
y
4
y
y = –P(x)
–3
1
3
b
y
y = P(x) – 2
x
(1, –2)
x
(–1, –2)
d
4
shift down 2 units
shift up 1 unit
stretch vertically by a factor of 2
reflect in x-axis and shift up 3 units
reflect in x-axis and stretch vertically by a factor of 3
reflect in x-axis and shift up 2 units
stretch vertically by a factor of 2 and shift down 5 units
reflect in x-axis, stretch vertically by a factor of 3 and shift
up 4 units
compress vertically by a factor of 12 and shift up 4 units
y = –P(x)
Chapter 15
–1
1
1
4 a
b
c
d
e
f
g
h
i
y
y = 2P(x)
x
–2
668
x
–18
x
(1, 1)
(–1, 1)
–1
1 3
–4
y = P(x) + 1
y
y = 2P(x)
y
(1, –3)(3, –3)
x
y
3
c
d
–12
1
(–2, 3)
2 a
y = P(x) – 3
x
(2, 3)
y = P(–x)
–1
x
–1
y = P(x) – 3
–2
–3 –1
x
1
x
SkillCheck
1 a SSS
2 a SSS
b SAS
b AA
c RHS
c RHS
d AAS
d SSS
e SAS
e SAS
f AAS
f AA
9780170194662
Answers
Exercise 15-01
1 a radius
2 a
b chord
c circumference
d tangent
segment
O
sector
b sector drawn from centre of circle and bounded by 2 radii
and arc. Segment is bounded by chord and arc
3 d ¼ 2r
4 D
5 a radius
b quadrant
c tangent
d diameter
e chord
f arc
g sector
h circumference
i segment
6 a diameter
b segment
c sector
d arc
Exercise 15-02
1
3
5
8
9
12
14
15
a Proof by SAS
2 a, b Proof by RHS
a Proof by SSS
4 c The centre of the circle
a, b Proof by SAS
6 5.74 cm
7 60 cm
a UC ¼ 4.5 m (the perpendicular from the centre bisects the
chord and the chords are equal as they are the same
distance from the centre)
b DE ¼ 12 m (chords of equal length subtend equal angles
at the centre of a circle)
c \UVO ¼ 58 (chords of equal length subtend equal
angles; angle sum of isosceles n )
d PQ ¼ 30 mm (Pythagoras: the line from the centre is the
perpendicular bisector of the chord)
e OM ¼ 21 cm (Pythagoras: the line from the centre is the
perpendicular bisector of the chord)
pffiffiffi
f OD ¼ 18 2 (Pythagoras: the line from the centre is the
perpendicular bisector of the chord)
52 cm
10 18.4 km
11 MN ¼ 4 cm
77 cm
13 34 cm, 20 cm
a AB ¼ 30 cm
b area ¼ 840 cm2
a 52 cm
b area ¼ 1920 cm2
Exercise 15-03
1 a
b
c
d
e
f
g
h
i
2 a
b
c
d
e
f
9
45 >
>
>
112 >
>
>
>
120 >
>
>
=
232 ðangle at the centre is twice
40 >
> the angle on the circumferenceÞ
>
74 >
>
>
>
>
63 >
>
;
104
90 (angle in a semicircle)
9
48 >
>
>
36 >
>
>
=
30 ðangles at the circumference of
35 >
> a circle standing on the same arcÞ
>
74 >
>
>
;
90
9780170194662
3 a reflex \ROT ¼ 216 (angles at a point), \S ¼ 108 (angle at
the centre is twice the angle at the circumference)
b x ¼ 43 (angles opposite equal sides in an isosceles triangle
are equal), y ¼ 86 (exterior angle of triangle equal to sum
of two opposite interior angles, or angle at the centre is
twice the angle at the circumference)
c n ¼ 37 (angles at the circumference standing on the same
arc are equal), m ¼ 74 (angle at the centre is twice the
angle at the circumference)
d p ¼ 37 (angles at the circumference standing on the same
arc equal)
e w ¼ 50 (angle at the centre is twice the angle at the circumference)
f h ¼ 113 (angle at the centre is twice the angle at the
circumference, co-interior angles on parallel lines supplementary)
4 a m ¼ 75 (opposite angles of cyclic quadrilateral)
b p ¼ 88 (opposite angles of cyclic quadrilateral);
q ¼ 121 (opposite angles of cyclic quadrilateral)
c x ¼ y ¼ 90 (angles in a semicircle)
5 a n ¼ 106 (exterior angle of cyclic quadrilateral)
b w ¼ 60 (angle in an equilateral triangle; exterior angle of
cyclic quadrilateral)
c x ¼ 84 (exterior angle of cyclic quadrilateral),
y ¼9
110 (exterior angle of cyclic quadrilateral)
6 a 23 =
ðangle in semicircle,
b 9
; angle sum of a triangle)
c 45
d 63 (opposite angles of a cyclic quadrilateral)
e 75
ðexterior angle of cyclic quadrilateralÞ
f 88
7 a x ¼ 75 (angle at the centre is twice the angle at the circumference)
y ¼ 33 (angles at the circumference standing on the same arc)
z ¼ 72 (angle sum of a triangle)
b x ¼ 108 (angle at the centre is twice the angle at the
circumference)
y ¼ 126 (opposite angles of a cyclic quadrilateral)
z ¼ 252 (angles at a point, or angle at the centre is twice
the angle at the circumference)
c x ¼ 70 (straight line)
y ¼ 110 (exterior angle cyclic quadrilateral)
z ¼ 70 (straight line)
d x ¼ 96 (angle at the centre is twice the angle at the
circumference)
y ¼ 42 (angles opposite equal sides of an isosceles n ,
angle sum of a triangle)
z ¼ 264 (angles at a point)
e x ¼ 140 (angles opposite equal sides of an isosceles n ,
angle sum of a triangle)
y ¼ 70 (angle at the centre is twice the angle at the circumference)
z ¼ 35 (angle sum of an isosceles n , and by subtraction)
f x ¼ 62 (angle in a semicircle, angle sum of a triangle)
y ¼ 118 (opposite angles of a cyclic quadrilateral)
z ¼ 31 (angle sum of an isosceles n )
8 WXYZ is a cyclic quadrilateral because
\W þ \Y ¼ 180 and \X ¼ \Z ¼ 180
i.e., opposite angles are supplementary
669
Answers
Exercise 15-04
1 a
b
c
d
2 a
b
3 a
4 a
\YMP
OP ’ AB (angle between a tangent and radius)
proof by angle sum of an isosceles triangle
proof by angle at centre is twice angle at circumference
angle between a tangent and radius
proof by angles on a straight line
proof by AA (equiangular triangles)
a ¼ 56 (the angle between the radius and the tangent is a
right angle)
b b ¼ 21 (radius is perpendicular to a tangent, and
Pythagoras’ theorem)
c c ¼ 134 (a tangent is perpendicular to the radius; angle
sum of a quadrilateral)
d g ¼ 67 (alternate segment theorem)
5 a 15
b 5
c 9
d 7
e 20
f 4
6 x ¼ 7 cm 7 a XP ¼ 10 cm b AB ¼ 24 cm
Exercise 15-05
1 \R ¼ \Q
\P ¼ \S
ðangles at the circumference
standing on the same arcÞ
[ n PYR ||| n SYQ (equiangular or AA)
RY
) PY
SY ¼ QY (matching sides in similar triangles)
[ PY 3 YQ ¼ RY 3 YS
2 \ADC ¼ \BEC (opposite angles of a parallelogram)
\ADC ¼ \CBE (exterior angle of a cyclic quadrilateral)
[ \BEC ¼ \CBE
[ n CBE is isosceles (two equal angles)
3 Construction: Draw a perpendicular from O to meet DG at P. Since
the perpendicular from the centre to a chord bisects the chord:
DP ¼ GP and EP ¼ FP.
) DE ¼ DP EP
\PQS ¼ x ¼ \SRP (angles at the circumference standing on
the same arc)
[ \PQS ¼ \PSQ ¼ x
[ n SPQ is isosceles (two angles are equal).
7 Join APX and BQX.
In n XPQ and n XAB:
\X is common
\XPQ ¼ \XAB (corresponding angles, PQ || AB)
[ n XPQ ||| n XAB (equiangular or AA)
PQ
) XP
XA ¼ AB (matching sides in similar n s)
but XP ¼ 12 XA (radius is half the diameter)
1
XA
) 2XA ¼ PQ
AB
) 12 ¼ PQ
AB
) PQ ¼ 12 AB
8 Let \PTX ¼ a
[ \R ¼ a (alternate segment theorem)
Now \QTY ¼ a (vertically opposite angles)
[ \S ¼ a (alternate segment theorem)
[ \R ¼ \S ¼ a
[ PR || SQ (alternate angles are equal).
Chapter 16
SkillCheck
y
1 a
670
y = x2 – 3
– √3
x
0
0
√3
x
–3
y
c
¼ GP FP
¼ FG
4 \THJ ¼ \HIJ (alternate segment theorem)
\THJ ¼ \HPI (alternate angles, HT || IP)
[ \HIJ ¼ \HPI
In n HIP and n HJI:
\HIJ ¼ \HPI (proved above)
\IHJ ¼ \IHP (common angles)
[ n HIP ||| n HJI (equiangular)
[ \HIP ¼ \HJI (third pair of equal angles in similar triangles)
5 In n UVX and n UWX:
\UXV ¼ 90 ¼ \UXW (angle in a semicircle, straight line)
UV ¼ UW (given)
UX is common.
[ n UVX ” n UWX (RHS)
[ VX ¼ VW (matching sides in congruent triangles)
[ circle bisects base of triangle.
6 Let \QRP ¼ x
[ \SRP ¼ x (PR bisects \QRS)
[ \PSQ ¼ x ¼ \QRP (angles at the circumference standing
on the same arc)
y
b
y = x2
y = x2 + 3x
–3
2 a
x
0
y
(2, 8)
y = x3
b
y
y = x3 + 3
(1, 4)
x
0
3
0
c
x
y
y = x3 – 1
0
1
–1
x
9780170194662
Answers
y
3 a
y
b
iii
y = 1x
(1, 1)
iv
y
y= 1
x–1
x = –2
x
0
0
–1
x
1
0
m¼0
1_
2
–2
y= 1
x+2
No gradient or the
gradient is undefined.
Exercise 16-02
y
4 a
y
b
y = 2x
(–1, 3)
(1, 2)
1
y = 3–x
1
x
0
x
0
y
c
0
–1
x
y = –4–x
(1, –4)
5 a x ¼ yþ1
2
pffiffiffiffiffiffiffiffiffiffiffi
c x¼ y4
b x ¼ 3y 1
1 a
c
e
g
i
2 a
3 a
4 a
5 a
6 a
i
b
7 a
b
8 a
9 a
d
10 a
c
f
i
l
11 a
i 6
ii 2
iii 0
b i 2 ii 2
iii 1
i 24 ii 4
iii 0
d i 17
ii 1
iii 1
pffiffiffi
i 3 ii 1
iii 3 f i 125 ii 13
iii 1
i 125 ii 13
iii 1
h i 2 ii 6
iii 1
i 60 ii 12
iii 21
0
b 28
c 9k 9k2
16
b 10
c 6d 20
d 12
e 256
4
b 12
c 2
d x ¼ 212
5
b 0
c 14
d t ¼ 2, 112
i 11
ii 19
iii 10
9 2y
ii 2
c 16
i 11
ii 5
iii 6
Teacher to check c m ¼ 3, 1
pffiffiffiffiffiffiffi
3
b 12
c
1 has no value d x ¼ 12
8
b 11
c 40
3k4 2k2 þ 3
e 3k2 þ 2k þ 3
f 4k
3 x 3; 0 y 3
b 4 x 0; 0 y 4
x 0; y 5
d x 1; y 0
e x 1; y 3
all x; y ¼ 3
g all x; y > 0
h all x; y ¼ 3
all x; y > 2
j all x; 1 y 1 k all x; y 4
all x; 0 < y 4
b
y
y
(1, 4)
Exercise 16-01
1 a
e
2 a
e
i
m
3 a
Yes
Yes
Yes
No
Yes
Yes
i
b
f
b
f
j
n
y
No
Yes
Yes
Yes
No
No
c
g
c
g
k
o
m¼3
9780170194662
Yes
No
No
No
Yes
Yes
ii
d
h
d
h
l
p
Yes
Yes
No
Yes
Yes
Yes
i All x
c
x
m ¼ 12
x
i All x
ii All y
d
y
ii y 1
y
(1, 2)
(2, 1)
1
0
3
x
0
i All x
x
0
0
1 12
x + 2y = 3
1
1
y
y = 3x – 2
(1, 1)
0
–2
0
b i, ii and iii
c i For all values of m. ii If m is undefined (a vertical line).
x
0
–2
x
y
c
y
4 y=4
ii y > 0
0
x
x
i x 6¼ 0
ii y 6¼ 0
671
Answers
e
f
y
d i
y
f 1(x) ¼ f (x) ¼ 4x ii
y
10
5
1
–3 0
5
y = 4x
(1, –1) x
0
–10
–15
(1. 4)
x
–5
10 x
5
–5
(1, –16)
–10
i All x
ii All y
g
i All x
ii y 16
h
y
e i
f
1
ðxÞ ¼
2xþ3
2
ii
y
(1, 7)
y = 4x + 3
x
0
y
3
2x + 3
y = _____ 2
2 1
0
–3 –2 –1
–1
4
2x − 3
y = _____
2
3
0
i All x
ii All y
i
i All x
x
f
i
f 1 ðxÞ ¼ 22x
3
ii
2 − 2x
y = _____
3
y
ii y > 3
2
1
y
7
−2 −1 0
−1
−2
x
0
ii y 2
Exercise 16-03
1 a i f
ðxÞ ¼
xþ5
2
ii
–4 –3 –2 –1 0
–1
x
y=2x–5
(x) ¼ 3x
ii
y
4
3
2
1
4 3x 2 110
_
y =
2
3
3
c i f 1(x) ¼ 6 2x
ii
y=3–
x
2
1 2 3 4
x
–2
–3
–4
y=x
b i f
y=x
4
3
2
1
y
x+5
y = __
2 =
0
1
x
2 a Teacher to check.
y
b
y=2–x
1
1 2
3x
y = 1 − __
2
(–3, 2)
i All x
1 2 3x
–2
–3
y = 3x
1 2 3 4x
The graph of f (x) ¼ 2 x is itself symmetrical about the
line y ¼ x.
3 b, c and h
4 a
y
y
6
5
4
3
2
1
y = x2 – 2
0
x
–2
0 1 2 3 4 5 6x
–6 –5 –4 –3 –2 –1
–1
672
–2
–3
–4
–5
–6
y = 6 – 2x
b No
9780170194662
Answers
c y¼
pffiffiffiffiffiffiffiffiffiffiffi
xþ2
y
y=
x2
3 Both graphs are increasing.
For y ¼ 2x, y-intercept ¼ 1, no x-intercept.
For y ¼ log2 x, x-intercept ¼ 1, no y-intercept.
y
4
y = 4x
– 2, x ≥ 0
y= x+2
0
–2
y = 3x
y = log3 x
x
1
y = log4 x
–2
0
x
1
y=x
pffiffiffiffiffiffiffiffiffiffiffi
d y¼ xþ2
y
y = x2 – 2, x ≤ 0
0
–2
x
–2
y= x+2
5 a
b No
c x 0 or x 0
y
3 y = x2 + 3
a They are all increasing graphs and have a y-intercept of 1.
For x > 0, y ¼ 4x is steeper than y ¼ 3x, which is steeper
than y ¼ 2x.
For x < 0, y ¼ 4x is closer to the x-axis than y ¼ 3x, which
is closer to the x-axis than y ¼ 2x.
b They are all increasing graphs and have a x-intercept of 1.
For x > 1, y ¼ log2 x is steeper than y ¼ log3 x, which is
steeper than y ¼ log4 x.
For x < 0, y ¼ log4 x is closer to the y-axis than y ¼ log3 x,
which is closer to the y-axis than y ¼ log2 x.
5 a 2x
b 4x
6 a log4 x
b log2 x
7 a 1.3010
b 2.7973
c 3.7345
d 0.9138
e 0.3979
f 0.1192
8 x
0.5
1
2
5
8
10
y
6 a
b x 2 or x 2
4
0
x
0.9
1
0
x
1 2 3 4 5 6 7 8 9 10
9 Teacher to check.
y
b No
c x 12 or x 12
2
Exercise 16-05
1 a
x
0
–4 –3 –2 –1
–1
c
y = f (x) + 1
1 2 3 4
y
4
3
2
1
–4 –3 –2 –10
–1
–2
–3
–4
x
d
4
3
2
1
–4 –3 –2 –10
–1
–2
–3
–4
y
b
–2
–3
–4
Exercise 16-04
1 y ¼ 2x
Interchange x and y and make y the subject.
[ x ¼ 2y
[ log2 x ¼ log2 2y
[ log2 x ¼ y log2 2 where log2 2 ¼ 1
[ y ¼ log2 x
2 a Domain: all x; range: y > 0 b Domain: x > 0; range: all y
c They have interchanged.
y
4
3
2
1
(– 12 , –6 14 )
9780170194662
0.7
2
1
–2 –1 0
–1
–2
(2, –4)
–3
0.3
y
y
7 a
0
0.3
x
0
1 2 3 4
x
1
x
y
4
3
2
1
1 2 3 4
x
–4 –3 –2 –1 0
–1
2
3
4
–2
–3
y = f (x) – 3
–4
y = f (x – 2)
673
Answers
e
y
3
2
1
4 a
y
4
3
2
1
0
–4 –3 –2 –1
–1
1 2 3 4
–3 –2 –1
–1
–2
–3
x
–2
y = f (x + 4) –3
–4
y
3
2
1
c
2 a
b
y
y
y = f(x) – 3
0
y = f(x) + 2
x
0
–3
d
y
y = f(x) – 1
0
3
f
y
y
y = f(x + 1)
0
–1
0
(–2, –1)
x
x
3 y = f(x + 2) –1
3 a
y = f(x – 1)
0
x
1
4
3
2
1
1 2 3x
–3 –2 –1
y = f(x) + 3
0
1 2 3
y
3
x
1 2
y = f(x + 1) – 3
y
b
0
–2
y = f(x) + 2
x
x
y
(1, 1) y = f(x – 1)
d
y
(2, 2)
y = f(x – 2) + 1
y
2
0
x
y = f(x) – 3
y = f(x) + 2
0
2
x
0
x
x
y
c
y = f(x + 2) + 1
(–2, 1)
–3
674
b
3 4 x
y
0
–3 0
c
y
1 2
d
–3 –2 –1–10
–2
–3
5 a
e
0
–2 –1
–1
–2
–3
1
y
y = f(x – 3)
x
0
–1
1 2 3x
y = f(x – 3)
y
e
c
y = f(x) – 2
0
y = f(x + 2)
–3 –2 –1
–1
–2
–3
2
x
y
4
3
2
1
b
0
x
9780170194662