Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007 187
Answers to Homework Book 8
STAGE
8
1 Fractions
Exercise 1.1H (page 1)1 a) 1 b) 1
c) 3 d) 7
e) 2
2 a) 2 b) 2
c) 2 d) 2
e) 1
3 a) 9 b) 1
c) 2 d) 7
e) 5 f) 9
g) 8 h)
4 a) 4 b) 7
5 13 m
6 5 cut off, 4 left, not enough
Exercise 1.2H (page 2)1 a) b) 4
c) 10 d) 8
e) 1 f) 5
2 a) 2 b) 2
c) 12 d) 2
e) f)
3 a) 9 b) 16
c) 9 d) 2
e) 8 f)
g) 9 h) 3
i) 5 j) 2
k) 3 l) 14
4 a) 2 b) 2
c) 5 d) 3
e) 6 f) 4
2 Cubic and reciprocalgraphs
Exercise 2.1H (page 3)1 a)
b)
c) x = 0, x = 2·2 or x = –2·2
0 1 2 3
y = x3 – 5x
–1–2–3 x
–5
–10
–15
15
10
5
y
4–9
3––10
3–4
1–3
26––55
1–3
7––17
6–7
5–8
9––22
1–3
16––41
2–5
1–5
1–2
3–4
48––77
1–2
17––20
11––12
8–9
1––10
9––10
1–4
1–5
3–4
7––20
13––20
3–4
1–5
7––18
27––40
5––14
34––35
7––18
7––16
17––24
11––24
5––12
7––10
9––10
1–8
11––24
1–5
7––30
1––10
8––15
17––20
7––10
x –3 –2 –1 0 1 2 3
x3 –27 –8 –1 0 1 8 27
– 5x 15 10 5 0 –5 –10 –15
y –12 2 4 0 –4 –2 12
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 187
188
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
2 a)
b)
c) x = –3·5, x = –1·6 or x = 1·1
3
4 a)
Three solutions
b)
No solution
y
O
x
y
O x
0 1 2 3 4
y = 3x
–1–2–3–4 x
–2
–4
–6
–8
–10
–12
12
2
4
6
8
10
y
0 1 2
y = x3 + 4x2 – 6
–1–2–3–4 x
–2
–4
–6
16
18
12
14
2
4
6
8
10
y
x –4 –3 –2 –1 0 1 2
x3 –64 –27 –8 –1 0 1 8
4x2 64 36 16 4 0 4 16
– 6 –6 –6 –6 –6 –6 –6 –6
y –6 3 2 –3 –6 –1 18
x –4 –3 –2 –1 –0·5 –0·25 0·25 0·5 1 2 3 4
y –0·75 –1 –1·5 –3 –6 –12 12 6 3 1·5 1 0·75
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 188
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
5
x = –2·5, x = –1·3 or x = 0·9
6
x = –2·2, x = 0 or x = 2·2
0 1 2 3
y = 5x – x3
–1–2–3 x
–2
–4
–6
–8
–10
–12
12
2
4
6
8
10
y
0 1 2
y = x3 + 3x2
y = 3
–1–2–3 x
2
4
6
8
10
12
14
16
18
20y
189
Answers to Hom
ework Book 8
STAGE
8
x –3 –2 –1 0 1 2
x3 –27 –8 –1 0 1 8
3x2 27 12 3 0 3 12
y 0 4 2 0 4 20
x –3 –2 –1 0 1 2 3
5x –15 –10 –5 0 5 10 15
– x3 27 8 1 0 –1 –8 –27
y 12 –2 –4 0 4 2 –12
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 189
190
3 Probability
Exercise 3.1H (page 4)1 a)
b)
2 a)
b) (i)
(ii) =
3 a)
b) (i)
(ii)
4 a)
b) (i)
(ii) =
(iii) =
Exercise 3.2H (page 5)1 a) = b) =
c)
2
3
4 a) b) =
5 a) 0·85b) 0·65
6 a) 0·003b) (i) 0·15
(ii) 0·01(iii)0·91(iv) 0·18
c) (i) 0·0081(ii) 0·0009
1––18
2––36
1––36
1–––169
1–4
49–––400
3–5
12––20
1–4
5––20
1–9
3––27
1–9
3––27
1––27
2nd spin
1
21
3
1st spin
1
2
3
1
2
3
3rd spin1
2
31
2
31
2
31
2
31
2
31
2
31
2
31
2
31
2
3
3
2
2–9
1–9
LunchtimeCanteen
GymCar
Shopping
Travel
Canteen
Gym
Shopping
Canteen
Gym
Shopping
Bus
Cycle
2–3
4–6
1–6
Food
Muesli
ToastTea
Grapefruit
Drink
Muesli
ToastCoffee
Grapefruit
1–6
Spinner
1
2H
3
Coin
1
2T
3
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 190
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
Exercise 3.3H (page 6)1 a)
b) (i) (ii)
2 a)
b) (i) (ii)
(iii) =
3 a)
b) (i) =
4 a)
b) (i) 0·064(ii) 0·288(iii)0·784
5 a)
b) (i) 0·15(ii) 0·1
6 a)
b) (i)
(ii) = 3–5
9––15
1––15
Drink
Mineral water15
ColaDailyGazette
Orange
Newspaper
25
13
23
25
Mineral water15
ColaDailyNews
Orange
25
25
LunchtimeCanteen
Gym
0.1
0.5
0.4
0.1
0.5
0.4
0.1
0.5
0.4
0.2
0.5
0.3
Car
Shopping
Travel
Canteen
Gym
Shopping
Canteen
Gym
Shopping
Bus
Cycle
Day 3Rain0.4
0.6 No rain
Rain0.4
0.6 No rain
Rain0.4
0.6 No rain
Rain0.4
0.6 No rain
Day 2
Rain0.4
0.6 No rain
Rain0.4
0.6 No rain
Day 1
Rain0.4
0.6No rain
11––40
110–––400
Second ball
R
G
W
1120
520
420
First ball
R
G
1120
520
R
G
W
1120
520
420
W
420
R
G
W
1120
520
420
176––––1125
528––––3375
484––––3375
1331––––3375
Third ball
R
W
Second ball1115
415
R
W
1115
415
R
W
1115
415
First ball
R
W
1115
415
R
W
1115
415
R
W
1115
415
R
W
1115
415
88–––225
16–––225
Second ball
R
W
1115
415
First ball
R
W
1115
415
R
W
1115
415
191
Answers to Hom
ework Book 8
STAGE
8
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 191
192
4 Equations andinequalities
Exercise 4.1H (page 8)1 x = 4 11 x = 1
2 x = 20 12 x =
3 x = 6 13 x = 15
4 x = 14 x = 12
5 x = 35 15 x = 6
6 x = 8 16 x = 2
7 x = 50 17 x = 23
8 x = 3 18 x = 2
9 x = 9 19 x = –3
10 x = –2 20 x = 5
Exercise 4.2H (page 9)1 x � 14 8 x � 30
2 x � 7 9 x � 8
3 x � 6 10 x � 14
4 x � 7 11 x �
5 x � 9 12 x �
6 x � 5 13 x � –5
7 x � 12 14 x � 12
Exercise 4.3H (page 9)1 b � 7 = 21, base = 6 cm
2 = + 2 , n = 24
3 a) x – 7 = x
b) x = 28, he had 28 m of rope
4 a) 80 – x � x
b) x > 60, £60·01
5 a) x + x + x – 50 = 180
b) x = 150°; 100°, 30°, 50°
6 a) (i) x
(ii) x + 30
(iii)x + 30
b) x + 30 > (x + 30)
c) x < 30, 29 or 29 years 364 days
7 a) x – 15 + x + 3 + x – 27 + x – 3 = 68
b) x = 40; 25 cm, 13 cm, 13 cm, 17 cm
5 Percentage increase anddecrease
Exercise 5.1H (page 11)1 a) 1·2(0) b) 1·07
c) 1·045 d) 1·0625e) 2·2(0)
2 a) 0·8(0) b) 0·93c) 0·65 d) 0·16e) 0·985
3 a) £946·08 b) £1024·92c) £1708·20 d) £2102·40e) £932·94
4 a) £595 b) £469c) £672 d) £210
5 £187·206 £1116·257 £10 937·508 a) £112·75
b) £114·95She will be £2·20 per week better off.
9 583·7 mm10 £244·80
Exercise 5.2H (page 12)1 £24 520 6 £62 £45 7 £423 £1440 8 £754 £13 500 9 £72 0005 28 million
6 Linear inequalities
Exercise 6.1H (page 13)1 a) y � 3
b) x � –1c) y � x – 3d) y � 3x – 1e) 5x + 2y � 10
2
0 x54321–1–2–3–4–5
5
4
3
2
1
y
–5 –4 –3 –2 –1
x = –3
1–2
1–4
2–3
1–3
1–3
1–3
1–5
1–3
1–3
3–4
n–4
n–3
1–2
1–2
4–5
3–7
1–2
1–2
1–3
1–2
2–7
7––15
1–2
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 192
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
3
4
5
6
Exercise 6.2H (page 15)1
2
3
4
0 x3 421–1–2–3
4
3
2
1
y
–3 –2 –1
y = 2x + 1
x = –2
y = 4
5
6
7
5 6 7
0 x54321–1–2–3–4–5
5
4
3
2
1
y
–5 –4 –3 –2 –1
y = –x x = 4
y = 3
0 x3 4 521–1–2–3
4
3
2
1
y
–3 –2 –1
x + 2y = 4
x = –1 5
0 x3 4 5 621
4
3
2
1
y
3x + y = 6
6
7
7
5
0 x3 4 5 621–1–2
4
3
2
1
y
–2 –1
4x + 3y = 12
6
5
0 x321–1–2–3–4
4
3
2
1
y
–3 –2 –1
y = 2x – 1
–5
5
0 x54321–1–2–3–4–5
5
4
3
2
1
y
–5 –4 –3 –2 –1
x + y = 3
0 x54321–1–2–3–4–5
5
4
3
2
1
y
–5 –4 –3 –2 –1
y = x
193
Answers to Hom
ework Book 8
STAGE
8
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 193
194
5
6 x � –1, y � 2, 5x + 3y � 15
7 Cumulative frequencyand box plots
Exercise 7.1H (page 16)1 a) Median = 23, LQ = 10, UQ = 39
b)
2 a)
b) Median = 265, LQ = 232, UQ = 295,interquartile range = 63
c) See diagram above.3 a) 190
b)
4 a)
b)
c) Median = 62, interquartile range = 17
20 40
LQ
M
UQ
Mass (g)
Cum
ulat
ive
freq
uenc
y
60 80 100
80
100
60
40
20
0
0 10 20Height (m)
30 40
200150 250
LQ
M
UQ
Weekly pay (£)
Cum
ulat
ive
freq
uenc
y
300 350 400 450
40
50
30
20
10
0
0 20 40Age
60 8010 30 50 70 90
0 x3 421–1–2
4
3
2
1
y
–2 –1
y = 2x + 1
x = 1
x + y = 5
5
6
7
8
5 6 7 8
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
Mass (m grams) Cumulative frequency
m � 40 7
m � 50 19
m � 60 43
m � 70 75
m � 80 93
m � 90 98
m � 100 100
Weekly pay (£ p) Cumulative frequency
p � 200 3
p � 250 18
p � 300 39
p � 350 46
p � 400 48
p � 450 49
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 194
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
5 a)
b) 200 – 180 = 206 a) and c)
b) Median = 30·5, interquartile range = 18·5d) 150 – 103 = 47
10 20
LQ
M
UQ
Height, h (cm)
Cum
ulat
ive
freq
uenc
y
30 40 50
d)
60
80
100
120
140
160
20
40
60
0
200 250
UQ
M
LQ
Taking (£t)
Cum
ulat
ive
freq
uenc
y
300 350 400
b)
450 500
100
150
200
50
0
195
Answers to Hom
ework Book 8
STAGE
8
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 195
196
8 Repeated percentageand proportionate change
Exercise 8.1H (page 20)1 a) £793·44
b) £1776·29c) £7010·85
2 a) £258·80b) £5255·35c) £3549·64
3 5034 a) £15 200
b) £15 058·33Simple interest by £141·67
5 £31466 a) £339·30
b) £245·157 56·3 million8 8·5 years or 9 years9 5·04 or 6 years
10 4·5%: £2604·525%: £2552·564·5% for 6 years is better
11 £7527·35
Exercise 8.2H (page 21)1 a) 1
b) 1
c)
d)
e) 1
2 a) £805·26b) £8926·54c) £15 444·96
3 a) £163·84b) £3681·63c) £1788·91
4 4465 a) £8109·15
b) 7·8 or 8 years6 7·4 or 8 days
9 Transformations
Exercise 9.1H (page 23)1
2
3 a) Rotation 90° clockwise about (1, 1)b) Reflection in x = 1c) Reflection in y = x
4
5
0x321 54
D
E
F–1–2–3–4
3
4
2
1
y
6 7 8 9
0x321 1054
B
C
A
x = 5
y = 1
–1–2–3
3
4
5
2
1
y
6 7 8 9
0 x321
S
TP3
4
2
1
y
–3–4 –2 –1
0 x3 421
R
QP3
4
2
1
y
–3–4 –2 –1
12
y = xx = –
4––15
11––12
1–3
7–8
1–4
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 196
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
Exercise 9.2H (page 24)1
2
3 a) Enlargement, scale factor 2, centre, (–4, 1)
b) Translation ( )c) Enlargement, scale factor , centre (2, 0)
4
5
6
Exercise 9.3H (page 26)1 Rotation, 180° about (5, 1)2 Rotation, 90° anticlockwise about (7, 3)
3 Translation by vector ( )4 Enlargement, scale factors –2, centre (0, 0)5
Reflection in x = 3
6
Enlargement, scale factor 2, centre (0, 6)
0x321 5 64
3
2
1
–1–2–3–4–5
y
4
5
6
A
A’
C’B’
A”
C”B”
CB
0x3
A
A’
C’B’
21 5 64
3
4
2
1
–1–2–3–4
y
A”
B”C”CB
12
–5–7 0 x321 5 64
3
2
1
–1–2–3–4–5–6–7
y
–1–2–3–4
4
5
6
–6
–5–6 0 x321 5 64
3
2
1
–1–2–3–4–5–6
y
D
E
F
–1–2–3–4
4
5
6
–5 0 x321 54
3
2
1
y
BA
C
–1–2–3–4
4
5
6
1–2
–61
0 x321 54
3
2
1
y
XY
Z
6 7–1–2–3–4
4
5
7
6
0 x321 54
T
–1–2–3–4
3
4
5
2
1
y
R
P QS
6 7 8–1–2–3–4
197
Answers to Hom
ework Book 8
STAGE
8
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 197
198
7
Reflection in y-axis (x = 0)
8
Rotation 90° clockwise about (4, –1)
9
Enlargement, scale factor –3, centre (1, 1)
10
Translation by ( )
10 Simultaneous equations
Exercise 10.1H (page 28)1
x = 2, y = 3
2
x = 2, y = 4
0 1 2 3 4 5
y = x + 2
y = 3x – 2
x
–2
6
8
10
12
14
4
2
y
0 1 2 3 4 5
y = x + 1
y = 4x – 5
x
–2
–4
–6
6
8
10
12
14
16
4
2
y
–22
0 x321
3
2
1
–1–2
y
A
BB’
B” C”
C’
A’
C
C”’B”’
–1–2–3
4
5
6
0 x321
4
2
1
–1–2–3–4–5–6
y
A
C
C’
C”
B’
B”
B
–1–2–3
3
0–1–2
x321 54
3
9
2
1
y
A
A’A” B”
C”
BB’
C
C’4
5
6 7 8
0 x3 421
3
4
2
1
y
A
BB”
C”
A”
C
C’
B’
–1–2–3
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 198
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
3
x = –1, y = 2
4
x = 1, y = 3
5
x = 1 , y = 31–2
0 1 2 3 4 5
4x + 2y = 12
y = 2x
x
–1
–2
–3
–4
3
4
5
6
7
8
9
10
2
1
y
0 1 2 3 4 5
x + y = 4
y = 4x – 1
x
–2
6
8
10
12
14
16
18
20
4
2
y
0 1–1–2–3 2 3
y = x + 3
y = 3x + 5
x
–2
–4
6
8
10
12
14
4
2
y
199
Answers to Hom
ework Book 8
STAGE
8
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 199
200
6
x = 2·7, y = 3·3
7
x = 2·2, y = 2·6
Exercise 10.2H (page 29)1 x = 3, y = 22 x = 2, y = –13 x = 13, y = –44 x = –2, y = –35 x = 6, y = –1
6 x = 3 , y = 2
7 x = 5, y = –108 x = 4, y = 3
9 x = 5, y =
10 x = 1 , y = 3
11 x = 5, y = –212 x = –2, y = –3
13 x = –1, y = 3
14 x = 2 , y = –
15 x = 3, y = –7
16 x = 1 , y = 2
17 x = 5, y = 318 x = 3, y = –2
Exercise 10.3H (page 29)1 x = 1, y = 42 x = 2, y = 33 x = –1, y = –34 x = 2, y = –1
5 x = –5 , y = 9
6 x = 3, y = –17 x = 3, y = –18 x = 4, y = 4
9 x = 1 , y = 3
10 x = –1, y = 1011 x = 4, y = 312 x = –3, y = –513 x = –2, y = 5
Exercise 10.4H (page 30)1 x + y = 40, x – y = 14, x = 27, y = 13
2 2 = –2m + c, 1 = 4m + c, c = 1 , m = –
, y =
–x + 1
3 2a + 4c = 27, a + 3c = 17, adult £6·50, child£3·50
4 3p + 2r = 135, 4p + 3r = 190, pen 25p, ruler30p
5 a = 2c, 2a + 3c = 84, adult £24, child £126 a) x + y = 46
b) y + 1 = 3(x + 1)y – 3x = 2
c) Alan 11 years old, mother 35 years old
2–3
1–6
1–6
2–3
1–2
1–2
1–2
1–3
5–7
1–7
1–2
1–2
1–2
1–2
1–2
0 1 2 3 4 5
2x + y = 7
2y = x + 3
x
–1
–2
–3
3
4
5
6
7
2
1
y
0 1 2 3 4 5 6
x + y = 6
y = 2x – 2
x
–1
–2
3
4
5
6
7
8
9
10
2
1
y
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 200
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
11 Significant figures andstandard form
Exercise 11.1H (page 31)1 a) 9 b) 10
c) 60 d) 0·8e) 500 f) 7g) 700 000 h) 0·08i) 0·005 j) 0·0009
2 a) 19 b) 790c) 7800 d) 79 000e) 90 f) 0·31g) 0·057 h) 0·0047i) 0·031 j) 0·99
3 a) 7·39 b) 72·5c) 19 100 d) 236e) 17 900 f) 8·24g) 67·1 h) 0·893i) 0·0490 j) 2·72
Exercise 11.2H (page 31)1 a) 6 � 104 b) 8·4 � 103
c) 8·63 � 105 d) 7·25 � 107
e) 9·02 � 106 f) 7·8 � 101
g) 8·56 � 105 h) 5·63 � 102
i) 6 � 106 j) 1·36 � 108
2 a) 8 � 10–2 b) 9·6 � 10–3
c) 3·08 � 10–4 d) 6·3 � 10–5
e) 4·8 � 10–6 f) 2·3 � 10–8
g) 8·6 � 10–1 h) 3·62 � 10–6
3 a) 3000 b) 46 000c) 0·000 02 d) 720 000e) 0·000 19 f) 5 780 000g) 287 000 000 h) 0·000 005 13i) 0·002 07 j) 72 800 000k) 0·000 063 4 l) 0·0838
4 4·4 � 1013
Exercise 11.3H (page 32)1 a) 1·8 � 1010 b) 2 � 103
c) 3·6 � 104 d) 6 � 10–7
e) 4 � 104 f) 1·5 � 106
g) 1·4 � 1010 h) 4 � 10–5
i) 7·2 � 10–3 j) 7·5 � 104
k) 7·98 � 105 l) 6·03 � 108
m) 5·2 � 10–3 n) 5·83 � 10–5
2 b) because 4 � 105 � 9 � 103 = 3·6 � 109
3 c) because 5 � 10–3 � 4 � 10–4 = 2 � 10–6
4 a) 4 � 105 � 2 � 104 = 8 � 109, 6·7332 � 109
b) 4 � 106 � 2 � 10–3 = 8 � 103, 6733·2 or6·7332 � 103
c) 4 � 10–4 � 2 � 10–5 = 8 � 10–9, 6·7332 � 10–9
5 a) 1 � 107 ÷ 6 � 102 = 0·17 � 105 = 1·7 � 104,23 000 or 2·3 � 104
b) 1 � 105 ÷ 6 � 10–3 = 0·17 � 108 = 1·7 � 107,23 000 000 or 2·3 � 107
c) 1 � 10–5 ÷ 6 � 10–2 = 0·17 � 10–7 = 1·7 � 10–8,0·000 000 023 or 2·3 � 10–8
6 a) 1·188 � 1012 b) 1·495 � 109
c) 5·89 � 107 d) 2·35 � 106
e) 9·36 � 108 f) 6·85 � 104
g) 5·835 � 105 h) 1·404 � 108
i) –3·3373 � 10–3 j) 287·35 � 104
12 The equations of astraight-line graph
Exercise 12.1H (page 34)1 a) 3 b)
c) –2 d) –3
e) – f) 1
g) –3
2 a) 6 b) 4
c) 1 d) –1
e) f) –2
g) – h) 0
i) –4 j) 2
k) –3 l) –1
3 100, speed = 100 km/h80, returning home at 80 km/h
4
The lines are parallel.Gradient = –2
0 1 2 3
y = –2x + 3
y = –2x
–1–2–3 x
–4
–2
–6
8
4
10
6
2
y
1–4
7–4
1–2
1–2
3–7
1–2
1–2
201
Answers to Hom
ework Book 8
STAGE
8
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 201
202
5
a) Gradient = 3
b) Gradient =
c) Gradient = –2
6 Gradient of AB = –
, gradient of BC = –1 ,
gradient of CA = 1
7 Gradient = 0·65, representing the cost inpounds per kilogram
8
a) Gradient = b) Gradient = c) Gradient = 5 d) Gradient = 5e) Gradient = –2 f) Gradient = –2
Exercise 12.2H (page 37)1 a) Gradient = 4, y-intercept = 2
b) Gradient = –3, y-intercept = 5c) Gradient = 2, y-intercept = –3d) Gradient = 5, y-intercept = 4e) Gradient = –5, y-intercept = 4
f) Gradient = – , y-intercept = 2
g) Gradient = – , y-intercept = 3
h) Gradient = , y-intercept = –
i) Gradient = , y-intercept = –
j) Gradient = – , y-intercept = 55–4
8–3
2–3
7–3
2–3
1–2
2–3
1–2
1–2
0 1 2 3
y = –2x + 4
y = 5x – 4
y = 5x
y = –2x
y = x + 312
–1–2–3 x
–5
–10
–15
–20
10
5
15
20y
y = x12
1–2
1–2
1–2
1–2
0 1 2 3
y = –2x + 7
y = 3x – 2
y = x + 112
–1–2–3 x
–4
–2
–6
–8
–10
–12
8
4
10
12
14
6
2
y
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 202
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
2
3
4 Accept any value of k for each part except thevalue given in the question.a) y = 2x + kb) y = –4x + kc) y = k – 3x
d) y = x + k
e) y = k – x
f) 3x + y = kg) x + 5y = kh) 3x – 2y = k
13 Similar figures
Exercise 13.1H (page 38)1 x = 4·8 cm2 A and B; length is 1 � width or equivalent
statement (scale factor = 1·25)C and E; length is 1 � width or equivalent statement (scale factor = 0·75)
3 x = 4·2 cm4 ST = 4·8 cm, SU = 4·2 cm5 AB = 3 cm, EF = 8·75 cm
6 a) Angle A is common.Angle ABC = Angle ADE(Corresponding angles.)Angle ACB = Angle AED(Corresponding angles.)So all the angles are equal, so the trianglesare similar.
b) BD = 2·8 cm, CE = 3·6 cm7 Angles are the same but 6 ÷ 4 = 1·5 and
10 ÷ 7 = 1·43 or equivalent explanation8 a) In first triangle,
3rd angle = 180 – (72 + 66) = 42°So both triangles have angles 42°, 66°and 72°, so the triangles are similar.
b) x = 10 cm9 a) PSR = 85°
b) AB = 10·5 cm, SR = 10 cm
14 Comparingdistributions
Exercise 14.1H (page 41)1 a) Alice: median = 15·5, range = 18
Bob: median = 15, range = 25b) On average Alice’s scores were higher,
and more consistent.2 a) Seashore: mean = 8·96, range = 5·9
Clifftop: mean = 2·88, range = 9·8b) Seashore gets more sunshine on average
and is more consistent.3 a) Men: median = £320,
interquartile range = £150Women: median = £200, interquartilerange = £100
b) Men have higher wages and a widerspread of wages.
4 a) English: median = 47, interquartile range = 11·5Maths: median = 52, interquartile range = 24
b) Maths marks were, on average, higher buthad a wider spread. English marks weremore consistent.
5 Girls spend longer on average (girls’ median = 64 seconds, boys’ median = 36 seconds); the spread of times for the boys isvery slightly less than the spread for the girls(girls’ interquartile range = 35 seconds; boys’interquartile range = 34 seconds).
1–3
1–2
1–2
1–4
014 4
y = –2x + 8 y = 4x + 1
y = x + 3
–6 – x
3
1
8
y
12
0 1 6
y = –x + 6
y = 3x – 5y = 2x + 5
x
–5
5
6
y
12
–2 23
203
Answers to Hom
ework Book 8
STAGE
8
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 203
204
6 Duane if you want the chance of a really fasttime as his mean time is faster.Matt if you want to rely on his time as he ismore consistent.
7 a)
b) Boys are, on average, taller (the median ishigher) and have a greater spread (boys’interquartile range = 19 cm, girls’interquartile range = 15 cm).
8 Boys have slightly larger heads on average(median = 54·7 cm as opposed to 54 cm forgirls) and have a greater spread ofcircumference (boys’ interquartile range = 3 cm, girls’ interquartile range = 2 cm).
9 a) Make B – if you are buying one batteryyou need it to be a reliable one.
b) Make A – if you are buying a largequantity the spread is less important andthe higher average life is more important.
15 Trigonometry
Exercise 15.1H (page 45)1
2
3
4
5
6
Exercise 15.2H (page 46)1 a = 6·34 cm
b = 5·60 cmc = 11·8 cmd = 25 cme = 35·2 mf = 13·4 cmg = 11·9 cmh = 18·4 cm
2 a) w = 30·3 cmb) h = 62·5 cm
3 a) a = 14 cmb) b = 24·25 cmc) c = 12·61 cmd) 258 cm2
4 a) 180 kmb) 126 km
AH
O
θ
AH
O
θ
A
HO
θ
A
H
O
θ
A
H
O
θ
A
H O
θ
120 130
Boys
Girls
140Height (cm)150 160 180 190170
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 204
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
Exercise 15.3H (page 48)1 a = 2·60 cm
b = 12·2 mc = 99·7 cmd = 10·1 me = 9·20 mf = 5·35 cmg = 42·7 cmh = 15·3 m
2 l = 2·32 m3 a) a = 21·1 cm
b) 84·2 to 84·4 cm2
4 16·8 km
Exercise 15.4H (page 50)1 a = 34·5°
b = 32·6°c = 8·6°d = 61·5°e = 46·7°f = 53·4°g = 71·8°h = 32·5°
2 33·7°3 120·2°4 x = 108·7°
16 Dimensions
Exercise 16.1H (page 52)1 Volume2 Area3 None4 Length5 Area6 None7 None8 Volume9 None
10 Area11 Area12 Volume13 Length14 None15 Volume16 None17 None18 Volume19 Volume20 Area21 Length22 None23 Area24 Area25 Volume
26 None27 Area28 Volume29 Area30 None31 Square32 Square33 Cube34 Power four
17 Quadratics
Exercise 17.1H (page 54)1 x2 + 9x + 82 x2 + 10x + 243 a2 + 2a – 354 b2 + 7b – 305 x2 – 8x + 126 a2 – 13a + 227 c2 – 368 y2 + 14y + 499 a2 – 18a + 81
10 a2 – 2511 b2 + 11b + 2812 6 + 5c + c2
13 a2 – 11a + 2414 9 – 6d + d2
15 c2 + c – 3016 a2 – 2a – 3517 t2 – 13t + 3018 s2 – 12119 a2 – 99a – 10020 d2 + 30d + 200
Exercise 17.2H (page 54)1 (x + 3)(x + 1)2 (x + 4)(x + 1)3 (x + 4)(x + 3)4 (x – 1)(x – 1) or (x – 1)2
5 (x – 1)(x – 4)6 (x – 10)(x – 2)7 (x + 20)(x + 1)8 (x – 14)(x – 2)9 (x + 9)(x + 1)
10 (x + 3)(x + 3) or (x + 3)2
11 (x + 5)(x + 4)12 (x + 12)(x + 2)13 (a – 8)(a – 1)14 (b – 2)(b – 1)15 (a – 2)(a – 8)16 (s – 12)(s – 2)17 (y – 6)(y – 5)18 (y + 10)(y + 3)19 (x – 16)(x – 1)20 (c – 16)(c – 2)
205
Answers to Hom
ework Book 8
STAGE
8
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 205
206
Exercise 17.3H (page 55)1 (x + 5)(x – 3)2 (x – 7)(x + 4)3 (x + 7)(x – 1)4 (x – 4)(x + 3)5 (x – 7)(x + 2)6 (x – 10)(x + 1)7 (x + 9)(x – 4)8 (x – 12)(x + 3)9 (x + 10)(x – 1)
10 (a + 4)(a – 2)11 (a + 6)(a – 2)12 (y – 5)(y + 3)13 (b + 8)(b – 3)14 (a + 6)(a – 4)15 (c – 9)(c + 4)16 (x – 14)(x + 2)17 (x + 14)(x – 1)18 (y + 8)(y – 6)19 (a – 7)(a + 3)20 (x + 25)(x – 4)
Exercise 17.4H (page 55)1 (x + 3)(x – 3)2 (x + 8)(x – 8)3 (x + 14)(x – 14)4 (x + y)(x – y)5 (5 + y)(5 – y)6 (4 + c)(4 – c)7 (a + 100)(a – 100)8 (9 + s)(9 – s)
18 Time series and movingaverages
Exercise 18.1H (page 56)1 a) and c)
b) 29, 29, 30·5, 31·25, 31·75, 32·75, 33, 33,33·25
d) There are seasonal fluctuations. Generaltrend is a slight increase.
2 a) and c)
b) 96, 96, 104, 109, 110, 108, 109, 113, 119, 119
d) There are some variations. General trendis an increase in occupancy during theyear.
0
20
40
60
80
100
120
140
J F MMonth
A M J
Num
ber
of g
uest
s
J A S O N D
0
10
20
30
40
50
60
70y
1 2
Year 1
3 4 x1 2
Year 2
Prof
it (£
0,00
0s)
3 4 1 2
Year 3
3 4
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 206
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
3 a) and c)
b) 1500, 1518, 1498, 1506, 1527, 1530, 1531, 1549, 1556, 1567, 1579, 1600, 1615, 1630, 1640, 1655,1652, 1668, 1663, 1671, 1679, 1693
d) Fairly steady increase in customers. Highest on Saturday and Sunday, much lower in the week,except Wednesdays.
e) Wednesday4 a) and c)
b) 136·75, 134·5, 135·5, 137·75, 147·25, 151, 146, 148, 144·25d) Number of units of gas used is fairly constant. Heaviest use is in the first quarter and the
lightest in the third.
0
50
100
150
200
250
1 2 3 4
Year 1
Uni
ts o
f gas
1 2 3 4
Year 2
1 2 3 4
Year 3
0
500
1000
1500
2000
2500
3000
3500
S M Tu W
Week 1
Num
ber
of c
usto
mer
s
Th F Sa S M Tu W
Week 2
Th F Sa S M Tu W
Week 3
Th F Sa S M Tu W
Week 4
Th F Sa
207
Answers to Hom
ework Book 8
STAGE
8
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 207
208
5 a) and c)
b) 113·7, 112·2, 108·7, 106·5, 106·8, 108·7, 103·8, 104·7, 104·2, 107·2, 108, 110·7, 113d) Overall trend is fairly constant. Highest always Saturday, lowest Monday or Wednesday.e) 76
19 Equations and formulae
Exercise 19.1H (page 59)1 x = –3 or x = –1 13 x = 2 or x = –1 25 x = 11 or x = –112 x = –5 or x = –1 14 x = 1 or x = 18 26 x = 1 or x = –223 x = 6 or x = –2 15 x = 3 or x = –4 27 x = 0 or x = 34 x = –5 or x = –3 16 x = 0 or x = –7 28 x = 2 or x = 95 x = 5 or x = –2 17 x = 2 or x = –5 29 x = 0 or x = 46 x = 4 or x = 5 18 x = 15 or x = –2 30 x = 2 or x = –117 x = 8 or x = –1 19 x = 0 or x = 5 31 x = 5 or x = –28 x = 7 or x = –3 20 x = 7 or x = –7 32 x = 5 or x = –79 x = –2 or x = –3 21 x = –6 or x = –2 33 x = 1 or x = –10
10 x = 6 or x = –5 22 x = 10 or x = –2 34 x = 5 (repeated)11 x = 1 or x = 7 23 x = –4 (repeated)12 x = 0 or x = –4 24 x = 0 or x = 8
Exercise 19.2H (page 60)1 r = 2 a = P – 1 3 c = a2 – b2
4 x = 4y 5 u = 6 r =
7 r = 8 x = 9 t =
10 x = 11 v = 2as + u2 12 t =
13 a) 183 cm3 b) r = c) 3·9 cm3V–––πh
30 – 2s––––––a
y + 4–––––3
2s––––––2u + a
qy–––––q + p
pq + p––––––q – 1
pq––––s + t
fv––––f – v
A––––2πh
0
40
80
120
160
20
60
100
140
180
M Tu W Th
Num
ber
of p
eop
le
F S M Tu W Th F S M Tu W Th F S
Week 1 Week 2 Week 3
Answ
ers
to H
omew
ork
Book
8
Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007
8STAGE
17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 208