0521681774_homework10_Ans.

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Cambridge University Press © Greenwood, Robertson 2006

Answers
1 Length, area and volume 2 Linear algebra and linear
Homework Sheet A relations
1 a 434 cm b 0.000 714 km Homework Sheet A
c 200 mm2 d 10 000 000 m3 1 a 7st b 8xy  5y 2
2 694 cm/sec c 6m2n3 d 4h2i 4
3 a 12.57 cm b 1.91 m 2 a 3a  3b b 2bc  4b 2
4 a 50 cm b 40.85 m c 18x  4 d 2c 2  4c
c 74 m d 33.99 m 15  4a 8  3b
5 a 8.06 mm b 12.09 m 3 a b
20 4b
c 10.20 m d 4.24 m 5x  8 x  14
6 a 1.54 cm2 b 10.4 m2 c d
6 12
c 39.45 m2 d 30.90 cm2 8x  6
e
(x  7)(x  3)
Homework Sheet B
7
1 a 4 a x b x  2
5
8
c x1 d x
3
5 a x  18 b x5
13
b c x  17 d x
2
6 a x5 x
5
b x  4 x
−4
c x5 x
5
c d x2 x
2
e x  6 x
−6
2
7 m
3
2 a 66 cm2 b 132 m2 8 a m  3, c  7
2
c 471.24 mm d 25.65 m2 b m undefined, no y- intercept
2
e 50.27 km f 235.62 mm2 c m  0, c  2
3 a 35.63 m 3
b 720 mm3 d m  2, c  4
c 35.65 mm3 d 54.10 cm3 e m  4, c  0
3 y
4 a 137.3 m b 2.88 m 9 b
c
5 8.125 kg/m3 4 a
3
6 150 mL 2
7 a 158 b 7.6 m2 c 7.87 m 1
x
−4 −3 −2 −1
−1 1 2 3 4
d
−2
−3
−4

Essential Mathematics VELS Edition Year 10: Answers 1

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Cambridge University Press © Greenwood, Robertson 2006

10 a y b y d y
(4, 5)
6
x x
−2 4 7
x −7 3
4 (−2, −13)
c y d y
3 Geometry
Homework Sheet A
x 3 1 a x  40 b x  60
−6 x c x  80 d x  160
e x  18 f x  15
11 a y  x  4 b yx3 2 a 360 b 1080 c 540
c y4 d x2 3 a x  50 b x  60
e y  7x f y  3x c x  11 d x  65
12 a y  4x  1 b y  2x  12 4 i a  70; b  110; c  70; d  70
ii e  60; f  35
Homework Sheet B 5 a No b Yes SAS
1 a (1, 2) b None 6 a x  5.2; y  2.6
c (0, 4) b p  0.83; w  0.42
2 a No point of intersection. 7 a diameter b radius
b No point of intersection. c minor arc d minor sector
3 a (1, 1) b (1, 3) 8 a 3.49 m b 9.08 m2
4 a (4, 2) b (1, 1)
5 22 emus, 6 wombats Homework Sheet B
6 a y 1 a x  130, y  70 b p  100
c x  90 d e  30
2 a y  40; x  50 b d  47
3 3 a (1, 1) b (4, 7)
x c (2, 3) d (3, 2)
−3
2 e (3, 2) f (1, 3)
b y g (2, 21)
4 a y

(−2, 1) 1
x
9 x
−1
7 y
b y
7
2 x x
−4 8 −1
−7 (2, −3)
(−1, −2) (1, −2)

8 a i 13 ii 5 iii x3

b [2, 4] c [13, 5]

2 Essential Mathematics VELS Edition Year 10: Answers

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Cambridge University Press © Greenwood, Robertson 2006

c y Homework Sheet B
1 13, 17
(−2, 1)
2 a 2 12 b 5 13
x
−1 111
(−2, −1)
c 6 12 d
3
121
y e
d 12
3 a 2 15  17 b 6  3 16
c 30 12  4 16 d 15  18 12
(2, 2) 17 115
(−2, 2) 4 a b
1 7 5
x 10 5 111  177
c d
5 a y  2x  3 b y  2x  1 9 11
1 5 a x  1.3 b y  15.6
c y x1 d y  6x  3
2 6 a 4 b 2 c 2
4 1
d e 1 f 
3 11
4 Indices and surds 7 a x  1.61 b x  0.68
Homework Sheet A 8 a A  A0(1.05)n b A  A0(0.93)n
1 a x8 b 6x8y9 9 a i $25 400 ii $20 432
k 2t 2 iii $15 066.56
c c4 d
3 b 6 years c $3254.73
2 a m6 b 64m 6 10 a (0, 1) (1, a) b y 0
c 4m6 d 27x6y3z6 11 a x  1.50 b x  2.37
e 1 12 a 9.0 b 1.5 c 0.2
3 a 1 b 4
c 1 d 6
e 1 5 Statistics
4 a 2x 2ty4 b 16a8t 8 Homework Sheet A
1 a Points scored Frequency
1
c 0–9 4
2m 10–19 8
1 2 20–29 5
5 a b 30–39 1
x4 t3
1 b, c Frequency
c x4 d
xy 10
1
e
8m6
1 1 5
6 a 5 b c
3 10
2t 3 2a6
7 a b
5 t4 0
1 10 20 30 40
5m
c d Points scored
y 81h14k9
9 d 10–19
e
zb3

Essential Mathematics VELS Edition Year 10: Answers 3

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Cambridge University Press © Greenwood, Robertson 2006

2 a 6 01223445677788999 11 a 3 b 9
7 0113379 c 6 d 12
8 25567 12 a IQR and min. b Set A
9 1 9 |1 means 91 beats per minute c Set A is an even distribution
b Set B has 50% of its data between 11
and 12
13 a
60 70 80 90 11 19 21.5 23 31

3 a 17 students b 44 b 4
c 31 d 32 years c
4 a 2 11 13 19 21.5 23 26 31
b UK, Australia, New Zealand, Russia, d Outliers at 11, 31
Armenia, Costa Rica, Indonesia 14 a 0 b 0.02
c UK, Australia, Russia, New Zealand, c 0.04 d 0.08
Armenia, Cost Rica, Indonesia e 0.10
5 a Relative frequency: 0.28, 0.28, 0.24, 0.2;
Percentage frequency: 28, 28, 24, 20 Homework Sheet B
b 50 1 a N b Y
c 0.24 c N d Y
d 44% 2 a Yes b decrease
6 a 1, 4, 14, 25 b 4 c 14 c x9 d negative
d 56% e 24 f 96% 3 a 14
7 a Cumulative frequency: 3, 10, 14, 20;
Percentage cumulative frequency: 15, 50, 12

70, 100 x
10 x
b 3
c 10 8 x
d 10 x
e 50% 6 x
8 a Cumulative frequency: 2, 6, 18, 25; x x
Percentage cumulative frequency: 8, 24, 4 x
x
72, 100
2
b Cumulative frequency

25 100%
20 1 5 10
75%
15
10
50%
b yes, positive
25%
5 4 a i Positive Result
Cost
40 80 120 160 200 240 ii (2, 9) 70

b i none
c i 126 ii 162 60
ii none
iii 180 iv 202 50
5 a, b graph
d
80 162 180 202 240 c i 20 years 40

ii 15 years 30
9 a 5.583 b 5 c 6.5
d 43
d 3.5 e 2 f 12 20

g 3 10

10 a 0.685 b 0.3 c 0.55 0

d 1 e 0.7 f 1.4 0 5 10 15
Age
20 25 30

4 Essential Mathematics VELS Edition Year 10: Answers

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Cambridge University Press © Greenwood, Robertson 2006

6 a y  2x  4 b y  3x  50 1 1 1
2 a b c d 1
7 a 8 3 6
x 1.0 1.3 1.5 1.6 1.7 1.7 1.8 1.8 1.9 1.9 2.0 2.2 1 1 3 1
3 a b c d
y 16 14 13 13 10 11 9 12 8 9 6 16 8 2 8 2
1 1 1 3
b (1.5, 12.8) (1.9, 10) 4 a b c d
4 13 52 13
c y  7x  23.3
8 b y = 2.1x  11.4 c 41C 17 33
5 a i ii
d 36C 50 50
b i 17 times ii 340 times
6 a i Depends on simulation results
6 Quadratic expressions
b Results depend on the simulation
Homework Sheet A
1 1 5
1 a 3x  9 b x2  x  20 c i ii iii
c x2  8x  16 d 9x2  4 6 2 6
2 a 4(x  3) b (3x  5)(3x  5) 7 a 1 2 3 4 5
c (x  6)(x  3) d 12(5x  1)(5x  1) 1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5)
3 a (3x  1)(x  3) b (3x  2)(3x  5) 2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5)
c (3x  2)(2x  3) 3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5)
x5 x7 4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5)
4 a b x4 c 5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5)
x3 x5
1
x1 3x  4 b 25 c
5 a b 5
2x  3 2x  3
1
6 2x2  2x  5 d i ii 0
5
7 a (x  2  12)(x  2  12) 2 3 22
b (x  3  111)(x  3  111) e i ii iii
25 25 25
1
/ 1
Homework Sheet B 8 a 2 R RR 4
1
1 a 2 solution b 2 solutions R
/
3
G RG 1
1/ 1 6
c 1 solution 2
/
6
B RB 1
2 a x  2, 3 b x  3, 4 12
c x  2
1
d no real sltn. /
2 R GR 1
1/ 6
3 a x  4 and x  1 3 1
/
3 1
G G GG
b x  5 and x  3 1
/
9
c x  13 and x  9
6
B GB 1
1/ 18
4 a x  0, 2 b x3 6 1
/
c x  3 d x  6, 1 2 R BR 1
12
1
e x  7, 2 B
/
3
G BG 1
1 18
3  117
/
6
5 a x B BB 1
36
2
7
b x   12 b i 0 ii
6 a x6m b x8m 18
c x4m d x9m 5 11
iii iv
9 18
7 Probability 2 3 8
9 a b c
Homework Sheet A 3 11 33
1 3 3 1 16 17
1 a b c d d e
8 4 8 2 33 33

Essential Mathematics VELS Edition Year 10: Answers 5

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Cambridge University Press © Greenwood, Robertson 2006

Homework Sheet B 2 7 4
c i ii iii
1 a A B 5 30 15
1 1 1
4 a i ii iii
8 3 4
1 2 1
b i ii iii
5 5 2
b 1 1 1
A B c i ii iii
9 4 5
2 4 2
d i ii iii
5 5 3
5 part b.
c 6 Depends on simulation results.
A B

8 Quadratic graphs
Homework Sheet A
1 a (3, 0) (0, 0) b (0, 0)
d
A B c (1.5, 4) d x  1.5 e [4, 5]
2 x intercepts at (1, 0) (4, 0)
turning point at (2.5, 2, 25)
axis of symmetry x  2.5
y- intercept at (0, 4)
2 a 20 18 16
A B 3 x intercepts at (1, 0) (3, 0)
9 2 y intercept at (0, 9)
3 turning point at (2, 3)
5 7
1 11 13
14 axis of symmetry x  2
17 19 4 a ii b iii
15 c i d iv
5 a y
4 6 8 10 12

b i {1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19}

ii {3, 5, 7, 11, 13, 17, 19} 4
iii {1, 9, 15}
x
1 11 7 −2
c i ii iii y
2 20 20 b
d No
1 1
e i ii
2 20 1,
1
3 a 2
H M
x
7 5 10
c y
8

b H H' x
M 5 10 15 3

M' 7 8 15
12 18 30 −9

6 Essential Mathematics VELS Edition Year 10: Answers

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Cambridge University Press © Greenwood, Robertson 2006

6 a 3 b 9 c 21 iii (3, 0) (8, 0)

7 a y iv y
(5, 4)

x
3 8
x
−2 8
−21
−16
y
c i minimum at (–3, 0)
b
ii (0, 18)
iii (3, 0)
iv y

x
−2 2
18
−12
x
Homework Sheet B −3
1 a turning point at (2, 5)
3 a (0.60, 2.20)
axis of symmetry is x  2
b No intercepts
x intercepts at (1, 0) (4, 0)
c (0, 4)
y intercept at (0, 3)
4 a Two x intercepts
b turning point at (2, 0)
b (0, 2)
axis of symmetry is x  2
c (1, 1)
x intercept at (2, 0) y
5
y intercept at (0, 1)
c turning point at (3, 3)
axis of symmetry is x  3
no x intercepts (0, 1)
x
y intercept at (0, 5)
d turning point at (1, 6)
−5 − √17 −5 + √17
axis of symmetry is x  1 ,0
4 4
x intercepts at (1, 0) (3, 0)
y intercept at (0, 4) −5, −2 1
2 a i minimum at (4, 9) 4 8
ii (0, 7)
iii (1, 0) (7, 0) 6 a 0 x 300
iv y b x 0 50 100 150 200 250 300
h 25 66.67 91.7 100 91.7 66.67 25
c h
7
100

x
1 7 25
(4, −9)
b i Maximum at (5, 4) x
ii (0, 21) 150 300

Essential Mathematics VELS Edition Year 10: Answers 7

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Cambridge University Press © Greenwood, Robertson 2006

d 25 metres Homework Sheet B

e 100 metres 1 a 1.69 metres b 3.63 metres
7 a i 3500 m ii 3480 m iii 3000 m 2 x  5.00
b 20 seconds y  8.66
c h (m) w  5.00
z  7.07
3500 3 21
4 a 288 b 167
1500 5 a 24.43 km b 8.89 km
6 a 71.565 b 3.16 cm
t (sec)
c 72.5, 72.5, 35.1
20 7 a b  c
d  e  f 
9 Trigonometry g 
Homework Sheet A 8
1  and Degrees only Trigonometric
25 30 25.5 function sin cos tan sin cos tan
32 24 32.4 7 5
1 45 150 100
6 3 4
17 17
11 5
147 15 147.25 2 135 210 280
6 3 4
12 39 12.645
2 Degrees Radians 10 Variation and modelling
180 c Homework Sheet A
c 1 a A r c b S r r3
90
2 1 x
c D r d Y r 2
c t y
30
6 2 a direct b inverse c partial
3 c 3 a b  3a b q  2p
135 4 a y  5x b x  10 c y  250
4
5 a r  4t2 b r  100 c t  10
5 c
300 6 7.5 kPa
3 4
7 y  1x
3 a 0.7379 b 0.5934 5
c 3.0777 d 0.4339 8 a C  50n  120 b $245
x y c 15.6 hours
4 a tan  b cos  15x 4
y x
9 a y b
x 1z 15
c sin 
y c 100
5 a x3 b x  4.70
c x  3.20 d x  3.85 Homework Sheet B
6 a x  4.73 b x  10 1 a quadratic b exponential
c x  1.80 d x  0.41 2 a linear b exponential
7 a   37.00 b   60.00 c quadratic d linear
c c  1.16 d c
 1.05 3 a y  1.65x  106.87 b 190 cm
8 a  38 40 b  34 51 4 a quadratic
c  55 9 b y  900x2  2400x  37100
9 2986 metres c $2600

8 Essential Mathematics VELS Edition Year 10: Answers

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Cambridge University Press © Greenwood, Robertson 2006

11 Consumer mathematics Homework Sheet B

Homework Sheet A 1 $10.85
1 a 0–15 people: $80/day, 30 people: 2 a $119 b $139.68
$70/day, 50 people: $61/day, 75 people: c $258.68 d 7.7 cents/km
$56/day 3 a $1600 b $18 400
b $2450 c $10 400
c $4087 4 a $340 b 53.97%
2 $27521.56 5 a large: $4.8
3 3% small: $2.72
4 $717.60 b $21.40
5 a $1140 b $0.96 6 a $19950 b $554.17
6 a 7.83% b 0.79% 7 $997.50
7 a mortgage $237.60, bills $237.60, 8 14.29%
savings $63.36 9 a P  $3000 R  3.0% r  0.25%
recreation $118.80, clothing $39.60, t  60
travel $95.04 b P  $10 000 R  7.4% r  0.14%
b $25.34 t  208
c $316.80 c P  $1000 R  9.36% r  0.36%
d 21.43% t  52
10 a $17 956.35 b $18 023.90

Essential Mathematics VELS Edition Year 10: Answers 9