Answers - Weeblymelba10maths.weebly.com/uploads/1/0/9/9/10997732/18_answers.pdf · Answers Answers...

An

swer

s

Essential Mathematics VELS Edition Year 10 Gold378

1 a 177, 184, 188, 189, 196, 203b shortest: 177 cm, tallest: 203 cmc 26 cm

2 a 3.6, 3.7, 3.8, 3.8, 3.8, 3.8, 3.9, 3.9, 4.0b lightest: 3.6 kg, heaviest: 4.0 kgc 0.4 kg

3 a 30°, 32°, 35°, 37°, 38°, 39°, 40° b 2 days4 a

bc 3 d 8 m2

5 a

b

c 4 d

1 a 2.4 b 2 c because there are noextreme values to affect the mean

2 a b 6 c because there are

no extreme values to affect the mean3 a $5.38 b $4 c because the $20

value has a large effect on the mean

4 a b 4 days c because the

10 value has a large effect on the mean5 a i 70 ii 68 b i 70 ii 75

c psychology6 a mean b median c mean d mean7 a median, the large value (1 700 000) has a

large effect on the mean

1

2 a

b No, there are no extreme values.3

4 a

b yes—a large IQR and range5 a 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9,

10, 11, 11, 13, 20, IQR � 6

Q1 � 3, Q2 � 6, Q3 � 9,

maximum � 32, IQR � 17Q3 � 21,minimum � 1, Q1 � 4, Q2 � 11,

maximum � 1.9, IQR � 0.6minimum � 0.8, Q1 � 1.0, Q2 � 1.1, Q3 � 1.6,

maximum � 82, IQR � 8.5Q3 � 78.5,minimum � 67, Q1 � 70, Q2 � 74.5,

IQR � 7maximum � 12,Q3 � 9,Q2 � 6,Q1 � 2,minimum � 1,

1CExercise

4 23

days

6 23

hours

1BExercise

824

�13

2024

1824

,1724

,1624

,1524

,1424

,1224

,

1724

1824

,1224

,1424

,1524

,2024

,1624

,

20 m2, 21 m2, 22 m2, 25 m2, 28 m220 m2, 21 m2, 28 m2, 22 m2, 25 m2

1AExerciseb 0.5, 0.9, 1.2, 1.4, 1.5, 1.6, 1.7, 1.8, 1.8, 2.1,

3.2, 3.4, 3.9, 4.3, 5.3, 5.4,

c 25, 26, 35, 42, 43, 43, 43, 44, 44, 47, 47, 47,48, 48, 51, 61,

d 0.01, 0.01, 0.01, 0.02, 0.02, 0.03, 0.04, 0.04,0.05, 0.05, 0.07,

1 a 7, 8, 10, 11, 12, 14, 15, 17, 18, 21, 26, 27, 32,41 b

c

d The top 25% of sales are over 26 shirts perday.

2 a 1, 1, 2, 3, 4, 5, 5, 6, 7, 8, 9b

c

d The bottom 25% of sales are below twomotor cycles per day.

3 ab

c Middle 50% are between 28 and 62.4 a

b

c Middle 50% are between 4 and 9.5 a

b

c Middle 50% are between 12 and 23.5.6 a

b

c Bottom 25% are below 8.5.7 a i

6 15 18119

Q1 � 9, Q2 � 11, Q3 � 15

6 16 22118.5

Q1 � 8.5, median (Q2) � 11, Q3 � 16

8 23.5 3217.512

Q1 � 12, Q2 � 17.5, Q3 � 23.5

2 9 1274

Q1 � 4, Q2 � 7, Q3 � 9

15 624028 85

Q1 � 28, Q2 � 40, Q3 � 62

1 752 9

maximum � 9Q3 � 7,minimum � 1, Q1 � 2, Q2 � 5,

7 2611 16 41

Q3 � 26, maximum � 41minimum � 7, Q1 � 11, Q2 � 16,

1DExercise

Q3 � 0.05, IQR � 0.04Q1 � 0.01, Q2 � 0.03,

Q3 � 47.5, IQR � 5Q1 � 42.5, Q2 � 44,

Q2 � 1.8, Q3 � 3.65, IQR � 2.2Q1 � 1.45,

9780521681780ans_p378-408.qxd 06/20/2007 03:23 PM Page 378 pinnacle 204:CUAT071:ans:

SAMPLE

Uncorrected Sample Pages • Cambridge University Press • © Greenwood, Robertson and Del Porto

An

swers

Answers 379

ii

iii

b year 3 c year 3

1 ab c 24 is an outlier.

2 ab 7.5, 27.5 c 7 is an outlier.

3 a no outliersb 28, 38, 39 are outliers.c no outliersd 0.3, 0.3 are outliers.

4 2 bags—30 and 31 will be checked.5 2 fridges—350 and 1700 are outliers.6 2.1 is unusual (an outlier).

1 a

b 2 is an outlier.c

2 a

b 3.8 and 3.9 are outliers.c

3 a i 8 ii 15 iii 16 iv 19v 24 vi 4 b yes, 8

c

4 a i 1 ii 2 iii 5.5 iv 9v 20 vi 7 b yes, 20

c

1195.51 220

19

*

1916148

*

1524

2.61.6 2.02.2 2.7 3.9

3.8

* *

maximum � 3.9, IQR � 0.6Q3 � 2.6,minimum � 1.6, Q1 � 2.0, Q2 � 2.2,

82 18139 10

*

maximum � 18, IQR � 4minimum � 2, Q1 � 9, Q2 � 10, Q3 � 13,

1FExercise

IQR � 0.3;IQR � 0.55,IQR � 1;IQR � 6,

Q1 � 15, Q3 � 20, IQR � 5�3, 21Q1 � 6, Q3 � 12, IQR � 6

1EExercise

9 17.5 2514.511

Q1 � 11, Q2 � 14.5, Q3 � 17.51 14 228.53

Q1 � 3, Q2 � 8.5, Q3 � 14 5 a 2 and 29 are outliers.b

c 94.5

Multiple-choice questions

1 D 2 C 3 B 4 D 5 A6 B 7 B 8 C 9 A 10 E

Short-answer questions

1 a 4, 6, 9 b 3.5, 5, 8.5 c 3.5, 5, 7.5

2 a 5, 6 b 57 c 1.6, 1.2

3 a 27 b 28, 38, 394 a 41, 47, 49, 51, 53, 55, 62, 64

b lightest 41, heaviest 64 c 23 kg5 a 26, 29, 32, 32, 33, 37, 38, 40, 41, 43, 48,

76, 87 b 43.23 c 38d because the mean is affected by the high ages

of 76 and 876 a

bc

Extended-response questions

1 a $25, $30, $50, $60, $80, $80, $80, $100,$120, $130, $150, $160, $200, $260, $300

bc

d The top 25% of profits were above $160.2 a 2, 8, 10, 10, 11, 12, 12, 13, 13, 15, 24;

b c 2, 24d

*outliers

1 a 240 km b 3 hours c 360 km2 a 360 km b 4 hours c 540 km3 a 300 deer b 100 deer c 200 deer4 a 1800 people b 450 people

c 1350 people5 a i $10 000 ii $40 000

b increased c $30 000

2AExercise

2 8 10 13 15 24

**

12

IQR � 3Q1 � 10, Q2 � 12, Q3 � 13

25 16010060 300

Q1 � $60, Q2 � $100, Q3 � $160

IQR � 10Q1 � 6, Q2 � 14, Q3 � 16minimum � 2, maximum � 23

28 13

,

15.52 7 11 19 22 29

**

13.5


SAMPLE


An

swer

s


6 a i 50 cm ii 45 kgb i 10 ii 3

7 a decrease b 300 kg c 50 kg8 a

b

1 a 80 cm b 50 cm c approx. 2 a 400 m b approx. 250 m

c approx.

3 a $10 000 b $0 c 12 years4 a 200 g b 200 g

c (2 hours 15 min)

5 a 75 cents b approx. 60 centsc approx. $2 d $2.40 US e $0.07

6 a (30 min) b i 1 pm

ii approx. 1:20 pm iii approx. 1:10 pmiv approx. 1:30 pm c iii approx. iii approx. d i 0 m ii iiie i 12:45 pm ii 1:15 pm iii 2:05 pm

7 a

140

0 2.000.50 1.00Cost ($)

Lol

lies

(g)

100

60

20

1.50

�360 m�160 m�52 m�80 m

�120 m

12

hour

2 14

hours

3 12

days

2 14

months

2BExercise

2.0

1.5

1.0

0 2515 20Employees

Pro

fit (

mil

lion

s $) 2.5

25

0 21Time (hours)

Dis

tanc

e (k

m)

b i approx. 100 g ii approx. 50 giii 85 g c i approx. $0.60 ii $1.10iii approx. $1.50

1 a 20 km b 2 hours c approx. 17 km2 a 200 m b 80 s c i approx. 38 m

ii 75 m iii approx. 150 m3 a i 3 m ii 2 m iii 2 m

b the lawn c i 1.5 m ii approx. 4 miii 6 m

4 a i 10 s ii 17.5 s iii 20 sb phase 3 c i approx. 40 mii approx. 85 m iii approx. 160 m

5 a i 40 kg ii 50 kg iii 80 kg

b c 1st hour

6 a 10 km b 20 km c 27 min d 9 min

1

2

3 a 20 km b 22 minc

20

48

1216

0 2016 244 8 12Time (min)

Dis

tanc

e (k

m)

15

5

10

0 4010 20 30Time (s)

Dis

tanc

e (k

m)

100

50

0 20.5 1 1.5Time (hours)

Dis

tanc

e (k

m)

2DExercise

12

hour

2CExercise


SAMPLE


An

swers

Answers 381

4

5 a i

ii

b i

ii 18 s6

1 a i 60 km ii 60 km/hourb i 60 km/hour ii 0 km/hour

iii 90 km/hour2 a i 15 km ii 15 km/hour

b i 0 km/hour ii 30 km/hour

2EExercise

40

10

20

30

0 1 2Time (hours)

Dis

tanc

e (k

m)

30

61218

0 20 255 10 15Time (s)

Dis

tanc

e (k

m)

24

314

hours

50

2010

3040

0 12 1 2 31

Time (hours)

Dis

tanc

e (k

m)

12 21

2 312 33

4

20

51015

0 54 761 2 3Time (hours)

Dis

tanc

e (k

m) 3 a i 2 L ii 0.5 L

b i 0.2 L/s ii 0.05 L/s iii 0.05 L/s4 a i 1.5 L ii 0.5 L b i 0.15 L/s

ii 0.05 L/s iii 0.15 L/s5 a 3 km b 4 s

c i 0.5 km/min ii 0.75 km/miniii 0.5 km/min iv 0.25 km/min

6 a

b 60 km7

44 s

1 a i 8 s ii 8 s iii 4 sb approx. 8 m/s

2 a i 50 m ii 300 m iii 50 mb 5 m/s

3 a 3 b i 20 m ii 4 m/sc 35 and 40 s

4 a i 100 m ii 900 m b i 50 m/sii 300 m/s c approx. 85 m/s

5 a because the top part of the flask is narrowerb i ii

Time

Hei

ght

0Time

Hei

ght

0

2FExercise

60

102030

0 5 10 15 20 25 30 35 40 45Time (s)

Hei

ght (

m)

5040

60

102030

0 1 32 4 5Time (hours)

Dis

tanc

e (k

m)

4050


SAMPLE


An

swer

s


Date Deposit Withdrawal Balance1 May $3010

3 May $490 $3500

5 May $2300 $1200

17 May $490 $1690

18 May $150 $1540

20 May $50 $1490

25 May $218 $1272

31 May $490 $1762

iii iv

Multiple Choice

1 E 2 C 3 B 4 A 5 E 6 D7 B 8 A 9 A 10 C

Short Answer

1 a 40 km b 2 hours c 60 km2 a i $6000 ii $8000 iii $9000

b i $2000 ii $4000 iii $5000c 10 years

3 a 15 km b 3 hours c i 6 kmii 6 km iii 9 km iv 15 km

d

4

Extended Response

1 a i 30 km ii 10 km/hourb i 20 km/hour ii 0 km/hour

iii 20 km/hour2 a i 2 min ii 1 min iii 2 min

b 750 km c 750 000 m/min

1 a $13 750 b $11250 c no2 $60.88 3 13.43%4 a $342.55 b $2137.51 c 11.68%5 a $7756 b $3878 c $149.156 a food $86.40

recreation $43.20transport $56.16savings $108.00taxation $108.00clothing $51.84

3AExercise

60

20

40

0 155 10Time (s)

Dis

tanc

e (m

)

3 12

hours

Time

Hei

ght

0Time

Hei

ght

0

b $70.20 c 30% d approx. 10%e $810.00

1 a 200 tea bags b 400 tea bags2 daily3 a Mon–Thurs—$87

Fri–Sat—$93.50weekly—$71.43

b weekly4 a 200 mL bottle $0.011 75 500 mL bottle

$0.010 48 b 500 mL bottle c $2.10d $0.25 e cost of packaging

5 $6.406 80 cents7 a 0–15 $40

30 people $3548 people $3273 people $32

b $945 c $19208 a i Tom $37, Peter $180

ii Tom $111, Peter $225b Peter

9 a $248 b $240, 6 containers10 a $15.18 b 100 tech screws, 200

countersunk screws, 300 self-tapping screws

1 a $4.50 b $1.26 credit2 a

May June July August September October$2.40 $3.00 $0.12 $5.00 $2.08 $0.73

b $13.33

3 a

b $4.90 c $1759.55 d wages4 a $1146.57 b $1790.62 c $511.00

d $1146.57 e $132.81 f $233.84g $443.22 h 15.65% i $20.30

3CExercise

3BExercise


SAMPLE


An

swers

Answers 383

Value at the Value at thestart of year Depreciation end of the year

Year 1 $27000 $4050 $22950

Year 2 $22950 $3442.50 $19507.50

Year 3 $19507.50 $2926.13 $16581.38

Year 4 $16581.38 $2487.21 $14094.17

Date Deposit Withdrawal Balance1st 217.63

7th 64.00 153.63

9th 140.00 293.63

11th 117.34 176.29

15th 0.51 175.78

20th 20.00 12.93 182.85

30th 140.00 322.85

5 a $98 822.90 b fee 0.23 c fee $8.00d $2400 e $378.50f $246 025 g $146 025

1 a $1200 b $15 360c $16 560 d $8560

2 a 1705 L b $2148.303 a $1650 b $1024

c city driving d $26744 a $210 b $666.505 a

b $14 094.17 c $12 905.836 a rate 1 b 1667 km


1 E 2 D 3 D 4 A 5 C6 A 7 E 8 D 9 B 10 C


1 a $7400 b $616.67 c $142.312 a $287.32 b $43.10 c 10.79%3 a 500 mL at $5.08 per litre

1 L at $5.20 per litre4 L at $4.10 per litre

b containers and containers

4 a $115, $72.50, $100, $128.57 b weekend5 a $12 325 b approx. 38%6 a $5.50 b $549.857 a $22 200 b $27 200 c $97008 a 3150 L b $3087


1 a

b $153.63 c $0.077

4 � 500 mL2 � 4 L

3DExercise

1 a bc d

2 a no b no c yes d yese no f yes

3 a 25 b 34 c 454 a 2 b 8 c 185 a 4, 2 b 25, 5 c 9, 3

1 a 5 b 17 c 13 d 252 a 5.83 cm b 7.28 mm c 18.03 m

d 11.18 km3 a 8.91 cm b 3.62 m c 5.02 km

d 13.95 mm4 35.3 m 5 13 m 6 5.28 m7 2.64 m 8 494.97 m10 a 100 m b c 103�08 m

1 a 4 b 7 c 8 d 52 a 7.1 m b 13.3 mm c 12.3 cm

d 6.2 km3 a 7.14 mm b 13.90 m c 3.87 cm

d 133.84 mm5 5.66 m 6 2.2 7 19.86 m 8 25.04 m9 a 11.18 m b 12.2 m10 horizontal: 45.25 cm, vertical: 71.66 cm

1 a 10.6 cm b 10.8 cmc 15.8 mm d 4.2 m

2 a 4.77 m b 4.90 cmc 9.37 cm d 14.92 mm

3 a 11.2 m b 8.06 cm4 a 1.41 cm b 1.73 cm5 a 4.2 cm b 3.39 cm6 a i 8.08 m ii 5.41 m iii 8.75 m

iv 9.25 m v 9.25 m b 12.4 m


1 B 2 B 3 C 4 A 5 A6 E 7 E 8 C 9 D 10 E

4DExercise

4CExercise

25 m

100 m

4BExercise

x2 � w2 � y2s2 � r2 � p2t2 � m2 � n2z2 � y2 � x2

4AExercise


SAMPLE


An

swer

s


Radius of spray (m) Area covered (m2)2 m

3 m

4 m 50.27 m2

28.27 m2

12.57 m2


1 no 2 15.17 m 3 4.13 cm4 a 9.5 mm b 17.0 m 5 6.157 m6 4.33 mm 7 6.41 m 8 7.3 cm

Extended Response

1 a 4.2 cm b 5.4 cmc i 2.1 cm ii 4.5 cm

Investigation

1 4 2 yes 3 5 6 doors6 family, meals, living 7 yes 8 4 9 210 tiles 11 timber

1 a 3 m b 5 m c 8 md 0.25 m e 0.70 m f 0.84 mg 12.5 m h 45.6 m i 34.29 mj 3 m k 5 m l 2 mm 0.37 m n 0.29 m o 0.184 mp 35 m q 57.6 m r 87.9 m

2 a 23.4 m b 22 m c 21.8 md 25.4 m

3 a 28.55 m b 15.98 m c 42.00 md 17.50 m e 34.55 m f 33.41 m

4 a 5.7 m b 7.7 m c 4.27 md 4.15 m 5 41.6 m 6 79.2 m

7 b triangles, c they are strong and stable

1 a i b i

ii 30.8 m ii 60 mc i ii 61.6 m

d i e i

ii 69.4 m ii 55.8 mf i ii 52.2 m

2 a 13 m b 13 m c 3 m d 20 m3 a 9.42 m b $423.90

2.5 m8.1 m 10.9 m

12.7 m

13 m

2.7 m 3.9 m2.4 m

12.5 m18.7 m

14.6 m

16 m 4.5 m

16.8 m

14 m3.5 m 4.7 m

15 m

15 m

10.6 m

4.8 m

5BExercise

5AExercise

4.5 m � 4.5 m

4 a 14.4 m b $197.285 a 14.8 m b $162.806 a 11 b $258.507 a i $35.12 ii $44.23 iii $61.14

1 a b $149.602 a b $491.403 a b c

d e f4

5 a b c6 a b $57 967.507 a $199.20 b $439.92 c 2.12 L

1 a b cd e f

2 a b cd 3 4

5 a b $1409.88

1 a b cd 2 3.6 L 3 a 5.116 Lb 10.232 L 4 24.933 L

5 a waterproof 13.76 L, anti-slip 22.86 Lb $553.46 6 a $424


1 C 2 D 3 A 4 E 5 E6 C 7 B 8 C 9 E 10 D


1 a 12.6 m b 27.6 m 2 46.05 m3 48 m4 a

b 69.2 m

19 m

16.6 m1.9 m

2.4 m

13.7 m15.6 m A

B

40.56 m2202 cm2168 m2240 m2

5EExercise

15.16176.8 m3132 m3163.2 m348 m354.6 m363.6 m3138.012 m333.54 m329.4 m362.4 m379.9 m340.7 m3

5DExercise

77.29 m2118.18 m2177.86 m2252.05 m2

8.3 m23.1 m239.3 m232.2 m250.3 m212.6 m2

7.56 m213.6 m2

5CExercise


SAMPLE


An

swers

Answers 385

5 a 28.90 m b 9.90 m 67 a b8 a b


1 a 61.2 m b i ii $514.08c d 48.96 L

1 a

bi $300 ii 4.5 hours

2 a

b i $20 ii 2.5 litres3 a

b

c i $450 ii 450 km4 a

100

300

500

700

300km

Cos

t ($)

1000 500

16243240

3Capacity (L)

Cos

t ($)

8

210 4 5

240280320

400

3Hours (n)

Cos

t ($)

200

360

210 4 5

6AExercise

24.48m230.24 m2

204 m3660 m34.54 m232.17 m2

96 m2 b

c i $65.60 ii 186 a

Paul

Sherry

b

c i $250 ii $150 iii 0.5 hoursiv 4.25 hours v 1.5 hours

d Paul is cheaper only for 1.5 hours or less.7 a

b

c 9:00 am d 7 hours e 8 hoursf 4 pm

100200300

800

3Hours

km f

rom

Moo

rban

k

400500600700

210 4 5 6 7 8

200300400500

3Hours

Cos

t ($)

100

210 54

39587796

15Deliveries

Cos

t ($)

20

1050 20

No. of km (k) 100 200 300 400 500

Cost (C) 300 400 500 600 700

No. of deliveries (d) 0 5 10 15 20Cost (C) 20 39 58 77 96

No. of hours work 0 1 2 3 4 5

Cost (C) 75 125 175 225 275 325

No. of hours work 0 1 2 3 4 5

Cost (C) 90 130 170 210 250 290

Time in hours (t ) 0 1 2 3 4 5 6 7 8

km fromMoorbank 720 630 540 450 360 270 180 90 0


SAMPLE


An

swer

s


1 a 1 b c

2 a b c

3 a 2 b 5 c d

e f 0 g 0 h undefined

i undefined

4 AB CD 1, EF GH

5

6 a 3 b 2 c

d e 0 f undefined

7 a 2 b c

d e 1 f

8 a 1 b 1 c d 0

e 11 f

10 a A, D b C, E, G c Dd B, F, H e A

1 a i 2 ii (0, 4) b i 6 ii

c i ii (0, 7) d i ii

e i ii f i 9, ii (0, �5)(0, �8)35

(0, �3)�7�23

(0, �7)

6CExercise

13

�35

�25

�2

�112

�1

�12

23

23

,32

,

43

�2�3

�31

15�

38

m

�35

14

6BExercise2a b

c d

e f

3a b

c d

y

x0

(0, 4)

y

x0

(0, 0)

(2, −4)

y

x0

(0, 0)

(1, 6)

y

x0

(0, 0)

(2, 6)

y

x0

(−4, 0)

(1, −5)(0, −4)

y

x0

(−2, 3)

(1, −12)(0, −7)

y

x0

(5, −5)

(1, 3)

(0, 5)

y

x0

(−4, 0)(0, 4)

(1, 5)

y

x0

(4, 0)

(0, −12)(1, −9)

y

x0

(1, 5)

(0, 3)

Line segment Rise Run Gradient

AB 1 2

AC 2 4

AD 3 6

BC 1 2

BD 2 4

CD 1 212

12

12

12

12

12


SAMPLE


An

swers

Answers 387

e f

g h

i

4 a bc de f

5 a 1, (0, 0) b (0, 3)c 0.5, (0, 4.5) d 0, (0, 4)e 0, (0, 7) f undefined, none

6 a iv b ii c v d ie vi f vii g iii h viii i ix

1a b

y

x0 (6, 0)

(0, 2)

y

x0

(2, 0)

(0, 3)

6DExercise

�1.5,y � �2xy � �4x � 3y � �3x � 5y � 5xy � 3x � 2y � 4x � 2

y

x0

(9, 0)

y

x0

(−2, 0)

y

x0

(5, 0)

y

x0

(0, 5)

y

x0

(0, −2)

c d

e f

g h

i

2a b

y

x0

(0, −2)

( , 0)23

y

x0(0, 1)(− , 0)1

2

y

x0

(0, 24)

(4, 0)

y

x0

(−18, 0)

(0, −10)

y

x0

(−8, 0)

(0, −4)

y

x0(−3, 0)

(0, 1)

y

x0(−7, 0)

(0, 2)

y

x0

(0, −10)

(4, 0)

y

x0

(0, −3)

(4, 0)


SAMPLE


An

swer

s


c d

e f

3 a iii b ii c i4 a ii b iii c i5 a vi b ii c i d v e iv f iii6 a b 0.2 c 2 d 0.57 a i (2, 0), ii

b i (0, 2) iic i iid i (0, 2) ii

1 a i b iii (0, 1) ii (0, 2)iii iii

c i d iii ii (0, 0)iii iii

e i f iii (0, 2) ii (0, 0)iii iii

2 a i 3 ii (0, 1) iiib i ii (0, 6) iiic i 5 ii (0, 21) iiid i 3 ii iiie i ii (0, 2) iii

f i ii iii

3 a b cd e f

4 a b c y �23

xy � 3xy � 2x

x � 7y � 2x � �2x � 3y � �1y � 4

y �12

x �32

a0, 32b1

2

y � �3x � 2�3y � 3x � 16(0, �16)y � 5x � 21y � �x � 6�1y � 3x � 1

y � 2xy � �x � 2

m � 2m � �1y � �4xy � 4x � 3

(0, �3)m � �4m � 4y � �3x � 2y � 2x � 1

m � �3m � 2

6EExercise

A � 4(�4, 0),A � 2.25(�1.5, 0), (0, �3)A � 2(�2, 0),A � 4(0, �4)

�2

y

x0

(0, −3)

(2, 0)

y

x0

(0, 1) (2, 0)

y

x0

(0, 2)(2, 0)

y

x0(0, −3)

(− , 0)34

d e f

5 a i 7 ii

b i ii

c i 1 ii

d i ii

e i 0 iif i undefined,

7 a

The lines are parallel.b

The lines intersect at

1 ab

c i $28 ii 23.5 kg

30

20

10

0 105

C

n

C � 2n � 10

6FExercise

(0, �1).

y

x0

y =

3x −

1y

= 2x

− 1

y = x

− 1

y = x − 134

y = x − 112

y

x0

y = 2x + 4y = 2x + 1y = 2xy = 2x − 2y = 2x − 3

x � 3y � 2

y � �32

x�32

y � x � 2

y � �32

x�32

y � 7x

y � �25

xy � �xy � �3x


SAMPLE


An

swers

Answers 389

2 ab

c i $820 ii 10 hours3 a

b

c i 87 kg ii 29 litres4 a (0, 1000)

b

c 1000 litresd i 360 litres ii 952 litres iii 664 litrese i 350 hours ii 407.5 hours

5 a (0, 5500)b

c $5500d i $3500 ii $4800 iii $2500e i 45 days ii 55 days

6 a

5500

0 55days

m

t

�100,

1000

0 500

w

t

�2,

10080

0 20

w

l

W � l � 80

1000

1000 15

hours

C

t

C � 60t � 100 b

c i $2100 ii $1400 iii $7250iv $8750

d Mandy’s is best for amounts Terry’sis equal to Lenny’s for $5000, but never thebest; Lenny’s is best for amounts � $5000


1 D 2 E 3 C 4 A 5 B 6 C7 D 8 D 9 E 10 A


1 a

b

c i $70 ii 17

2 a 1 b �1 c d

3 ab gradient � �2, y � intercept � (0, 0)

gradient � 3, y � intercept � (0, 4)

13

�2

110

100 20

C

d

� $5000;

1100013000

100030005000

0 10002000

30004000

50006000

7000

MM

TTLL

80009000

Parts (p)

Cos

t (C

) 90007000

p 0 1000 2000 3000 4000 5000 6000 7000 8000 9000MM 0 1400 2800 4200 5600 7000 8400 9800 11200 12600

TT 3000 3700 4400 5100 5800 6500 7200 7900 8600 9300

LL 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500

d 0 5 10 15 20C 10 35 60 85 110


SAMPLE


An

swer

s


4a b

c d

5a b

c

6 a i 2 ii (0, 0) iiib i ii (0, 16) iii

7 a i b iii c vi d ii e iv f v8 a

b

c i $130 ii 5.5 bins

170

50

0 6

E

n

E � 20n � 50

y � �4x � 16�4y � 2x

y

x0

(3, 0)

(0, −9)

y

x0 (3, 0)

(0, −6)

y

x0

(0, 3)

(4, 0)

y

x0(−1, 0)

y

x0

(0, 2)

y

x0

(0, 0)

(1, −4)

y

x0

(0, 3)

(1, 5)


1 a i 440 km ii 280 kmb i

ii

c i 160 km ii 2.25 hours

1 a i ii iii b i

2 a i ii iii b i

3 a i ii 0.5

b i ii 0.2

c i 0 ii 0

d i ii 0.9

e i 1 ii 1

f i ii 0.167

4 a b c d 1 e f

5 a b c d 1 e f

6 a b c d

7 a b c d e

9 a b c d e f 1

g h i

1 a i ii

iii iv

v vi4950

� 0.98 � 98%9

10� 0.9 � 90%

150

� 0.02 � 2%2

25� 0.08 � 8%

110

� 0.1 � 10%45

� 0.8 � 80%

7BExercise

713

413

12

213

12

126

14

113

13

16

110

12

130

12

12

14

13

38

12

12

12

18

13

712

712

512

112

16

910

15

12

16

18

14

15

14

13

7AExercise

520

0 6.5

D

t

D � �80t � 520


SAMPLE


An

swers

Answers 391

2 a i ii

iii iv

v vi

vii99

100� 0.99 � 99%

910

� 0.9 � 90%1

100� 0.01 � 1%

125

� 0.04 � 4%1

20� 0.05 � 5%

310

� 0.3 � 30%35

� 0.6 � 60% 3 a i ii

iii b yes

4 a

b i 0.04 ii 0.92 iii 0.96

120

� 0.05

15

� 0.2 � 20%1520

� 0.75 � 75%

No. of faults 0 1 2 3 4 5 Total

No. of items 35 8 3 2 1 1 50

Probability 0.7 0.16 0.06 0.04 0.02 0.02 1

No. of mistakes 0 1 2 3 4 5 6 7 8 9 10 Total

No. of essays 0 5 8 10 5 4 2 1 0 4 1 40

Probability 0 0.125 0.2 0.25 0.125 0.1 0.05 0.025 0 0.1 0.025 1

No. of faults 0 1 2 3 Total

Probability 0.5 0.2 0.2 0.1 1


Probability 0.4 0.3 0.2 0.1 1


Probability 0.4 0.2 0.0 0.4 1

5 a

b i 0.125 ii 0.125 iii 0.8 iv 0.4256 a Probability of faults is 0.7.

b Probability of faults is 0.7.

c Probability of faults is 0.6.

1 a b 30

2 a b 500

3 a b

c d

4 a i ii

iii iv

b Packaging Inc., because it has fewer faultsc 200

5 a b 1875

6 a b 506

120� 0.05

1580

� 0.1875

120

� 0.05150

� 0.02

125

� 0.043

100� 0.03

140

� 0.0259

200� 0.045

18

� 0.12515

� 0.20

120

� 0.05

3100

� 0.03

7CExercise

� 2

� 2

� 2

Results will vary.


1 C 2 E 3 A 4 B 5 C 6 B7 A 8 C 9 E 10 D


1 a i ii iii b i

2 a b c d e f

3 a b

c d

e f

4 a 0.08 b 80

5 a b 100


1 a b

1 supplemeantry, alternate,corresponding, vertically

opposite2 corresponding, alternate,

corresponding, verticallyopposite

d � 80°c � 80°b � 100°a � 100°

d � 160°c � 160°b � 20°a � 20°

8AExercise

16

15

130

99100

� 0.99 � 99%1920

� 0.95 � 95%

1100

� 0.01 � 1%125

� 0.04 � 4%

110

� 0.1 � 10%1720

� 0.85 � 85%

713

152

213

12

1213

113

16

110

13

7DExercise


SAMPLE


An

swer

s


3 a , b ,c , d ,

4 a b c de f

5 a , ,b , ,c , ,d , ,e ,f ,

6 a (a, d), (e, f ), ( f, g), (g, h), (c, b), (a, b), (c, d),(e, h) b (a, e), (d, f ), (b, h), (c, g)

c (d, h), (c, e) d (c, h), (d, e)e (a, c), (b, d), (e, g), (f, h)

7 a ° b ° c ° d ° e ° f °9 a 12 b 16 c 40

1 a bc d

2 a bc d

3 a b c4 a scalene b isosceles

c equilateral d isoscelese equilateral f scalene

5 a bc def

6 a b7 a i ii

b i iic i ii

1 a °b z � 70y � 110,x � 110,

x � 20

8CExercise

180°0°160°20°130°50°115°65

d � 40°c � 40°,b � 100°,a � 40°,d � 20°c � 45°, b � 115°,a � 115°,

b � 105°a � 35°,b � 70°a � 70°,a � 120°a � 7017,2567,60,80,25,

6030302040806558251070

8BExercise

303630107590

b � 120°a � 110°b � 130°a � 90°

c � 50°b � 130°a � 50°c � 135°b � 45°a � 135°

c � 90°b � 90°a � 90°c � 90°b � 90°a � 90°

30°50°115°100°20°60°

y � 120°x � 120°y � 105°x � 75°y � 140°x � 40°y � 110°x � 110° c

d e f2 a square, rectangle, rhombus, parallelogram

b rectangle, square, parallelogram, rhombusc rhombus, square, parallelogramd trapezium, e kite, f square, rectangle

3 abcdef

4 a It has two equal side lengths.b i iic It has two equal side lengths and two pairs of

equal angles and one pair of parallel sides.5 a

bcdef

6 b7 iii a same length, b same length, c not

same length, d not same length, e notsame length, f not same length,

iv a always b not c always d not e not f always

1 a 24 cm b c2 a 28 cm b c3 a b4 a b5 a b

c6 a b7 a b 25272

240°120°y � 225x � 45,

y � 60x � 60,y � 72x � 108,165.614432401620

1351080120720

8DExercise

9090,90,90,90,90,

65b � 80a � 10,b � 20a � 60,c � 70b � 50,

d � 110c � 50,b � 20,a � 40,d � 50c � 80,b � 100,a � 80,

e � 30d � 60,c � 60,b � 120,a � 30,

40120

y � 30x � 50,z � 30y � 140,x � 20,z � 30y � 22.5,x � 90,z � 80y � 100,x � 100,

y � 130x � 50,y � 80x � 120,

x � 25x � 30x � 125z � 30y � 150,x � 30,

Total angle Single internalPolygon No. of sides Diagram No. of triangles sum (s) angle (A)

Triangle 3 1

Quadrilateral 4 2

Pentagon 5 3

Hexagon 6 4

...

n-gon n180(n � 2)

n180 � (n � 2)n � 2

120720

108540

90360

60180

8 a


SAMPLE


An

swers

Answers 393

b i For a polygon with n sides the total anglesum S is given by

ii For a polygon with n sides a single internal

angle A is given by

1 a 4 b 1 c 02 a 6 b 1 c 23 a yes b no c yes4 a i 0 ii 1 iii no

b i 1 ii 1 iii noc i 3 ii 3 iii no

5 a b

c

6 a i 4 ii 4 iii yesb i 2 ii 2 iii yesc i 2 ii 2 iii yesd i 0 ii 2 iii yese i 0 ii 1 iii nof i 1 ii 1 iii no

7 a line, rotational point b line, rotational8 a i yes ii no iii yes

b i yes ii no iii yesc i yes ii yes iii nod i yes ii no iii noe i no ii yes iii yesf i no ii yes iii yes

9 a i ii

iii iv

b i y

x0

8EExercise

A �180(n � 2)

n.

S � 180(n � 2).ii iii

1 a ° b ° c °2 a ° b ° c °3 a ° b ° c °4 a

bc

56 a 2 b 2 c 2

d ° e ° f °7 a ° b ° c °

d ° e °8 a i 2 ii 2

b i 9 ii 3


1 B 2 A 3 D 4 C 5 E 6 B 7 E8 B 9 E 10 B


1 a bc de f

2 a ° b ° c °d ° e ° f °

3 a square, rectangle, rhombus, parallelogramb parallelogram, square, rhombus, rectanglec kite

4 a bc de f

5 a 10m b ° c °6 a i 3 ii 3 iii no

b i 1 ii 1 iii noc i 6 ii 6 iii yes

7 a ° b ° c °d ° e ° f °


1 a i 20° ii ° iii °iv ° v ° vi °

b i ° ii ° iii °iv ° v ° vi °

c The angle ABC is always twice the angle AOC.160808050120301206010040140

301060502045

108540a � 110b � 140a � 40,

b � 130a � 90,b � 30a � 110,a � 10a � 90

306020773020

x � 45y � 120x � 90,y � 150x � 30,y � 115x � 65,y � 120x � 120,y � 110x � 70,

122.567.567.522.5135255530

215c � 40b � 50,a � 90,c � 120b � 30,a � 60,

e � 120d � 30,c � 60,b � 60,a � 60,755860204370154530

8FExercise

y

x0

y

x0


SAMPLE


An

swer

s


1 b increases 2 b decreases 3 a ii increases b increases c ii decreases4 b D c yes5 a i 2174 ii 436

c As the number of photos increases, thenumber of words decreases.

1 a none b positive c negative d positive2 a ii none b ii positive3 a negative b positive c none4 b negative c decreases

1 b negative c (14, 4)2 b positive c (8, 1.0)3 a (3, 1) b (0.4, 100) c (5, 2) d (10, 1)4 b positive c (160, 10)5 a (8, 1) b (8, 20) c (3, 11)6 a b yes, positive

c

1 a 0.5 m b 7.5 m c 5 m d 50 m2 b positive d i 3.5 ii 1 iii 0.5 iv 83 b negative d i 13.5 ii 23 iii 9 iv 74 a iii 4 iv 11,

b iii 16 or 17 iv 5 or 5.55 c i 30 m ii 47 m iii 1.4 m iv 0.7 m

1 b i 350 ii 600 c i 13 ii 22 b i $450 ii $150 c i 2 ii 123 a increases c i 60 ii 15 degrees4 c i 25 cm ii 60 cm

d i 600 mm ii 700 mm5 b i 130 ii 140 c i 16 ii 22

d experiment 2


1 C 2 B 3 C 4 A 5 D6 D 7 A 8 E 9 A 10 D

9FExercise

9EExercise

(l � 12, w � 2.7), (l � 32, w � 4.1)

9DExercise

9CExercise

9AExercise Short-answer questions

1 b increases2 a negative b none c positive3 b negative c (34, 39) 4 2 m


1 b i 80 ii 150 iii 240c i 7 ii 16 iii 27

1 a i AC ii BC iii ABb i BC ii AB iii ACc i BC ii AB iii ACd i AC ii BC iii ABe i AB ii AC iii BCf i BC ii AB iii AC

2 a 0.17 b 0.64 c 0.87 d 0.94 e 0.77f 0.17 g 0.09 h 1.19 i 3.73 j 0.53k 0.95 l 1.96

3 a 0.87 b 0.71 c 0.26 d 0.644 a i 0.5, 0.87 ii 0.58

b i 0.97, 0.22 ii 4.33c i 0.93, 0.36 ii 2.61

5 a 0.5 m b 0.87 m6 a 0.68 b 0.35 c 1.738 a i 0.17, 0.17 ii 0.5, 0.5,

b They are the same.c They are complementary (add up to 90).d i ii

1 a b cd e f

2 a 2.11 b 4.01 c 1.883 a 5.36 b 1.27 c 0.524 a 5.49 b 8.51 c 9.235 a 3.76 b 2.12 c 2.80

d 4.94 e 4.14 f 0.756 a b

c7 a i 2.11 cm ii 4.53

b i 4.60 cm ii 1.95 cm9 1.5 cm

1 a 8.77 b 9.44 c 8.492 a 4.62 b 23.39 c 2.86

10CExercise

w � 2.57, l � 3.06w � 0.68, l � 1.88w � 1.27, l � 2.72

cos �cos �tan �tan �sin �sin �

10BExercise

cos40� � sin50�sin20� � cos70�

10AExercise


SAMPLE


An

swers

Answers 395

3 a 5.96 b 1.62 c 1.724 a 4.73 b 6.19 c 6.14

d 3.00 e 26.08 f 27.825 a

bc

6 a 7.464 m b 7.727 m7 a 30.5 m b 17.5 m9 a b 4.80 c 4.80

d either or

1 7.97 m 2 1 m 3 1.85 m4 3.06 m 5 a 1.95 m b 0.436 26.29 cm 7 7.54 m 8 66.74 m9 10 10 m12 4.70 cm 13

1 a b c2 a b c3 a b c4 a b c

d e f5 a b c

d e f6 a b

c de

7 a b

1 536.29 m 2 38.97 m 34 5 67 8 8.72 mm 9 280.04 m10 a b c 1.712 a i 500 m ii 600 m

b i 66 m ii 63 m iii 3 m c Peak A


1 B 2 C 3 E 4 C 5 D6 E 7 A 8 D 9 C 10 B


1 a i BC ii AB iii ACb i AC ii AB iii BC

60�30�25.84�

4.27�48.30�47.10�5.71�

10FExercise

36.87�46.66�21.8�68.2�,

63.4�26.6�,36.9�, 53.1�55.2�34.8�,53.1�36.9�,

15.1�53.1�47.7�32.7�58.6�30�68.20�53.13�48.59�64.16�45�60�83.29�36.87�63.43�63.61�53.13�60�22.02�30�19.47�

10EExercise

AB � 64.01 mx � 5.87 cm, y � 9.14 cm

10DExercise

cos �sin �30�

AB � 14.62, BC � 13.74AB � 5.32 m, BC � 1.82 mAB � 42.89 cm, BC � 20 cm

2 a 0.57 b 0.96 c 8.143 a 4.50 b 1.5 c 0.934 a 6.31 b 12.94 c 4.165 a 3.63 m b 1.69 m 6 567.13 m7 a b c8 a b 42.4 m


1 a b 130.25 m c 187 m

1 a $617.11 b $353.852 a $566.83 b $631.40 c $774.90

d $861.003 a $157.80 b $452.164 a $1186.24 b $30 842.24 c 2570.195 $878.40 6 $3437.50 7 3% 8 $365.709 a nil b $600 c $2100

d $6360 e $15 270 f $7095g $635.25 h $10 149.60

10 a $11 580 b i $3401.67 ii $785iii $1570 c $1572

1 a $6 b 60.00%2 a $41 b 65.85%3 a $123 b 70.73%4 a $2.20 b 122.22%

c $66 d 122.22%5 a $58.86 b $381.506 a $1225 b $24.507 a $2140.25 b $305.758 $11.99 9 $147.6010 a $84.13 b $94.8711 $104.71 12 a $106.15 b $148.6213 a $1952.24 b $211.24 c 12.13%

1 a $6650 b $184.72 per month2 a $5192.25 b $16 692.25 c $198.723 $1008 4 a $228 b $684 c $46845 16% 6 12.57 $66 666.67 8 $75009 a $1250, $2500 b $18 28.13, $1920.00

c $217.97, $331.11

11CExercise

11BExercise

11AExercise

54.46�

45�72.26�59.00�48.19�


SAMPLE


An

swer

s


4 a Principal Rate Overall Time Interest Amount$7000 5% 5 years $1750 $8750

$7000 10% 5 years $3500 $10 500

$3300 10% 3 years $990 $4290

$8000 10% 3 years $2400 $10 400

$9000 8% 2 years $1440 $10 440

$18 000 8% 2 years $2880 $20 880

5

5 $4200 6 $576.927 a $1050 b $12 000 c $60508 a $1600 b $1166.67 c $624.32

d $1071.77 e $636.70


1 a 15% p.a. simple interestb 15% p.a. simple interestc 15% p.a. simple interestd 10% p.a. compounded annually

6 a 8.45% b 8.19% c $8.12%7 a 4.2% b 8.66%


1 C 2 B 3 E 4 B 5 C6 D 7 C 8 B 9 C 10 E


1 a $346.68 b $290.65 2 $10 212.603 $35.55 4 a $11.40 b $3.80

b i interest is doubled ii no change iii interest is doubled

Principal Rate Period Overall Time Interest Amount$7000 4.56% annually 5 years $1750 $8750

$7000 8.45% annually 5 years $ 3500 $10 500

$9000 8% fortnightly 2 years $1559.00 $10 559.00

$18 000 8% fortnightly 2 years $ 3118.01 $21118.01

1 a $5973.17 b $11946.33 c $13 652.22d $9550.63

2 a $106 000 b $112 360 c $119 101.6d $133 822.56 e $179 084.77 f $239 655.82

3 $262 777.374 a 6, 3% b 60, 1%

c 52, 0.173% d 182, 0.202%5 a

bR � 30%, T � 2 yearsP � 5000, n � 24, r � 2.5%,R � 14%, T � 6 yearsP � 300, n � 12, r � 7%,

11DExercisec

d

e

6 $11 651.927 a $5075 b $5228.39 c $5386.428 a i $3239.42 ii $3348.15 iii $3446.15

iv $3461.88 v $3465.96 b $226.549 5.3% compounded bi-annually10 a i approx. 6 years ii approx. 12 years

iii approx. 9 years iv approx. 5 yearsv approx. 7 years vi approx. 4 years

b same as a i, ii c yes

R � 7.8%, T � 10 yearsP � 10 000, n � 10, r � 7.8%,R � 1.93%, T � 30 daysP � 3500, n � 30, r � 0.0053%,R � 0.936%, T � 2.5 yearsP � 1000, n � 65, r � 0.036%,

1 a i $7146.10 ii $6955.64 iii $6858.57iv $7260 v $7916.37

b $6000 at 5.7% p.a. for 5 years2 a i $7080 ii $7080 iii $7428

iv $7200 v $7710b $6000 at 5.7% p.a. for 5 years

11EExercise

3 a i I $240, $240 II $480, $494.40III $1200, $1352.90 IV $2400, $3163.39ii I $240, $243.60 II $480, $502.04III $1200, $1375.67 IV $2400, $3224.44iii I $240, $246.71 II $480, $508.64III $1200, $1395.40 IV $2400, $3277.59

b Compound interest c Compound interest


SAMPLE


An

swers

Answers 397

1 2 3 41 (1, 1) (1, 2) (1, 3) (1, 4)

2 (2, 1) (2, 2) (2, 3) (2, 4)

3 (3, 1) (3, 2) (3, 3) (3, 4)

4 (4, 1) (4, 2) (4, 3) (4, 4)

b 36 c i 2 ii 6 iii 15

d i ii

iii

iv

e She was not correct, Pr(at least 10) �16

Pr(at least 11) �1

12

Pr( � 2) �3536

Pr( � 5) �16

Pr(7) �16

1 2 3 4 5 61 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

b 9 c i ii iii iv

4 a

29

29

49

19

R B BR (R, R) (R, B) (R, B)

B (B, R) (B, B) (B, B)

B (B, R) (B, B) (B, B)

b 9 c

d

3 a

Pr(double) �13

Pr(1, 3) �19

1 2 31 (1, 1) (1, 2) (1, 3)

2 (2, 1) (2, 2) (2, 3)

3 (3, 1) (3, 2) (3, 3)

b 16 c

d

2 a

Pr(double) �14

Pr(2, 4) �116

1 2 3 41 (1, 1) (1, 2) (1, 3) (1, 4)

2 (2, 1) (2, 2) (2, 3) (2, 4)

3 (3, 1) (3, 2) (3, 3) (3, 4)

4 (4, 1) (4, 2) (4, 3) (4, 4)

Red (R) Blue (B) Yellow (Y)White (W) (W, R) (W, B) (W, Y)

White (W) (W, R) (W, B) (W, Y)

Red (R) (R, R) (R, B) (R, Y)

Blue (B) (B, R) (B, B) (B, Y)

b i 1 ii 2 iii 1c i 25% ii 50% iii 25%

5 a

b 16 c i 4 ii 6 iii 44 a

1 a

12BExercise

1 a

b 12 c 112 a

b 16 c 143 a

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , ) ( , ) ( , ) ( , )

( , )A

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

12AExercise

H TH (H, H) (H, T)

T (T, H) (T, T)

L E V E LL (L, L) (L, E) (L, V) (L, E) (L, L)

E (E, L) (E, E) (E, V) (E, E) (E, L)

V (V, L) (V, E) (V, V) (V, E) (V, L)

E (E, L) (E, E) (E, V) (E, E) (E, L)

L (L, L) (L, E) (L, V) (L, E) (L, L)b 25 c i 9 ii 16 iii 12

iv 24 v 17 a

b 12 c 2 d 7


SAMPLE


An

swer

s


5 a outcomes: 1-1, 1-2, 1-3, 1-4, 2-1, 2-2, 2-3, 2-4, 3-1, 3-2, 3-3, 3-4, 4-1, 4-2, 4-3, 4-4

b 16 c i ii d i

ii iii iv v

6 a outcomes: 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5,6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11,

7, 8, 9, 10, 11, 12 b i ii

iii iv

7 a outcomes: (A, E), (A, F), (A, G), (B, E), (B, F), (B, G), (C, E), (C, F), (C, G), (D, E),

(D, F) (D, G) b i ii

iii c

8 a i 8 ii 16 iii 32 b 1024c

1 a b c outcomes:

d e

2 a outcomes:

b i ii iii iv c

3 a outcomes:

b i ii

iii iv

4 a outcomes: (15,16, 25, 26)

b i ii iii c 2 d

5 a outcomes:

b 6 c i ii iii d12

14

16

112

16

, (B, G) �16

, (C, P) �14

, (C, G) �112

(A, P) �112

, (A, G) �14

, (B, P) �

59

49

29

29

12

13

13

16

W boat) �13

W boat) �13

, (W doll, P boat) �16

, (W doll,

(P doll, P boat) �16

, (P doll,

12

18

38

38

18

(B, yellow) �38

, (B, orange) �18

(A, yellow) �18

, (A, orange) �38

,

38

18

(A, purple) �14

, (B, blue) �18

, (B, purple) �38

(A, blue) �14

,14

12

12DExercise

63 � 216

13

14

112

112

512

16

136

136

58

316

14

18

116

14

116

b 16 c i 1 ii 8 iii 8

d i ii iii iv e

1 a outcomes: HH, HT, TH, TT b 4

c i ii iii

2 a outcomes: HHHH, HHHT, HHTH, HHTT,HTHH, HTHT, HTTH, HTTT, THHH, THHT,THTH, THTT, TTHH, TTHT, TTTH, TTTT

b 16 c i ii iii

3 a outcomes: TTT, TTF, TFT, TFF, FTT, FTF,FFT, FFF b 8

c i ii iii iv

4 a outcomes: 2, 3, 4, 3, 4, 5, 4, 5, 6,

b 9 c i ii iii iv23

13

13

19

78

38

14

18

1116

18

116

34

12

14

12CExercise

716

316

14

18

116

2.5 kg 5 kg 10 kg 20 kg2.5 kg 5 7.5 12.5 22.5

5 kg 7.5 10 15 25

10 kg 12.5 15 20 30

20 kg 22.5 25 30 40

b 21 c

7 a

Pr(double) �17

O L DC (C, O) (C, L) (C, D)

O (O, O) (O, L) (O, D)

L (L, O) (L, L) (L, D)

L (L, O) (L, L) (L, D)

E (E, O) (E, L) (E, D)

G (G, O) (G, L) (G, D)

E (E, O) (E, L) (E, D)

b

c

6 a

Pr(at least one is correct) �9

25

Pr(B, E) �1

25

5 a

A B C D EA (A, A) (A, B) (A, C) (A, D) (A, E)

B (B, A) (B, B) (B, C) (B, D) (B, E)

C (C, A) (C, B) (C, C) (C, D) (C, E)

D (D, A) (D, B) (D, C) (D, D) (D, E)

E (E, A) (E, B) (E, C) (E, D) (E, E)


SAMPLE


An

swers

Answers 399

b i

ii 4 iii

c

ii 9 iii 05

b i ii iii

7 a {1, 2, 3, 4, 5, 6}b

c i {1, 2, 3, 4, 5, 6} ii {5, 6}

d i ii iii e

1 a

b c yes d i ii

iii iv 0

2 a i

ii no iii 5 iv16

A

1 2

3 45 6

Bw

710

310

25

5 6 or �

5 7

94

8 10

2

3

6

1w

12FExercise

13

13

23

23

A

1

256 4

3

Bw

25

15

25

P S3 1

94

27

16 1518

2014121086

513 11

17 19

w

A B

2 1 3

75

04 6

8

w

17

7

A B

2 1 4

63

8

w

1 a

b i {4, 6} ii {2, 4, 5, 6, 7, 8, 9, 10}

c i ii iii

2 a

b i {2, 5, 8} ii {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

c i 7 ii 6 iii 3 iv 10

d i ii iii iv 1

3 a

b

c

d

4 a i

ii 5 iii16

3

6

1

2

4

5

w

A Bw

A Bw

A Bw

A Bw

310

35

710

10

1

7

4 2 36

958

A Bw

45

15

710

A

5 74

26

1

8 910 3

Bw

12EExercise


SAMPLE


An

swer

s


b i

ii no iii {5, 7} iv

c i

ii yes iii iv 0d i

ii no iii {i} iv

e i

ii yes iii iv 0f i

ii no iii {4} iv3 a i

ii no iii {1, 3}, {1, 2, 3, 4, 5, 7, 9}

iv

b i

ii no iii {a, t}, {a, b, c, e, l, t}

iv57

, 27

, 67

A

b at

le

d

c

Bw

59

, 29

, 79

A

5 13

79

6 8

2

4

Bw

17

A

19

164

818

32

Bw5 6 or �

w a bchij k

yx

A Be

f gwz

l m n o p q r s t u v

d

17

A B

fg

hi

j

k

w5 6 or �

A B

1 23 4

5

9 10

67 8

w

29

A

3

9

10

12

1121

75

Bw c i

ii yes iii {2, 5, 6, 8, 9, 10, 11,

12, 15, 16} iv

d i

ii yes iii , {2, 3, 4, 5, 7, 9}

iv

4 a 4 b 10, 12 c a, c, e d none5 a b c d

e f gh

6 a

b i ii iii iv 1 c B

1 a i (9, 11, 13, 15, 17, 19, 21, 23, 25}ii (9, 16, 25)

b

c i {9, 25} ii {9, 11, 13, 15, 16, 17, 19, 21,23, 25} d {10, 12, 14, 16, 18, 20, 22, 24)

e i ii iii

2 aBA

9

3 57

46

8102

1

w

817

217

917

BA

11151719

2325 16

22

20

24

9

21

10 12 14 18

13

w

12GExercise

15

25

45

Mandelone

A E

CB D

Taliminew

A � B � CA � B � CW � ZE � F

�A � BA � B�

310

, 0, 35

5 6 or �

A

3 45

27

910861

Bw

12

, 0, 1

5 6 or �,

A

12 108 5

166

2 9

1511

Bw


SAMPLE


An

swers

Answers 401

b i {5, 7} ii {1, 3, 4, 5, 6, 7, 8, 9}

c {2, 4, 6, 8, 10} d i ii

iii iv v vi

3 a i

ii

b i

ii

c i

ii

d i

ii

4 a

b i ii iii

iv v vi

5 a Mario

W CN

S

VM

Elisaw

12

112

23

34

13

14

X Y

A

C

B D G H J K

EL

FI

w

15

, 35

, 710

A

124

6

201482

1016

18

Bw

0, 34

, 12

A

a c

f he g

b d

Bw

14

, 1112

, 13

BA

12

13 4

5

2 6 910

1178

w

16

, 56

, 12

BA

8

4

6

3

75

w

12

12

45

15

12

12

b i ii iii

iv v

1 a

b i 15 ii 10 c i ii iii

2 a

b i 35 ii 25 iii 10 iv 5

c i ii

3 a

b

c

d

4 a M Bw

5

25 10 5

A Bw

A Bw

A Bw

A Bw

15

25

F N

25 10 10

5

w

110

310

12

Dogs

15 5 20

10

Catsw

12HExercise

13

23

16

23

13


SAMPLE


An

swer

s


b i 25 ii 5 c i ii

iii iv v

5 a

b

7

Three enjoy both cakes and tarts.


1 A 2 D 3 E 4 C 5 B6 E 7 C 8 B 9 A 10 A


1 a

b 12 c 102 a

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

w C T

4 3 5

w A B

8 5 6

w A B

3 2 5

19

29

89

29

79

3 a

b i ii iii iv

4 a b d e

5 a i {1, 2, 3, 4, 6, 12}ii {2, 4, 6, 8, 10, 12}

b

c i {2, 4, 6, 12}ii {1, 2, 3, 4, 6, 8, 10, 12}

d i 6 ii 6 iii 4 iv 8

e i ii iii

iv f 2, 4, 6, 12

6 a

b i ii iii

iv v vi


1 a

b i 30 ii 5 c i ii iii12

14

58

TVGround

10 20 5

5

w

12

112

34

23

14

13

YX

E

AC F G H J K

B DL

I

w

23

13

12

12

BA

1

3

26 4

8

10

11975

12

w

58

14

12

34

78

12

18

38

T

HH

H HHHHH TH T HH T TT HHT H TT T HT T T

THTHTHT

T

T

H

1 2 3 4 5 61 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

b 36 c i 5 ii 4 iii 3 iv 6

d i ii iii iv

e , he is wrong16

712

112

16

536


SAMPLE


An

swers

Answers 403

1 a 4 b c 3 d

2 a b 3 c 3 d 43 a b c

d e 5x f 4a

g 3r h i j

4 a 2 b 2 c 2 d 3e 4 f 4

5 a b c

d e

6 a 5x b 35y c

d e

7 a b c

8 a i 4x ii b i ii xy

c i ii

d i 4ab ii

e i ii

f i ii 2mn

1 a 3ac and b 4pq and 3qpc and and d and e and 4ba

f and g and

h and

2 a Y b Y c N d N e Y f Y3 a 10g b 5f c 8e d 0

e 5xy f 17 st g 3ts h 3jki

4 a 9t b 7 g cd e f

5 a b cd ef

6 a 6rs b 6hu c 16wh d 2lene f g 12 cm h 35 fli

7 a b c de f g h 48uvygi �3de3wx4

�18hi4j21j2kr2s6fgst3�6g2h532 e2f 220 h4p36c3d4

6r2s�10hv�8es

3kl � 10k2l2n4m3 2mn23fg � fg2

2de2 � de37de2 5de7x2y xy28gh � 3g2cd 3u 2x 3y

�st2

yx2, �xy, yxx2y

lm

413

lm4qp23p2q

�2ab�r22r22xy24yx2, �3xy27x2y

�2ac

13BExercise

mn 7

a2b2(a2 b)

(ab)2

5x

2x y 5

2(x y)x2

5r � 43x � yx � 3

x 1111m

500n

34

x � 1513

y 4

12

x � 56y 34x � 10

xy

34

m12

x

2x � 3

ab yy � 4x 2�4

�312

13AExercise 8 a b c de f g hi

1 a b cd e fg h i

2 a b cd e fg h i

3 a bc de f

4 a b cd e f

5 a b cd

6 a b 4 cd

7 a b c8 a b 17v c

d9 a b

1 a b cd e fg h ij k l


3 a b cd e fg h i


5 abcdefg 3x 4 � 16, x � 4

2(x � 5) � �10, x � 02x 3 � 9, x � 313 � x � 20, x � �7x � 5 � 5, x � 10x 12 � 8, x � �4x 4 � 6, x � 2

x � �4x � 5x � 3x � 2x � �3x � �2x � 5x � 3x � 2x � 5x � 8x � 2x � �18x � �20x � �32x � 90x � 35x � 20x � 56x � 0x � 9x � 5x � �3x � �2x � 8x � 8x � 4x � �9x � �1x � �2x � 3x � 3x � 1x � 7x � 21x � 20x � 50x � 4x � 3x � 10x � 14x � 10x � �11x � 9x � 3

13DExercise

2b(2a 3b)6(2a 7)27 � 3x

27a � 35x � 86x2 � 12xy6x2 � 2xy12x2 4xy

2m 711x 244s 5

12d 19f 227p 197x 18�19 � 5x�5 � 2x1 3x1 2x17 7x17 5x

12x2 18xy9x2 6xy�6x2 10xy�8x2 8xy�6x2 � 15xy�6x2 � 8xy

x y�x y�x � y�7w 7c�2m 2n�4x 4y�3w � 3c�5m � 5n�2x � 2y12x � 8y6x � 3y6x 4y5r � 5s2p � 2q3x � 3y5r 5s2p 2q3x 3y

13CExercise

20v2w518f 3s581l5x221j3sr26s2t4�6g732f 420h76c7


SAMPLE


An

swer

s


6 13 cm 7 22 mm8 a 11, 12 b 6 c 3 d 25, 44 e 8 m10 a b $280 c $112011 a b 3 minutes c 11 minutes

1 a b cd e fg h

2 a b cd e fg h

3 a b cd e fg h i

4 a b cd e fg h

5 a b c

d e f


1 D 2 B 3 C 4 A 5 E6 D 7 D 8 C 9 B 10 D


1 a 3 b c 7 d

2 a 3x b c

3 a i 4x ii

b i ii 3x4 a 7x b c d5 a b6 a b

c d7 a b c

d e fg h i

8 The length of the side is 16 cm.9 a b

c d


1 ab i

ii 20 cm, 27 cm, 37 cm, 7 cm, 30 cmc i 24 cm, 31 cm, 45 cm, 7 cm, 38 cm

ii 43 cm, 36 cm, 69 cm, 7 cm, 62 cm

x � 22P � 6x � 4

x � 14x � 13x � 8x � 2

x � �2x � �1x � 3x � 9x � 4x � 1x � 20x � 5x � 2

8s 115f 13�2x3x 11

6x2 15xy�6x � 8y2fx � 3g2d2ed 3c

x y 6

x2

d c

5h 2

�312

x � �8

17x � 3x � 8

x �125

x � �3x � 1

x � �8x � �9x � �6x � 5x � 28x � 60x � 18x � 12x � �2x � 8x � 6x � 5x � 10x � 11x � 13x � 6x � 13

x � �2x � 3x � 1x � 3x � 0x � 0x � 1x � 1

x � �1x � �2x � 2x � 3x � 2x � 3x � 2x � 1

13EExercise

x � 6t 5C � 60h 40

1 a SSS b SSS2 a SAS b SAS3 a AAS b AAS4 a RHS b RHS5 a no b yes—SAS

c yes—RHS d noe yes—AAS f yes—AAS

6 (d, g)7 a b

c def gh i

8 a RHS b 6 m c i ii

1 a Yes—AA b Yes—AA2 a Yes—PPP b Yes—PPP3 a Yes—PAP b Yes—PAP4 a b5 a AA, b AA,

c AA, 6 (c, d), (a, e, f)7 a (alternate),

(alternate), (vertically opposite)b i ii

1 a AA b 2 c 30 cm 2 a AA b 1.5 c 4.5 m3 a AA b 5 c 5 m4 a AA b 1.25 m5 1.90 m7 a AA b 1.2 c 13.2 m

1 a i 1000 m ii 20 mb i 2.5 cm ii 50 cm

2 a i 1 km ii 3 kmb i 10 cm ii 1 cm c 2 km

3 a 25 000 b 2.0625 km c 42 cm4 a 2 cm b 1500 c 5 cm d 75 m5 a 5 cm b 1500 c 4 cm d 60 m

14DExercise

¢ABD, ¢CBE;

¢ABC, ¢DEC;

14CExercise

AC � 6 cmDC � 6 cm�ACB � �DCE

�ABC � �CDE�BAC � �CED

x � 2.2x � 9x � 1.5

x � 21x � 8

14BExercise

53�37�a � 20, b � 70a � 30, b � 5c � 3, d � 4a � 70, b � 7

x � 6x � 55, y � 4a � 60, b � 7x � 3, y � 5a � 4

14AExercise


SAMPLE


An

swers

Answers 405

6 ab 20 m

7 ab

9 6 m, 8 m, 5 m, 14 m, 6 m

1 a b2 a b3 a b4 a b5 a i 3:4 ii 9:16 b6 a 1:8 b7 a i 2:3 ii 4:9 iii 8:27

b c9 a 1:27 000 000 b c


1 D 2 E 3 D 4 B 5 C6 A 7 A 8 D 9 C 10 B


1 a RHS b SSS c AAS d SAS2 a Yes—AA b Yes—PPP c Yes—PAP3 a b AA

c 2.5 d 7.5 m4 a AA b 6.25 c 187.5 cm5 a 2 cm b 5000 c 5 cm d 250 m6 a i 2:3 ii 4:9 iii 8:27 b


1 a b AA c 2.5d 8 cm e 4:25 f 6.25

1 a 43.2 mm b 0.327 km c 8.34 md 96 mm e 0.2975 km f 1.27 cm

2 a bc de f

3 a bc de f

4 a 118 mm b 147.3 cmc 453.258 km de fg h

5 5500 m 6 21.5 cm537 300 m3484 500 mm33739 m23251 cm215.5 cm2

0.762 m30.0283 km315 000 000 m35.7 cm3200 000 cm32000 mm323 000 mm253 700 mm22.98 m25 000 000 m25000 cm2300 000 mm2

15AExercise

60�, 60�, 30�

32 cm3

¢ABE, ¢ACD

9 m254 000 000 m354 cm390 cm2

240 cm3450 cm2

156.25 m3108 cm38 m32 cm33 cm23 mm245 cm216 cm2

14EExercise

AC � 7.5 mscale factor � 250AB � 4 cm,

scale factor � 400AB � 2 cm, 7 a 18.5 cm b c8 a 1 000 000 b 10009 a 8.8495 km b 4.5 feet

c 26.67 cm d 1.243 milese f 0.247 Lg 8200 mL h 5 500 000 mLi 1000 sq. feet j 2000 Lk 100 ha l

1 a 10 cm b 23 m c 11 kmd 12 m e 19.2 cm f 10 m

2 a 6.7 cm b 65 mm c 18 md 810 m e 9.4 km f 180 cm

3 a b c4 a b c5 a b

c6 a b

c de f

7 20 m 8 15 cm 9 10 3

1 a 18.85 m b 31.42 m c 31.42 km2 a 113.10 cm b 61.07 mm c 3.36 km3 a 27.42 m b 16.28 cm c 6.71 mm

d 12.22 cm e 14.71 m f 61.42 cm4 a 12.25 b 53.03 c 1.37

d 31.42 e 19.77 f 61.705 a i 3.14 m ii 47.12 m b 3.14 km6 a 94.25 cm b 942.48 cm c 9424.78 cm

7 318.31 times 8 a b i 5.57 cm

ii 0.29 m iii 0.04 km9 a 3.5 cm b i 21.99 cm ii 65.97 cm

iii 109.96 cm c 12.73 cm

1 a b cd e f

2 a b cd e f

3 a b4 1 and 24, 2 and 12, 3 and 8, 4 and 65 21 m2

9600 cm20.96 m2100 cm21.12 m20.03 mm21.82 km254.6 m225 cm22 m222.5 mm221 m211.76 m221 cm24 m2

15DExercise

r �C

2

15CExercise

x � 7.5P � 3sP � 4lP � a 2bP � x y zP � 2l 2wP � 4l

P � 4x 18P � 2x 30P � a b c

x � 0.1x � 8.8x � 3x � 6x � 2x � 4

15BExercise

0.152 m3

57 000 m2

4445 cm2555 cm2


SAMPLE


An

swer

s


6 a b cd e f

8

1 a b c2 a b c3 a b c4 a 12.6 b 28.3 c 39.3

d 4.9 e 24.1 f 1.95 67 a b c

d e f8 a 1.26 cm b 0.52 m c 5.75 km10 a 20 b c

d 5

1 a b c2 a b c3 4 567 a b c8 a 66.2 b 17.9 c 645.110 yes

1 a b 376.99c d

2 a b3 a b4 a b

c d5 6 78 a b9 a b 251.33 m2 c 6.28 m

d 159.15 times e

1 a b c2 a b c3 a b 45 a b c

d e f 196 cm330 km31583.36 m354.98 cm310500 m340 cm35890.49 cm390 cm320 cm24.83 mm319.63 m3113.10 cm30.18 m3480 m3240 m3

15HExercise

4000 m225.13 m2

65.0 cm251.8 m275.4 m2628.3 cm224.0 m2

52.9 cm231.6 m2217.8 m2173.9 cm26283.2 cm26.3 m2502.9 m22557.3 cm274.64 mm21225.22 cm2

100.53 m2

15GExercise

836.6 m296 mm28.64 cm23520 cm2

3880 cm212 000 m2384 cm216 m25 cm2105 cm234 m234 mm290 cm2

15FExercise

154.51 cm2565.49 cm2

5.0 m2578.5 km2103.34 mm28.7 m263.5 m234.8 cm2

157.1 cm243.2 m2

8.03 m269.81 cm213.09 m232.14 mm2178.54 m214.28 cm20.82 mm238.48 m228.27 cm2

15EExercise

All answers � 3x � 8.89h � 1.87a � 1.05h � 1.44l � 14.35w � 2.88 g h i

6 a b 4 cm7 a 4 cm b 8 cm c 0.8 cm8 a b

c 35 d9 a b

c


1 E 2 B 3 C 4 A 5 A6 B 7 E 8 D 9 B 10 C

Short-answers questions

1 a 5300 m b c2 a 13 b 24 cm c 38 m3 a 18.85 m b4 a i 19.42 m ii

b i 19.50 m iic i 14.28 m ii

5 a 10 b 25.9 c 17.56 a b 78 a b c


1 a bc d 100 530.96 L

1 a (0, 3) b (1, 2)c no point of intersection d (2, 8)e no point of intersection f (4, 3)g (2, 5) h (0, 4)i no point of intersection

2 a (2, 3) b (2, 8) c (0, 9) d3 a (2, 3) b4 a (3, 9) b5 a b6 a no b parallel lines

d7 a yes (0, 0) b same y-intercept

d

1 a (2, 10) b cd (1, 4) e (2, 2) f (2, 12)

2 a (2, 5) b (1, 3) c (2, 1)d (4, 3) e f (1, 6)g (4, 1) h (�1, �5)

(�5, �3)

(�4, �8)(�5, �15)

16BExercise

(�3, �3), (�6, �12), (6, 24)

(�6, �12), (�5, �11), (�4, �6), (�3, 3)

(1, 1)(1, �4)(1, �3)(3, �2)

(�3, 8)

16AExercise

100.53 m3150.80 m250.27 m2

21 cm3125.66 m340 cm343.75 m2136 cm2828 m2

12.28 m221.87 m226.14 m228.27 m2

40 mm32.7 m2

20.94 cm31500 m383.3 m33680.42 cm3384.85 cm317 150 cm3

25 cm22.15 m310 cm330 m3


SAMPLE


An

swers

Answers 407

3 a b c (4, 4)4 a (2,4) b c5 a (1, 5) b (4, 10) c (2, 1)

d (2, 9)7 a i Joe’s: $60, Paul’s $150

ii Joe’s: 20c/km, Paul’s 10c/kmiii Joe’s Paul’s

iv 900 kmb Joe’s if you are travelling less than 900 km

and Paul’s for more than 900 km

1 a (2, 5) b (2, 3) c (4, 2) d (2, 2)2 a (1, 1) b (2, 1) c3 a b (1, 1) c (2, 0) d (1, 1)4 a (1, 1) b (4, 2) c (3, 4)5 a (3, 1) b c d (0, 1)

e f6 a b

1 Bob: 36 years old, Francene: 20 years old2 Paul: 33 years old, Mary: 30 years old34 vanilla thick shake: $5, Fruity Twirl: $35 children: 2500, adults: 25006 tyre: $200, wheel balance: $47 a a: apples m: mangos

b apples: 50c mangos: $1.50 c $8.008 a m: multiple-choice s: short-answer

bc

9 abc

11 a i iibc Gary is 32 and his daughter is 1.


1 B 2 C 3 D 4 A 5 E6 B 7 D 8 A 9 A 10 E


1 a (1, 2) b (2, 3)c no point of intersection

2 a (1, 6) b (3, 2) c (0, 0)3 a (3, 2) b4 a b (2, 1)(�2, �3)

(5, �1)

g � d 31, g 30 � 2(d 30)d 30g 30

2x y � 12, x y � 7, x � 5, y � 2x y � 30, x � y � 10, x � 20, y � 10x y � 16, x � y � 2, x � 9, y � 7s � 6 m � 16

m s � 222m 3s � 50,

15a 4m � 135010a 5m � 1250,

length � 6 cm, width � 18 cm

16DExercise

y � 2x � 2,y � 2x � 1,(5, �2)(�1, 2)

(�2, �3)(1, �10)

(4, �3)(2, �1)

16CExercise

C � 0.1k 150C � 0.20k 60,

(7, �1)(�3, 2)(3, �1)(�1, 2) 5 a x: number of 20 cent coins; y: number of 50

cent coins; b

6 50 children


1 a i iib (5, 400)

1 a b cd e fg h i

2 a b cd e fg h i

3 a b d cd e l f

g h i

4 a b c

d e f 2q2

g h i

5 a b c m

d e f

g7 a 1, 2, 4, 8, 16, 32... b 1.41, 1.26, 1.19...

c 0.5, 0.25, 0.125...

1 a 1 b 3 c 1d 0 e 1 f 2g 3 h 1 i 6

2 a b m c

d e f

g h

3 a b cd e f

4 a b c8p5

325r4

327s6

5

4c185c183x6k21f 20b12

r2272

c4

43

b46y52a2b2

r4s7xy2

17BExercise

4w4

92

x8y42a2b2r4s7

xy283

ab2

25

cd3r2s2xy3

53

h4d4t3r

13

nd22m4x2p2

5n3

3

f

24d2

b3c4r2a2d6f 42r7s82p4c318e9r36x3y315a3b628v5z818d 9f 56a5b86s116c82p5f3g4d 5t9p7x7

17AExercise

C � 100 60tC � 70t 50

y � 60x � 100,x y � 160, 20x 50y � 5000


SAMPLE


An

swer

s


d e f

5 a b c

d e f

g h y6 a 1 b

c i 2 ii 0 iii

1 a b c

d e f

g h i

j k l

2 a b c

d e f

g h i

3 a b c

d e f

g h i

4 a b c

d e f

5 a b c

d e f

6 a b c

d e f

g h i

1 a bc d A � A0(1.25)nA � A0(0.97)n

A � A0(0.95)nA � A0(1.17)n

17DExercise

27x

2y

h2r7

m5a2b18

2s2y14

x5

324r11

s4a8b3

16p4

9q254x5y11a7b2

2p7

3q3

15m3

7w3

2s2

r

4b3

a2

3x2

y4

2a2

b6

4r3s5

34m

7n3

x

2y

p

q2r

m2

n2

a2

b2

1r

q

p5

a

b3

18b4

a2

6

a5b2

3t2

w7

y2

a3

1xy

1a

s3

3t4

4r3

3d4

2p4

3s4

4s5

53s2

7

2p2

3

7z45y33r4

2y3z

3x2

3r3

4s4

2x2

5y3

2r2

s4

6z4

x3

4p2

q2

5

s10

3

r7

2

p4

1

z7

1

y5

1

x3

17CExercise

�2�1

2r6

32

d10c421s3y22m10n4

48r9y12108a9b62p3q7

r8

625s12

81n12

f 20

16s8

t12

e f

g

2 ab i 13254 L ii 10348 Lc 769.53 L d approx. 55 hours

3 ab i iic approx. 6.6 years

4 a b 90000 km c yes5 a 3000 cells b i 7800 cells

ii 52728 cells iii 1809017 cellsc 10 hours 11 minutes

6 ab i iic 30 seconds d 1 minute 25 seconds


1 D 2 A 3 A 4 E 5 C6 E 7 A 8 D 9 C 10 B


1 a b c d

2 a b

3 a 4 b 1

4 a b c d

5 a b c

d e f

6 a b c d

7 a b

8 a b

9 a b10 a

b i iic


1 a 20 bc e 29 yearsf red 18 years, grey 8 years

N � 100(1.04)tN � 20(1.1)t

t � 37.4 weeksA � 3.0772 m2A � 2.3762 m2

A � 2(1.09)tA � A0(0.85)nA � A0(1.08)n

x3

6y234s3t2x5

2s4

r2

10y3

x2

t 4

3d 24s92y4z

3x2

3r4

s2

32

c4d10252

x3y25n4

ry

336a8b53s3q7

243c10

h20

a4

f 68v65b6

54

y6x7y7

23

xy3g212x4x7

76.2°C79.4°CT � 90 (0.92)t

D � 10(0.875)n

V � $403115.58V � $68 381.55V � 50 000 (1.11)n

V � 15 000 (0.94)t

A � A0 a 12b n

A � A0(2)nA � A0(0.90)n


SAMPLE


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