Answers to maths yr 11 i think

P1: FXS/ABE P2: FXS0521672600Xans.xml CUAU034-EVANS October 11, 2011 7:26

AnswersChapter 1

Exercise 1A

1 a Categorical b Numerical c Categoricald Numerical e Categorical f Categorical

2 a Numerical b Categorical3 a Discrete b Discrete c Continuous

d Continuous e Discrete

Exercise 1B

1 FrequencySex Count PercentFemale 5 33.3Male 10 66.7Total 15 100.0

2 FrequencyShoesize Count Percent7 3 158 7 359 4 2010 3 1511 2 1012 1 5Total 20 100

3 a 69; 8.7%, 26.1% b 7 students c 10.1%d Hamburgere 25

2015105N

umbe

r of

stud

ents

Hambu

rger

s

Chick

en

Fish an

d chi

ps

Chine

sePizz

a

Other

Food type

0

4 a 53; 16.4%, 20.7% b 21 people c 50.4%d Strongly disagree

e15010050

Num

ber

of

resp

onse

s

Strong

ly ag

ree

Strong

ly di

sagr

ee

Agree

Don’t

know

Disagr

ee

Attitude to capital punishment

0

5 a 38.4%, 6.5%, 100.0% b 42 films c 22.8%d 232 filmse 100

50

Comed

y

Dram

a

Mus

ic

Horro

r

Other

Type of film

Num

ber

ofbo

rrow

ers

0

6 a 200 students b 4% c Watch TVd

Read

Other

Leisure activity

Perc

enta

geof

stu

dent

s

Phone

frien

ds

Watc

h a vi

deo

Listen

to m

usic

Watc

h TV

50

25

0

Exercise 1C

1Number of Frequencymagazines Number Per cent

0 4 26.71 4 26.72 3 20.03 2 13.34 1 6.75 1 6.7

Total 15 100.1

536ISBN: 9781107664623 © Peter Jones, Kay Lipson, David Main, Barbara Tulloch 2012 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party


An

swers

Answers 537

2 Amount of Frequencymoney ($) Number Per cent0.00–4.99 13 655.00–9.99 3 15

10.0 –14.99 2 1015.00–19.99 1 520.00–24.99 1 5

Total 15 100

3 a i 2 students ii 3 students iii 8 studentsb i 32.1% ii 39.3% iii 89.3%c

28Length of line (cm)29 31 3330 32 34

108642F

requ

ency

0

4 a 4 students b 2 childrenc 5 students d 28 students

5 a 0 students b 48 studentsc 60–69 marks d 33 students

6 a

b i $7.00 ii 5 booksiii $7.00 − <$9.00

7 a

b i 11◦C ii 1 cityc

d i 2 cities ii 15◦C to <20◦C

8 a

b i 8 books ii 20 to < 25 and 25 to < 30

9 a

Batting averages

1

2

3

4

Fre

quen

cy

00 5 10 15 20 25 30 35 40 4550 55

b Batting average Cum Freq (%)less than 5 14.3less than 10 23.8less than 15 38.1less than 20 38.1less than 25 52.4less than 30 61.9less than 35 76.2less than 40 95.2less than 45 95.2less than 50 95.2less than 55 100.0

10 a

marks

No.

of s

tude

nts

02468

10 20 30 40 50 60 70 80 90100

b Mark Cum Freqless than 30 1less than 40 3less than 50 8less than 60 16less than 70 21less than 80 26less than 90 27

less than 100 30

c 73%11 a

Length of hole

No.

of h

oles

024

026

028

030

032

034

036

038

040

042

0

2368

101214

ISBN: 9781107664623 © Peter Jones, Kay Lipson, David Main, Barbara Tulloch 2012 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party


An

swer

s538 Essential Standard General Mathematics

b Length (m) Cum Freqless than 260 1less than 280 6less than 300 8less than 320 17less than 340 30less than 360 33less than 380 45less than 400 47less than 420 50

Exercise 1D

1 a Centre b Neither c Both2 a Positively skewed b Negatively skewed

c Symmetric3 a Symmetric b Positively skewed

c Negatively skewed

Exercise 1E

1 a

0 1 2 3 4 5 6 7Children in family

b 2 children

2 a

0 1 2 3 4 5 6Times shopped at supermarket

b 7 people

3 a

0 1 2 3 4 5 6Goals scored

b 0 goals4 a

0 2 4 6 8Number in queue

b Around 12.25 pm

5 a

48 51 54 57 60 6663Monthly rainfall (mm)

b8

87 7720

0

9 99 9

654Monthly rainfall (mm)

5|0 represents 50 mm.

c 2 months

6 a

2

3

4

6

5

7

8

9

1 7

3 3 6

6

8

8

8 9

9

9

6

9

9

9

7

6

2 5 5

5

9

4

4

3 4

2

4

8

3

3

0

1

5

3

2

English marks

5|0 represents 50 marks.

b 21 students c 17 marks7 a 40 people b Symmetric c 21 people

8 a

11 2 4 5 6 6 7 7 8

74331161

234

47 9

0

00 00

Battery time (hours)

2|5 represents 25 hours.

b 9 batteries

9 a

112

0 0

0

00

00

4

4

5

5 5

6

6

66

7

773 3

3

3 99

98

Homework time (minutes)

4|6 represents 46 minutes.

b 2 students c Positively skewed

10 a

2 5 8

3 5 6 9

4 5 6 925

6 8

7 5 5 6 8 9

428

9 5

10

11

12

13

14

15

9

Price ($)

16|4 represents $164 (truncated).

b Approximately symmetric with an outlier($149)

11 a

Females Males9 0

5 0 1 3 67 2 1 4 5 6 7

7 1 3 43 0 4 0 7

0 56

9 70 | 4 represents 40 years 4 | 0 represents 40 years

b Both distributions are approximatelysymmetric, with a possible outlier for the



An

swers

Answers 539

females (79). The females tend to be olderthan the males, with the ages of males centredin the 20s and the ages of females centred inthe 30s. The age spread for females is greaterthan that for males.

12 aClass B Class A

2 93 12 23 9

5 7 845 5 8

5 89 61 6 7 9 97001223346

0011234488 89

9 | 6 represents 69 marks 7 | 1 represents 71 marks

55 922101 98 1

b Six students in class A and two students inclass B

c Class B performed better overall as morestudents scored in the higher values of 70s to90s.

13 aJapan Australia

3 2001

5 77 59

3 3 3 4 45 5 6 7 7 8 91 1 44 4 2

9 7 6 5 5

12 1 3

6 23

9 83234

6|2 represents 26 1|5 represents 15

4

23 3 2

b Both distributions are positively skewed.Japanese tourists tend to spend more nightsaway from home than Australian tourists. Thespread for Japanese tourists is also greaterthan the spread for Australian tourists.

Exercise 1F

1 a 5 b 5 c 15 d 101 e 2.82 a 5 b 4.5 c 15 d 99.5 e 2.13 a x̄ = 12.5 ha, M = 7.4 ha

b The median, as it is typical of more suburbs4 a x̄ = $393 386, M = $340 000

b The median, as it is typical of more houseprices

5 a IQR = 10.5, R = 21 b IQR = 8, R = 11c IQR = 7, v = 12 d IQR = 4.5,R = 8e IQR = 1.1,R = 2.7

6 x̄ = 365.8, s = 8.4, M = 366.5,

IQR = 12.5, R = 317 x̄ = 214.8, s = 35.4, M = 207.5,

IQR = 42, R = 1458 x̄ = 3.5 kg, s = 0.6 kg, M = 3.5 kg,

IQR = 1 kg, R = 2.4 kg9 a i x̄ = 6.79, M = 6.75

ii IQR = 1.45, s = 0.93b i x̄ = 13.54, M = 7.35

ii IQR = 1.8, s = 18.79c The error does not affect the median or

interquartile range very much. It doubles themean and increases the standard deviation by afactor of 20.

Exercise 1G

1 a and b

120 130 140 150 160 170 180Height (cm)

c The distribution of heights is approximatelysymmetric, centred at 154 cm, with the middle50% of heights ranging from 141.5 cm to161.5 cm.

2 a and b

0 4 8 12 16 20 24Weeks in charts

c The distribution is slightly positively skewed.Singles appear to stay in the charts for around8 weeks, with the middle 50% staying in fromaround 4 to 13 weeks.

3 a and b

Pocket money ($)0 5 10 20 2515

c The distribution is approximately symmetricand centred on $12. The middle 50% ofstudents receive pocket money of about$7.75–$15.

4 a and b

0 5 10 15 20 25 30Years employed

c The distribution is positively skewed, centredat 7.5 years. Half of the employees have beenemployed by the company for 4 to 14.5 years.

5 a and b

0 10 20 30 40Time (seconds)

c The distribution is positively skewed, centred at8 seconds. While 50% of the children take from6 to 11 seconds to tie a shoelace, there were 3students who took 29, 35 and 39 seconds.

6 a Year 12; higher medianb Year 12; larger IQR

7 The distributions of ages in both groups areslightly positively skewed, with the mothers in1970 (M = 24.5) being generally younger thanthe mothers in 1990 (M = 28). The variability inboth groups is the same (IQR = 10 for bothgroups).

8 a

0

female

male

10 20 30 40 50 60 70Smoking rate



An

swer


b The distribution of smoking rates is slightlynegatively skewed for females, andapproximately symmetric for males. Ingeneral, the smoking rates for females(M = 19%) are much lower than the smokingrates for males (M = 39.5%). The variabilityin both groups is the same (IQR = 14.5).

Exercise 1H

1 a m = 3, Q1 = 0, Q3 = 13, min = 0, max = 52

b 38, 52c

0 10 20 30 40 50

* *

d The distribution of number of books borrowedis positively skewed, centred at 3. While 75%of people borrowed 13 books or less, onestudent borrowed 38 books and anotherborrowed 52.

2 a* * *

2 000 000 8 000 0006 000 0004 000 0000

b The distribution of winnings is extremelypositively skewed with a median value of$737 508. The middle 50% of players wonfrom $650 325 to $1 131 026. There were threeoutliers, Roger Federer with winnings of$2 502 919, Rafael Nadal with winnings of$5 250 169 and Novak Djokovic with winningsof $7 608 673.

3 a

0 10 20 30 40 50

** *

60

b The distribution is positively skewed, centredat 8 seconds. While fifty percent of thestudents take from 6 to 11 seconds to completethe puzzle, there were three students who took29, 39, and 60 seconds respectively.

4 a

0 100 200 300 400 500

*

600 ’000

b The distribution is approximately symmetric,centred at about 210 000, with an outlier at570 000. The middle 50% of papers havecirculations of about 88 000–270 000.

5 a

0 10 20 30 40 50

*

* *After

Before

b The distribution for the number of sit-ups isnegatively skewed before the course, centred at26. After the course, the distribution is moresymmetric, centred at 30, indicating that thecourse has been effective. The distributionafter the course is more variable than beforethe course, showing the course has not had the

same effect on all participants. There is oneoutlier in the before group, who can achieve 46sit-ups, and two in the after group, recording50 and 54 sit-ups respectively.

6 a

Male

Female

40 50 60 70 80 90

*

*

b The distribution of life expectancy isapproximately symmetric for both males andfemales. There is one outlier, Afghanistan,which has extremely low life expectancy of 43years for both males and females. In general,life expectancy is higher for females (median= 77) than for males (median = 74). Thevariation in life expectancy is also slightlylarger for females (IQR = 10) than for males(IQR = 6).

Multiple-choice questions1 D 2 D 3 C 4 B 5 D6 D 7 D 8 D 9 D 10 E

11 D 12 A 13 C 14 C 15 A16 B 17 B 18 B 19 C 20 A21 C

Short-answer questions1 a Numerical b Categorical2 a Categorical b 7.5%3

05 10 15 20 25 30 35

2

4

6

8

10

12

Cigarettes smoked

Fre

quen

cy

4 a20 30 40 50 60 70

Time (minutes)

b

2345

67

4 5 7 94 5 6 6 7 911

2930

5 8 92

Time (minutes)

2 2 4|7 represents 47 minutes.

c M = 52 minutes, Q1 = 47 minutes,Q3 = 57 minutes

5 x̄ = $283.57,

s = $122.72, M = $267.50, IQR = $90,

R = $495

6 x̄ = 178.89 minutes, s = 13.99 minutes



An

swers

Answers 541

7

0 5 10 15 20 25SMS messages

8 a

0 20 30 40 5010Students absent

b 14.5 students c 27.8%

Extended-response questions1 a Numerical

b

1

2

3

5

4

0

4

5

2

3

4

0

4

6

2

5

5

7

6

8

8

6

9

8 9

Divorce rate (%)

3|2 represents 32%.

c

100 20 30 40 50Divorce rate (%)

d Positively skewede 21.05%

f x̄ = 20.05%, M = 18%g

10

1

2

3

4

5

6

020 30 40 50 60

Divorce rate (%)

Fre

quen

cy

i Positively skewed ii 5 countries

2 a

2

4

6

8

10

12

0959085807570656055

Fre

quen

cy

Travel time (minutes)

i 9 daysii Positively skewed

iii 38.1%

b x̄ = 69.60 minutes, s = 9.26 minutes,Min = 57 minutes, Q1 = 62 minutes,M = 68 minutes, Q3 = 76 minutes,Max = 90 minutes

c i 69.60 ii 68 iii 33, 14 iv 76 v 9.26

d

50 60 70 80Travel time (minutes)

90 100

Met

HillsideTrains

e The distributions of travel times are bothpositively skewed. The travel times for the Met(M = 70 minutes) tend to be longer than thetravel times for Hillside Trains(M = 68 minutes). The spread of times is alsolonger for the Met (IQR = 24 minutes)compared to Hillside Trains (IQR = 14).

3 a

50 60 70 80 90 100

Method 1

Method 2

Method 3

Test score40

b The distributions of scores are negativelyskewed for Methods 1 and 3 and approximatelysymmetric for Method 2. The scores forMethod 1 are centred higher than for Methods2 & 3 (M = 90, 79 & 70 respectively), and arealso less variable than Method 2 & 3.

c Thus training Method 1 would berecommended as it consistently produceshigher scores.

4 a

50

First-born

Second-born

Third-born

Level of independence403020100

b The distribution for first-borns’ Level ofindependence is symmetrical, while forsecond- and third-borns the distributions arepositively skewed. The centre for first-borns ishigher than the centre for second-borns, whichis higher than the centre for third-borns(M = 35, 21 and 12 respectively). Thevariability is greatest for first-borns, followedby second-borns and then third-borns.



An

swer


5 aNo

Yes

Mark20 25 30 35 40 45 50

b The distributions of marks for both groups areapproximately symmetric, and in each group50% of the students scored 36 or more in theessay. However, the marks for the students whowere able to choose their topic were much lessvariable (IQR = 8.5) than those for studentswho were not able to choose (IQR = 16).There are no outliers.

Chapter 2Exercise 2A

1 a $1400 b $1500 c $1425

2 380 km3 a $10.50 b $14.40 c $30

4 a 157.08 cm b 18.85 mmc 33.93 cm d 45.24 m

5 a P = 14 b P = 46 c P = 236 a A = 4 b A = 14.25 c A = 5.67

7 a 10◦C b −17.8◦Cc 100◦C d 33.3◦C

8 a $2400 b $180c $375 d $2014.50

9 a 15 points b 37 points c 68 points10 a t6 = 13 b t11 = 23 c t50 = 101

Exercise 2B

1 x 40 41 42 43 44 45 46 47 48 49 50

C($) 86 88.15 90.3 92.45 94.6 96.75 98.9 101.05 103.2 105.35 107.5

2 r (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

A(cm2) 0 0.031 0.126 0.283 0.503 0.785 1.131 1.539 2.011 2.545 3.142

3 n 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

C($) 49 50.8 52.6 54.4 56.2 58 59.8 61.6 63.4 65.2 67 68.8 70.6 72.4 74.2 76

4 M(kg) 60 65 70 75 80 85 90 95 100 105 110 115 120

E(k J ) 650 695 740 785 830 875 920 965 1010 1055 1100 1145 1190

5 n 3 4 5 6 7 8 9 10

S 180◦ 360◦ 540◦ 720◦ 900◦ 1080◦ 1260◦ 1440◦

6 a n 0 1 2 3 4 5 6 7 8 9 10

E($) 680 740 800 860 920 980 1040 1100 1160 1220 1280

b 6 cars

7 T (years) 1 2 3 4 5 6 7 8 9 10

I ($) 750 1500 2250 3000 3750 4500 5250 6000 6750 7500

8 t(years) 5 10 15 20 25

A($) 6535 8541 11 162 14 589 19 067

Exercise 2C

1 a x = 9 b y = 15 c t = 5 d m = 6e g = 6 f f = 19 g f = −3 h v = −5i x = −1 j g = 1 k b = 5 l m = −2

m y = 6 n e = 3 o h = −5 p a = −4q t = −10 r s = −11 s k = 7 t n = 4

2 a x = 3 b g = 9 c n = 4 d x = −8e j = −4 f m = 7 g f = 5.5 h x = 3.5i y = 5 j s = −3 k b = −5 l d = −4.5

m r = 12 n q = 30 o x = 48 p t = −12q h = 40 r m = 21 s a = 2 t f = −2

3 a a = 2 b b = 6 c w = 2 d c = 2e y = 7 f f = 2 g h = 5 h k = 3.3i g = 8.5 j s = 20 k t = 2.2 l y = 2

m x = −2 n g = 37 o p = 2

Exercise 2D

1 a P = 27 + x b P = 4xc P = 2a + 2b d P = 19 + y

2 a P = 22 + m b 8 cm3 a P = 4y b 13 cm

4 a n + 7 = 15 b 8 5 6 6 597 a P = 4x + 12 b 18 cm c 24 cm, 18 cm

8 140 tickets 9 145 minutes

10 Anne $750, Barry $250

Exercise 2E1 a x = 22 − 7y b x = 11 + 4y

c x = 5 − 6y d x = 5y + 12e x = 2y − 5 f x = 8 − 4yg x = 2y − 3 h x = 2

3 y + 53

i x = 5 − 2.5y j x = −6 − 3yk x = 6 + 1.5y l x = 7

5 y − 8

2 r = C

2�3 a n = S + 360

180b 7 sides

4 a t = v − u

ab 3.6 seconds 5 h = 2A

b

6 C = 5(F − 32)

97 a T = 100I

PRb 5 years

Exercise 2F1 a C = 0.5x + 0.2y b $16.502 a C = 40x + 25y b $13 8753 a C = 1.6x + 1.4y b $141.204 a C = 1.75x + 0.7y b $52.155 a C = 2.5x + 4y b $2346 a C = 30x + 60y b $34807 a N = x + y b V = 0.5x + 0.2y c $37.908 6.67 m

Exercise 2G1 a 16 b 81 c 49 d 27 e 8

f 216 g −125 h 256 i 10 000



An

swers

Answers 543

2 a a = ±3.46 b b = ±8.49 c c = ±23.83d d = 4.24 e e = 6.69 f f = −9.12

3 a x = ±2.83 b y = ±2.24 c a = ±2.35d f = ±2.35 e h = ±2.18 f c = ±2.61g x = 4.33 h r = 2.62 i y = 4.58j r = 2.92 k m = 2.67 l b = 1.38

m p = ±2.12 n q = 3.17 o r = ±4.90

4 1.43 cm 5 15.7 cm6 a 5 cm b 10 cm

Exercise 2H1 200, 188, 176, 164, 1522 a $3900 b $63003 a i $10 000 ii $8400 iii $3600

b 1 year, 11 months4 a i $31 700 ii $33 350

b 10 years5 a $525 b 12 days6 16 000 fish 7 $41 258.738 8 years 9 $9144.22

Exercise 2I

1 a (−1, −1) b (3, −2) c (1, 1) d (1, −1)2 a (2, −4) b (−3, 2) c (1.5, 2.5)

d (2, 1) e (0, 6) f (7, 2)g (0, 3) h (1, 5) i (0.4, −2.6)j (7, 25) k (−8, −20) l (−3, 10)

Exercise 2J

1 a (2, 1) b (2, 5) c (3, 4)d (9, 1) e (3, 2) f (1, 1)g (4, 3) h (2.4, 3.4) i (−1, 4)j (−2, 5) k (−2, −1) l (3, 2)

2 a (2, 4) b (4, −1) c (−2, 10)d (−2, 3) e (−2, 3) f (−7, 0)

Exercise 2K

a (4, −1) b ( 12 , 2) c (−1, −2)

d ( 12 , −2) e (3, −1) f ( 32

17 , 2817 )

g (2,3) h ( 43 , 7

2 ) i (−1.5, 2.25)j ( 1

5 , − 15 ) k (1.5, −0.6) to 1 d.p.

Exercise 2L

1 a 5t + 6p = 1275 and 7t + 3p = 1380b Texta $1.65, pencil $0.75

2 Petrol $1.16/L, motor oil $7/L3 Banana 35c, orange 60c4 Nails 1.5 kg, screws 1 kg5 12 emus, 16 wombats6 6 cm, 12 cm 7 22, 308 Bruce 37, Michelle 339 Chocolate thickshake $5, fruit smoothie $3

10 Mother 44, son 12

11 77 students12 10 standard, 40 deluxe13 252 litres (40%), 448 litres (15%)14 126 boys, 120 girls15 7542 litres unleaded, 2658 litres diesel16 $10 000 at 5%, $20 000 at 8%

Multiple-choice questions1 C 2 B 3 D 4 B 5 A6 A 7 D 8 B 9 D 10 B

11 C 12 D 13 C 14 D 15 A16 A 17 D 18 D 19 D

Short-answer questions1 a x = 10 b x = 11 c x = 8 d x = 6

e x = 1 f x = 7 g x = −6 h x = 11i x = 3 j x = 3 k x = 15 l x = −24

2 a P = 40 b P = 1303 a A = 30 b A = 544 94.25 cm5

x −20 −15 −10 −5 0 5 10 15 20 25

y −716 −551 −386 −221 −56 109 274 439 604 769

a x = 10b x = −5

6 a a = ±7 b b = ±94 c c = ±8 d d = 3e e = −4 f f = 3 g g = ±2 h h = 5

7 1 8 59 a (1, 3) b (4, 1) c (5, 1)

10 a (2, 8) b (3, 2.5) c (5, −2)d (5, 2) e (2, 1)

11 14, 31, 48, 65, 82, 9912 75, 146, 288, 572, 1140, 2276, 4548, 9092

Extended-response questions1 a $57 b 7 hours2 a

n 60 70 80 90 100 110 120 130 140 150 160C 55 60 65 70 75 80 85 90 95 100 105

b $1053 a C = 80 + 45h b $2154 a 3a +5c = 73.5

2a +3c = 46.5b $12 c $7.50

5 a $3200 b $1400 c 17 months6 End of first year: $3090

End of second year: $3182.70End of third year: $3278.18End of fourth year: $3376.53End of fifth year: $3477.82

7 3 m8 Indonesian 28; French 42; Japanese 35.


1 a (0, 4), (2, 6), (3, 7), (5, 9)b (0, 8), (1, 6), (2, 4), (3, 2)


An

swer


2 a x 0 1 2 3 4y 1 3 5 7 9

10

0

6

4

4

2

2

8

31

a y = 1 + 2x

x

y

b x 0 1 2 3 4y 2 3 4 5 6

10

0

6

4

4

2

2

8

31

b y = 2 + x

x

y

c x 0 1 2 3 4y 10 9 8 7 6

10

0

6

4

4

2

2

8

31

c y = 10 – x

x

y

d x 0 1 2 3 4y 9 7 5 3 1

10

0

6

4

4

2

2

8

31

d y = 9 – 2x

x

y

3 a i ii

b i ii

c i ii

d i ii

e i ii

f i ii

ISBN 978-1-107-66462-3 Photocopying is restricted under law and this material must not be transferred to another party.

© Peter Jones, Kay Lipson, David Main, Barbara Tulloch 2012 Cambridge University Press


An

swers

Answers 545

Exercise 3B

1 A negative, B positive, C not defined, D zero2 A −2.3, B 1.75, C 13 A 2, B −3, C 04 a 2 b −1 c 2

d 1.8 e 2 f −1

Exercise 3C

1 a y-intercept 5, slope 2b y-intercept 6, slope −3c y-intercept 15, slope −5d y-intercept 5, slope −2e y-intercept 10, slope −3f y-intercept −5, slope −2g y-intercept 0, slope 3h y-intercept 6, slope 3i y-intercept −5, slope 2j y-intercept = −10, slope = 5k y-intercept = 10, slope = −1l y-intercept = 0, slope = 2

2 a y = 2 + 5x b y = 5 + 10xc y = −2 + 4x d y = 12 − 3xe y = −2 − 5x f y = 1.8 − 0.4xg y = 2.9 − 2x h y = −1.5 − 0.5x

3 a

(0, 5)(5, 15)

y = 5 + 2x

Ox

y b

x

(5, 30)

(0, 5)

y

y = 5 + 5x

O

c

x

y

(0, 20)

(10, 0)

O

y = 20 – 2x

d

x(1, 0)

(0, –10)

y

y = –10 + 10x

e

(5, 20)

xO

y

y = 4x

f

(0, 16)

(8, 0)

Ox

y

y = 16 – 2x

Exercise 3D

1 A: y = 10 − 2.25x B: y = 2 + 1.75x

C: y = x2 A: y = 4 + 2x B: y = 8 − 1.5x

C: y = 2 + 0.6x

Exercise 3E

1 A: y = 14.5 − 4.5x B: y = −5 + 5x

C: y = 3x − 52 A: y = 11.5 − 1.5x B: y = −10 + 10x

C: y = 2 + 1.2x

Exercise 3F

1 Same as Exercise 3D, Question 12 Same as Exercise 3D, Question 23 Same as Exercise 3E, Question 14 Same as Exercise 3E, Question 2

Exercise 3G

1 a $20 b $35 c C = 20 + 0.15nd $65 e $0.15 (15 cents)

2 a 500 mL b 400 mL c 200 minutesd V = 500 − 2.5t e 212.5 mL f 2.5 mL/min

3 a F = 32 + 1.8C (or as more commonlywritten: F = 9

5 C + 32)b i 122◦F ii 302◦F iii −40◦Fc 1.8

4 a I = 160 − 1.6Fb i 96 per 100 000 ii 64 per 100 000

iii 8 per 100 000c 1.6

5 a i 300 L ii 450 L iii 750 L iv 1150 Lb

Ot

V = 150 + 10t (100, 1150)

(30, 450)

V = 15t

V

Multiple-choice questions1 E 2 D 3 A 4 D 5 C6 C 7 E 8 C 9 B 10 E

11 C 12 B 13 B 14 A 15 C

Short-answer questions1 a x 0 1 2 3 4

y 2 7 12 17 22

y

25

20

15

10

5y = 2 + 5x

x1 2 3 40


An

swer


b x 0 1 2 3 4y 12 11 10 9 8

x

y

5

10

15

1 2 3 4

y = 12 – x

0

c x 0 1 2 3 4y −2 2 6 10 14

x

y

5

10

15

1 2 3 4

y = –2 + 4x

0

–5

2 a i ii

b i ii

c i ii

3 A −1.2, B 0.64 A 2.25, B −2.67

Extended-response questions1 a $200 000 b After 60 months (5 years)

c V = 300 − 5t d $120 000e $5000

2 a $80 billionb A = 0.16N (with A in billions, N in thousands)c $96 billion d $240 billion e $0.16 billion

3 a H = 80 + 6.25A b 98.75 cm c 6.25

4 a i $13 ii $17 iii $49b i $0.40 (40 cents) ii $1.60c

x

C

(0, 5)

(30, 17)

(50, 49)

C = –31 + 1.6x

C = 5 + 0.40x

O

Chapter 4

Exercise 4A

1 2

3 4

5

Exercise 4B

1 a Related; positive b Related; positivec Related; negative d No relationshipe Related; positive f Related; negative

2 a i Not related, outlierb i Related, no outliers ii Positive

iii Strongc i Related, no outliers ii Positive

iii Moderated i Related, no outliers ii Negative

iii Stronge i Related, no outliers ii Negative

iii Weakf i Related, outlier ii Positive

iii Strong (ignore outliers)

Exercise 4C

1 a No relationshipb Weak negative relationshipc Strong negative relationshipd Weak positive relationshipe Strong positive relationshipf Strong negative relationship




An

swers

Answers 547

g Strong positive relationshiph No relationshipi Strong negative relationshipj Weak positive relationshipk Strong positive relationshipl Moderate negative relationship

2 a q = 0.5 b q = 0 c q = 0.6d q = −0.45 e q = 0 f q = −0.67

3 a q = −0.67 b q = −0.17 c q = 1

Exercise 4D

Note: Answers will vary for lines drawn by eye.

1 y = 160 − 1.6x ; infant death rate= 160 − 1.6 × female literacy rate

2 y = 72 + 0.4x ; height = 72 + 0.4 × age3 y = 18 + 0.9x ; daughter’s height

= 18 + 0.9 × mother’s height4 velocity = 18.4 + 1.362 × time5 price = 17 652 − 1211 × age6 airspeed = 695 + 0.29 × number of seats

Exercise 4E

1 a interpolation b extrapolation2 a 88cm, interpolation

b 94cm, interpolationc 100cm, extrapolation

3 a 59.1kg, extrapolationb 65.7kg, interpolationc 72.3kg, interpolation

4 a $175, extrapolationb $523, interpolationc $691.20, interpolation

5 a 171.2cm, interpolationb 196.7cm, extrapolationc 159.4cm, interpolation

Multiple-choice questions1 D 2 B 3 D 4 E 5 D6 C 7 A 8 B 9 E 10 C

11 B 12 B 13 A 14 C 15 C16 E

Short-answer questions1 a

Scor

e (p

oint

s)

140

120

100

80

60

40

30 40 50 60 70 80Inside 50 m

b Moderate positive relationship2 q = 0.7 (to 1 d.p.)3 weight = −200 + 2 × height4 errors = 15.7 − 0.578 × time

Extended-response questions1 a IV = exam score,

DV = number of new clientsb 11

10

9

8

7

6

5

60 65 70 75 80 85Examination score

Num

ber

of n

ew c

lien

ts

c Strong positive relationshipd q = 1, strong positivee number of new clients = −8.7 + 0.239 ×

examination scoref 15 new clients g Extrapolating

2 a IV = assignment mark,DV = final exam mark

bF

inal

exa

m m

ark

85

80

75

70

65

60

55

50 55 60 65 70 8075Assignment mark

c Strong, positive, possible outlierd q = 1, strong positivee The statement is incorrect as it is a causal

statement. It can only be said that there is arelationship between the assignment mark andthe final exam mark.

f final exam mark= 4.66 + 0.986 × assignment mark

g 54 h Interpolating3 a IV = number of times played,

DV = weekly salesb

Wee

kly

sale

s

4500

4000

3500

3000

2500

2000

25 30 35 40 45 5550Number of times played



An

swer


c Strong positive d q = 1, strong positivee weekly sales = 98.5 + 79.268× number of

times playedf 4855 g Extrapolating

4 a IV: Year ; DV: Distanceb 9.00

8.50

8.00

7.50

7.00

6.50

6.00

1900 1920 1940 1960 1980 2000Year

Dis

tanc

e

c There is a strong positive association betweenyear and distance. There are two outliers.

d q = 1, very strong positivee distance = −25.57 + 0.01718 × yearf 8.93 metresg Quite reliable, since we are only extrapolating

one time period outside the data.5 a Hours is the IV and Test score is the DV.

b

Hours

Test

sco

re

0 10 20 3010

20

30

40

c There is a strong, positive linear relationshipbetween hours of instruction and test score.

d q = 1, stronge test score = 10 + 1 × hours f 20


1 a 4.9 cm b 83.1 cm c 24 mmd 2.4 mm e 15.8 mm f 7.4 cmg 6.4 cm h 141.4 mm i 15.4 m

2 2.9 m 3 3.8 m 4 5.3 m 5 48.88 km6 15 km 7 12.81 km 8 20 cm 9 9.4 m

10 61.717 m 11 4.24 cm

Exercise 5B

1 a 4.243 cm b 5.20 cm2 a 10.77 cm b 11.87 cm c 6.40 cm3 a 27.73 mm b 104.79 mm4 9.54 cm

5 a i 8.5 cm ii 9.1 cmb i 10.6 cm ii 3.8 cm

6 17 cm 7 13 cm 8 25 cm

Exercise 5C

1 a i 60 cm ii 225 cm2

b i 22.4 cm ii 26.1 cm2

c i 312 cm ii 4056 cm2

d i 44 cm ii 75 cm2

2 a 56.2 m2 b 16.7 m2 c 103.6 cm2

d 73.8 cm2 e 28 cm2 f 35.9 cm2

g 29.9 m2 h 312.5 m2

3 100 m2 4 63 375 m2 5 40 tiles 6 3 L

Exercise 5D

1 a i 31.4 cm ii 78.5 cm2

b i 53.4 cm ii 227.0 cm2

c i 25.6 m ii 52.3 m2

d i 49.6 mm ii 196.1 mm2

e i 47.1 cm ii 176.7 cm2

f i 1.3 m ii 0.1 m2

2 a i 25.71 cm ii 39.27 cm2

b i 1061.98 mm ii 14167.88 mm2

c i 203.54 cm ii 2551.76 cm2

d i 53.70 mm ii 150.80 mm2

3 a 343.1 cm2 b 34.9 m2

c 19.2 cm2 d 177 377.5 mm2

4 a 1051.33 m b 37 026.55 m2

Exercise 5E

1 a 125 cm3 b 49 067.8 cm3 c 3685.5 cm3

d 3182.6 mm3 e 29 250 cm3 f 0.3 m3

g 6756.2 cm3 h 47.8 m3

2 424 cm3 3 516 cm3

4 a 20 319.82 cm3 b 20 L5 20.785 cm3

Exercise 5F

1 a 9500.18 cm3 b 16.36 m3

c 59.69 m3 d 2356.19 mm3

2 a 153.94 cm3 b 705.84 m3

c 102.98 cm3 d 1482.53 cm3

3 392.699 cm3

Exercise 5G

1 a 26.67 cm3 b 420 m3 c 24 m3 d 68.64 cm3

2 213.333 cm3 3 1 694 000 m3

4 a 335.6 cm3 b 66.6 cm3



An

swers

Answers 549

Exercise 5H

1 a 523.60 mm3 b 229.85 mm3 c 7238.23 cm3

2 a 179.59 cm3 b 11 494.04 cm3 c 33.51 cm3

3 a 8578.64 cm3 b 7679.12 cm3 c 261.80 cm3

d 4.09 m3

4 14 L

Exercise 5I

1 a 1180 cm2 b 40 m2 c 383.3 cm2

d 531 cm2 e 2107.8 cm2 f 176.1 m2

2 a 3053.63 cm2 b 431.97 cm2 c 277.59 m2

d 7.37 m2 e 242.53 cm2 f 24.63 m2

g 235.62 m2 h 64.40 m2

3 15 394 cm2 4 25 133 cm2

5 141 cm2

Exercise 5J

1 a i3

1ii

9

1

b i2

1ii

4

1

2 a Similar,3

1b Similar,

2

1c Not similar

3 a Not similar b Similar,4

1c Not similar

d Similar1

3

44

15 a 3 cm b

9

16 112 cm2 7 864 cm2

Exercise 5K

1 a SSS b AA c SAS or SSS or AA2 a x = 27 cm, y = 30 cm

b x = 26 m, y = 24 m3 a 28 cm, 35 cm b 119 cm

4 a AA b1

8 c 8 m

5 1.8 m 6 72 cm2

Exercise 5L

1 27 times

2 a4

1b

64

1

327

14 a 9 cm b

125

15 a

27

1b 3240 cm3

Exercise 5M

1 a

b

c

d

e



An

swer


f

g

h

i

2 a 2 b 3 c 5 d 3 e 2f 8 g 2 h 6 i 2

3 a Antigua and Barbuda, Argentina, Armenia,Austria, Belgium, Bulgaria, Burkino Faso,Burundi, Cambodia, Columbia, Costa Rica,Ecuador, Estonia, Ethiopia, France, Ghana,Haiti, Honduras, Hungary, Israel, Italy,Jamaica, Japan.

b Austria, Costa Rica, Dominican Republic,Great Britain, Honduras, Israel, Jamaica, Japan

Exercise 5N

1 a and d Tessellate, as angles at corners add to360◦

b and c Don’t tessellate, as angles at cornersdon’t add to 360◦

2 No. 360◦ is not a multiple of 144◦.3 Many answers possible, e.g. regular heptagon,

regular nonagon, regular decagon. Angles atcorners do not add to 360◦.

4 Teacher to check 5 Yes

6 Teacher to check 7 Teacher to check

Multiple-choice questions1 B 2 D 3 D 4 B 5 A6 B 7 C 8 B 9 D 10 C

11 E 12 D 13 C 14 B 15 C16 C

Short-answer questions1 a 58 cm b 30 m2 36 m 3 68 cm4 a 9.22 cm b 9 cm5 a 140 cm2 b 185 cm2

6 37.5 cm2

7 a 31.42 cm b 75.40 cm8 a 78.54 cm2 b 452.39 cm2

9 a 30 m2 b 15 m2 c 5.83 m d 69.97 m2

e 421.94 m2

10 33.32 m3

Extended-response questions1 a 154.30 m2 b 101.70 m2 a 61.54 m b 140 m2 c 120 m3 d 128 m2

3 13.33 m 4 a 15.07 m b 1.89 m3

5 a1.96

1or 1 : 1.96 b

2.744

1or 1 : 2.744

c 63 cm3


1 a $86.40 b $180 c $0.58 d $73.08e $10.43 f $7.22 g $23.40 h $234.30

2 a $280.80 b $756.84 c $49.40 d $1182.50e $1771.75 f $28 000 g $20

3 a 4.89% b 30% c 28.42% d 0.92%e 33.33% f 11.11% g 3.62% h 0.13%

4 a $291.20 b $626.40 c $68 d $6318e $57.78 f $10 638 g $294.64 h $2301.04

5 a $1865.50 b $11.14 c $27.72d $10 282 e $847.70 f $2631.20g $12 136.10 h $142.88 i $593.12

6 a $60 b $50 c $71.43 d $887 a $13.30 b $62.22 c $104.50 d $4993.908 $212.75 9 $58.82

Exercise 6B

1 a $80 b $300 c $600d $384.38 e $4590 f $324.38g $29.95 h $14.43 i $6250

2 a $600 b $932.10 c $1243.50d $2411.25 e $2597.26

3 a $1950 b $11 9504 $30 800 5 $1243.50 6 $9041.107 a $118.75 b $2750 c $2463.19

d $24 000 e $1983.63 f $13 617.928 a $4500 b $13.33


An

swers

Answers 551

9 $3.12 10 $1.8811 a March $650.72, April $650.72, May $900.72

b $6.88

Exercise 6C

1 6.5 years 2 $1210 3 12%4 $45 552 5 15% 6 354 days7 a $180 b $780 c 3 years d $1051.60

e 7% f $1335.15 g $4500 h $4650i 5% j $3698.63 k 3 years l $220.50

m $1448.28 n $1500.788 4 years 9 20 years

10 a $18 000 b 6.67%11 18.125% 12 $4350 13 15 months

Exercise 6D

1 $4466.99 2 $2523.42 3 $1552.874 $105.10 5 $27 722.41 6 $1494.657 a $16 000 b $17 623.42 c $18 061.11

d $18 166.97 e $18 219.398 a i $61 440 ii $93 503.42 iii $88 254.96

iv $79 287.58 v $70 662.90b Compound interest at 12% per annum,

calculated annually9 $971.14 10 $579.52

11 $6890 12 $17 820

Exercise 6E

1 a $2350 b $10 2002 a $1020 b $64603 $18 0054 a $234 b 12%5 a 11.25% b $48 750

c

6 a $1125 b $6875c

d 11 years7 a $8750 b 10.3%

c

8 a $15 358.75 b $61 435c

d 8 years

Exercise 6F

1 $16 800 2 $272.16 3 $74514 a $613 b $887

c

5 a $184.40b

6 a $1260 b $43 740 7 a $25 725 b $41 2508 a

Book value ($)Year Reducing balance at 40% Flat rate at 17%

0 41 000 41 0001 24 600 34 0302 14 760 27 0603 8 856 20 0904 5 314 13 1205 3 188 6 150

b Reducing balance method

Exercise 6G

1 a $366 b $36 2 a $26.40 b $3243 a $1210.20 b $313.20 4 14.82%5 a $242 b 17.6%6 a $57.60 b $633.60 c $158.407 a $85.50 b $2218 a $41 771.80 b 12%



An

swer


Revision1 a 0.15 b 0.28 c 0.08 d 0.77

e 0.065 f 1.25 g 0.005 h 0.00642 a $86.40 b $180 c 58 cents d $73.083 a 25% b 75% c 10% d 11.11%4 a $291.20 b $626.40 c $68 d $63185 a $1865.50 b $11.14 c $27.72 d $10 282

Multiple-choice questions1 B 2 B 3 A 4 E 5 C6 E 7 A 8 C 9 E 10 D

11 A 12 B 13 B 14 B 15 B

Short-answer questions1 a Rabbit Easter Eggs b 0.7%2 $137.50 3 $791.89 4 $10 992.655 a $1802.24 b $649.446 a $220 b 12.9%

Extended-response questions1 a $612.50

b i $87.50 ii $437.50iii $765.63 iv 25%

2 a $13 000 b $13 157.04 c 6.3%3 a and b

c i Plan A ii Plan B4 a $11 000 b 9.2% c $21 3725 a $11 400 b $11 938

c i

ii 5.5 years6 a 12.5% b i $190 ii 27.1%


1 Answers are in order: hypotenuse, opposite,adjacent.a 13, 5, 12 b 10, 6, 8 c 17, 8, 15d 25, 24, 7 e 10, 8, 6 f 13, 12, 5

2 Answers are in order: sin �, cos �, tan �.a 5

13 , 1213 , 5

12b 6

10 , 810 , 6

8c 8

17 , 1517 , 8

15

d 2425 , 7

25 , 247

e 810 , 6

10 , 86

f 1213 , 5

13 , 125

3 a 0.4540 b 0.7314 c 1.8807 d 0.1908e 0.2493 f 0.9877 g 0.9563 h 1.1106i 0.9848 j 0.7638 k 5.7894 l 0.0750

Exercise 7B

1 a 20.74 b 20.76 c 32.15 d 8.24e 26.63 f 7.55 g 17.92 h 15.59i 74.00 j 17.44 k 32.72 l 37.28

2 a 78.05 b 25.67 c 8.58 d 54.99e 21.32 f 11.59 g 30.67 h 25.38i 63.00 j 62.13 k 4.41 l 15.59

3 a 12.8 b 28.3 c 38.5 d 79.4 e 16.2f 15.0 g 14.8 h 37.7 i 59.6

Exercise 7C

1 a 28.8◦ b 51.1◦ c 40.9◦ d 30.0◦

e 45.0◦ f 45.0◦ g 60.0◦ h 68.2◦

i 33.0◦ j 73.0◦ k 17.0◦ l 30.0◦

m 45.0◦ n 26.6◦ o 30.0◦ p 70.0◦

2 a 32.2◦ b 59.3◦ c 28.3◦ d 55.8◦ e 46.5◦

f 48.6◦ g 53.1◦ h 58.8◦ i 22.6◦ j 53.1◦

k 46.3◦ l 22.6◦ m 32.2◦ n 41.2◦ o 48.2◦

3 a 36.9◦ b 67.4◦ c 53.1◦ d 67.4◦

e 28.1◦ f 43.6◦

Exercise 7D

1 6.43 m 2 21.0◦ 3 10 m 4 16 m5 a

3 m

2 m

θ

b 33.7◦

6 a

3.8 km x

52°

b 3.0 km

7 a2 km

17°

b Horizontal distance 1.91 km, height 0.58 km8 70.5◦ 9 78.1 m 10 5.77 m



P1: FXS/ABE P2: FXS0521672600Xans2.xml CUAU034-EVANS October 11, 2011 7:28

An

swers

Answers 553

Exercise 7E

1 413 m 2 11 196 m 3 33 m4 164.8 m 5 244 m 6 14◦

7 a 44.6 m b 36◦

8 a 16.2 m b 62◦

9 a 35 m b 64 m c 29 m10 507 m

Exercise 7F

1 a S45◦E, 135◦ b S45◦W, 225◦

c N45◦W, 315◦

2 a N25◦E, 025◦ b S70◦E, 110◦

c S30◦W, 210◦ d N80◦W, 280◦

3 a 25◦ b 18 km c 7.61 km4 a S56◦W, 236◦ b N56◦E, 056◦

5 130◦

6 a 4.2 km b 230◦

7 a 10 km, 15 km b 5 km c 8.7 kmd 10 km e 319◦, 13.2 km

8 a 12.9 km b 15.3 km c 17.1 kmd 42◦ e 138◦, 23.0 km

Exercise 7G

1 a a = 15, b = 14, c = 13b a = 19, b = 18, c = 21c a = 31, b = 34, c = 48

2 a C = 50◦ b A = 40◦ c B = 105◦

3 a 5.94 b 12.08 c 45.11 d 86.8◦

e 44.4◦ f 23.9◦

4 a 41.0◦ b 53.7◦ c 47.2◦ d 50.3◦

5 a 19.60 b 30.71 c 55.38 d 67.676 a 4.45 b 16.06 c 67.94 d 67.847 a c = 10.16, B = 50.2◦, C = 21.8◦

b b = 7.63, B = 20.3◦, C = 39.7◦

c a = 52.22, c = 61.01, C = 37◦

d b = 34.65, c = 34.23, C = 54◦

8 39.09 9 43.2◦ 10 49.6911 a = 31.19, b = 36.56, A = 47◦

12 A = 27.4◦, C = 22.6◦, c = 50.2413 a = 154.54, b = 100.87, C = 20◦

14 a

A B

C

60°

10°

5 km

NN

b 2.66 km from A, 5.24 km from B15 409.81 m16 a 19.89 km from naval ship, 18.16 km from

other shipb 1.21 h (1 h 13 min)

17 a Airport A b 90.44 km c Yes

18 a

A B

C

25° 50°80 m

b 130◦ c 25◦ d 145.01 m e 61.28 m

Exercise 7H

1 a 36.72 b 47.62 c 12.00 d 14.55e 29.95 f 11.39

2 a 33.6◦ b 88.0◦ c 110.7◦ d 91.8◦

e 88.3◦ f 117.3◦

3 17.41 4 27.09 5 51.51 6 50.5◦

7 63.2◦ 8 40.9◦ 9 B = 46.6◦

10 B = 73.2◦

11 a 60◦ b 42.51 km12 5.26 km 13 33.6◦ 14 11.73 km15 4.63 km 16 45.83 m

Exercise 7I

1 a 102 cm2 b 40 cm2 c 24 cm2

d 52 cm2 e 17.5 cm2 f 6 cm2

2 a 25.7 cm2 b 65.0 cm2 c 26.0 cm2

d 32.9 cm2 e 130.5 cm2 f 10.8 cm2

3 a 36.0 km2 b 9.8 m2 c 23.5 cm2

d 165.5 km2 e 25.5 cm2 f 27.7 cm2

4 a 10 cm2 b 23.8 cm2 c 63.5 cm2

d 47.3 m2 e 30 m2 f 30.1 m2

g 100.9 km2 h 21.2 km2 i 6 km2

5 224 cm2 6 1124.8 cm2 7 150.4 km2

8 3500 cm2

9 a 6 m2 b 4.9 m2 c 6.9 m2

10 a 33.83 km2 b 19.97 km2 c 53.80 km2

11 a 43.30 cm2 b 259.81 cm2

12 a i 12 km2 ii 39 km2 iii 21 km2

b 29.6◦

Multiple-choice questions1 D 2 C 3 B 4 E 5 B6 A 7 A 8 D 9 C 10 B

11 B 12 D 13 E 14 D 15 B16 D 17 E

Short-answer questions1 35.87 cm 2 117.79 cm 3 4◦

4 14.02 m 5 76.3◦ 6 A = 40.7◦

7 54.17 km 8 760.7 cm2 9 27.7 m2

Extended-response questions1 a 50.95 m b 112.23 m



An

swer


c

T B

h

18°

Height of tree = 36.47 m2 a 50◦

b First group 3.68 km, second group 3.39 kmc 290◦

3 a 45 km b 54 km c 110◦ d 81.26 km4 a 44.4◦, 57.1◦, 78.5◦ b 14.70 m2

c $426.305 a 24 000 m2 b 48 000 kg c $744 000 0006 a 21.75 km2 b 7.71 km c 37.6◦ d 32.4◦

e 4.40 km f 10.34 km2 g 32.09 km2


1 a 19 b 6 c 64 d March e 1f 3 g −17 h 125 i i j ♣k 81 l ⇒ m 48 n ↑ o C

2 a 6 b 16 c 11 d 21 e 26 f 313 a b 3, 5, 7, . . . c 9, 11

4 a

b Position 1st 2nd 3rd 4th 5thNumber of dots 1 4 7 10 13

5 a

b Position 1st 2nd 3rd 4th 5thNumber ofmatch sticks 4 12 24 40 60

Exercise 8B

1 a 3, 5, 7, . . . b 9, 112 a 7, 12, 17, . . . b Yes, d = 5

c 22, 27 matchsticks3 a 3 c −4 d −3 f 9

h −2 i 0 k 9 l 1b, e, g, j, Not arithmetic

4 a d = 6, t5 = 29 b d = −4, t5 = 1c d = 4, t5 = 27 d d = −4, t5 = −8e d = −5, t5 = 15 f d = 0.5, t5 = 3.5g d = 2, t5 = 8.5 h d = 0.1, t5 = 2.4i d = 0.3, t5 = 7.6 j d = 16, t5 = 91

k d = −19, t5 = −33 l d = 23, t5 = 200m d = −7, t5 = −4 n d = 1

3 , t5 = 2o d = 1

4 , t5 = 32

5 a 41, 47 b 2, −1 c 0, − 12 d 59, 67

e −15, −27 f 2, 2.3 g 7.8, 7.3 h 35, 39i 11, 7 j 25, 30 k 5

6 , 1 l 6 12 , 8

6 a 28, 33 b −10, −16 c 33, 42d 13, 8 e 11, 19 f 13, 21g 29, 18 h 29, 15 i 23, 39, 55

7 a 48 b −61 c 31.5d −22.3 e −980 f −815

8 a i 9ii n 1 2 3 4

tn 3 5 7 9

iii tn

n

10

5

10 2 3 4

iv Points lie on a line with positive slope.b i 2

ii n 1 2 3 4tn 11 8 5 2

iii tn

n

10

15

5

10 2 3 4

iv Points lie on a line with negative slope.

Exercise 8C

1 a a = 7, d = 4 b a = 8, d = −3c a = 14, d = 9 d a = 62, d = −27e a = −9, d = 5 f a = −13, d = −6g a = 2.4, d = 0.3 h a = 8.1, d = −0.9i a = 28, d = 17

2 a 119 b −38 c 39 d −141 e 2.0 f 6.53 a 120 b 306 c −441 d 436 e −119

f 25.3 g −198 h −7.44 323 5 1908 6 −33 7 $123 8 15.25 m9 68.4, 68.1, 67.8, 67.5 seconds

10 $43 11 a 10 logs b 61 logs12 a 6th b 49 13 a 5th b 22nd14 20 weeks15 a 100, 107, 114, 121 songs

b tn = 100 + 7(n − 1)c 261 songs d 36th month

16 a $865 b After the 24th week17 a $73 800 b In the 6th year

c In the 12th year



An

swers

Answers 555

Exercise 8D

1 a 50 pairs b 101 c 50502 a a = 1, n = 100, l = 100 b 50503 a 1044 b 5160 c −152 d 105

e 168 f 171 g 302.6 h −23104 a n = 50, a = 2, l = 100 b 25505 10756 a 55 km b 720 km7 a 183 b 24758 a $194 000 b $4 640 0009 a i 1 + 2 + 3 + 4

ii 1 + 2 + 3 + 4 + · · · + 11 + 12b a = 1, d = 1, n = 12 c 78 boxes

10 a 15 + 14 + 13 + · · · + 7b i 15 ii 9 iii −1 c 99 logs

11 $53 50012 a i 12 ii 324 b i 15 ii 390

c i 50 ii 2550 d i 33 ii 1683e i 50 ii 2500 f i 19 ii 412.3

13 a a = 100, d = 50, l = 1000b 19 bets c $10 450

Exercise 8E

1 a Number of folds 1 2 3 4 5Number of areas 2 4 8 16 32

b a = 2, r = 2 c 128 areas2 a 2 b 1

4 c 5 d −3 e 12

f 13 g −2 h 7 i 2

33 a 2 b −2 d 3 e −3

h 12 c, f, g, i Not geometric

4 a 56, 112 b 6, 2 c −135, 405d −6, 3 e 2.7, 0.81 f 49.13, 83.521g −9.261, 19.4481 h 2

9 , 427 i 3

8 , 932

5 a 3 906 250 b 5120 c −1024 d 14

e 256 f 81 g 3125 h 15366 a 375, 1875 b 48, 96 c 216, 96

d 36, 20.25 e −8, 16 f −6, 18g 3, −6 h 12, 108 i 486, 216

7 a i 24ii n 1 2 3 4

tn 3 6 12 24

iii tn

n

10

15

20

25

5

10 2 3 4

iv Curve v Diverge

b i 1ii n 1 2 3 4

tn 8 4 2 1

iii tn

n

10

5

10 2 3 4

iv Curve v Convergec i −8

ii n 1 2 3 4tn 1 −2 4 −8

iii tn

–10

–5

0 1

2

3

5

4 n

iv Neither (it zig-zags)v Diverge and oscillate

d i − 12

ii n 1 2 3 4tn 4 −2 1 − 1

2

iii tn

4

–4

–2

0 1 2 3

2

4

n

iv Neither (it zig-zags)v Converge and oscillate

Exercise 8F

1 a 384 b 5th c −192 d 3rd position2 a a = 12, r = 2 b a = 6, r = 3

c a = 2, r = 4 d a = 56, r = 12

e a = 36, r = 13 f a = 3, r = −3

g a = 5, r = −2 h a = 100, r = 0.1i a = 27, r = 2

33 a 78 732 b 1536 c −3 906 250

d −786 432 e 196 830 f 14 a a = 3, r = 4 b a = 5, r = 2

c a = −3, r = 7 d a = 200, r = 1.10e a = 6, r = −3 f a = −4, r = −5

5 a 1 b 1152 c 524 288 d 531 441e 1

3 f 0.0001 g 6561 h −0.125



An

swer


6 3072 7 3172.62 8 5.739 a tn = 9 × (2)n−1 b tn = 54 × ( 1

3 )n−1

c tn = 7 × (−3)n−1 d tn = −3 × (−4)n−1

e tn = (1.1)n−1 f tn = (0.8)n−1

10 a 10 935 b 10th11 1 cm, 3 cm, 9 cm, 27 cm12 a 100, 95, 90.25, 85.74

b 100, 120, 144, 172.8c 5000, 5150, 5304.50, 5463.64d 7000, 6720, 6451.20, 6193.15

13 $4267.2514 a $95 212.46 b Start of 11th year15 a a = 2000, r = 0.90 b tn = 2000 × 0.90n−1

c 774 people d 14 years16 a i Geometric ii Divergent iii B

b i Arithmetic ii Divergent iii Cc i Geometric ii Convergent iii Ad i Arithmetic ii Divergent iii Fe i Geometric ii Divergent, oscillating iii Df i Geometric ii Convergent, oscillating iii E

Exercise 8G

1 a a = 3, r = 4 b 1 048 5752 6 291 4503 a 59 048 b 196 605 c −1705 d 44 287

e 127.97 f 238.79 g 9309.74 h −725.31i 57.27 j 19.15

4 a $151 279.98 b $1 839 279.565 a 5, 25, 125, 625 letters

b 9 765 625 letters c 12 207 030 letters6 a $321 156.30 b $2 051 960.517 a 2, 4, 8, 16 descendants b 256 descendants8 a 50, 100, 200, 400 dollars b $25 5509 About 1.84 × 1019 or

18 400 000 000 000 000 000 grains

Exercise 8H

1 a a = 54, r = 13 b 80.96 c 81

2 a 144 b 121.5 c 81 d 96 e 426.67f 333.33 g 4000 h 156.25 i 356.67

3 a 85.25 b 85.332 c 85.333 . . .

4 No, as S∞ = 1080 m 5 10 m6 a 24 cm b 184 cm7 a 5, 4.5, 4.05, 3.65 L b 17.20 L

c 43.92 L d 50 L e 8 years

Exercise 8I

1 a 7, 10, 13, 16 b 28, 22, 16, 10c 19, 27, 35, 43 d 67, 54, 41, 28e 9.8, 10.2, 10.6, 11 f 14.6, 12.9, 11.2, 9.5g 1

2 , 14 , 0, − 1

4 h 16 , 1

2 , 56 , 7

6i 106, 69, 32, −5 j −8, −6.5, −5, −3.5

2 a 4, 12, 36, 108 b 3, −6, 12, −24c −6, −12, −24, −48 d −1, −5, −25, −125e 1, −3, 9, −27 f 24, 12, 6, 3g 54, −18, 6, −2 h 125, 25, 5, 1

3 a 4, 7, 10, 13 b 2, 10, 50, 250 c 6, 19, 45, 97d 8, 23, 68, 203 e 100, 92, 84, 76 f 1, −2, 4, −8g 2000, 1900, 1790, 1669h 3000, 3650, 4332.5, 5049.13i 3, 9, 81, 6561 j 256, 16, 4, 2 k 4, 14, 34, 74l 4, 14, 34, 74 m 1, 15, 85, 435 n 1, 15, 85, 435o 1, 2, 6, 42 p 3, 6, 30, 870

4 a tn+1 = 2tn + 5, t1 = 3 b tn+1 = 3tn + 7, t1 = 4c tn+1 = 5tn + 2, t1 = 1 d tn+1 = 6tn − 9, t1 = 2e tn+1 = t2

n + 2, t1 = 15 a 3, 11, 27, 59 b 4, 19, 64, 199 c 1, 7, 37, 187

d 2, 3, 9, 45 e 1, 3, 11, 1236 a 57 b 67 c 196 608 d 59 049

e −2043 f 234 374 g 4892.63 h 8121.89i 3 263 442 j 547 008

7 a tn+1 = 3tn − 7, t1 = 10b 10, 23, 62, 179, 530 fish

8 a tn+1 = 1.05tn + 2000, t1 = 10 000b 10 000, 12 500, 15 125, 17 881.25 dollarsc $37 566.41

9 a tn+1 = 1.06tn − 70 000, t1 = 800 000b 800 000, 778 000, 754 680, 729 960.80 dollarsc $57 280.18

Multiple-choice questions1 B 2 C 3 C 4 A 5 B6 D 7 B 8 C 9 C 10 E

11 D 12 D 13 B 14 B 15 A

Short-answer questions1 83 2 45, 75, 105, 135 seconds3 1536 4 48, 24, 12, 6 metres5 717.57 6 880 7 112 8 659.08 9 16

10 a B b E c A d F e D f C

Extended-response questions1 a 37 squares b 21st2 a a = 300, r = 2 b 38 400 bacteria

c Day 12 d Day 203 a a = 65 000, r = 1.09

b $514 220.41 c $5 505 558.26d 6th year e 15th year

4 a 34 b 210.4 cm c Yes, as S∞ = 256 cm

5 a 14.7 m b 171.5 mc Time (s) Height (m)

1 53.92 983 132.34 156.85 171.56 176.47 171.58 156.89 132.3

10 9811 53.912 0

d 176.4 m e 6 seconds f 12 seconds



An

swers

Answers 557


1 a < b > c = d <

e > f < g < h <

2 a

876543210–1–2x

1 ≤ x ≤ 4

b 0 < x < 4

876543210–1–2x

c x < 4

876543210–1–2x

d x ≥ 4

876543210–1–2x

e –1 ≤ x < 4

876543210–1–2x

f 3 < x < 5

876543210–1–2x

3 a x ≤ 7 b x ≥ 1 c 0 < x ≤ 6d 3 < x < 6 e −1 ≤ x < 4

4 a x ≥ 5

876543210–1x

b x < 5

876543210–1x

c x > –2

6543210–1–2–3x

d x ≥ 4

876543210–1x

e –2 ≤ x < 4

6543210–1–2–3x

f 2 < x ≤ 5

876543210–1x

5 a 13 ≤ x < 20b

x0 5 10 15 20 25

13 ≤ x < 20

6 a 0 ≤ x ≤ 5 (x = 0 allows for a person with nohand luggage.)

b 0 ≤ x ≤ 5x

0 5 10

7 a

x

y

(1, 0)O

≤ 1x

x = 1

b

xO

x > – 2

(–2, 0)

y

x = –2

c y

xO

(0, 5)

y ≤ 5

y = 5

d

(0, 1)

y > 1

x

y

O

y = 1

e

(2, 0)

x < 2

x

y

O

x = 2



An

swer


f

x

y

(0, 2)

(0, –2)

–2 ≤ y ≤ 2

y = 2

y = –2

y

O

g

(2, 0)

O

(–1, 0)

–1 < x < 2 x = 2x = –1

x

y

h

(3, 0)

O

(5, 0)

x = 5x = 2

3 < x ≤ 5

x

y

i

–3 ≤ y < 0

x = 0

y = –3(–3, 0)

x

y

O

Exercise 9B

1 a Yes b Yes c No d No e No f Yes2 a Yes b No c Yes d No e Yes f Yes3 a

y – x = 5

(0, 5)

(–5, 0)

y – x ≤ 5

x

y

O

b

x

y

O

(0, –4)

(2, 0)

2x – y = 4

2x – y ≤ 4

c

O

(0, –3)

(3, 0) x – y = 3

x – y < 3

x

y

d

(0, 10)

O y + x = 10

y + x ≥ 10

x

y

(10, 0)

e

(0, 9)

(3, 0)O

3x + y ≤ 9

3x + y = 9

x

y

f

5x + 3y = 15

5x + 3y ≥ 15

(0, 5)

(3, 0)x

y

O



An

swers

Answers 559

g

(0, 5)

(–3, 0)

3y – 5x < 153y – 5x = 15

x

y

O

h

2y – 5x > 5

2y – 5x = 5

(0, 2.5)

(–1, 0)

O

y

x

i y

y – x > –3y – x = –3

x(3, 0)

(0, –3)

O

Exercise 9C

1

x

(0, 10)

x + y = 10

O

y

(10, 0)

Feasibleregion

2 y

x

Feasibleregion

O

(0, 4)

2x + 3y = 12

(6, 0)

3 y

x(5, 0)

(0, 3)

3x + 5y = 15

O

Feasibleregion

4

x

y

Feasibleregion

O (6, 0)

(7.5, 0)

(3, 3)

(0, 6)

(0, 5)

2x + 3y = 15

x + y = 6

5 y

xO (2, 0)

(0, 6)

(1, 3)(0, 3.5)

(7, 0)

Feasibleregion

x + 2y = 7

3x + y = 6

6

(4, 0) (6, 0)

(3, 2.5)

(0, 5)

(0, 10)

x

y

Feasibleregion

O

5x + 2y = 20

5x + 6y = 30

7

O (3, 0) (10, 0)

(2, 4)

Feasibleregion

4x + y = 12

3x + 6y = 30

x

y

(0, 5)

(0, 12)



An

swer


8

Feasibleregion

x + y = 30

x

y

O (0, 0)

(0, 30)

(30, 0)

(10, 20)

2x − y = 0

Exercise 9D

1 P = 24 at (6, 0) 2 P = 54 at (2, 12)3 C = 18 at (6, 0) 4 C = 6 at (2, 4)5 P = 50 at (10, 20)6 C = 10 at (0, 5) and (5, 0) and at all points on

the line between these two points

Exercise 9E

1 a y ≥ 02x + 4y ≤ 24 (Machine 2 time)

b B(0, 6), 2x + 4y = 24, (12, 0); intersection atC(4, 4)

c P = 200x + 360yd 4 Wigits and 4 Gigits; $2240

2 a x ≥ 0, y ≥ 02x + 2y ≤ 520 (material availability)2.4x + 3.2y ≤ 672 (worker time availability)

b (0, 260), 2x + 2y = 520, D(260, 0);2.4x + 3.2y = 672, (280, 0); intersection atC(200, 60)

c P = 36x + 42yd $9720; 200 Polarbear and 60 Polarfox

3 a 45x + 30y ≥ 450 (people)3x + 4y ≥ 36 (equipment)

b (0, 10), 3x + 4y = 36; (9, 0),45x + 30y = 450; intersection at B(8, 3)

c C = 3600x + 3200yd 8 Redhawks and 3 Blackjets; $38 400

4 a x ≥ 0, y ≥ 02x + 2y ≤ 8 (sawing)3x + 6y ≤ 18 (planning)P = 500x + 600y

b

(0, 4)

(0, 3)(2, 2)

(0, 0) (4, 0) (6, 0)

3x + 6y = 18

2x + 2y = 8

Feasibleregion

x

y

c 2 cubic metres of each; $2200

5 ax ≥ 0, y ≥ 012x + 20y ≥ 15 (vitamin B1)40x + 25y ≥ 30 (vitamin B2)C = 5x + 4.5y

b

x

(0, 1.2)

(0, 0.75)

(0.45, 0.48)

O

(0.75, 0) (1.25, 0)

Feasibleregion

y

40x + 25y = 30 12x + 20y = 15

c 0.45 kg of Healthystart and 0.48 kg ofWakeup; $4.41

Multiple-choice questions1 B 2 B 3 D 4 B 5 D 6 A7 D 8 D 9 D 10 D 11 A 12 C

13 D 14 A 15 C 16 D

Short-answer questions1 −2 ≤ x < 4

876543210–1–2–3x

2

xO

(0, 1)

(0, 5)

y

y = 1

y = 5

1 ≤ y < 5

3

x

y

O

(8, 0)

(0, 10) 5x + 4y = 40

5x + 4y ≤ 40

4

3x + 5y = 60

(0, 12)

(0, 0)

(20, 0)x

y

Feasibleregion



An

swers

Answers 561

5

(0, 10)

(20, 0)(15, 0)

(12, 2)

(0, 5)

O

x + 4y = 20

2x + 3y = 30

x

y

Feasibleregion

Extended-response questions1 a x ≥ 0, y ≥ 0

0.8x + 0.7y ≤ 56 (nitrate)0.2x + 0.3y ≤ 21 (phosphate)P = 600x + 750y

b

(0, 70)

(0, 0)

(21, 56)

(105, 0)(70, 0)

(0, 80)

0.8x + 0.7y = 56

0.2x + 0.3y = 21

x

y

Feasibleregion

c 21 tonnes of Standard Grade and 56 tonnes ofPremium Grade; $54 600

2 a x ≥ 0, y ≥ 03x + 5y ≥ 15 (vitamin A)4x + 3y ≥ 12 (vitamin B)C = 0.3x + 0.24y

b

(0, 3)

O

(1.36, 2.18)

(5, 0)(3, 0)

(0, 4)

4x+3y = 12 3x + 5y = 15

x

y

Feasibleregion

c 1.36 kg of Food A and 2.18 kg of Food B;$0.93


1 a No path possibleb Several answers are possible.

Example:

2 a i 4 vertices ii 5 edges iii 2 iv 3 v 2 oddb i 4 vertices ii 7 edges iii 3 iv 4 v 2 oddc i 5 vertices ii 6 edges iii 3 iv 1 v 4 odd

3 No answers – exploration

Exercise 10B

1 a Graphs 1 and 3 b Graphs 2 and 3c Graphs 1 and 2 d Graphs 1 and 3e Graphs 1 and 3

2 A, D, F3 Many answers are possible.

Examples:a b

c d

4 Many answers are possible.Examples:a b

c d

5 3 edges

Exercise 10C

1 A, B, D, F2 Many solutions are possible.

Examples:a A B

CD

b A

B

D

C

c

D

A

C

EB

d

D

A

B

C



An

swer


e

D

E

F

B

C

f

D

E F

GH

A B

C

3 a i v = 4, e = 4, f = 2ii v − e + f = 4 − 4 + 2 = 2

b i v = 7, e = 9, f = 4ii v − e + f = 7 − 9 + 4 = 2

c i v = 7, e = 12, f = 7ii v − e + f = 7 − 12 + 7 = 2

d i v = 7, e = 10, f = 5ii v − e + f = 7 − 10 + 5 = 2

4 a f = 2 b v = 3 c e = 4 d v = 4e f = 4 f v = 4 g f = 7 h e = 19

Exercise 10D

Other paths are possible in each case.1 Not traversable; more than two

vertices odd2 Traversable; all vertices even

Start/Finish

3 Traversable; two vertices odd,the other even

StartFinish

4 Traversable; two vertices odd,the rest even

Finish

Start

5 Traversable; all vertices even

Start/Finish

6 Not traversable; more than twovertices odd

7 Traversable; all vertices even

Start/Finish

8 Traversable; two vertices odd,the rest even

Finish

Start

9 Not traversable; more than twovertices odd

Exercise 10E

1 Other paths are possible in each case.a Euler circuit: all even vertices

Start/Finish

b Neither: more than twoodd vertices

c Euler path: two odd vertices,rest even

StartFinish



An

swers

Answers 563

d Euler path: two odd vertices,the rest even

Start

Finish

e Euler circuit: all even vertices

Start/Finish

f Euler path: two odd vertices,the rest even

StartFinish

g Euler circuit: all even vertices

Start/Finish

h Euler path: two odd vertices,the rest even

Start

Finish

i Neither: more than two oddvertices

2 a Yes, all vertices even.b Other routes are possible.

Town C

Town D Town BTown ETown A

Start /Finish

3 a No; not all even verticesb Yes; two odd vertices, the rest even. Two routes

are possible.A

H

G

B

C

F

D

EFinish

Start

4 a A B

CD

b An Euler path does not exist. The graph hasmore than two odd vertices.

c One possible solution is shown.

A

B

C

D

A B

CD

Start

Finish

The bridges can now be crossed only once in asingle walk because an Euler path now exists.The graph has two odd vertices and the rest areeven.

Exercise 10F

1 Other answers are possible.a A-F-G-B-C-H-E-Db F-A-B-C-D-E-H-G

2 Other answers are possible.a A-B-C-D-E-F-Ab A-B-C-D-E-Ac A-F-E-D-C-B-G-Ad A-B-C-F-I-H-E-G-D-Ae No Hamilton circuit exists.f A-E-F-G-H-D-C-B-A

Exercise 10G

1 a A-B-D-C-E-A; 105 kmb A-B-C-E-D-A; 26 km

2 A-B-C-E-F-D-A; 63 minutes3 A-C-D-E; 11 units4 A-F-E-D-C-G-B; length 24 units

Exercise 10H

1 8 vertices, 7 edges2 A, B, D



An

swer


3 Other answers are possible.a

b

c

4 a A

B

C

D

E

2

4

7

5

Length = 18

b A

B

C

D

E

2

2

4

3

Length = 11

c

A

B

C

D

E

4

53

7

3

F

Length = 22

d

A

B

CD

E

15

15

1020

Length = 60

e

A

B C

F

GD

E

2

4

5

3

3

3

Length = 20

f A

B

C

D

E

2

2

4

1

Length = 9

5 Outlet A Outlet B

Outlet C

Outlet DOutlet E

Outlet FOutlet G Tank

7

8

66

510

2

Length = 44 m6

11

10

8 1517

9 18

6

H

BC

DE

FG

A

Power station

Length = 94 km

Multiple-choice questions1 C 2 E 3 C 4 D 5 B 6 E7 B 8 E 9 B 10 B 11 D 12 C

13 B 14 B 15 C 16 E 17 B 18 B19 C 20 A 21 B 22 C 23 B 24 D25 E 26 C

Short-answer questions1 Many answers are possible.

Examples:a b c

2 Other answers are possible in each case.a

BA

CD

b A

B C

D

c

A

BC

D

E



An

swers

Answers 565

3 a deg(C) = 3 b 2 odd, 2 evenc Other answers are possible, ending at C and

tracing each edge once only. Example:B-A-C-B-D-C

4 a deg(C) = 4 b All evenc Other answers are possible, ending at A and

tracing each edge once only. Example:A-B-C-D-E-B-A-E-C-D-A

5 a 27 units b 24 units6 a 23 units b 17 units

Extended-response question1 a No edges intersect, except at vertices.

b v = 9, e = 14, f = 7; 9 − 14 + 7 = 2c 750 m d No odd, 9 evene i Yes, all vertices are even.

ii Many answers are possible. Example:P-C1-C8-C2-C1-C4-C2-C3-C4-C5-C7-C8-C6-C5-P

f i 1270 mii

140

350250

160

600

150

280

80

110

130400120

230200

Park Office

140

350250

160

600

150

280

80

110

130400120

230200C1

C2

C3

C4

C5

C6C7

C8

g i Hamilton circuit ii C7-Park Officeiii P-C1-C2-C3-C4-C5-C6-C8-C7-P, or the

same route in reverse


1 a 3 × 4b i 16 ii 3 iii 5

2 a i 2 × 3 ii 6, 7b i 1 × 3 ii 2, 6c i 3 × 2 ii −4, 5d i 3 × 1 ii 9, 8e i 2 × 2 ii 15, 12f i 3 × 4 ii 20, 5

3, 4 a 9 b 2 c 3 d 10 e 85 a 32 students b 3 × 4

c 22 Year 11 students preferred football.6 a A 4 × 3, B 2 × 1, C 1 × 2, D 2 × 5

b a3,2 = 4, b2,1 = −5, c1,1 = 8, d2,4 = 77 a i 75 ha ii 300 ha iii 200 ha

b 350 hac i Farm Y uses 0 ha for cattle.

ii Farm X uses 75 ha for sheep.iii Farm X uses 150 ha for wheat.

d i f2,3 ii f1,2 iii f2,1

e 2 × 3

8 a$70 $80 $90

SatSun

[100 150 17560 0 200

]

b i $34 750 ii $22 200 iii $56 950

Exercise 11B

1 a

A B CABC

⎡⎣0 2 0

2 0 10 1 0

⎤⎦ b

A BAB

[2 11 2

]

c

A B CABC

⎡⎣0 1 0

1 2 10 1 0

⎤⎦ d

A BAB

[0 33 2

]

e

A B CABC

⎡⎣0 1 1

1 0 21 2 0

⎤⎦ f

A B CABC

⎡⎣0 2 1

2 0 11 1 0

⎤⎦

2 Many answers are possible.Examples:a A B b

A B

c

A B

d

A B

e

A B

f

A B

3 a

A B C DABCD

⎡⎢⎢⎣

0 1 0 11 0 1 10 1 0 01 1 0 0

⎤⎥⎥⎦

b Compare the sums of the rows (or columns).The person with the highest total has met themost people.

c Person Bd Person C

4 a

A B C DABCD

⎡⎢⎢⎣

0 2 1 22 0 1 01 1 0 12 0 1 0

⎤⎥⎥⎦

b Compare the sums of the rows (or columns).The landmass with the highest total has themost connections to it.

c They are the same.d Yes. The numbers of odd and even vertices can

be seen from the sums of the rows (orcolumns). The network is not traversable (i.e.every bridge cannot be crossed just once)because all these sums are odd.



An

swer


Exercise 11C

1 a a = 4, b = 15, c = −2, d = 6b a = 8, b = 4, c = 5, d = −1c a = 2, b = 10, c = 5, d = 3d a = 5, b = 8

2 a = 5, b = 8, c = −3, d = −2, e = 9

Exercise 11D

1 a

[9 106 3

]b

[7 8

13 3

]c

[3 57 0

]d

[98

]

e

[3 41 6

]f

[4 −23 9

]g

[12 7

]h

[0 0

]i[0 0

]j[ −2 2 3 −9

]

2 a

[8 53 7

]b

[8 53 7

]c

[−2 −91 1

]

d

[2 9

−1 −1

]e Not possible

f

⎡⎣3 7

5 −24 −1

⎤⎦ g Not possible

h

⎡⎣−9 3

3 − 2−2 15

⎤⎦

3Liberal Labor Democrat Green

MenWomen

[43 42 10 537 37 17 9

]

4 aAida Bianca Chloe Donna

Weight (kg)Height (cm)

[6 8 −2 75 8 7 6

]

b Bianca c Bianca

Exercise 11E

1 a

[14 −2

8 18

]b

[0 −10

25 35

]c

[−64 12−6 −14

]

d

[2.25 0−3 7.5

]e

[18 21

]f

[ −1230

]

g

[2 3 00 1 1

212

]h

[−3 −6 8]

2 a

[9 −126 15

]b

[2 28

−6 −28

]c

[1 −328 33

]

d

[0 00 0

]e

[21 18

3 −12

]

3 a

[79 −3168 −36

]b

[−121 50−84 103

]

c

[13 −236 53

]d

[69 −2760 −30

]

4 a

Clothing Furniture ElectronicsStore AStore BStore C

⎡⎣6 2 9

5 1 94 −1 5

⎤⎦

b

Clothing Furniture ElectronicsStore AStore BStore C

⎡⎣1.8 0.6 2.7

1.5 0.3 2.71.2 0 1.5

⎤⎦

Exercise 11F

1 a Defined, 2 × 1,

[3819

]b Not defined

c Defined, 3 × 1,

⎡⎣ 17

32−10

⎤⎦

d Not defined

e Defined, 2 × 2,

[42 1421 7

]f Not defined

g Not defined

h Defined, 3 × 2,

⎡⎣ 15 5

24 8−3 −1

⎤⎦

2, 3 a

[2233

]b

[6453

]c

[0 −84 2

]

d

[ −4 −3−14 −20

]e

[8 35 2

]f

[16 1416 14

]

g

⎡⎣ 31

3521

⎤⎦ h

⎡⎣ 11

17

⎤⎦ i [83]

j [21] k [8] l [4] m [30] n [36] o[3 3

]4 a

[19 2243 50

]b

[23 3431 46

]c No

5 a

[104 70

80 54

]b

[9 87 6

]c

[17 1713 13

]

d

[8 64 2

]e

[14 14

6 6

]

6 a

[376 118 154 420643 117 281 523

]b [722]

c

⎡⎢⎢⎣

−496 752 976 −224−310 470 610 −140−744 1128 1464 −336

558 −846 −1098 252

⎤⎥⎥⎦

d

⎡⎣−131 −264 176

467 62 535697 279 406

⎤⎦

e

⎡⎢⎢⎣

102 22090 87

166 43167 −84

⎤⎥⎥⎦ f

⎡⎢⎢⎣

3 4 5 53 2 3 31 3 2 04 5 5 3

⎤⎥⎥⎦

7 a$

AnnBill

[405540

]b

$ CouponsJeansShirts

[60 245 1

]

c$ Coupons

AnnBill

[405 11540 16

]

8 5800 kJ



An

swers

Answers 567

9 a $32 b $30

c$

TomLouise

[4438

]

10Wheels Seats

SmithJones

[14 1312 9

]

11 aRawFood FastFood

Aubrey’sBettie’s

[35 1842 23

]

b$ Packets

RawFoodFastFood

[30 220 3

]

c$ Packets

Aubrey’sBettie’s

[1410 1241720 153

]

Exercise 11G

1 D2, 3 a i 1 ii

[3 −1

−5 2

]

b i 2 ii

[2 −2.5

−1 1.5

]

c i 4 ii

[0.5 −1.5

−0.25 1.25

]

d i −1 ii

[−2 71 −3

]

e i 0 ii No inverse

f i −2 ii

[−0.5 21 −3

]

g i 0 ii No inverse

h i −4 ii

[0.5 −0.751 −2

]

4 b, d, e, h

5 a

[3 −7

−2 5

]b

[1 −2

−2 4.5

]

c

[−4 91 −2

]d

[−1.5 3.51 −2

]

e

⎡⎣ 0.5 −0.5 0.5

0.5 0.5 −0.5−0.5 0.5 0.5

⎤⎦

f

⎡⎣ 0.1 −0.2 0.35

0.4 0.2 −0.6−0.1 0.2 0.15

⎤⎦

g

⎡⎣ 16 10 −15

−8 −5 83 2 −3

⎤⎦

h

⎡⎣−0.25 0.125 0.5

0 0.5 00.5 −0.25 0

⎤⎦

Exercise 11H

1 a

[23 18 33 7717 16 24 50

]

b

[38 17 51 7425 16 35 47

]

c

[8 33 13 597 17 8 32

]

d

[39 38 43 2133 29 29 17

]

e

[55 50 69 28 51 9 44 2841 35 42 21 30 8 26 24

]

f

[27 30 37 50 69 10 42 4714 25 32 30 42 9 28 33

]

2 a

[A I MH I G H

]b

[I T SJ A N E

]

c

[F L YH O M E

]d

[R U NA W A Y

]

e

[D O N T G ON O T S A F E

]

f

[F R E D I SN O T D E A D

]

3 a

[9 1 9 15 11 6 8 8

15 1 14 23 20 9 8 15

]

b

[6 1 7 7 4 0 8 31 9 1 6 8 0 4 9

]

4 Other student to check

Exercise 11I

1 x = 2, y = 3 2 x = 1, y = 23 x = 1, y = −2 4 x = 4, y = 65 x = 9, y = 2 6 x = −2, y = 3

Multiple-choice questions1 B 2 E 3 C 4 E 5 A6 D 7 D 8 C 9 A 10 E

11 D 12 B 13 E 14 A 15 D16 E

Short-answer questions1 2 × 4 2 13

[38 34 47 54

]4 2 × 1

5

⎡⎣0 2 0

2 0 30 3 2

⎤⎦

6 w = 2, x = 5, y = 4, z = 8

7 a

[9 3

12 6

]b

[3 6

11 8

]c

[−3 43 4

]

d

[6 7

15 10

]e

[0 00 0

]f

[7 21

14 32

]



An

swer


g

[20 1045 19

]h

[1 −0.5

−2 1.5

]i

[13 520 8

]

j

[3 14 2

]k 2 l

[1 00 1

]

Extended-response questions1 a 40 pigs b 320 sheep c Farm A2 a 21 pies b $2

c

[104103

]

d Value of sales for each shope Shop A, $104

3

a

Hours Hourswalking jogging

PatsyGeoff

[4 13 2

]

b$ kJ

WalkingJogging

[2 15003 2500

]

c$ kJ

PatsyGeoff

[11 850012 9500

]

4 a

[4 1 8 4 8 5 2 53 1 6 3 5 3 1 4

]

b

[2 3 1 4 0 2 2 11 0 1 1 2 3 0 2

]

5 a 6x + 5y = 14 b Apple $1.50, banana $1


1 a 0.9 b 0.7 c −0.6d −0.1 (estimates could vary by ± 0.2)

2 a none b weak negativec strong negative d weak positivee strong positive f moderate negativeg moderate positive h nonei weak negative j weak positive

k perfect positive or strong positivel perfect negative or strong negative

Exercise 12B

1 a

Tim

e

00

20

40

60

80

100

10 20 30 40 50Distance

b r = 0.850c For this sample of students there is a strong

positive linear relationship between distancetravelled and time taken. Students who travelfurther tend to take longer to get to school.

2 a IV = number of hours spent gambling, DV= amount spent gambling

b

Am

ount

0 10 20Hours

30 40

0

1000

2000

3000

4000

5000

c r = 0.922d For this sample of gamblers there is a strong

positive linear relationship between thenumber of hours spent gambling and theamount of money spent gambling. Those whogambled for longer tended to spend more ongambling.

3 a Either variable could be the IV.

b

Fem

ale

Male40

45

50

55

60

65

70

75

50 60 70 80

c r = 0.894d There is a strong positive linear relationship

between the percentage of males with eyedisease and the percentage of females with eyedisease. Those countries with high percentagesof males with eye disease also tended to havea high percentage of females with eye disease.

4 a IV = age, DV = price



An

swers

Answers 569

b

Pri

ce

Age0

0

5000

10000

15000

20000

25000

2 4 6 8 10 12

c r = −0.755d There is a strong negative linear relationship

between the age and price of motorbikes.Older motorbikes tended to have a lower price.

5 a Either variable could be the IV

b

Hus

band

Wife15

15

20

25

30

35

40

45

20 25 30 35

c r = 0.607d There is a moderate positive linear

relationship between the age of a wife and herhusband. Men and women tend to marrypartners of a similar age.

Exercise 12C

2 a height = 68.2 + 0.464 × age (correct to 3sig. figures)

b On average, the children’s height increased by0.464 cm for each one month’s increase intheir age. Because the data specifically relatesto girls aged 36 to 60 months, the intercept isunlikely to give a meaningful prediction aboutbirth height (length).

c i 87.7 cm ii 101.6 cm3 a daughter’s height = 50.2 + 0.715 × mother’s

height (correct to 3 sig. figures)b On average, the height of the daughters

increased by 0.715 cm for each 1 cm increasein the height of the mothers.

c 171.8 cm4 a IV: number of DVD players

b Cost = 3629 + 24.00 × number of DVDplayers

c $3629 d $24

5 a weight = 19.8 + 5.50 × shoe size(correct to 3 sig. figures)

b On average, the weight of adult malesincreased by 5.50 kg for each unit increase inshoe size.

c 74.8 kg6 a time = 14.52 + 4.408 × distance

(correct to 4 sig. figures)b On average, travel time increased by 4.4

minutes for each extra kilometre travelled. Theintercept has no meaningful interpretation.

c 27.7 minutes7 a response time = 51.3 – 8.70 × drug dose

(correct to 3 sig. figures)b On average, the time to experience pain relief

decreases by 8.70 minutes for each extramilligram of drug taken. The time taken forthe patient to experience pain relief if no drugis taken is predicted to be 51.3 minutes

c −0.9 minutes, no8 a DV: income

b income = 4607 + 18.83 × amount spent oninternet advertising

c On average, income increased by $18.83 foreach additional dollar spent on internetadvertising. The predicted income with noadvertising is $4607.

d $51 682

Exercise 12D

1 a (2, 5) b (3, 2) c (2.5, 2.5)d (3, 2) e (4, 3) f (2, 3)

2 a (2, 2, 2) b (4, 3, 4) c (3, 4, 3)d (7, 8, 7)

3 a 2 b 2.5 c −3 d −0.54 a (38, 85.5), (48, 91) and (58, 95)

b slope = 0.475c

3680828486889092949698

100

38 40 42 44 46 48Age (months)

Hei

ght (

cm)

50 52 54 56 58 60

5 a (157, 160), (164.5, 170.5) and (173, 178)b slope = 1.125



An

swer


c

150150

160

170

180

155 160 165 170 175Mother’s height (cm)

Dau

ghte

r’s

heig

ht (

cm)

6 a (8, 70), (9.5, 69.5) and (10.5, 80)b slope = 4c

750

60

70

80

90

8 9Shoe size

Wei

ght (

kg)

10 11

7 response time = 40 – 6 × drug dose (correct to1 sig. figure)

8 travel time = 10 + 7 × distance (correct to1 sig. figure)

Multiple-choice questions1 D 2 E 3 A 4 D 5 B6 E 7 C 8 C 9 A

Short-answer questions1 r = 0.9272 a (22, 65), (62, 92) and (96, 94)

b slope = 0.4

Extended-response questions1 a r = 0.4865

b score = 18.4 + 1.38 × inside 50s (correct to3 sig. figures)

c 129; extrapolating2 a errors = 14.9 – 0.533 × time (correct to 3

sig. figures)b slope = −0.533; the average number of

errors made is reduced by 0.533 for everyextra second taken to complete the task. Theintercept does not have a meaningfulinterpretation.

c 9.6 errors3 a number of new clients = −3.99 + 0.173 ×

exam score (correct to 3 sig. figures)b On average, the number of clients attracted by

the graduates increased by 0.173 for eachextra 1 mark obtained on the final exam. Theintercept has no sensible interpretation.

c 13d Not very reliable: you are making a prediction

that takes you well beyond the range of thedata.

4 a The statement is questionable because itimplies causality. The existence of even astrong relationship between two variables isnot, by itself, sufficient information toconclude that one variable causes a change inthe other.

b exam mark = 24.7 + 0.699 × assignmentmark (correct to 3 sig. figures)

c Intercept: on average those who score 0 on theassignment will score about 25 on the finalexam. Slope: on average students’ exam markswere 0.7 marks higher for each additionalmark they obtained on the assignment.

d 60e Reliable: you are making a prediction that

falls well is within the range of the data.


Answers to maths yr 11 i think

Documents

Transcript of Answers to maths yr 11 i think