Maths A Textbook - Answers

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CHAPTER 1 Earning money

Skills check

1

75

2

12.6

3

3825

4

11.4%

5

400 km

6

20.8 days

Exercise 1A — Calculating salary payments

1

$1700

2

$960

3

$4500

4 a

$745

b

$1490

c

$3228.33

5

$1653.84

6

7

$23 920

8

$32 500

9

$69 600

10

C

11

$14.28

12 a

$634.62

b

$17.63

13 a

$688

b

Karina ($16.38 per hour)

14

45 hours

Exercise 1B — Calculating wages

1

$518

2

3 a

$424.80

b

$566.40

c

$501.50

4 a

$432

b

$499.50

c

$600.75

5 a

$17.34

b

$225.42

6

D

7

$9.68

8

39

9

10

$12.54

11

C

12

D

13

$422.62

14

$548.80

15 a

$349.65

b

43 hours

16

$11.78

10 Quick Questions 1

1

$344.16

2

$518.70

3

$218.40

4

$95.04

5

$12.87

6

$903.85

7

$2692.31

8

$4706.67

9

$846.15

10

$24.18

Exercise 1C — Commission and royalties

1

$ 2000

2 a

$260

b

$327

c

$568.79

3 a

$400

b

$1200

c

$1360

4

$1425

5

$4140

6

B

7

C

8

$8125

9

$800

10 a

$4125

b

$5375

c

$16 875

11

$950

12 a

$390

b

$490

c

$649

13

B

14 a

$400

b

$500

c

$8000

d

$8125

15

$625

16 a

$300

b

$345

c

$406.80

17

D

18

$15 500

19

$510

20

$810

Exercise 1D — Payment by piece

1

$75.95

2 a

$103.50

b

$94.50

c

$85.50

d

$81

3

$175

4

$135

5

$325.50

6

$327

7 a

$92

b

$138

c

$87.40

d

$114.08

8 a

$57.75

b

$125.13

c

$103.95

9

$22.80

10 a

$11

b

$27.80

c

$19.32

11 a

$134.40

b

$16.80

12 a

$174

b

$21.75/h

c

$29.00/h

13

24


1

$455.84

2

$346.15

3

$740.38

4

$3307.69

5 $32 406.40 6 $487.207 $570 8 $208.55 9 $60.30

10 $1840

Exercise 1E — Working overtime1 $16.95 2 $22.84 3 $28.704 $142.56 5 $157.206

Answers

Annual salary Weekly pay

Fortnightly pay

Monthly pay

$30 000 $576.92 $1153.84 $2500.00

$39 500 $759.62 $1519.23 $3291.67

$42 250 $812.50 $1625.00 $3520.83

$54 350 $1045.19 $2090.38 $4529.17

$86 475 $1662.98 $3325.96 $7206.25

NameHourly

rateHours

worked Wage

A. Smith $14.52 40.5 $580.80

B. Brown $16.45 38.5 $625.10

N. Tran $15.95 37.5 $598.13

A. Milo $20.10 41.5 $824.10

L. McTavish $18.04 36.5 $649.44

Name WageHours

workedHourly

rate

A. White $416.16 36 $11.56

B. Black $538.80 40 $13.47

C. Green $369.63 37 $9.99

D. Brown $813.96 42 $19.38

E. Scarlet $231.30 15 $15.42

F. Grey $776.72 38 $20.44

NameOrdinary

rateOvertime

rateHours

worked Pay

A. Nguyen $8.90 Time and a half

4.5 $53.40

M. McDonnell $9.35 Double time

6.5 $112.20

F. Milosevic $11.56 Time and a half

7.5 $121.38

J. Carides $13.86 Time and a half

6.5 $135.14

Y. Robinson $22.60 Double time

5.5 $248.60 1A

1E

MQ Maths A Yr 11 - Ans Page 560 Thursday, July 5, 2001 8:08 AM

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7 C 8 A 9 B10 $543.52 11 $721.60 12 $596.2513

14 C 15 A 16 $595.2017 a $705.28 b $788.80 c $92818 $455.78 19 $492

Exercise 1F — Additions to and deductions from gross pay1 $385.202

3 $389.804 a $2519.23 b $1585.23 5 $7.586 $56.027 a $511.10 b $5.11 c $407.268 a $2153.85 b $44.84 c $1448.419 $18.71

10 $106.4411 a $422.56 b $23.24 c $331.1412 a $2884.62 b $137.02 c $69.60

d $1668.7813 a $516.80 b $2428.9614 a $880.77 b $4139.6215 a $466.20 b $81.59 c $464.5516 a $5269.23 b $922.12 c $96.15

d $4315.28

Chapter review1 $761.54 2 $2592.31 3 $15 912 4 $22.295 a $522 b $594.70 c $588.246 a $442.80 b $220.807 $11.40 8 43 hours 9 $395.20

10 $798.50 11 $534 12 $340.7513 $9814 a $21.30 b $28.4015 a $98.10 b $10916 a $368.60 b $426.80 c $426.80

d $485

17 $590.24 18 $333.25 19 $4.0520 a $1855.77 b $83.5121 a $631.55 b $13.26

c $22.10 d $455.89

CHAPTER 2 TaxationSkills check1 20.4 2 15% 3 $1104 17.8 litres 5 4.05 hrs

Exercise 2A — Calculating allowable deductions1 $1153.90 2 $1624.553 $1070.10 4 $1540.365 a $914 b $1208.77 c $811.72

d $1560.206 a $1000 b $600 c $3607 $3087.508 a i $30 000 ii $18 000 iii $10 800

b 2005–069 $960 10 $18 760

11 $712.27 12 $40 074.50

Exercise 2B — Taxable income1 $43 754.252 a $16 879.20 b $15 736.503 $43 568.344 a $24 219.40 b $22 262.605 a $20 503.60 b $20 075.206 a $42 500 b $2600 c $39 9007 a $34 262.30 b $498.24 c $32 204.068 a $74 280 b $8737.46 c $65 542.549 a $25 649 b $1470 c $1540

d $1349.40 e $21 289.6010 A

10 Quick Questions 11 $2260 2 $1581.22 3 $16504 $1105.50 5 6 years 6 $36 5207 $41 771 8 $22 660 9 $37 525.80

10 $24 570

Exercise 2C — Medicare levy1 $598.052 a $648.75 b $851.18 c $14103 a $23 491 b $352.37

Exercise 2D — Calculating tax1 $70152 a Nil b $2154.75 c $5755

d $9676 e $14 677 f $23 303.043 a $17 039.36 b $1876.634 $3897.405 a $7060 b $534.00 c $75946 a $2402.50 b $8646.10 c $18 662.507 $81.148 $230.699 B 10 B 11 D

12 a $38 674.10 b $8562.31 c $291.69 refund13 a $38 942.80 b $166.28 c $8252.67

d $393.89 refund

NameOrd. rate

Normal hours

Time and

a half hours

Double time

hours Total pay

W. Clark $8.60 38 4 $378.40

A. Hurst $9.85 37 .5 6 $482.65

S. Gannon $14.50 38 5 2 $717.75

G. Dymock $16.23 37.5 4 1.5 $754.70

D. Colley $24.90 36 6 8 $1518.90

Gross pay Deductions Net pay

$345.00 $89.45 $255.55

$563.68 $165.40 $398.28

$765.90 $231.85 $534.05

$1175.60 $429.56 $746.04

$2500.00 $765.40 $1734.60

1A

2D


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14 a

Gross annual pay

=

$44 650,PAYG tax

=

$11 940.50

b

$41 513.40

c

$9456.72

d

$2483.78

15 a

$392.05

b

$4751.14 debt

16

1590

17

Pay $180


1

$600

2

$360

3

$442.01

4

$385.05

5

$502.62

6

Nil

7

$2305.20

8

$6130.00

9

$14 603.80

10

$25 920

Investigation — Tax offsets

1

The amount appears correct ($52.50)

2

$1115

Exercise 2E — Calculating GST and VAT

1

$3.56

2 a

23c

b

$6.89

c

$9.85

d

13c

e

$8.99

3 a

80c

b

48c

c

9c

d

63c

e

34c

4

$123.75

5 a

$126.39

b

$32.89

c

$16.17

d

$5.45

e

$6.47

6 a

$30

b

94 cents

c

$47

d

$2.94

e

$9.86

7

$98.50

8 a

$1.90

b

19c

9

$348.10

10 a

$1.08

b

$80.63

c

$193.29

d

$49.21

e

$6.95

11 a

$33 550

b

$36 630

c

$34 705

d

$38 885

Chapter review

1

$2865

2

$2148.43

3 a

$12 600

b

$9072

c

$6531.84

4

6 years

5

$27 057.35

6

$43 883

7

$70 420

8 a

$28 483.60

b

$26 465.60

9 a

$34 409.30

b

$32 366.15

10

$585

11 a

$232.50

b

$375

c

$412.50

d

$502.60

e

$570

12

$9730

13 a

Nil

b

$2270.69

c

$7081

d

$15 160

e

$24 040

14 a

$33 987.20

b

$6576.16

c

$509.81

d

$7085.97

e

$136.27

15

$291.66

16 a

$40 255

b

$9060.33

c

$1100.93

17

$99

18 a

$1.13

b

$36.90

c

12c

d

$3.75

e

$1.25

19

$22

20

$112.50

CHAPTER 3 Spending money

Skills check

1

33.75

2

237.6

3

306

4

$360

5

$53.45

Exercise 3A — Discount

1

2

3

One item is discounted by just over 30% but the others range from a 10.00% to a 28.59% discount.

4

5

6

9

10

11

No, as the 12.5% is calculated from different amounts. For example, a $60.00 item reduced by 12.5% ($7.50) is $52.50. A $52.50 item increased by 12.5% ($6.56) is $59.06.

Exercise 3B — Profit and loss

1

2

5

Children’s $14.40; Adults’ $20.40; Extra large $22.80

a

25%

b

49.3%

c

27.7%

d

28.8%

e

11.5%

f

26.5%

g

25.2%

h

28%

i

10%

j 20%

a i $10.05 ii 25.16%b i $7.05 ii 23.54%c i $17.05 ii 42.68%d i $7.95 ii 19.90%

a 25.02% b 11.12% c 10.00% d 28.59%e 22.23% f 20.01% g 30.78%

a i $4.98 ii 19.88%b i $10.57 ii 9.46%c i $5.91 ii 7.78%d i $4.65 ii 14.19%e i $16.99 ii 11.77%f i $8.35 ii 10.30%

Item

Original price($)

% dis-count

Discount($)

Saleprice($)

a Microwave 300 10% 30 270

b Furniture set 2030 5% 101.50 1928.50

c Mirror 40 30% 12 28

d Necklace 1560 12.5% 195 1365

e Fridge 760 20% 152 608

f Stereosystem

480 33 % 160 320

g Washingmachine

564 25% 141 423

h Car 7500 50% 3750 3750

a $119 b $101.15 c $17.85

7 A 8 D

a $11.94 b $1.79

a $175 b $8.75

a 74.94% b 40.63% c 80.08% d 50%e 55.26% f 197.5% g 45% h 63.64%a 80% b 78% c 85.71% d 92.48%e 85.71% f 70% g 75% h 95.83%

3 $70, 140% 4 $79.75; 53.26%

6 4 years 7 $150 8 $25 each

13---

1F

3B

MQ Maths A Yr 11 - Ans Page 562 Monday, September 24, 2001 7:16 AM

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10 Quick Questions 11 25% 2 $105 3 12.5% 4 $23.805 50% 6 $21.60 7 $40 8 236%9 $780 10 $180 000

Investigation — Dealing in diaries1 $2.40 2 $30 3 25%4 58.3% 5 $50 6 41.7%7 $130 8 $80 9 61.54%

Exercise 3C — Budgeting12 Answers will vary.3 a

b $34.834

5 a $320.83b Income = $809.50 per month; New expenses =

$677 per month, so she can afford to move out.6 Answers will vary.7 a

b $600 c 2.36%

Exercise 3D — Cost of services1 a $348.50 b 1/3/01

c Previous $375.55, down $27.05d 7/11/00, 7/02/01e $3.79 f $26.60g Tariff 11 up, Tariff 33 down

2 a 2253 b 52 964 c $24.13d $241.31 e 10.7 cents

3 a 1904 b 1352 c $319.354 a $100.70 b $9.40 lower

c Approx. same d $1.12 e $408.40f $34.03

5 a 134 b × by MJ factorc $9.16 d 2.397c/MJe $101.48

6 a 6370 b $106.26 c $10.63d $116.89

7 $138.668 a $166.09 b $181.09 c Pensioner

d $367.27 e $664.36 f $55.369 a 62 kL b $0.80 c 248 kL

10 $138.6011 a $10 000 b 15%12 a Call charges + Service and equipment charges −

Flexi-Planb 28.2% c Flexi-Plan d $144.15

13 a 404 @ 25c b 17.7% c 35.6d 22.8c e 7 pm

Exercise 3E — Credit cards1

4 a 53 days, 48, 40, 34 and 26 days b Very beginning5 $17.706 a 28 days b $22.10

c No, since it was paid on 29/4, which was less than 25 days from the end of the statement

d The balance is over $25, but under $1000, so the minimum amount due is $25.

e Credit limit − Closing balance: $1000 − $650 = $350

7

Exercise 3F — The exchange rate1 a 58.29 b 38.27 c 119 900 d 4062 a $373.83 b $821.14 c $630.32 d $74.573 a 50 504 yen b $784.59 c $15.414 a 800 b 320 c $257.825 $15.41

10 Quick Questions 21 Fixed, variable 2 $8.463 $46 800 4 3110 kWh5 0.0493% 6 4th May7 The total amount owing is $540.65.8 Selling 9 7.81 Pounds 10 $150.28

a $1565 b $785 c $1450 d 2.07 months

Monthly income ($) Monthly expenses ($)

AustudyBirthday money

502.6720.83

Board and foodTransportBooks and stationery

InsuranceEntertainmentEnrolment feeClothes

216.6763

4024552565

Total: 523.50 Total: 488.67

ItemCost

($ per week)Rent 138.46Food 90Electricity 32.31Gas 4.62Phone 27.69Car registration 8.27Car insurance 9.62Health insurance 13.46Contents insurance 2.40Clothes 23.08Entertainment 18.46Total: 368.37

Income ($) Expenses ($)

Government subsidy

Membership fee

Profit from auction

Profit from stalls

Profit from concerts

4 200

16 250

400

920

3 600

RentNewsletterSunday SchoolBillsPublic liability and insurance

AdvertisingStationeryComputerUnexpected

6 000960

7 2002 640

1 860360250

3 5002 000

Total: 25 370 Total: 24 770

a $17.50 b $25 c $25 d $25e $33 f $57 g $87 h $54i $58 j $80

2 $4.95 3 $0.75

a $19.89 b $29.08

2E

3F


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sChapter review1 $35 2 16.7% 3 $2504

5 $256.20 6 $2007

8 a Rent $100; Electricity $10; Gas $7; Phone $23; Car registration $8; Car insurance $9; Contents insurance $3; Health insurance $9; Food $100; Sport $30; Entertainment $20; Clothes $28; Holidays $23; Total $370 b $5200

9 $45.42 10 $400.97 11 $401213 65.03 pounds

CHAPTER 4 Length, area and volumeSkills check1 The shortest measured distance between two points.2 mm, cm, m, km.3 The distance around the boundary of an object.4 a 24 cm b 28 m c 15 m d 18.85 m5 The amount of space within the boundary of a two-

dimensional closed figure.6 mm2, cm2, m2, km2, ha7 a 36 cm2 b 40 m2 c 10.83 m2 d 28.27 m2

8 a Square b Rectangle c Triangled Trapezium/trapezoid e Parallelogramf Kite

9 a 2.13 b 1.75 c 79.51 d 3.0610 ‘Volume’ is the amount of space within, or occupied

by, a 3-D object. ‘Capacity’ is the quantity of liquid or gas which a 3-D container could hold.

11 a mm3, cm3, m3

b mL, L, kL, ML12 a 0.6 cm b 250 mm

c 0.004 m2 d 450 me 0.3 L f 0.005 m3

g 0.025 kL h 5000 mm3

l 0.1 L j 25 m3

Exercise 4A — Changing units and calculating perimeters1 a 7 cm b 6 m c 5 km d 90 mm

e 1200 cm f 9000 m g 8.6 cm h 9200 mi 2.4 km j 64 mm k 1125 cm l 22 mm

2 5200 mm long2400 mm wide2500 mm high

3 a 28 m b 34 m c 84 cmd 42 mm e 24 m f 510 m

4 a 108 m b 12.1 m c 71.7 md 334.3 mm e 79 cm f 139 m

5 E6 C

Exercise 4B — Calculating areas1 a 0.7 cm2 b 0.6 m2 c 30 000 cm2

d 2 500 000 m2 e 45 000 m2 f 300 ha2 a 64 cm2 b 841 mm2 c 12.96 km2

d 27 m2 e 1026 mm2 f 2914 cm2

g 20.37 m2 h 26.46 km2 i 6.845 m2

j 216.32 km2 k 3306 mm2 l 6.4 m2

m 60 m2 n 5.84 m2 o 26.82 cm2

p 161.2 cm2 q 26.9 mm2 r 438.7 m2

s 14.14 cm2 t 4.19 m2 u 65.45 mm2

3 a 140 m2 b 36 m2 c 104 m2

4 a 144 m2 b 68.5 cm2 c 10 m2 d 80 m2

5 B 6 A 7 B8 a 34.56 m2 b $960.779 a b 180 m2

c 18 m long and 15 m wide d 90 m2

10 a C b E11 107 cm2

12 30.6 cm2

13 a 2474 cm2 b 34.4%

10 Quick Questions 11 452.4 cm2 2 31.2 m2

3 184.3 cm2 4 13 939.2 mm2

5 306 cm2 6 625 cm2

7 1428.3 m2 8 1147.6 cm2

9 17 121.8 mm2 10 670.9 cm2

Investigation — Effect of scale factors on perimeter and area1 Pentagon2 All angles 108°. Figure is regular pentagon.3 Larger knot has twice the side length of smaller knot4 S = 25 Larger knot has twice perimeter of smaller knot6 Area of larger knot is four times area of smaller knot7 Perimeter is 3 times as long; area 9 times as large8 Perimeter is ‘S’ times as long; area is ‘S2’ times as

large9 a Parallelogram

b 4 trapeziumsc Perimeter of larger knot twice as long and area 4

times as large as smaller knot. Supports conclusion in 8.

Exercise 4C — Total surface area1 a iii Triangular prism

b iii Square-based pyramidc iii Triangle-based pyramid

ItemCost price

($)

Per-centage discount

Discount($)

Selling price

($)

a 200 12% 24 176b 150 5% 7.50 142.50c 98 10% 9.80 88.20d 130 12.5% 16.25 113.75e 416 20% 83.20 332.80f 228 33 % 76 152

a 80% profit b 124.14% profitc 37.5% loss d 44.44% loss

a $35 b $39.89

13---

1.5 m

15 m

12 m

3C

4C

MQ Maths A Yr 11 - Ans 64 Thursday, July 5, 2001 8:08 AM

A n s w e r s 565

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2 a

b

c

3 a Square pyramid

b Triangular prism

c Cone

4 a 150 cm2 b 486 cm2 c 6144 cm2

d 95.98 cm2 e 1444 cm2 f 1274 mm2

5 11.92 m2 6 28 125 cm2

7 a 17.5 m2 b 70 c 42.5 m2

d 17.5 m2 e 5 L8 a 4.9 m2 b 9148.3 mm2 c 2945 cm2

9 360 cm2 10 28 cm2 11 B12 36 cm2

13 a 15.5 cm2

b 3267.3 cm2

c 879.6 cm2

14 a 58.1 cm2

b 39.3 m2

c 374 mm2

15 2 cm16 No. If the side length was doubled, the area would be

four times as large.17 95.6 m2

18 50 m2

19 99 m2

20 C 21 B 22 E 23 A24 a Cylindrical loaf

b 108.7 cm2

10 Quick Questions 21 0.44 m2 2 29.52 m2

3 4224 m2 4 Triangular prism5 Square pyramid 6 Triangular pyramid7 486 cm2 8 236 cm2

9 568 cm2 10 160 cm2

Exercise 4D — Volume and capacity1 a 350 mm3 b 0.0048 m3 c 56 litres

d 1500 cm3 e 1600 litres f 2.3 mm3

g 570 cm3 h 0.14 litres i 250 cm3

2 a 750 mL b 0.8 L c 2500 mL d 40 Le 6 000 000 cm3 → 6 000 000 mL → 6000 Lf 12 000 L g 4.2 kL h 7.5 kL → 7500 Li 5.2 cm3 j 6000 cm3

k 20 000 mL = 20 000 cm3 l 5.3 m3

3 a 125 cm3, 125 mL b 13.824 m3, 13.8 kLc 2197 m3, 2197 kL d 56.448 m3, 56.4 kLe 4050 mm3, 4.1 mL f 4228.125 m3, 4228.1 kLg 1357.2 cm3, 1357.2 mL or 1.4 Lh 339.3 m3, 339.3 kL i 29 772.9 cm3, 29.8 L

4 a i 12 cm2 ii 60 cm3

b i 24 cm2 ii 288 cm3

c i 4.59 m2 ii 6.885 m3

d i 12.48 m2 ii 156 m3

5 B 6 D 7 D8 a 504 000 cm3 b 504 L 9 101.25 kL

10 a 150.796 m3 b 150 800 L11 a 175 m2 b 17.5 m3 c $2546.2512 a 2.8 m3 b 2800 L c 24 429 L

d 27.5 cm13 a 96 cm3 b 560 cm3 c 120 m3

d 100 cm3

14 a 262 cm3 b 1810 cm3 c 2212 mm3

d 77 585 cm3

15 254.5 cm3

16 a 904.8 cm3 b 2144.7 cm3c 8181.2 m3

d 137.3 m3

17 6.37 cm3 18 A 19 C 20 D 21 a i 200 cm2 ii 2000 cm3

b i 99 m2 ii 792 m3

c i 204 cm2 ii 1224 cm3

d i 153 m2 ii 1836 m3

22 335.1 cm3

23 a 7 cm b 2144.7 cm3 c 1436.8 cm3

d 707.9 cm3

24 a 565.5 cm3 b 84.8 cm3 c 480.7 cm3

25 14.3 cm3

26 a 52.4 cm3 b 65.4 cm3 c 85.1 cm3

Chapter review1 a 19 cm b 1.9 cm2 c 0.19 cm3

d 0.5 L e 0.0005 kL f 50 000 Lg 200 000 cm3 h 2000 cm2 i 20 cmj 120 mL k 0.12 L l 300 000 cm3

2

3

45 a b c

a i 97.98 mm2 ii 48 mmb i 8.55 cm2 ii 16.44 cmc i 168 cm2 ii 54 cmd i 32 cm2 ii 49.3 cme i 8.8 m2 ii 13.4 m

a i 540 cm2 ii 106 cmb i 60.7 m2 ii 45.7 mc i 29.7 cm2 ii 21.4 cma C b E

4A

4D


566 A n s w e r san

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s6 Triangular prism7 a 105.84 cm2b 25.98 m2 c 19.44 m2

d 18.18 m2

8 a 54 m2 b 352 cm2 c 340 m2

9 a 301.6 cm2 b 23.1 m2 c 2670.4 cm2

10 a 247 m2 b 2463 mm2 c 879.6 cm2

11 a 452 cm2 b 763 mm2 c 157 cm2

12 a 75 m2 b 1650 m3 c 1 650 000 Ld 1316.2 m2

13 37.5 m2

14 a 274.625 cm3, 274.6 mLb 24 389 mm3, 24.4 mLc 202.768 m3, 202.8 kLd 984 cm3, 984 mLe 368 cm3, 368 mLf 57 906 mm3, 57.9 mL

15 585 cm3

16 a 48 cm3, 48 mL b 798 mm3, 0.8 mLc 5.29 m3, 5.29 kL

17 a 10 800 m3 b 10.95 m3 c 19 658 mm3

d 2339 mm3 e 50 965 mm3 f 179 594 cm3

18 a 6.1 m3, 6.1 kLb 123 717.1 cm3, 123.7 Lc 2356.2 cm3, 2.4 L

19 a 179.6 cm3

b 808.2 cm3

c 269.4 cm3

20 58.1 cm2 21 226.19 cm2

22 129.2 cm2 23 452 cm2

24 77.47 cm2 25 5.37 cm2

26 2073 cm2 27 21.237 cm2

28 2100.6895 cm3 29 536 cm3

CHAPTER 5 Right-angled triangles and trigonometryHistory of mathematics1 Samos Island2 Egypt and Babylonia3 c2 = a2 + b2 or hypotenuse2 = base2 + height2

4 Patterns in music5 Plimpton 3226 A set of numbers that obeys Pythagoras’ theorem

Skills check1 a AB b DF c GI

d No hypotenuse (as the triangle is not right-angled)

2 In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sideshypotenuse2 = base2 + height2

3 a a = 10 m b b = 4.47 m c c = 14.14 cm4 a 15 b 2 c 0.75

d 12.55

6 a a = 56° b b = 63°

7 a 35°30′ b 27°13′48″ c 68°7′30″8 a 45.45° b 84.59° c 64.01°9 In a right-angled triangle

a sine =

b cosine =

c tangent =

10 a b

c

11 a 0.7071 b 0.8660 c 0.4142d 0.9222 e 0.7871

12 a

b

c

13 a x = 2.08 b x = 1.56

Exercise 5A — Pythagoras’ theorem1 a PR b YZ c AB2 a 13 cm b 170 mm c 61 m3 a 10.82 cm b 6.93 m c 14.20 km4 a 10.4 cm b 1.9 m c 3.9 m5 a 8.9 cm b 22.1 cm c 47.4 mm

d 37.3 m6 a Right b Right c Obtuse

Angle of elevation

Shadow

opposite side lengthlength of hypotenuse--------------------------------------------------

adjacent side lengthlength of hypotenuse--------------------------------------------------

opposite side lengthadjacent side length------------------------------------------------

Opp

osite

Adjacent

HypotenuseOpposite

Adjacent

Hypotenuse

Opposite

Hyp

oten

use

Adjacent

Angle of elevation

Angle ofdepression

Angle ofelevation

4D

5A


A n s w e r s 567

answ

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➔

7 B 8 C9 a Yes b No c Yes

d No e Yes f Yesg No h No i Yesj Yes k Yes l No

10 a 9, 12, 15 b 7, 24, 25 c 1.5, 2.0, 2.5d 3, 4, 5 e 11, 60, 61 f 10, 24, 26g 9, 40, 41 h 0.7, 2.4, 2.5

11 a 15 c 50 e 1.0 f 25i 61 j 26 k 20

12 E13 B14 13 m15 3.23 m16 3.73 m17 2.2 m18 7.5 m19 7.07 cm

Exercise 5B — Shadow sticks1 a 5.7 m b 15.6 m c 5.3 m d 7.8 m2 5.4 m 3 6.4 m 4 8.1 m5 16 m 6 B 7 D

Exercise 5C — Calculating trigonometric ratios1 a 1.540 b 17.663 c 40.460

d 0.6572 a 0.602 b 2.092 c 15.246

d 51.8933 a 0.707 b 0.247 c 6.568

d 5.8964 a 0.500 b 0.966 c 1

d 548.643 e 64 f 1.301g 5.306 h 1.374 i 15.772

5 a 0.42 b 1.56 c 0.09d 5.10 e 2.87 f 0.38g 7.77 h 73.30 i 0.87

6 10°7 a 44° b 80° c 57°8 86°40′9 a 42°57′ b 31°21′ c 16°5′

Exercise 5D — Finding an unknown side1 a

b

c

2 148.1 mm3 5.08 m4 30 cm5 a 12.1 cm b 55.2 m c 9.4 km

6 a 12.5 m b 89.3 mm c 10.1 m7 a 5.4 m b 1.4 km c 2.1 km

d 18.4 mm e 3.2 cm f 66.5 mg 5.4 m h 5.4 km i 0.2 mj 41.6 km k 84.4 m l 13.2 cm

8 D 9 A 10 A 11 C12 6 m 13 4.2 m 14 20 km15 a b 6 m

16 a b 1.6 m

17 9.65 m18 a b 58 m

c 15.5 m

10 Quick Questions 11 17 cm 2 22.4 m 3 26.5 km4 21.5 m 5 32.9 cm 6 25.3 m7 12.5 mm 8 177.8 mm 9 97.5 m

10 17 m

Exercise 5E — Finding angles1 a 30° b 75° c 81°2 a 32°48′ b 45°3′ c 35°16′ 3 a 53°8′ b 55°35′ c 45°27′4 a 50° b 32° c 33°

d 21° e 81° f 34°5 a 39°48′ b 80°59′ c 13°30′

d 79°6′ e 63°1′ f 19°28′6 A 7 B 8 C 9 37°

10 75°31′ 11 8°38′ 12 13° 13 4°35′

10 Quick Questions 21 13 cm 2 17.0 cm 3 22.4 cm4 6.409 m 5 0.8290 6 10.967 133.55 8 30° 9 73°

10 63°26′

Exercise 5F — Angles of elevation and depression1 26.8 m 2 3984 m 3 190 m 4 39.2 m5 42.1 m 6 100 m 7 15 km8 Yes, the ladder needs to be only 28 m long.9 a 914 m b 868 m

10 39° 11 21°12 a b 85 m

c 40°

Chapter review1 a 13.01 m b 18.65 cm c 3.58 m

d 15.65 cm e 2.30 km f 2.47 m

hypopp

adjθ

hyp

opp

adjα

hyp

oppadjγ

24°13.5 m

60°

1.4 m

15°60 m

12°400 m

5A

5F


568 A n s w e r san

swer

s2 98 km 3 66 m4 a Right-angled b Right-angled

c Obtuse d Acute5 b and c6 11.25 metres7 a 0.7193 b 4.2303 c 2.7400

d 8.1955 e 21.9845 f 14.29988 a 54° b 51° c 53°9 a 78°31′ b 26°34′ c 14°54′

10 a 37.9 cm b 3.8 m c 13.6 cmd 11.7 cm e 14.7 cm f 14.6 mg 1.5 m h 4.9 cm i 15.6 mmj 7.5 m k 10.7 m l 5.3 km

11 8.5 m 12 2.5 km 13 63.9 m14 a 57° b 27° c 68°15 a 23°4′ b 61°37′ c 59°35′16 39° 17 24° 18 23 m 19 57°

CHAPTER 6 Earth geometrySkills check1 Latitude — imaginary lines which circle the Earth in

an east–west direction parallel to the equator.Longitude — imaginary lines circling the Earth joining the North and South Poles and running perpendicular to the equator.

2

3

4

5 The shortest distance between two points on a sphere is represented by the length of an arc of a circle.

6 40 030 km7 a Greenwich Mean Time (GMT) — the standard

time in Greenwich (England) which is used as the basis for calculating the time in all other parts of the world.

b The meridian of longitude 180° from the Greenwich Meridian. When we cross the International Date Line, the date will be different.

c Eastern Standard Time — the time adopted by the eastern States of Australia (Qld, NSW, Vic and Tas) and the ACT.

8 Three — EST (Eastern Standard Time), CST (Central Standard Time), WST (Western Standard Time).

9 Clocks are put forward 1 hour during summer.10 EST is 10 hours ahead of GMT.

Exercise 6A — Latitude and longitude1 a Cairo b Shanghai c Darwin

d Montreal e London f Aucklandg Tokyo h Beijing i Rio de Janeiroj Oslo

2 a (38°S, 145°E) b (40°N, 75°W)c (18°N, 76°W) d (26°S, 28°E)e (42°N, 12°E) f (35°S, 57°W)g (33°N, 44°E) h (55°N, 40°E)i (2°N, 104°E) j (18°S, 178°E)

Exercise 6B — Distances on the Earth’s surface1 50°2 a 40° b 40° c 71° d 21° e 80°3 60°4 3336 km5 a 3892 km b 15 012 km

c 4337 km d 10 675 km6 6672 km7 5226 km8 6600 km9 a 4337 km b 4003 km c 3781 km

10 D 11 A12 a 110° b 12 200 km13 20 016 km14 a 28° b 3114 km15 3892 km16 17 792 km17 a 6894 km to South Pole

b 4559 km to North Polec 4893 km to North Poled 8896 km to South Pole

18 a 2470 km b 3233 kmc 2859 km d 425 kme 16 301 km f 6452 km

Exercise 6C — Time zones1 10 h2 a 14 h b 7 h c 11 h d 22 h3 11:00 pm Monday

1–2

North Pole (90° N)

South Pole (90° S)

Tropic of Cancer (23 ° N)

1–2Tropic of Capricorn (23 ° S)

Equator (0°)

S

N

50° W 0° 20° E

Equator

Tropic of Capricorn

N

S 5B

6C


A n s w e r s 569

answ

ers

➔

4 a 8:00 pm b 1:00 pm Fridayc 5:00 pm Wednesday d 11:00 pm Tuesdaye 3:45 pm Monday

5 5:00 am Saturday6 11:00 pm Tuesday7 10:00 am Monday8 a 10:00 pm b GMT+11

c i 3:00 pm Monday ii 8:00 am Friday9 a 18 h b 19 h c 17 h

10 7 h11 a 10 h 20 min b 24 min c 2 h 48 min12 C 13 D14 2:00 pm Tuesday LAX local time15 a 4:00 pm Wednesday b 8:00 am Sunday16 a 1:00 am Wednesday b 3:00 am Wednesday

Chapter review1 a 207.3 cm b 44.0 cm c 57.8 m2 56.5 km3 71 cm4 a Manila b Lima c Santiago5 a (41°N, 3°W) b (1°N, 104°E)

c (43°S, 147°E) 6 58°7 a 16° b 1779 km8 5671 km9 a 14 481 km b 18 425 km

10 a 8 h b 11 h c 17 h11 3:00 am Thursday 12 3:30 am Tuesday13 a 11:00 am the same day

b 11:00 am the same day14 7:00 pm the same day

CHAPTER 7 Basics of constructionSkills check1 a 1 : 0.75 b 1 : 4 c 1 : 25 d 1 : 402 a Enlargement b Reduction

c Reduction d Reduction3 a 1 m b 2.5 cm4 a P = 40 m, A = 80 m2 b P = 56 m, A = 128 m2

5 a 0.6 m3 b 1 m3

6 a 3394 mm b 1.8 m7 a 34.4° b 43.3°8 a 3.46 m b 11.22 m9 a 7.18 m b 2784 mm

10 a 76 m2 b 18.97 m2

Exercise 7A — Scale drawings1 a 8.215 m b 3.5 m c 89 000 m

d 0.026 m e 0.04 m f 6400 m2 a 45 mm b 67 mm c 58 mm3 a Reduction b Reduction c Enlargement

d Reduction e Enlargement f Reduction4 a 1 : 5000 b 1 : 200 000 c 10 : 15 a 1.8 m b 6.75 m c 22.5 m d 3.375 m6 a 2.4 cm long × 1.4 cm wide

b 3 cm × 1.8 cm c 4.4 cm × 2 cm7 1 : 5508 a 4.75 m b $3034 c 18.75 m9 a Approx. 70 m b Approx. 1000 m

c Approx. 2 km2

Exercise 7B — Building plans1 a 630 m2 b 30 m, 21 m

c Approx. 1 : 1750 e 632 m2

f i 1063 m2, $58/m2 ii 850 m2 is largerg i Lot 110

ii Does it front a main road? Is it low lying?Slope of land, views, aspect.

2 a 2100 m2, 83 perches b 104 m2

c Approx. 1 : 1000 d i Rising ii 1.4°3 a 77.8 m2 b Approx. $265

c in order, 10.85 m2, 11.25 m2, 6.84 m2, 5.04 m2

Exercise 7C — Floor plans and elevations1 a No doors and 1 window

b 9 (D4–D12)c Kitchen and dining roomd 2400 mm (2.4 m)e At 4 corners of house, downpipesf 1490 mm (1.49 m)g 290 mm, 90 mmh Shower, bath, vanity unit, toileti Refrigerator, pantry, oven, broom cupboard, hot

plates, sink, benchesj i No doors and 1 window, window is 310 mm wide

ii 8990 mm, 7790 mmk

10 Quick questions 11 1 : 250 2 NE 3 20 m × 25 m4 10 m × 15 m 5 4.4 m 6 1 :1257 5.6 m × 3.75 m 8 Bed 1 9 3.75 m square

10 2.5 m

Exercise 7D — Pegging out the perimeter1 a 1697 mm b 45°2 Acute angle3 12 m square4 No — it could be a parallelogram.5 The shed could be rectangular or square.6 17.7 m7

The wall at X is 2 cm below horizontal level of wall at Y.

Exercise 7E — Footings and slabs1 a 8.855 m3 b 5.016 m3 c 20.832 m3

2 7.43 m3

3 a 10 lengths b 5.28 m3

2090

2400 40

00

79908990

310

w5

2 cm

Wall Wall

WaterX

Y

6A

7E


570 A n s w e r san

swer

s4 8.6 m3

5 a i 12.579 m3 ii 24 lengths iii 12.75 m3

b i 14.679 m3 ii 28 lengths iii 16 m3

Exercise 7F — Bracing1 a 6.46 m b Angle is 21.8° c 4 m2 Yes, brace is at 45° to base.3 a 1697 mm b 45° c Yes4 3839 mm, 38.7°5 a 40.6° and 43.8°

b 3688 and 3467 mm = 7155 mm6 a 34.18 m b 13.8 m

Exercise 7G — The roof1

2

3 a 13.4° b 16.9° c 36.9° d 36.9°4 a 1 : 3, 18.4° b 1 : 1.67, 31°5 a 43.8° b 33.6°

Exercise 7H — Cladding the roof1

2 a EF = 18 m, FH = 6 mb ∠CAB = 20°c AB = 3 md AC = 3.2 m BC = 1.1 me CD = 12 mf 48 m2

g 9.6 m2

h 115.2 m2

i $5184 (≈$5200)

3 a QR = 18 m, PQ = 6 m, ∠TQV = 20°b VQ = 3 mc TV = 1.1 m TQ = 3.2 md 57.6 m2, 115.2 m2

e $51844

5

6 a

i There is no ridge — all faces meet at a point.ii 148.8 m2

b 148.8 m2

7 $3577.508 a and b

c

Exercise 7I — Brickwork1 a 1680 b 3000 c 3000 d 19202 a 210 b 19553 a 50 b 25 c 194 a 43 cm b 1.892 m c 4.73 m5 a 25 b 10 c 1206 a 15 b 35 c 525

d 542 This is an estimate and allows for breakages.7 4056

Chapter review1 a 1 : 140 b 4

c 3.8 m × 3.6 m with ensuite containing shower, handbasin and toilet, walk-in wardrobe with hanging space and shelves

d 5.8 m × 6.09 me Living–dining room and hallway near bathroomf 231.45 m2

g Vanity basin, broom cupboard, washing machine, water closet, walk-in wardrobe, wall oven, range hood, hot plates, drain pipe

Pitch ratio Pitch angle

1 : 22.9 2.5°

1 : 57.3 1°

1 : 7.6 7.5°

1 : 5.7 10°

1 : 1 45°

1 : 2.7 20°

1 : 1.43 35°

1 : 1.08 42.8°

Roof pitchBuilding

widthKing post

heightRafterlength

10° 8 m 705 mm 4062 mm

12° 10 m 1063 mm 5112 mm

18.4° 12 m 2 m 6325 mm

25° 27.19 m 6339 mm 15 m

10.8° 31.4 m 3 m 16 m

34.6° 14 m 4822 mm 8.5 m

Hip roof

Triangles

Trapeziums

Gable roof

Rectangles

12 m

4 m5.8 m

8 m18°

8 m

4.2 m

18°

12 m

12 m

12 m

15°

15°

12 m12 m

10 m

10 m2.7 m

2.7 m 2.7 m

5 m20° 20°

10 m20° 20°

10 m

2.7 m

2.7

m 2.7 m

2.7 m 2.7 m5 m5 m

2.7 m

7A

7I


A n s w e r s 571

answ

ers

➔

4 a East b Rectangularc 21.3 m × 28.175 m d Sweetapple Crescente 1.5 m f 4.5 mg 38.6%

5 a Garage b Northc North-west d 1e Panel lift f 4g Concrete tiles h 21°i Gable j Brickk 1000 mm l 600 mmm 2400 mm n Standard Type Ao 2.67 m × 3.6 m p 70 mmq 220 mm

6 a 200 mm b 100 mm c 900 mmd The floor of the garage falls 50 mm from back to

front.e Internal footingsf No, garage is 1 step down from house.g 40 mm h

i Down western side of allotment, 600 mm8 a 6.4 cm × 4 cm b 12.8 cm × 8 cm9 4.48 m 10 $46.57

11 1.67 m3 12 613 $470 14 3988 mm15 3042 mm 16 1 : 2.617 a No b 10.9°18 1441 mm 19 $288020 $907.20 21 100022 11 23 2824 a 308 b 312

Both methods give approximately the same number.

CHAPTER 8 Construction: The finishing touchesSkills check1 a b

c

2 a 37.5 m2 b 29.64 m2

3 a

b 96 m2

c

d 100 m2 e 4 m f 53°g h

4 a 11.847 m2 b 5.79 m2

5 a 471.24 m3 b 21.6 cm

Exercise 8A — Painting and wallpapering1

b 150 m2 c 25 L d 7 e $2522 $243 3 1.3 L4 3 tins 5 81.6 L6 a 3.6 L white undercoat; 4.8 L blue enamel

b 3.3 L white undercoat; 5 L acrylicc $198.40

7 a

b 14 m c 28 d 2.4 m e 67.2 m f 78 99 Wallpaper $405

Paint $19210 Wallpaper $4.50/m2

Painting $1.44/m2

So it is cheaper to paint.

Exercise 8B — Tiling, carpeting and kitchen planning1 $73802 a $234.78 b $123.123 a 24 m b 24 m4 a

b 116 tiles c 22.8 m d 21.6 m5 $127.80/m6 a i 1226 mm

ii 820 high, 700 wide, 495 deepiii 720 high, 595 either side of corner

b i 2135 high, 800 wide, 590 deepii 875 mmiii Cabinet O — Deep corner floor cabinet 900 iii and narrow corner floor cabinet 750iv 400 wide or 800 wide, 2135 high

c 0.354 m2 d 590 mm e 315 mm7 Check with your teacher8 a 1.296 m2 b 1.0206 m2 c 0.567 m2

d 1.6686 m2 e 4.5522 m2 f 910 mL

3 m

6 m10 m 6 m10 m

10 m

5 m5 m

6 m

10 m

6 m

3 m

5 m

10 m

15 m

3.5 m

2.4 m 2.4 m

12 m

11.4 m

5.4 m6 m

Tiles(30cm × 30cm)

Carpet

7F

8B


572 A n s w e r san

swer

s10 Quick questions 11 30 m × 34 m 2 128 m3 $416 4 10.8 m × 14 m5 151.2 m2 6 SW7 42 m 8 43.2 m9 85.68 kL 10 75 m2

Exercise 8C — Landscaping1 a 2.4 m b 3 c 200 mm d 5

e 15 f $44.40 g $6662 a 1.8 m b 4 c 100 mm d 10

e 40 f $9.45 g $3783 a 1.8 m b 4 c 150 mm d 7

e 28 f $18.27 g $511.565 a i 75 mm wide and 38 mm thick

75 mm wide and 50 mm thickii 75 × 50 mmiii 6 cmiv 10 m

b i 100 × 38 mm and 100 × 50 mmii 75 × 38 mm and 75 × 50 mmiii 2850 mm2 and 5000 mm2

iv 100 × 38 mm6 a 20 PRP

b or

or other combinations

c or

or other combinationsd 78.5%

7 a 0.288 m3 b 0.375 m3 c $86.19d 16 m2 e 1.125 m2 f 3.99 m2

g 21.115 m2 h $253.38 i $339.57

Chapter review1 a $32.60 b 1 : 25 c $42 d $2102 a 32 m2 b $1216

c i $456ii $850 laid horizontally

$680 laid vertically3 a Sink, oven and refrigerator arranged in triangle

b 2 × 800 and 2 × 900c 0.2 m3

d Approx. 356 mm

4 a 60 b $2664 c 57.6 m3 d $17285 a 600 b $990 c 450 m2 d No, 574

e 568f The closer the rectangle approaches a square

shape, the smaller the perimeter, and fewer palings would be required.

6 a Sand, clayb Compete with plants for water and nutrientsc Makes them too thirstyd Thick grass requires too much water and water has

difficulty reaching the roots.e Couch/kikuyu/buffalo — the broad leaf helps it

absorb water.f Clay soil does not absorb as well, so requires a

longer watering time. Once the clay is wet, it retains the water for a longer period of time than sandy soil does.

g They sprinkle a further distance.h Water runs off surface.

7 a 0.1 m3 b $13 c 5.65 m2 d $84.75e $97.75 f 1.13 m3 g 1.96 m

CHAPTER 9 Collecting and entering dataSkills check1 Qualitative — some quality or feature (not involving

numbers or measurements).Quantitative — involving some quantity or number which can be measured.

2 a −2, −1, 0, 1, 3, 6.5, 8, 12, 25b −2, 25, 3

3 a

b c

4 a 0.196 c/g b $0.88/L c 0.76 c/g5 1 L for $2.50

Exercise 9A — Types of data1 a Numerical b Categorical c Numerical

d Categorical e Numerical f Numerical2 a Continuous b Discrete c Continuous

d Continuous e Discrete

4 6 4 6+ + +

4 4 4 4 4+ + + +

4 4 4 4 4+ + + +

4 4 3 3+ + + 3 3+ +

6 m

6 m

Year Students

8 117

9 102

10 92

11 77

12 62

Year 9 Year 8

Year 12Year 10

Year 11

No.

of

stud

ents

Year level8 9 10 11 12

0102030405060708090

100110120

8A

9A


A n s w e r s 573

answ

ers

➔

3 a Numerical and discreteb Categoricalc Categoricald Numerical and continuouse Numerical and continuous f Numerical and discrete

4 Categorical, ordinal 5 Categorical, ordinal6 Numerical and discrete 7 B8 Categorical 9 Numerical and continuous

Exercise 9B — Collecting data1 Open questions — no boundaries for response.

Closed questions — answer within category.2 A variety of categorical responses suitable; check

with your teacher.3 A variety of categorical responses is suitable; check

with your teacher.4 a Vague — weekly? yearly? all jobs?

b Vague — define ‘exercise’, ‘regularly’.c What do abbreviations stand for?d Emotional language.e Capable of being answered? What is the PM’s

policy?g Double-barrelled question.h Leading question suggesting a particular response.i Emotive language.

5 Check with your teacher.

Exercise 9C — Organising and displaying data using column and sector graphs1

2

3

4 Check with your teacher.5

6

7

8

9 Check with your teacher.10

10 Quick Questions 11 Qualitative2 Quantitative and discrete3 Quantitative and discrete4 Quantitative and continuous5 40 6 Married 7 15 8 11 9 28

10

Make Tally Frequency

Holden |||| ||| 8

Ford |||| ||| 8

Nissan || 2

Mazda ||| 3

Toyota |||| || 7

Mitsubishi || 2

Mark Tally Frequency

4 || 2

5 |||| 4

6 |||| | 6

7 |||| |||| 9

8 |||| 5

9 ||| 3

10 | 1

Mark Tally Frequency

40–49 | 1

50–59 || 2

60–69 |||| |||| 9

70–79 |||| ||| 8

80–89 ||| 3

90–99 || 2

Holden

Ford

Nissan

Maz

da

Toyota

Mits

ubish

i

Freq

uenc

y

Make of car

0123456789

HoldenFordNissanMazdaToyotaMitsubishi

Make of car

04 5 6 7 8 9 10

123456789

Num

ber

of s

tude

nts

Spelling test results

10

0

40–4

9

50–5

9

60–6

9

70–7

9

80–8

9

90–9

9

123456789

Num

ber

of s

tude

nts

Maths exam mark

40–49

50–59

60–69

70–79

80–89

90–99

Marks on maths examNumber of students

Married

Widowed

SeparatedDivorced

Nevermarried

8C

9C


574 A n s w e r san

swer

sExercise 9D — Graphical methods of misrepresenting data1 Check with your teacher.2 Horizontal axis uses same division for 5 and 7 year

periods3 a Check with your teacher

b No4 a 20.5

b 18.2, country schools have smaller class sizes5 Check with your teacher6 Check with your teacher7 a 0.2 b 71.5° c 80°

d The perspective appears to magnify some sections of the pie chart and diminish others.

8 a It is a circle viewed on an angle to produce an ellipse.

b No, because it causes some angles to be larger and others to be smaller.

Exercise 9E — Histograms and freauency polygons1

2

3

4 a

b

5

6 a

b

Exercise 9F — Stem-and-leaf plots1

2

3

4

No. of matches in a box Frequency

47 3

48 5

49 10

50 15

51 7

52 5

53 4

54 1

00246

1 2 3 4 5Number of mistakes

(score)

Num

ber

of d

rive

rs(f

requ

ency

)

8101214

10123

2 3 4 5 6No. of children in family

Freq

uenc

y

456 7 8 9

180246

19 20 21 22 23Age

No.

of

mem

bers

81012

24 25

14 16

53 54470246

48 49 50 51 52No. of matches in a box

Freq

uenc

y

810121416

Time taken (seconds) Class centre Frequency

6 to <8 7 1

8 to <10 9 4

10 to <12 11 15

12 to <14 13 18

14 to <16 15 12

16 to <18 17 8

18 to <20 19 2

304.5314.5

324.5334.5

344.5354.5

0

510

15

Length of fish (mm)

Freq

uenc

y 20

1970246

9 11 13 15 17Time taken (s)

Freq

uenc

y

81012141618

Key 0 | 6 = 6 errors

Stem01234

Leaf63 5 7 80 0 5 6 6 7 8 91 2 2 83 6

Key 3 | 6 = 36 min

Stem345678

Leaf6 7 8 8 9 90 0 1 2 2 2 2 2 3 5 6 7 7 8 8 80 2 2 2 3 4 5 7 8 96 8 81 2 52

Key 10 | 1 = 101 wpm 10* | 6 = 106 wpm

Stem8*9*9*

10*10*11*11*12*12*13*

Leaf6 825 5 5 6 6 6 8 92 2 2 37 7 7 8 80 1 250 1 1 4

0

Key 14 | 3 = 14.3 V 14* | 8 = 14.8 V

Stem13*14*14*15*15*

Leaf8 90 2 3 35 6 6 7 7 8 81 2 25 6 7 9 9B

9F


A n s w e r s

575

answ

ers

➔

5

1.95 g

6 a

8.4 s

b

Lower quartile

=

7.8 s, upper quartile

=

8.85 s

c

1.05

7

D

8

A

9

D

10

B

11 a

b

22.9 cm

c

Lower quartile

=

21.75 cm, upper quartile

=

24.1 cm

d

2.35 cm

12 a

b

99.5 cm

c

Lower quartile

=

92 cm, Upper quartile

=

110 cm

d

18 cm

Exercise 9G — Five-number summaries and boxplots

1

8, 15, 16.5, 18, 25

2 a

23, 44, 81.5, 83.5, 92

b

1, 2, 4, 6, 7

c

8, 29, 45, 72, 93

3 a

13

b

5

c

26

4 a

122

b

6

c

27

5

6 a

147

b

56

c

90

d

91

e

28

7 a

58

b

31

c

43

d

27

e

8

8

B

9

C

10

D

11 a

22, 28, 35, 43, 48

b

12 a

10 mm, 13.5 mm, 22 mm, 33.5 mm, 45 mm

b

Chapter review

1 a

Categorical

b

Numerical

c

Numerical

d

Numerical

e

Categorical

2 a

Discrete

b

Continuous

c

Continuous

d

Discrete

e

Continuous

3 a

Double-barrelled question

b

Double negative

c

Emotional language

d

Abbreviations

e

Leading question

4

5

6

7

Key 20 | 6 = 20.6 cm

Stem202122232425

Leaf2 74 6 7 82 8 8 80 1 2 6 66 6 7 81

Key 8 | 2 = 82

Stem89

10111213

Leaf2 4 5 5 80 1 2 3 4 6 6 7 8 91 1 3 3 7 80 0 1 4 5 76 62

35 40 45 50 55 60

20 25 30 35Scales

40 45 50

10 15 20 25Rainfall (mm)

30 35 40 45

Score Tally Frequency

1 ||| 3

2 |||| | 6

3 |||| | 6

4 |||| | 6

5 ||| 3

6 ||| 3

Number of CDs TallyNumber of

students

0–4 ||| 3

5–9 |||| |||| 9

10–14 |||| |||| 9

15–19 ||| 3

20–24 |||| 4

25–29 | 1

30–34 0

35–39 | 1

01 2 3 4 5 6

12345

67

Freq

uenc

y

Number of people in a household

1

2

3

4

5

6

Number of peoplein a household

10

00–

45–

910

–1415

–1920

–2425

–2930

–3435

–39

123456789

Num

ber

of s

tude

nts

Number of CDs purchased

0–4

5–9

10–14

15–19

20–24

25–29

30–34

35–39

Number of CDspurchased

9D

9G


576

A n s w e r s

an

swer

s

8

Check with your teacher

9

10 a

b

11

12 a

28

b

38

c

12.5

13

6, 24, 41, 69, 91

14 a

43

b

43

c

14

15

16

20

17

11

18

7.5

19

7

20

21

45

22

15

23

35

24

7

25

Check with your teacher

CHAPTER 10 Describing, exploring and comparing data

Skills check

1 a

3, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9

b

11

c

6th

d

5

e

3 to 9 or 6

f

5.55

g

6, 5

h

4

i

Mean = 5.5, median = 5, mode = 4. The mean takes into account all scores, the median is the middle score (arranged in order), the mode is the most frequently occurring score. These values would only be the same for a symmetrical (or near symmetrical) distribution.

j

4, 7

2

Central tendency is a measure of how the scores tend to be grouped around the centre of the data. The measure represents a typical score in the data set.

3

Range, interquartile range

4

The median is the second or middle quartile.

5

b, d

6

Consult your teacher.

Exercise 10A — Calculating and interpreting the mean

1

Average, total, number, central, median, mode.

2 a

5

b

26.5

c

74.25

d

7.72

e

376

3

72.6, 3, 2

4

73.4 c/L, yes, 3 above and 4 below5 1.81 m, 36 a Yes, mean mass is 45.035 g.

b Both the same distance from the mean7 a Mean is 10 greater; that is, 13

b Mean is 10 times as large; that is, 30.

Exercise 10B — Mean, from frequency distribution tables1 a

b 131.36 mm

2 a

b 7 c 10

Class Class centre Frequency

5000–9999 7 500 1

10 000–14 999 12 500 5

15 000–19 999 17 500 9

20 000–24 999 22 500 3

25 000–29 999 27 500 2

30 000–34 999 32 500 2

600246

1 2 3 4 5Number of sales

Freq

uenc

y

81012

0

7500

12 500

17 500

22 500

27 500

32 500

246

No. of people at a football match

Freq

uenc

y

810

Key 2 | 1 = 21

Stem234

Leaf1 1 3 4 8 8 8 9 9 90 3 4 5 5 5 6 8 8 8 8 90 0 0 1 1 2 2 4 5 5 5 6 8 9

2 6 10 14 180 4 8 12 16 20

0 5 10 15 20 25

Score (x) TallyFrequency

(f) fx

119 | 1 119

124 | 1 124

125 | | 2 250

126 | | 2 252

127 | 1 127

128 | | 2 256

129 | 1 129

130 | 1 130

131 | | | | 5 655

132 | | | 3 396

134 | | | 3 402

135 | | 2 270

136 | 1 136

138 | | 2 276

139 | | 2 278

141 | 1 141

Σ f = 30 Σ fx = 3941

Score Tally Frequency fx

4 | | 2 8

5 | | | | 4 20

6 | | | | 5 30

7 | | | | | | | | 9 63

8 | | | 3 24

9 | | | | 5 45

10 | | 2 20

Σ f = 30 Σ fx = 210

9G

10B


A n s w e r s 577

answ

ers

➔

3 a

b 20.4

4 a

b 2.3c 31 below, 19 above — could be a better measure

5 a

b 12c Size 12 not available, perhaps a better measure

could be used.

6 D7 B8 C

Exercise 10C — Mean, from grouped data1 a

Mean = 131.6 mmb Slightly larger — scores not evenly spread

around each class centre.

2 a

b 68.17 c 61–70 class

3 a

b 53.1c 39 — remember faster is lower time

4 Check with your teacher. 5 a 14.1 b 3.4 c 44.4

No. of televisions sold No. of weeks fx

16 4 64

17 4 68

18 3 54

19 6 114

20 7 140

21 12 252

22 8 176

23 2 46

24 4 96

25 2 50

Σ f = 52 Σ fx = 1060

Score (x) Frequency (f) fx

0 4 0

1 9 9

2 18 36

3 10 30

4 5 20

5 4 20

Σ f = 50 Σ fx = 115

Score (x) Frequency (f) fx

8 2 16

10 7 70

12 11 132

14 6 84

16 2 32

18 2 36

Σ f = 30 Σ fx = 370

13---

13---

ClassClass

centre (x) TallyFrequency

(f) fx

119–121 120 | 1 120

122–124 123 | 1 123

125–127 126 | | | | 5 630

128–130 129 | | | | 4 516

131–133 132 | | | | | | | 8 1056

134–136 135 | | | | | 6 810

137–139 138 | | | | 4 552

140–142 141 | 1 141

Σ f = 30 Σ fx = 3948

Class

Class centre

(x) TallyFrequency

(f) fx

31–40 35.5 | 1 35.5

41–50 45.5 | | | 3 136.5

51–60 55.5 | | | | 4 222.0

61–70 65.5 | | | | | | 7 458.5

71–80 75.5 | | | | | | | | | 11 830.5

81–90 85.5 | | 2 171.0

91–100 95.5 | | 2 191.0

Σ f = 30 Σ fx = 2045

TimeClass centre

No. of swimmers fx

50.01–51.00 50.5 4 202.0

51.01–52.00 51.5 12 618.0

52.01–53.00 52.5 23 1207.5

53.01–54.00 53.5 38 2033.0

54.01–55.00 54.5 15 817.5

55.01–56.00 55.5 3 166.5

Σ f = 95 Σ fx = 5044.5

10A

10C


578 A n s w e r san

swer

s6 a 6.6 b 30.677 166.258 a 12.5, 13.5, 14.5, 15.5, 16.5 b 14.49 a

b 46.4 c 33

Exercise 10D — Median and mode

1 Middle, arranged in order, , average,

cumulative frequency.2 63 814 a 5 b 5.4 c 62 d 1025 a 4 b 5.6

c The median is a better measure because one large score makes the mean larger than what is typical.

6 a

b 207 3 8 1 9 C 10 C 11 A

12 a

b 10–1413 Most frequent, bimodal, modal class.14 a 5 b 8 c 11

d 0.4 e 110

15 a 17 b 148, 151 c No moded 72 e 2.6

16 a 4 b 8 c 42, 4417 1718 a 17–20 b 22–28

19 a

b $350–$399

10 Quick Questions 11 5.5, 15.5, 25.5, 35.5, 45.5 2 5, 20, 49, 86, 973 48 4 865 Grouped 6

7 8 29

9 21–30 10 31–40

Exercise 10E — Best summary statistics1 a $215 000 b $170 000 c $150 000

d The median, as the mean is inflated by one large score and the mode is the lowest price.

2 a 7.1 b 7 c 7d The mode, as it is the size that sells the most.

3 a 23 550 b 20 000–30 000 c 10 000–20 000 d Median

4 B

5 a

b 6.8 c 0–4 d 0–4

Class Class centre Frequency

1–10 5.5 12

11–20 15.5 6

21–30 25.5 5

31–40 35.5 7

41–50 45.5 9

51–60 55.5 9

61–70 65.5 5

71–80 75.5 5

81–90 85.5 5

91–100 95.5 7

Score FrequencyCumulative frequency

17 4 4

18 9 13

19 6 19

20 12 31

21 8 39

22 5 44

23 4 48

24 2 50

Days sickness FrequencyCumulative frequency

0–4 10 10

5–9 12 22

10–14 7 29

15–19 6 35

20–24 5 40

25–29 3 43

30–34 2 45

n 1+2

------------

ClassClass centre Frequency

Cumulative frequency

$200–$249 224.5 8 8

$250–$299 274.5 4 12

$300–$349 324.5 6 18

$350–$399 374.5 6 24

$400–$449 424.5 4 28

$450–$499 474.5 2 30

$500–$549 524.5 6 36

$550–$599 574.5 4 40



0–4 2 16 16

5–9 7 6 22

10–14 12 4 26

15–19 17 2 28

20–24 22 1 29

25–29 27 1 30

5.5 15.5

25.5

35.5

45.5

05

1015

Score

Freq

uenc

y

2025303540

5.5

15.5

25.5

35.5

45.5

05

1015

Score

Freq

uenc

y

2025303540

10C

10E


A n s w e r s 579

answ

ers

➔

6 Check with your teacher; answers depend on groupings used.

7 a

b 42.2 c 16–30 d 16–30

e Nof Check with your teacher.

8 a Player A: 34.3 Player B: 41.8b Player B c Player A: 32.5 Player B: 0d Player Ae Check with your teacher.

9 a The statement is true but misleading as most employees earn $18 000.

b Check with your teacher, but you should quote $18 000 as the median and the mode salary and that only 15 out of 80 (less than 20%) earn more than the mean.

Exercise 10F — Range and interquartile range1 Dispersion, spread, lowest, highest, outlying,

interquartile, upper, lower, median, quarter, quarter, four, scores.

2 a 5 b 9 c 1d 6.94 e 89

3 a 4 b 5 c 64 a 49 b 30 c 235 a Sydney — 120 Collingwood — 40

b Collingwood, because the range is lower.6 a 9 b 8

c The range for machine A is large, only because of one extreme score.

7 a 5 b 25 c 53d 15 e 74

8 a 5 b 9 c 2d 4 e 32

9 A 10 B 11 D 12 B

Exercise 10G — Standard deviation1 Spread, mean, σn (or σx), σn – 1 or Sn,

consistent/reliable, low.2 a 2.29 b 2.19 c 20.17

d 3.07 e 42.443 a 26.94 b 2.14 c 57.51

d 0.26 e 96.044 a Sample b Population c Population

d Sample e Population5 a 616.6 b Sample c 270.976 a $1.44 million b Population c $0.48 million7 a x– = 4.9, σ = 1.0 b x– = 48.3, σ = 1.2

c x– = 78.3, σ = 2.3

8 a x– = 17.45, σ = 3.69 b x– = 14.95, σ = 7.49 c x– = 56.02, σ = 14.26

9 a Brianna: x– = 75, σ = 3.69Katie: x– = 74, σ = 18.28

b Brianna is more consistent because she has a lower standard deviation.

10 B 11 C12 x– = $1825, sample SD = $79713 a 500 hours

b x– = 455.3 h, sample SD = 88.9 h14 Crinkle, because the standard deviation in the weight

of each pack is lower and therefore you are more likely to get the correct amount.

10 Quick Questions 21 23.3 2 21.5 3 16 4 29 5 196 24 7 5 8 7.939 Median, because the outlier inflates the mean.

10 The outlier makes the range very large.

Exercise 10H — Comparing sets of data1

2 a Text b Textc The ‘text’ group showed more variability.

3

4 a

5 a

6 a Smith: (0, 17.5, 57.5, 62, 85), Jones: (3, 31.5, 39, 46, 61)

b

11 a Before: (20.3, 20.75, 21.1, 21.45, 21.8)After: (19.3, 19.7, 20.1, 20.95, 22.2)

b

12 a Key: 2 1 = 21 fruit

b



1–15 8 1 1

16–30 23 13 14

31–45 38 2 16

46–60 53 0 16

61–75 68 5 21

76–90 83 4 25

a Brand A b Brand A c Brand Bd Brand A e Brand A f Brand Bg Brand A

7 C 8 E 9 B 10 C

Unsprayed SprayedLeaf

9 9 8 7 59 7 5 4 3 2 1 0

8 6 2 1 08 8 5 3 2 2

1

Stem2345678

Leaf1 7 8 9 92 3 4 4 5 82 2 5 84 91 2 2 61 3 65

10 15 2520 30 35 Scale

Group XGroup Y

15 2520 30 35 40 Age

WomenMen

5 1510 20 25 30 Words per sentence

Children's bookGeography textNewspaper

0 4020 60 80100 Runs

SmithJones

19 20 21 22

Beforekg

After

20 40 60 80

Sprayed

Fruit

Unsprayed 10D

10H


580 A n s w e r san

swer

s13 a Key: 2 3 = 23 hours

Key: 2* 5 = 25 hours

b

Chapter review1 a 5.2 b 64.875 c 7.7 d 35.82 a 31.1 b 23.2 c 0.4453 a 7.025 b 9.464

Mean = 38.25 a 29.9 b 26.4 c 18.66 a 27 b 6 c 3.2

d 5.5 e 1287 a 2 b 56 c 68.5

8 a

b 50–59 9 a 2 b 23, 27 c No mode

10 a 2 b 15, 1811 46–49 12 a 27.8 b 24.5 c 28

d Median

13 Check with your teacher.14 a 7 b 159 c 1.415 a Population b 17.316 a Sample b 0.8917 a x– = 0.81, σ = 0.42 b x– = 67.25, σ = 75.3

c x– = 28.1, σ = 1.2 d x– = 27.5, σ = 7.0318 C 19 D20 a Key: 3* 9 = 3.9

b (3.9, 4.4, 4.9, 5.85, 6.8)c

21 a Elena: 2, 6, 11.5, 15, 25; Victoria: 3, 14, 20, 25, 35

b

22 a Key: 1 3 = 13

b Text A: (13, 35, 59, 82, 98);Text B: (37, 55, 63.5, 70, 82)

c

CHAPTER 11 Scatterplots and time seriesSkills check1 An independent variable is one whose variation does

not depend on changes in another variable. A dependent variable is one whose variation responds to changes in the independent variable.

2 Independent variable

3 a Height b Distance travelledc Temperature d Reaction timee Test results f Overtime payg Value of car h Travelling time

4 a Increase b Increase c Decreased Decrease e Increase f Increaseg Decrease h Decrease

Starlet Glow-wormLeaf8 6

49 82 1

6 6 53

7 64

9 548

2 2

Stem1*22*33*44*55*66*7

Leaf

3 37 815 5 8 91 1 25 7 8 8 90 2 4

ClassClass centre Frequency fx

21–24 22.5 3 67.5

25–28 26.5 9 238.5

29–32 30.5 17 518.5

33–36 34.5 31 1069.5

37–40 38.5 29 1116.5

41–44 42.5 25 1062.5

45–48 46.5 19 883.5

49–52 50.5 10 505.0

Σ f = 143 Σ fx = 5461.5



30–39 34.5 18 18

40–49 44.5 34 52

50–59 54.5 39 91

60–69 64.5 45 136

70–79 74.5 29 165

80–89 84.5 10 175

90–99 94.5 5 180

10 30 50 70

Glow-worm

Hours

Starlet

Stem3*44*55*66*

Leaf90 0 2 35 6 7 8 80 35 8 8 91 2 28

Text B Text ALeaf

9 78 2

9 9 8 8 5 5 3 28 8 8 6 5 4 4 3 2

9 9 5 2 22 1

Stem123456789

Leaf31 2 5 85 54 82 5 6 94 92 2 61 3 4 44 5 8

3.5 4.5 6.55.5 kg

0 10 3020

Elena

Number oflessons

Victoria

0 20 40 60 80100

Text A

Result

Text B

10F

10H


A n s w e r s 581

answ

ers

➔

5 a b

c d

e f

g h

Exercise 11A — Scatterplots1

2

3

4 a

b The greater the English mark, the greater the history mark, generally. However, as the points on the scatterplot do not form a straight line, the relationship is not linear.

5 a

b The greater the temperature, the fewer pies are sold. The points on the scatterplot approximate a straight line and so the relationship can be said to be linear.

6 a

b More workers on the team reduces the amount of time taken to unload the ship and, as the points on the scatterplot approximate a straight line, the relationship is linear.

7 D8 A9 Check with your teacher.

Exercise 11B — Regression linesNote: Best fit lines are indicated as a guide only.1 a b

c d

e

2

3 a y = 5x + 12 b y = 70 − 0.4xc y = 80x + 750

4 a b L = 0.05M + 220

5 a b V = 0.05T + 3.2

6 a b S = 1.25B + 21

7 a $17.40 b $8.40 c 20 km d 8.5 km

8 a 159.7 cm b 178 cmc 31.15 cm d 25.74 cm

9 a 755 b 295 c 20°C d 38°C

Hei

ght

Age

Dis

tanc

e

Time

Tem

pera

ture

Elevation

Rea

ctio

ntim

e

Blood alelevel

Test

res

ults

IQ

Ove

rtim

epa

y

Hoursworked

Val

ue o

f ca

r

Age

Tra

velli

ngtim

e

Speed

0

40

80

0 40 80

Geo

grap

hy

History

0

200

400

0 20 40

Num

ber

atci

nem

a

Temperature (°C)

00

100

200

200

400

600

800A

mou

nt s

pent

on

ente

rtai

nmen

t ($)

Wages ($)

0

40

80

0 40 80

His

tory

English

0

80

0 20 40Num

ber

ofpi

es s

old

Temperature (°C)

0

10

20

30

0 10 20 30

Hou

rs ta

ken

Number in work team

x

y

x

y

x

y

x

y

x

y

0

40

80

0 40 80

Mat

hs

English

0

240

280

040

080

0

Len

gth

of s

prin

g (m

m)

Mass (g)

20–20–60 60

2468

Temperature (°C)

Volume (L)

0

20

40

60

0 10 20 30 40

Lif

t tes

t (kg

)

Circumference ofbiceps (cm)

11A

11B


582 A n s w e r san

swer

s10 a, b c C = 0.4d + 2100

d i $8100 ii $2500 iii 14 750 km iv 34 750 km11 a, b c N = 135 − 20p

d i 73 000 ii 43 000e $2.75 f $1.75

12 a b A = 0.45d + 280

c i $582 ii $1236 iii $740 iv $1762

10 Quick Questions 11 $1152 $2353 $854 3 h 30 min5 6 h6 2 h 45 min7 808 359 2 h

10 4 h 30 min

Exercise 11C — Time series and trend linesNote: Your answers to questions 2 to 8 may vary slightly because you are using the ‘eye’ method.

1 a Seasonalb Randomc Secular, upwardsd Random or cyclicale Cyclical

2 Definite secular trend downward

3 Although there are some random variations, the trend could also be secular.

4 Prediction is about $5.40 (see dotted line at right). This price is an extrapolated value (outside the plotted values) and can only be treated as an approximate value at best.

5 Impossible to fit a trend line, given cyclical nature of the data.

6 a b Prediction for t = 25 is about $92.

7 Difficult to fit an accurate trend line, due to likely cyclical nature of software sales business.

8 At current rate (about 300/month), bank will have no employees in another year! Although not likely, there is a clear downward trend.

Chapter review1

2 a

b There appears to be a positive relationship which is linear.

3 a

b There is no apparent relationship.4 D 5 D 6 C7 a, b c y = 99 − 5x

8 a $242 400 b $73 0009 a b F = 107 − 8I

c 73 d 13.4 mg

00

8 000

16 000

10 00

0

20 00

0

30 00

0A

nnua

l cos

t ($)

Distance (km)

0

80

160

0.00

2.00

4.00W

eekl

y sa

les

(× 1

000)

Price ($)

0

800

1400

010

0020

0030

00

Pric

e ($

)

Distance (km)

Days

Tem

p. (

°C)

10152025303540

0 1 2 3 4 5 6 7 8 9 10 t

0

10

20

0 2 4 6 8 10 12 t

y

23456

0 2 4 6 8 10

Pric

e ($

)

12 t

y

Pric

e (c

ents

)

204060

80100

0 5 10 15 20 25 t

Sale

s (×

100

0)

240220200180160140120100

1999 2000 2001

Num

ber

of e

mpl

oyee

s

7000

6000

5000

4000

3000

2000

1000

01086

Months420 t

0

10

20

0 20 40Maximum

temperature (°C)

Min

imum

te

mpe

ratu

re (

°C)

0

4

8

12

0 2 4 6Number of childrenN

umbe

r of

sic

k da

ys

0

2

4

0 2Number of cars

Num

ber

ofte

levi

sion

s

0

40

80

0 8 16

y

x

0

40

80

120

0 4 8 12Amount of insecticide (µg)N

umbe

r of

blo

wfl

ies

11A

11C


A n s w e r s 583

answ

ers

➔

10 C11

Impossible to fit a trend line as trend is seasonal. Summer uniform bought at the end of the year and then the beginning of the year. Winter uniform bought near winter.

CHAPTER 12 Introduction to probabilitySkills check1 a 50-50 b Almost impossible

c Almost certain d Not very likelye 50-50 f Impossible

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

3 a

b 8 c 2 d 34 a 0.833 b 0.667 c 0.167

d 0.077 e 0.4175 a 83.3% b 66.7% c 16.7%

d 7.7% e 41.7%

6 a , 0.125 b , 0.444 c , 0.875

d , 0.938 e , 0.875 f , 0.009

Exercise 12A — Informal description of chance1 a Probable b Unlikely c Impossible

d Fifty-fifty

2 a Impossible b Certain c Even chanced Even chance e Probable f Unlikelyg Impossible h Even chance

3 Check with your teacher.4 More likely during school term5 a More likely b Equally likely c Less likely

d More likely e Less likely6 Rolling a 6

Rolling a number less than 3Rolling an even numberRolling a number greater than 2

7 Winning a raffle with 5 tickets out of 30Selecting a court card from a standard deckDrawing a green marble from a bag containing 4 red, 5 green and 7 blue marblesRolling a die and getting a number less than 3Tossing a coin and having it land Heads

8 Australia9 Carl Bailey because he has better past performances.

10 A 11 B 12 C13 Probable 14 Unlikely 15 Fifty-fifty

Exercise 12B — Sample space1 S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}2 a S = {Heads, Tails}

b S = {1, 2, 3, 4, 5, 6}c S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}d S = {a, b, c, d, …, y, z}e S = {Sun, Mon, Tue, Wed, Thu, Fri, Sat}f S = {Jan, Feb, Mar, …, Dec}

3 a 52 b 15 c 45d 1500 e 901 f 11

4 a S = {M, I, S, S, I, S, S, I, P, P, I}b 11 c 4

5 a 52 b i 4 ii 2 iii 136 a S = {1, 2, 3, 4, 5, 6} b E = {5, 6}7 a 100 b 408 D 9 B 10 D

11 a S = {NSW win, Qld win, draw}b 3c No, because the teams may not be of equal

ability.12 a S = {20, 20, 20, 20, 20, 10, 10, 10, 10, 5}, 10

b S = {20, 20, 20, 20, 10, 10, 10, 10, 5}c S = {20, 20, 20, 20, 20, 10, 10, 10, 5}d S = {20, 20, 20, 20, 20, 10, 10, 10, 10}

13 Check with your teacher.14 Check with your teacher.

10 Quick Questions 11 Unlikely 2 Fifty-fifty 3 Probable4 100 5 18 6 37 10 8 1 9 0

10 4

Exercise 12C — Tree diagrams1 S = {HH, HT, TH, TT}2 S = {11, 12, 13, 21, 22, 23, 31, 32, 33}

Child 1 Child 2 Child 3

Boy Girl Girl

Boy Boy Girl

Boy Girl Boy

Boy Boy Boy

Girl Boy Boy

Girl Boy Girl

Girl Girl Boy

Girl Girl Girl

6Month

42 12108

50

30

110

90

70

10Num

ber

of u

nifo

rms

sold

Impossible

b d a ce

f

Certain

18--- 4

9--- 7

8---

1516------ 7

8--- 9

1024------------

11C

12C


584 A n s w e r san

swer

s3 S = {BBB, BBG, BGB, BGG, GBB, GBG, GGB,

GGG}4 a 12 b No5 S = {13, 14, 18, 31, 34, 38, 41, 43, 48, 81, 83, 84}6 S = {DZ, DM, DK, DS, ZD, ZM, ZK, ZS, MD, MZ,

MK, MS, KD, KZ, KM, KS, SD, SZ, SM, SK}7 S = {AM, AS, AL, PM, PS, PL, YM, YS, YL}8 S = {CA, CR, CL, CK, AR, AL, AK, RL, RK, LK}9 a Check with your teacher.

b S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

c 610 C 11 D 12 B13 The statement is not correct because there are 4

elements to the sample space. The one Head and one Tail can occur in either order.

14 a S = {22, 25, 27, 28, 52, 55, 57, 58, 72, 75, 77, 78, 82, 85, 87, 88}

b S = {25, 27, 28, 52, 57, 58, 72, 75, 78, 82, 85, 87}

15 a 12 b 24 c 2416 a S = {TJ, TS, TR, TM, JT, JS, JR, JM, ST, SJ, SR,

SM, RT, RJ, RS, RM, MT, MJ, MS, MR}b 20 c 2 d 6 e 12

17 a 36b

c 6

Exercise 12D — Equally likely outcomes1 No. The players are not of equal ability.2 No. The runners are not of equal ability.3 Yes. The number is chosen randomly.4 a Yes b No c No d Yes5 a True. The letter is chosen randomly.

b False. On a page of writing, each letter of the alphabet does not occur equally often.

6 B7 No, there are two chances of a boy and a girl, as they

could be born in either order.8 a S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

b No9 a 24

b No. The chance of each combination depends on people’s taste.

10 a 10b No. Each horse has a different rider and ability.c Yes. Yes. The selection of horse is made

randomly.

10 Quick Questions 21 Unlikely 2 8 3 34 1 5 Yes6 S = {BB, BG, GB, GG}7 S = {AL, AM, AJ, SL, SM, SJ}8 9 9 6 10 No

Exercise 12E — Using the fundamental counting principle1 50 6252 a 4 b 36 c 123 1000 4 7776 5 6 760 0006 D 7 B 8 18339 72

10 a 64 b 144 c 168 d 112 e 384

11 a 3 200 000 b 24012 a 5408 b 67613 3614 a 100 000 000 b 80 000 000

c 1 000 000 d 2 000 00015 9616 C17 a 1200 b 55018 20 00019 307 328 000

Investigation — Q-lotto: frequencies1 Unlikely2 Almost impossible3 Less likely4 No5 {1, 2, 3, 4, . . . 44, 45}, 456 {4, 5, 8, 15, 22, 30, 23, 35}7 8, no8 No, at least 3, plus either bonus9 {4, 5, 8, 15, 22, 30}

10 Yes, they occur only once each11 No12 6013 314 28, 7615 6, 4316 {10, 20, 21, 25, 38, 40, 41, 43}

2 supplementary or bonus numbers17 {9, 11, 27, 28, 29, 38, 43}

6 of these18 {2, 5, 8, 12, 15, 37}

Exercise 12F — Relative frequency1 0.74 2 0.79 3 0.3754 a 0.45 b 0.555 4%6 a 0.03 b 0.977 a 0.96 b 0.048 A 9 A

10 a 0.525 b 0.4375 c 0.037511 a 6.67% b 8012 a 0.02 b $40013 Yes, the relative requency is 27%.14 a 2.5% b 51.5% c 17.5%15 40 000 km

16 a

b Win = 0.375, Loss = 0.35, Draw = 0.275

Total 2 3 4 5 6 7 8 9 10 11 12

No. of elements 1 2 3 4 5 6 5 4 3 2 1

Result Number

WinLossDraw

151411

12A

12F


A n s w e r s 585

answ

ers

➔

Exercise 12G — Single event probability1 S = {Heads, Tails}, 12 a S = {1, 2, 3, 4, 5, 6}, 1

b S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, 3c S = {a, b, c, d, e, … y, z}, 5d S = {Sun, Mon, Tue, Wed, Thu, Fri, Sat}, 2e S = {Jan, Feb, Mar, … Nov, Dec}, 3

3 a 26, 52 b 1, 15 c 1, 45d 5, 1500 e 3, 11

4

5 a b c

d e f

6 a b c

d e f

g g i

7 a b c

d e f

8 a b c

9 a b c

d e f

10

11 a b c

d e

12 C 13 C 14 C 15 D

16 a b

17 a b c

18 a b c

d e f

19 Check with your teacher.20 a Because there are two numbers which could go in

the last place.b A number greater than 400

10 Quick Questions 31 2 3 4 5

6 True 7 False 8 0.2 9 0.75 10 0.5%

Exercise 12H — Writing probabilities as decimals and percentages1 0.52 37.5%3 a 0.5 b 50%4 a 0.17 b 0.5 c 0.335 a 16.7% b 50% c 83.3%6 a 0.02 b 0.25 c 0.08

d 0.5 e 0.23

7 a 1.9% b 25% c 7.7%d 50% e 23.1%

8 A 9 D 10 B11 a 0.2 b 0.4 c 0.6

d 0.812 a 20% b 40% c 40%

Exercise 12I — Range of probabilities1 a Even chance b Probable c Unlikely

d Certain e Probable f Unlikelyg Probable h Impossible i Unlikely

2 a 0, impossible b 1, certain

c , even chance d , even chance

e , unlikely f 0, impossible

g , even chance

3 Check with your teacher.

4 , , , ,

5 A, D, C, B, E6 D 7 B 8 D9 a b Unlikely

10 , very probable

11 a Very unlikely b Even chancec Probable d Unlikely

12 a True, as there are 4 Aces from 52 cards in the deck.

b False, as each letter does not occur equally often.c False, as each student is not of equal ability.d True, as the name is chosen randomly.

10 Quick Questions 41 2 3 , , 4 62.5%

5 0.375 6 0.154 7 23.1% 8 19 0 10 Probable

Exercise 12J — Complementary events1 a S = {1, 2, 3, 4, 5, 6}

b c 1

2 a i ii iii

b 13 a Losing a race

b Failing a testc Your birthday not falling on a Monday

4 A coin landing Heads A coin landing TailsAn odd number on a die An even number on a dieA picture card from a A non-picture card from a

standard deck standard deckA red card from a A black card from a

standard deck standard deckWinning 1st prize in a Not winning 1st prize in

raffle with 100 tickets the raffleMaking the last 4 teams A team not making the

in a 20-team last fourtournament

12---

16--- 1

6--- 1

2---

12--- 2

3--- 1

3---

145------ 1

45------ 22

45------

2345------ 1

5--- 1

3---

1945------ 2

9--- 2

15------

152------ 1

13------ 1

4---

12--- 3

13------ 3

13------

112------ 1

3--- 7

12------

14--- 1

4--- 1

4---

34--- 1

2--- 3

4---

56---

14--- 3

4--- 1

4---

14--- 1

2---

1200--------- 4

999---------

3384160 000------------------- 6768

160 000------------------- 10 152

160 000-------------------

15--- 1

5--- 4

5---

15--- 4

5--- 1

5---

16--- 1

13------ 7

11------ 33

100--------- 5

9---

36--- 26

52------

452------

612------

1320------ 7

13------ 9

18------ 8

19------ 6

25------

502000------------

98100---------

12--- 1

4--- 4

9--- 1

2--- 10

19------

16---

720------ 8

20------ 5

20------

12D

12J


586 A n s w e r san

swer

s5 a , , , , ,

b , , , , ,

c 16 a Rolling an odd number

b Rolling a number less than 4c Rolling a number greater than 2d Not rolling a 6e Rolling a 1

7 a Choosing an even-numbered ballb Choosing a ball numbered greater than 19c Choosing a ball that has a number less than 24d Choosing a ball that is not a multiple of 5

8 a Selecting a coloured ballb Selecting a black ballc Not selecting a pink ball; that is, selecting a

black or orange ball9 A 10 C

11 a b

12 a b

13 a b c

d e f

14 a b c

d e

15 a b

16 a b c

17 0.318 a 91% b 9%

10 Quick Questions 51 S = {heart, club, diamond, spade}

2 3 4

5 6 7

8 9 10

Investigation — Q-lotto: conclusion1 45 × 44 × 43 × 42 × 41 × 40 = 5 864 443 2002 6 × 5 × 4 × 3 × 2 × 1 = 7203 5 864 443 200 ÷ 720 = 8 145 060

4

Chapter review1 Marcia will probably get a higher card.2 a Probable b Impossible c Even chance

d Unlikely e Unlikely3 Check with your teacher.

4 Hot weather5 Rolling a die and getting a number greater than 1

Selecting a blue marble from a bag containing 14 blue, 15 red and 21 green marblesSelecting a picture card from a standard deckWinning the lottery with 1 ticket out of 100 000 tickets sold

6 Mark is most likely to win based on past performances.

7 S = {S, A, M, P, L, E}8 a S = {Heads, Tails}

b S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}

c S = {ace club, ace spade, ace diamond, ace heart}

d S = {black, black, black, black, white, white, white, green, green, green, green, green}

9 a S = {1, 2, 3, 4, 5, 6}b E = {5, 6}

10 a i 2 ii 1b i 52 ii 32 c i 15 ii 11

11 S = {HH, HT, TH, TT}12 3613 a S = {56, 57, 59, 65, 67, 69, 75, 76, 79, 95, 96, 97}

b 914 a S = {MN, MP, MR, MS, NM, NP, NR, NS, PM,

PN, PR, PS, RM, RN, RP, RS, SM, SN, SP, SR}

b 815 a S = {TCB, TCM, TCZ, TDB, TDM, TDZ, THB,

THM, THZ, TIB, TIM, TIZ, KCB, KCM, KCZ, KDB, KDM, KDZ, KHB, KHM, KHZ, KIB, KIM, KIZ}

b 1516 a 8

b No. Each greyhound is not of equal ability.17 a Each is equally likely, as the winning ticket is

selected randomly.b Each outcome is not equally likely, as the teams

have different abilities.c Each letter is not equally likely, as each letter is

not used equally often.18 759 37519 2020 27221 16022 a 10 000 b 50023 a 100 000 000 b 94 109 40024 0.0225 a 0.15 b $75026 S = {1, 2, 3, 4, 5}, E = {3, 4, 5}

27 a b c

d e f

28 a b c

d e f

29 a b c

12--- 1

2--- 3

13------ 1

2--- 1

100--------- 1

5---

12--- 1

2--- 10

13------ 1

2--- 99

100--------- 4

5---

18--- 7

8---

15--- 4

5---

920------ 11

20------ 3

20------

1720------ 3

5--- 2

5---

25--- 3

10------ 3

5---

710------ 3

10------

720------ 13

20------

325------ 21

50------ 29

50------

110------ 1

8--- 1

10 000----------------

815------ 7

15------ 3

10------

15--- 4

5--- 4

5---

18 145 060-----------------------

125------ 1

25------ 13

25------

15--- 9

25------ 16

25------

152------ 1

13------ 1

4---

12--- 4

13------ 10

13------

720------ 1

10------ 3

4--- 12G

12J


A n s w e r s 587

answ

ers

➔

30 a b c

d e

31 a b

32 a 0.025 b 0.5 c 0.75

33 a 50% b 33 % c 66 %

34 Probable

35 . It is probable that the car will have a defect.

36 a Tossing a coin that lands Headsb Rolling a die and getting a number greater than 4c Not choosing a blue ball

37 a b

38 39

124------ 3

4--- 1

4---

34--- 1

2---

1400--------- 4

1999------------

13--- 2

3---

78---

310------ 7

10------

512------ 18

25------


Maths A Textbook - Answers

Economy & Finance

Transcript of Maths A Textbook - Answers