Heinemann Maths Year 9 VELS Answers

answers 513

Answers

Solutions to Laugh Zones, Maths in Actions, Maths@Works, Problem solving tasks, Investigations, VELS Design Tasks, VELS Assignments, DIY Summaries and Challenge Maths are available in the Teacher Edition and Teacher Worked Solutions.

Chapter 1Prep zone (p. 2)

1 (a) 0.17 (b) 0.057 (c) 0.003212 (a) (b) (c)

3 (a) (b) (c) (d)

4 (a) 8.7 (b) 9.1 (c) 7.8 (d) 206.675 (a) 3 : 5 6 2 : 1 7 Anh $15, Kiao $58 (a) 1 m (b) 6.35 km (c) 3.982 cm9 (a) 65 (b) 48

Exercise 1.1 (p. 6)

1 (a) (b) (c) (d)

(e) (f) (g) (h) (i)

2 (a) −21.96 (b) 18.52 (c) −0.314 (d) −0.75(e) −1.8125 (f) −11.43 (g) −14.3902(h) 10.0256 (i) 0.104

3 (a) −2.4 (b) 3.125 (c) −12.875 (d) 21.8(e) −123.75 (f) 321.375

4 (a) (b) (c) (d)

(e) (f)

5 D 6 C7 (a) 33.33% (b) 20% (c) 33.33%

(d) 18.18% (e) 15% (f) 31.25%(g) 35.56% (h) 17.5% (i) 37.65%

8 (a) 1725 (b) 1875 (c) 2175 (d) 33009 (a) 1980 (b) 1320 (c) 748 (d) 110

10 (a) $40 (b) $70 (c) 2200 minutes(d) 300 minutes

11 (a) E (b) B (c) C12 Any number divisible by 3 between 45 and 84

inclusive

13 (a) 0.5, 50%, 1 : 2 (b) 45%, 9 : 20

(c) 0.72, 18 : 25 (d) 0.4, 40%

(e) 56%, 14 : 25 (f) 0.375, 37.5%

14 (a) 700 (b) 96615 (a) 18 (b) 20%16 (a) (i) 120 (ii) 96 (b) (i) 390 (ii) 273

(c) Increasing by a certain percentage and then decreasing by the same percentage does not get you back to where you started.

17 (a) (i) 125 (ii) 100 (b) (i) 400 (ii) 300(c) Multiplying by a certain ratio and then applying the reverse ratio gets you back to where you started.

Exercise 1.2 (p. 13)1 (a) $20.40 (b) $38.40 (c) $262.502 B3 (a) 16.7% profit (b) 28.6% profit (c) 3.7% loss

(d) 5.3% loss 4 C5 (a) $69.60 (b) $96 (c) $520.80

(d) $6259.206 6.01% profit7 (a) $2.00 (b) $27.57 (c) $295.68 (d) $42.058 (a) $40 (b) $60 (c) $91.76 (d) $78.829 D 10 E 11 $735 12 $88.80

13 14.9% profit 14 18.7% profit 15 $15.7116 (a) $16.80 (b) $2117 (a) Students’ own answers but will need to be

between 19.9% and 24.9%. (b) Students’ own answers but will need to be between 18.3% discount on $3000 to a 23.4% discount on $3200.

18 (a) (i) $1090 (ii) $600 (iii) 31.2% discount(b) $7857

19 (a) 39.4% profit (b) $120 370 (c) $137 670

Exercise 1.3 (p. 19)1 (a) 27 (b) 38 (c) 512 (d) p9 (e) 6x6

(f) 11y16 (g) 3j11 (h) 72e6 (i) 14m8

2 (a) a9b2 (b) g4h7 (c) e11f 2 (d) m11n11

(e) p3q4 (f) t8u10 (g) 5v13w3 (h) 9x3y7

(i) 12a9b10 (j) 56c14d14 (k) 6e10f 7 (l) 54g6h8

3 (a) 72 (b) 35 (c) 23 (d) 5a4 (e) 5g4

(f) 3h2 (g) 4c11 (h) 12d2 (i) (j)

(k) (l) (m) 5m3n7 (n) 6v3w2

(o) (p) (q) 6c4d2 (r) 3e6f 6

(s) (t) (u)

79100--------- 3

1000------------ 7

500---------

334--- 2 2

15------ 12

5--- 111

16------

−1720-------- −1 5

12------ 524

35------ −41

3---

−12057------ 5 1

12------ 21

2--- 1 7

25------ 52

99------

−2153200--------- 7149

200--------- −151011

1250------------ 194993

5000------------

−4536180------ 6321631

2500------------

920------,

1825------, 2

5---,

1425------, 3

8---,

e4

6---- f 2

9---

j3--- 3k

11------

x2y2

4---------- a7b2

7----------

x8y2z2

5--------------- ab8c6

9------------- p2q5r3

4---------------

HMZVELS9EN-Answers Page 513 Monday, June 30, 2008 1:14 PM

HEINEMANN MATHS ZONE 9514

4 (a) C (b) C5 (a) 22 × 52 (b) 2 × 32 × 7 (c) 22 × 3 × 61

(d) 22 × 33 × 5 (e) 22 × 33 (f) 34 × 52

(g) 22 × 17 (h) 32 × 52 × 76 Coefficients must be 2 and 6, 1 and 12 or 3 and 4.

Sample answers: 2x7 × 6y3; x3y × 12x4y2

7 (a) x16, x4 (b)

8 (a) x9 (b) (c) 12a8 (d) 2q3 (e) c7

(f) j 5 (g) (h) q6 (i)

9 (a) A (b) C10 (a) a3 + 3a (b) 42k3 − 7k4 (c) b4 + ab

(d) 45p4 + 5p5 (e) 18x3 + 24x7 (f) 12v3 − 24v8

(g) 25xy3 − 10y9 (h) 45p4 + 18p3q5

(i) 15s2t3 − 6s4

11

(a) 15 625 (b) 78 125 (c) 6 103 515 625(d) 1 953 125 (e) 125 (f) 3125(g) 15 625 (h) 15 625 (i) 390 625

Exercise 1.4 (p. 23)1 (a) 1 (b) 7 (c) 8 (d) b2 (e) c3 (f) k

(g) −3a4 (h) −8g11

2 (a) 1 (b) 3 (c) 3x4 (d) k8 (e) a3

(f) 3 (g) (h)

3 All answers must contain x3.4 (a) 4096 (b) 531 441 (c) a12 (d) b21

(e) x9 (f) 70 = 1 (g) k0 = 1 (h) p0 = 15 (a) y17 (b) k27 (c) m20 (d) y23

(e) m12 (f) f 20

6 Values for m and n must multiply to give 24.7 (a) 1 (b) (c) (d) 1 (e)

(f) (g) (h)

8 (a) C (b) B9 (a) m3 (b) p14 (c) k3 (d) n10

10 (a) A (b) C11 (a) 7 (b) 18 (c) 10 (d) 7 (e) 3 (f) 1

Exercise 1.5 (p. 27)1 $1530 2 $179.90 3 B 4 E 5 A6 $527.05 7 D8 (a) $771 (b) $555.15 (c) $331.35

(d) $187.50 9 E

10 (a) (b) (c) 22% 11 $713

12 (a) $1700 (b) $2600 (c) $3450 (d) $4350(e) $4950 (f) $6000 13 $89.76

14 Adam: $433.20; Britta: $444.60; Con: $433.20; Deng: $307.80

15 (a) $900, $1956.75, $23 481(b) $335, $1456.69, $17 480.30(c) $622.84, $1245.69, $2708.33(d) $725, $3152.54, $37 830.50(e) $832.50, $1665.01, $43 440(f) $1360, $2956.87, $35 482.40

16 $150 00017 (a) 40 hours (b) 44 hours (c) 50 hours

(d) 19 hours overtime is exactly the same18 (a) (i) $78.75 (ii) $1057.50 (b) $2937.5019 (a) Option A: $40 000; Option B: $35 714

(b) $25 000 (c) If Bruce expects sales less than $25 000 per week he should choose Option A

Exercise 1.6 (p. 36)1 (a) $683.30 (b) $3123.45 2 $507.923 (a) $0 (b) $225 (c) $975 (d) $2100

(e) $11 460 (f) $13 859.7 (g) $15 360(h) $23 118 4 B 5 E

6 (a) $44 765 (b) $9289.57 (a) Answers need to be less than $45 550.

(b) Answer will be less than $9525.8 (a) $32 769.04 (b) $31 904.04 (c) $5431.219 (a) $12 210 (b) $1044.46 (c) $234

(d) $5754.9 (e) $163510 (a) $21 060 (b) 26% (c) $15 720 (d) 20%

(e) $5340 (f) If the income was split with their spouse/partner each individual would get the benefit of the tax-free threshold. There is a flaw in the tax system as applied to sole income earners.

Exercise 1.7 (p. 40)1 $2972 (a) $176 (b) $37.80 (c) $132.84 (d) $10.20

(e) $2234.40 (f) $453.753 B 4 $13 427.13 5 B6 (a) $3.93 (b) $7.59 (c) $1.08 (d) $2.587 (a) $2.03 (b) $1.04 8 (a) $1.37 (b) $0.239 8.9% 10 22.8% 11 5.8 years

12 B 13 B14 (a) 9.0% (b) 14.0% (c) 11.5% (d) 10.0%15 (a) 7.9 years (b) 3.8 years (c) 5.3 years

(d) 2.2 years16 (a) $200 (b) $1350 (c) $2129.61

(d) $42 760.8517 $1455.23 18 (a) $45 (b) $240019 $8036 20 (a) $4.36 (b) $2.7121 (a) (i) $0.74 (ii) $3.29 (b) $2.55

51 552 2553 12554 62555 3 12556 15 62557 78 12558 390 62559 1 953 125510 9 765 625511 48 828 125512 244 140 625513 1 220 703 125514 6 103 515 625

6y10

y7---------- , 6y3

t3---

f 3

8--- 2x2

5--------

3f 2

4------- 5s9

9-------

35--- 4

7--- 5

2---

e6

6---- d

10------ q5

15------

813---% 62

3---%


answers 515

22 207 days23 $24 000 24 $36 930.46 25 $4657.1426 Sample answers: R = 4%, T = 2; R = 8%, T = 1

27 (a)

(b) July $531; August $531; September $910; October $910 (c) $6.60(d) July $975; August $531; September $1516; October $910 (e) $9.01 (f) 36.5% increase(g) The timing of withdrawals needs to be carefully considered as even the small changes seen in this question have resulted in significant increases in the amount of interest earned.

28 (a) $2250 (b) $17 250 (c) $479.17 (d) 13%(e) $1500 (f) $1000(g) Part (e) assumes the $15 000 is owed for the whole 3 years whereas part (f) doesn’t.

Exercise 1.8 (p. 50)1 (a) $4 (b) $5.50 (c) $10 (d) 15.252 (a) (i) $18 (ii) 5 weeks

(b) (i) $9 (ii) 4 weeks(c) (i) $60 (ii) 6 weeks(d) (i) $34 (ii) 5 weeks

3 (a) $3 (b) $724 (a) $2050.40 (b) (i) $1250 (ii) $13135 Students’ own answers, but the cost price will

always be seven times the payment.6 (a) (i) $1890 (ii) $12 502

(b) $2667.50 (c) 4 years

Exercise 1.9 (p. 55)1 (a) $4.21 (b) $3.38 (c) $0.98 (d) $1.74

(e) $4.78 (f) $1.792 B 3 (a) $5.97 (b) $5.704 (a) $25 (b) $25 (c) $71.25 (d) $62.63

(e) $30 (f) $108.755 (a) (i) $100 (ii) $1055 (b) (i) $65 (ii) $705

(c) (i) $120 (ii) $1255 (d) (i) $245 (ii) $25056 (a) $893 (b) $2267 (a) Answers must be $375 or less.

(b) Answers will be $3.14 or less.8 (a) $5247 (b) $2572 (c) $65909 (a) If you were able to pay your credit card bill

completely each month then Card A is the better choice.

(b) Card B is better if you think you will need to have some on-going debt associated with your credit card. With this card you get more days without interest being charged.

Chapter review (p. 58)

1 (a) (b) (c) (d)

2 (a) $52.50 (b) $26.24 (c) $237 500 3 E4 (a) 12x15 (b) 5x4 (c) 45a7b11 (d) 2a3b2

5 (a) x12 (b) q26 (c) 4 (d)6 (a) $59.15 (b) $101.40 (c) $29.58

(d) $80.287 (a) $0 (b) $10 227 (c) $14 6948 (a) (i) $1.11 (ii) $0.58 (b) $0.539 C 10 (a) $16 (b) 5 weeks

11 (a) $735 (b) $171 12 $7.7513 (a) 16 700 (b) 23 380 (c) 40%14 (a) $105 (b) $94.50 (c) 26% 15 $945.7516 (a) $44 874.80 (b) $43 434.80 (c) $8890.4417 (a) $5750 (b) $958.33 18 $270019 (a) $2062.50 (b) 10 years 20 $62521 (a)

(b) $400 000: 4.9% $600 000: 5.28%(c) (i) $2440 (ii) $4960 (iii) $11 260(iv) $77 000 (d) (i) $2340 (ii) $3915(iii) $7590 (iv) $62 490 (e) Certainly all of the examples shown here indicate that Victoria is higher. However, NSW seems to collect stamp duty for properties of all values while Victoria starts at $20 000.

22 (a) $10 794 (b) $8095.50 (c) $1169.80(d) $3147 (e) $6477.20(f) Within a further two years

Replay (p. 62)1 (a) 6 h 45 min (b) 8 h 32 min2 (a) 5 × 5 (b) 2 × 2 × 3 (c) 2 × 3 × 73 (a) −33 (b) −47 (c) 74 (a) 78° (b) 42° (c) 1°5 (a) 5 : 2 (b) 11 : 21 (c) 3 : 86 (a) (b) (c) 67 (a) 2, 5, 11, 23, 47, 95, 191

(b) 80, 55, 30, 5, −20, −45, −708 (a) 20.2 cm (b) 36 cm (c) 23 cm9 (a) 21.3 cm2 (b) 60 cm2 (c) 26.5 cm2

10 (a) x = 11 (b) x = 7 (c) x = 15

11 (a) (b) (c) 12 5


1 (a) 72.1 (b) 18 210 (c) 15.7123(d) 0.000 074

2 (a) 6 (b) 32 (c) 0 (d) 140

Balance

Jul 11728

Aug 11929

Sep 628

Oct 162131

BalanceDepositWithdrawalDepositDepositWithdrawalDepositWithdrawalDepositWithdrawalBalance

$197$641$299$862$176$194$800$426$400

$975$1172$531$830$1692$1516$1710$910$1336$936$936

State/Territory Vic NT SA WA Tas Q’land ACT NSW

Rate (%) 3.83 3.4 3.42 2.92 2.84 2.8 2.76 2.75

−216--- −1 1

20------ −214

15------ −33

50------

75---

415------ 71

2---

13---

14--- 1

13------ 1

52------



3 (a) (i) 5 m (ii) 1.6 mm (iii) 15.1 cm(b) (i) 16 m (ii) 9 mm (iii) 62.1 cm

4 (a) E (b) B (c) A (d) D (e) C5 (a) 112 cm2 (b) 96 cm2 (c) 154 cm2

Exercise 2.1 (p. 68)1 (a) 3 cm (b) 8500 cm (c) 7500 (d) 140 mm

(e) 640 000 cm (f) 28 mm (g) 0.78 m(h) 671 cm (i) 9500 m

2 (a) centimetre (b) metre (c) metre(d) kilometre (e) millimetre (f) metre

3 (a) C (b) E (c) B (d) H (e) G (f) F(g) A (h) D

4 C 5 B 6 D 7 C 8 D 9 12 cm10 2.25 km: the claim is not correct. 11 $25.9012 Film for a camera. The film is 35 mm wide.13 (a) 12 m (b) 300 cm

Exercise 2.2 (p. 78)1 (a) 75.6 cm − 76.4 cm (b) 1.53 km − 1.61 km

(c) 19.3 m − 19.9 m (d) 7.59 cm − 7.69 cm(e) 12.3 m − 13.3 m (f) 1.089 km − 1.091 km

2 (a) (i) 0.000 (ii) 0.05% (b) (i) 0.001(ii) 0.14% (c) (i) 0.001 (ii) 0.12%(d) (i) 0.009 (ii) 0.87%

3 (a) 84 ± 1.5 m (b) 48 ± 0.9 cm (c) 656 ± 16 cm(d) 4760 ± 15 m

4 (a) 102.4 ± 1.6 cm (b) 150 ± 1 m(c) 705 ± 7.5 mm 5 2000 ± 56 cm2

6 (a) 15.5 m (b) 8.5 cm(c) 74.5 mm (d) 76.45 and 76.55 m

7 A 8 (a) B (b) A9 (a) length 0.04, width 0.0625

(b) length 4%, width 6.25% (c) 16.04 ± 1.64 cm2

10 (a) maximum 28.8 m, minimum 28.0 m (b) 1.4%(c) maximum 50 m2, minimum 47 m2 (d) 84 bags

11 (a) two cans of paint(b) maximum 36 m, minimum 32 m

12 (a) 1306 ± 72.4 m2 (b) 35 boxes13 Students’ own answers14 (a) −2.5% (b) 82 km/h

(c) Too high. Then you are actually travelling below the speed limit if the speedometer indicates that you are driving at the speed limit.

Exercise 2.3 (p. 82)1 (a) 825 cm2 (b) 1853 cm2 (c) 1750 mm2

(d) 506 cm2 (e) 600 cm2 (f) 628 cm2

(g) 143 cm2 (h) 240 cm2

2 (a) D (b) C (c) B3 (a) 1408 m2 (b) 176 kg4 (a) 451 cm (b) 1546 cm2 (c) 62%5 (a) (i) 311.1 m2 (ii) 69.1 m2 (b) 81.8%6 The area of the top of the pizza is 616 cm2, so any

rectangle that gives this area with integer values. Sample answers: 25 × 25; 22 × 28; 31 × 20 etc.

7 (a) (i) 3 cm (ii) 2 cm (b) They are the same.

Exercise 2.4 (p. 87)1 (a) 117 cm2 (b) 120 mm2 (c) 140 mm2

(d) 66 cm2 (e) 240 cm2 (f) 7.5 m2

(g) 27.5 cm2 (h) 130 mm2 (i) 12 km2

(j) 84 mm2 (k) 350 m2 (l) 360 mm2

2 (a) E (b) A (c) D3 (a) 625 cm2 (b) 96 tiles4 (a) 200 cm2 (b) 14.1 cm5 4.5 m2 6 B7 Any product whose product is 3208 1.26 m, 3.16 m 9 586 m2

10 (a) 90 m2 (b) $2070

Exercise 2.5 (p. 94)1 (a) 180 m2 (b) 780 cm2

(c) 3.913 m2 or 39 130 cm2 or 3 913 000 mm2

2 (a) (b) 54 cm2

3 (a) 700 cm2 (b) 78 cm2 (c) 1560 cm2

(d) 560 mm2 (e) 150 cm2 (f) 720 cm2

(g) 1360 cm2 (h) 4320 cm2

4 (a) C (b) E (c) E 5 6550 cm2

6 Type 1 uses 352 cm2; Type 2 uses 372 cm2

7 (a) 60 cm long, 50 cm wide (b) 15 cm8 Four times larger9 Any of these combinations (length, width, height) in

centimetres: (2,2,119), (4,4,58), (6,6,37), (8,8,26), (10,10,19), (12,12,14), (16,16,7), (20,20,2)

10 (a) 158 m2 (b) 110.86 m2

(c) 9 hours 14.3 minutes11 (a) 832 cm2 (b) 24 cubes

(c) 2304 cm2 (d) 36.1%

Exercise 2.6 (p. 98)1 (a) Yes (b) No (c) Yes (d) No (e) No

(f) No (g) Yes (h) No2 (a) 600 cm3 (b) 1260 mm3 (c) 210 cm3

(d) 512 m3 (e) 28 274 cm3 (f) 63 m3

(g) 1080 cm3 (h) 9600 mm3

3 (a) 600 cm3 (b) 560 m3

4 (a) E (b) B (c) A (d) A5 (a) 12 m3 (b) 12 000 litres = 12 kL6 3040 m3 7 50 cups8 (a) 200 cm (b) 419 days 9 5654.9 cm3

10 Any of these combinations (length, width, height) in metres: (1,1,36), (1,2,18), (1,3,12), (1,4,9), (1,6,6), (2,2,9), (2,3,6), (3,3,4)

11 (a) 15 944 cm3 (b) 62 cm12 (a) 76 027 mL (b) 14 451 cm3 (c) 547.4 kL

Chapter review (p. 102)1 (a) D (b) C (c) B (d) E2 (a) 6.3% (b) They are the same.

(c) 6662 ± 33.5 cm2


answers 517

3 (a) 180 cm2 (b) 3848.45 cm2 (c) 1480.44 m2

(d) 12 355.84 cm2

4 (a) 6.51 m2 (b) 500.85 cm2 (c) 315 cm2

(d) 338 cm2 (e) 162 cm2 (f) 10.935 m2

5 (a) 348 cm2 (b) 190.5 cm2

6 (a) 360 cm3 (b) 2011 cm3 (c) 1380 cm3

(d) 3000 cm3 (e) 110 mm3 (f) 450 m3

7 (a) 18.3 cm, 25.4 cm (b) 18.7 cm, 25.8 cm(c) 87.4 cm, 89.0 cm (d) 465 cm2, 482 cm2

8 5.03 cm2

9 (a) 61.3 m2 (b) 12.3 m2

10 (a) 143 m2 (b) 14 900 tiles (c) 145 200 L11 (a) 32 cm (b) 12.16 L (c) 17 cm

Replay (p. 106)1 STEM | LEAF

1 | 7 82 | 5 63 | 1 3 4 94 | 0 25 | 1

2 (a) 3 h 15 min (b) 10 h 30 min (c) 6 min3 (a) −33 (b) 12 (c) −6004 (a) 212.5 (b) $0.08 (c) 725 (a) 8 (b) 81 (c) 26 (a) 1 (b) − (c) 257 (a) 15a − 12ab (b) 60xy + 17x − y (c) 8j − 2k8 (a) 80gh (b) −36k2 (c) 54e3fg9 (a) −8x − 16 (b) 30y − 55y2 (c) 3p2 + 4p + 63

10 (a) 4(m − 7) (b) 7d(ed + 5) (c) (g − 3)(f + 5)11 (a) (i) 0.4 (ii) 40% (b) (i) 0.38 (ii) 37.5%

(c) (i) 0.42 (ii) 41.67%12 (a) x8 (b) x4 (c) x4

Mixed revision one (p. 107)1 (a) (i) $83.20 (ii) $883.20

(b) (i) $3553 (ii) $13 0532 (a) 14.29% (b) 75% (c) 12.5% (d) 250%3 132 cm2 4 $678.90 5 358 cm2

6 (a) 38.3 cm2 (b) 2045.2 cm2

7 (a) $14 (b) 4 weeks8 (a) 2 cm (b) 2 367 000 cm (c) 7 m9 (a) $48.50 (b) $77.60 (c) $92.15

(d) $145.5010 (a) 1 (b) 5 (c) 1 (d) 511 (a) 178.5 cm2 (b) 92 m2 (c) 198 cm2

12 $3.4013 (a) 60.3 m to 63.7 m (b) 5.645 km to 5.675 km14 (a) 17.4 cm2 (b) 47.1 cm2 (c) 100 cm2

15 (a) $45 (b) $1890 (c) $10 155 (d) $14 55016 (a) 7238.2 cm3 (b) 7238.2 mL17 (a) 12g4h4 (b) 120a7b11 (c)18 7.1 m2

19 The area is between 1323.875 cm2 and 1376.375 cm2

20 216 days 21 $1156.25 22 12 cm, 24 cm23 (a) $22 907.02 (b) $22 227.02 (c) $2528.1124 (a) 0.8 m (approx) (b) 12 days

25 (a) $364 (b) $487.50 (c) $606.25(d) $649.95 26 $1280

27 (a) $2035 (b) 7 years and 1 month28 $7809.5029 Surface area is multiplied by four

30 (a) 2 (b) (c) 5x5y7

31 (a) Option A: at least $16 000Option B: at least $12 666.67 (b) $6000(c) Option A is better if Bettina expects to sell less than $6000 worth of goods per week, but this is less than her minimum expectations.

32 (a) 21.46% (b) 21.46%(c) They are equally efficient


1 (a) equilateral (b) isosceles (c) scalene2 (a) 45.79 (b) 12.23 (c) 4.553 (a) 144 (b) 3025 (c) 1406.254 (a) 9 (b) 13 (c) 165 (a) 8.06 (b) 25.65 (c) 17.936 (a) x = 6 (b) x = 81 (c) x = 337 (a) x = ±6 (b) x = ±6.24 (c) c = ±18.03

Exercise 3.1 (p. 117)1 (a) Yes (b) No (c) No (d) No (e) Yes

(f) Yes (g) Yes (h) Yes (i) No

2 (a)

(b) For right-angled triangles, allowing for measurement errors, a2 + b2 = c2.

3 (a) C (b) A (c) D (d) E

4

5 (a) Yes (b) No (c) No (d) Yes (e) Yes(f) Yes (g) Yes (h) Yes (i) Yes (j) No(k) Yes (l) No

313---

xy5

3--------

a b c a2 b2 c2

(a) 21 36 42 441 1296 1764

(e) 18 24 30 324 576 900

(f) 26 26 36 676 676 1296

(g) 19 28 34 361 784 1156

(h) 22 30 37 484 900 1369

a b c a2 b2 c2 a2 + b2 = c2

(a) 36 36 51 1296 1296 2601 yes

(b) 23 33 38 529 1089 1444 no

(c) 23 36 43 529 1296 1849 yes

(d) 31 36 43 961 1296 1849 no

(e) 18 39 43 324 1521 1849 yes

(f) 23 34 41 529 1156 1681 yes

(g) 23 34 41 529 1156 1681 yes

(h) 22 27 27 484 729 729 no

(i) 9 51 52 81 2601 2704 yes

3p5q7

2--------------



6

a2 + b2 = c2

7 Students’ own answers

Exercise 3.2 (p. 124)1 (a) 15 m (b) 50 mm (c) 13 cm

(d) 25 cm (e) 2.5 m (f) 8.5 mm2 (a) 12 mm (b) 24 m (c) 24 cm

(d) 16 cm (e) 12 m (f) 6 cm3 (a) 26 (b) 9.43 (c) 15 (d) 17.89

(e) 19.21 (f) 130 (g) 13.89 (h) 17.034 (a) C (b) B 5 (a) C (b) A6 (a) Yes (b) Yes (c) Yes (d) No

(e) No (f) Yes (g) No (h) No7 192 cm8 (b) 19, 180, 181; 36, 323, 325; 60, 221, 229

Exercise 3.3 (p. 130)1 (a) 13 (b) 10 (c) 15 (d) 39 (e) 26

(f) 652 (a) 13.60 (b) 13.42 (c) 6.12 (d) 16.74

(e) 8.54 cm (f) 21.26 mm3 B 4 4.50 m 5 (a) D (b) D6 (a) 17 cm (b) 34 m (c) 10 cm

(d) 5 m (e) 35 m (f) 10 cm7 (a) 9.90 cm (b) 27.46 mm (c) 19.21 cm

(d) 10.20 m (e) 5.52 km (f) 13.89 m8 C9 (a) x = 10 cm, y = 14.42 cm

(b) x = 12.21 cm, y = 12.81 cm(c) a = 9.43 m, b = 8.94 m(d) x = 25.61 mm, y = 28.28 mm(e) a = 5.83 cm, b = 8.37 cm(f) a = 8.06 cm, b = 9 cm, c = 9.85 cm

10 C11 (a) = 14.14 cm; 1.414 = (b)12 (a) Sample answers

(b) 55.90 m

Exercise 3.4 (p. 135)1 (a) 35 (b) 24 (c) 9 (d) 40 m

(e) 48 cm (f) 77 mm

2 (a) 25.40 (b) 19.74 (c) 31.43(d) 118.76 (e) 11.18 m (f) 17.05 m

3 2.42 m 4 (a) A (b) D5 (a) x = 9 (b) x = 9.80 (c) x = 3 (d) x = 8

(e) x = 7.48, y = 8.31 (f) x = 6.63, y = 17.326 (a) 14.14 cm (b) 8.49 m (c) 70.71 cm

(d) 24.75 m

Exercise 3.5 (p. 140)1 5.83 m 2 A3 (a) 44.82 m (b) 18.18 m 4 B 5 0.51 m6 3.47 m 7 A 8 C 9 11.31 cm

10 1.88 km 11 3.14 m 12 11.95 cm13 Through mountains $157 429;

Around mountains $132 500 14 $1621.5015 A → B → C → D → E → F → A (or the reverse order)16 6.89 m extra wood; first new design 9.48 m extra;

second design 4.5 m extra. The last design is the cheapest.

Chapter review (p. 144)1 (a) Yes (b) No (c) Yes2 (a) 30 mm, 30 mm, 48 mm, No

(b) 20 mm, 50 mm, 54 mm, Yes(c) 26 mm, 45 mm, 52 mm, Yes

3 (a) No (b) Yes4 (a) 20 cm (b) 50 m (c) 30 m5 (a) 75 (b) 38.83 (c) 12.56 (a) 75 cm (b) 24.60 mm (c) 63.64 m7 (a) 40.82 (b) 10.308 (a) x = 27.33 (b) x = 78.33 (c) x = 15.239 (a) 9.64 (b) 13 10 E

11 (a) 3.8 m (b) 6.6 m (c) 4.97 m12 Ming wins by 1.58 s 13 7 m 14 132 m15 (a) 19.71 m, 10 sleepers (b) $35016 (a) 2 m

(b) Possibly—many races are won by less than 2 m17 (a) 4 cm (b) 5.66 cm (c) 21.66 cm

Replay (p. 148)1 (a) −197 (b) −35 (c) 652 (a) −5 (b) 47 (c) −553 64 cm3 4 (a) 90° (b) 55° (c) 168°5 (a) 8 (b) 44 (c) 259

6 (a) −8 (b) (c) −

7 (a) (b) (c) 12 (d)8 (a) x13 (b) x3 (c) x6

9 (a) $216.75 (b) more than 16010 (a) $50 (b) $20.6311 (a) 140 cm2 (b) 81.7 cm2 (c) 207.5 cm2


1 (a) 14x (b) 8y (c) k2

2 (a) 4h + 2y (b) 8y3 + 6x2 − 2x3 (a) 12xy (b) 20k2 (c) −60g3

a b c a2 b2 c2

(a) 3 cm 4 cm 5 cm 9 16 25

(b) 12 cm 16 cm 20 cm 144 256 400

(c) 60 mm 80 mm 100 mm 3600 6400 10 000

(d) 7 cm 24 cm 25 cm 49 576 625

(e) 24 mm 90 mm 93 mm 576 8100 8649

Distance from corner, y m

1 2 5 10 15 20 25

Total distance swum, x m

50.01 m 50.04 m 50.25 m 50.99 m 52.20 m 53.85 m 55.90 m

200 2. 2

50 m

y m 13s----- st

3----

25--- 1

3--- 19

7------


answers 519

4 (a) 4x2 (b) 4x2y (c) 2x2

5 (a) 6 (b) 9 (c) 46 (a) (i) 20 cm (ii) 25 cm2 (b) (i) 22 m

(ii) 18 m2 (c) (i) 16 mm (ii) 12 mm2

Exercise 4.1 (p. 154)1 (a) 7 (b) 21 (c) 2 (d) 8 (e) 0 (f) 21

(g) −18 (h) 25 (i) 8 (j) 1 (k) 27 (l) 12 (a) 13 (b) 31 (c) −20 (d) 3 (e) 18

(f) −3 (g) 13 (h) 73 (i) 21 (j) 24(k) −27 (l) 22

3 (a) 129 (b) −7 (c) −8 (d) −9 (e) 95(f) 11 (g) 24 (h) −42 (i) −21 (j) 36(k) −53 (l) 67

4 D 5 A 6 B7 (a) (i) 32 (ii) 41 (iii) 86

(b) (i) 197.9 (ii) 294.5 (iii) 3357.7(c) (i) 2.4 (ii) 180 (iii) 10 125

8 6.4 joules 9 282.8 cm2

10 d must be a negative number divisible by 6.11 (a) (i) 5 (ii) 5 (iii) same answers

(b) (i) 65 (ii) 65 (iii) same answers(c) (i) (x5 − y5)(x5 + y5)(ii) 310 − 210 = (35 − 25)(35 + 25) = (211)(275)

Exercise 4.2 (p. 159)1 (a) 2x + 10 (b) 8x − 16 (c) 9x − 18

(d) 4a + 36 (e) 8b + 24 (f) 3k − 12(g) 2m − 6 (h) −5n − 30 (i) −3d − 18(j) −7x − 7 (k) −4d − 32 (l) −6x + 18(m) −9c + 54 (n) −2x + 10 (o) −5x + 30

3 (a) x2 + 3x (b) m2 + 5m (c) x2 + 9x(d) s2 − 7s (e) −x2 − x (f) −x2 − 6x(g) −x2 + 8x (h) −x2 + 4x (i) −n2 + 9n

5 (a) 3x2 + 6x (b) 2u2 − 12u (c) 5x2 − 5x(d) 11m2 + 33m (e) 9x2 + 18x (f) −4x2 + 16x(g) −2x2 − 14x (h) −7q2 − 7q (i) −9b2 + 54b

6 −15x + 67 (a) 10x + 2 (b) 15q − 10 (c) −24x + 30

(d) −12p + 14 (e) 63 − 18u (f) 24 − 32x(g) 12n2 − 16n (h) 10r2 − 35r (i) −10x2 − 15x(j) −12x2 − 8x (k) 16x − 14x2 (l) 35k − 30k2

8 (a) 2x + 10 (b) 3y + 5 (c) 2a2 + 3ab − 2a(d) −12p + 6q − 3 (e) 6k2 + 21k − 4(f) 10x2 + 20xy − 15xz + 5x(g) 2dc − 6d2 + 10df − 12d (h) −36y + 7y2

9 (a) 5x + 2 (b) 8 − y (c) 2x − 11 (d) 5a + 13(e) 2a2 − 3a + 10 (f) 3x2 + 10x − 4(g) 7y2 − 26y − 10 (h) 9k2 + 27k

10 E 11 D 12 A

13 (a) (b) 6x + 18(c) (i) 48 cm (ii) 130.2 cm(iii) −66 (d) Not possible. No negative values can be used, nor can 0.(e) 2x(x + 9) cm2

(f) (2x2 + 18x) cm2

(g) (i) 1160 cm2

(ii) 504 cm2 (iii) 0 cm2; not possible in real life

14 (a) 2400 m (b) 10(3y − 2) (c) y(2y + 3)(d) (i) 14 m (ii) 702 m (iii) 2849 m (e) 5

15 (a) x(x + 3) (b) 10x − 12 (c) 3 cm, 4 cm16 Two possible methods are to substitute values for x

and to use areas of rectangles.

Exercise 4.3 (p. 163)1 (a) xy + 5x + 6y + 30 (b) xy + 7x + 4y + 28

(c) ce + 3c + de + 3d (d) rt + 8r + st + 8s(e) ab − a + 2b − 2 (f) pq − 2p + 3q − 6(g) x2 + 4x + 3 (h) y2 + 11y + 18(i) ax + 3x − ap − 3p (j) ay + 4a − by − 4b(k) mn − 6m − 2n + 12 (l) km − 4k − 5m + 20

2 x2 + x − 123 (a) 2ab − 6a + b − 3 (b) 3x2 + 5x − 2

(c) 3mn − 3m + 2n − 2 (d) 4y2 + 2y − 2(e) 10k2 − 29k − 21 (f) 8a2 + 14a − 15(g) 4mp + 4np + mq + nq (h) 7ax + 7kx + ay + ky(i) 12p2 − 11p + 2 (j) 10g2 − 47g + 9(k) a2 − b2 (l) p2 − q2

4 E 5 B 6 D7 (a) (x + 7)(x + 2) cm2 (b) 204 cm2 (c) 6

(d) x2 + 9x + 148 (a) (i) (15 + x) m (ii) (3 + x) m

(iii) (15 + x)(3 + x) m2 (iv) (45 + 18x + x2) m2

(b) New garden bed has (18x + x2) m2 more area.(c) 40 m2 extra area

9 a + b = 1; e.g. +

10 (a) (i) x2 (ii) x − 4 (iii) x − 2 (iv) (x − 2)(x − 4)(b) 6x − 8

Exercise 4.4 (p. 168)1 (a) k2 + 4k + 4 (b) m2 + 10m + 25 (c) d 2 − 2d + 1

(d) p2 − 6p + 9 (e) x2 + 16x + 64(f) y2 + 24y + 144 (g) m2 + 2mn + n2

(h) w2 − 2wk + k2 (i) a2 − 8a + 16(j) y2 + 12y + 36 (k) x2 + 18x + 81(l) k2 − 14k + 49

2 (a) 16y2 + 24y + 9 (b) 4w2 + 36w + 81(c) 9x2 − 30x + 25 (d) 36k2 − 12k + 1(e) 49 − 28a + 4a2 (f) 9 − 48d + 64d 2

(g) 1 − 8c + 16c2 (h) 36 + 84y + 49y2

(i) 16g2 − 8gh + h2 (j) 9a2 + 6ad + d2

(k) 4a2 − 12ab + 9b2 (l) 25m2 + 80mn + 64n2

3 (a) c2 − 25 (b) a2 − 16 (c) k2 − 64(d) m2 − 49 (e) x2 − y2 (f) c2 − d 2

(g) 81 − x2 (h) 9 − y2 (i) 1 − k2

(j) 36 − w2 (k) p2 − q2 (l) h2 − g2

4 (a) 4m2 − 1 (b) 9x2 − 16 (c) 36b2 − 49(d) 25y2 − 1 (e) 64 − 25a2 (f) 9 − 4d 2

(g) 16a2 − 25c2 (h) 9m2 − 4n2 (i) 4x2 − 49y2

(j) 16a2 − 25b2 (k) 9 − c2d2 (l) 25 − j2k2

5 B 6 E 7 D 8 A 9 E10 (a) (i) True (ii) False (iii) False (iv) True

(b) True11 (a) (i) x2 + 14x + 49 (ii) 4x2 − 12x + 9

(b) (i) 121 cm2 (ii) 25 cm2

x + 9

2x

14--- 3

4---



12 (a) x2 m2 (b) (x2 − 4) m2

(c) Square playing field is larger by 4 m2.13 d2 + 2ad + a2 14 4c2 + 12ch + 9h2

15 (a) Filomena: 3x, Stan: 6y (b) 36y2 − 36xy + 9x2

16 (a) m (b) 1 g (c) m − 1 g

(d) m2 − mg + g2

17 S1 = 4πR21, S2 = 4πR2

2S1 − S2 = 4πR2

1 − 4πR22

= 4π(R21 − R2

2)= 4π(R1 − R2)(R1 + R2)

18 π(R − r)(R + r)19 Sample answers: a = 5 b = 4; a = 13 b = 5;

a = 10 b = 6; any Pythagorean triad where a = length of hypotenuse and b = either of the other side lengths.

20 (a) B2 − b2 (b) (B − b)(B + b)

(c) (i) 12b2 (ii)

Exercise 4.5 (p. 173)1 (a) 3 (b) 4 (c) 2 (d) 3 (e) a (f) q

(g) 3g (h) 4ab (i) m (j) p (k) 5x(l) 3ab

2 (a) 3(x + 3) (b) 12(y + 2) (c) 6(1 + 7a)(d) 4(1 + 2b) (e) 2(k − 3) (f) 4(m − 5)(g) 7(4p − 1) (h) 4(4k − 1) (i) a(3 + b)(j) w(y + 5) (k) 2(a + 2b − 4c)(l) 3(x − 5y + 3)

3 (a) 5(2x + 5) (b) 4(2y + 9) (c) 7(2a − 5)(d) 6(2d − 3) (e) 9(2 − 3m) (f) 3(2 − 5k)(g) a(3 + 2b) (h) y(5x + 2) (i) 3g(3f − 4h)(j) 2b(12ac − 5) (k) k(5m − 3n + 2gh)(l) c(1 + 4b + 2a)

4 (a) x(x + 3) (b) y(y + 6) (c) k(5 − k)(d) m(8 − m) (e) p(4p + 7) (f) a(9a + 5)(g) 3d(2 − 3d) (h) 2g(11 − 7g) (i) 2a(ab + 2)(j) 6h(gh + 3) (k) 8xy(2x − 5y) (l) 6ab(3 − 7a)

5 (a) −2(m + 6) (b) −4(k + 6) (c) −y(y + 3)(d) −x(x + 1) (e) −4(4a − 1) (f) −7(3b − 1)(g) −8(3p − 5) (h) −2(9w − 8)(i) −3x(2x + 1) (j) −7y(2 + 7y)(k) −2(4d + 2f + 3g) (l) −5(3a + 2b + 1)(m) −4x(3x + 4 –5y – z) (n) −2k(m – 2m2 + 3 + 4k)

6 (a) (a + 3)(x + 5) (b) (n − 2)(m + 9)(c) (y − 1)(4 + w) (d) (x + 5)(3 + y)(e) (q + 5)(p − 2) (f) (f − 1)(d − 6)(g) (2x + 3)(y − 1) (h) (3p + 5)(a − 1)(i) (d − 2)(5d − 4) (j) (m − 6)(3m − 7)

7 (a) True (b) False (c) False (d) True(e) False (f) False

8 (b) 3x − 6xy = 3x(1 − 2y)(c) a(b + 2) − 3(b + 2) = (b + 2)(a − 3)(e) 4p + 3k cannot be factorised or 4p + 3kp = p(4 + 3k)(f) −3y2 − 9y + 12xy = −3y(y + 3 − 4x)

9 C 10 B 11 D 12 C 13 A

14 5(3a − 2b2) 15 (a) 8ab + 12a (b) 4a(2b + 3)16 (a) (c + 2)(d + 5) (b) c = d + 317 Sample answers: 3x + 12xy; 6x + 9xb; 12abx + 15cx18 (a) x(4x − πx + y) (b) x2(5 − π)

(c) 5 − π must be greater than zero, so π must be less than 5

Exercise 4.6 (p. 177)1 (a) (x + 4)(y + 3) (b) (p + 1)(q + 5)

(c) (m + 2)(n + 9) (d) (a + f )(b + d)(e) (p + t)(q + r) (f) (m − 3)(k + 6)(g) (p − 7)(n + 1) (h) (a − 5)(b + 1)(i) (m − 2)(n − 7) (j) (a − 6)(b − 4)(k) (x + 2)(x − 8) (l) (y + 4)(y − 6)

2 (a) (k + 2)(p + 3) (b) (m + p)(n + q)(c) (d + 6)(c + 2) (d) (a + k)(d + h)(e) (x − 4)(y + 2) (f) (e − 1)(g + 3)(g) (b + 1)(c − 1) (h) (y + 3)(x − 1)(i) (k − 3)(m − n) (j) (d − 6)(f − g)(k) (a − 4)(a + 5) (l) (k − 2)(k + 5)

3 D 4 C 5 A 6 C7 (a) de + 2d + ce + 2c (b) (d + c)(e + 2)8 (a) x2 − 4x + 12 − 3x (b) (x − 4)(x − 3)9 (a) y2 + 12y + 36 (b) (y + 6)2

(c) Square of side length y + 610 Sample answers: 2x + 2a to give (x + a)(x + 2),

xy + ay to give (x + a)(x + y)11 (a) (a + 7)(b + c + d) (b) c + d = 7.

Sample answers: c = 1, d = 6

Exercise 4.7 (p. 180)1 (a) (x − 4)(x + 4) (b) (y − 5)(y + 5)

(c) (d − 8)(d + 8) (d) (a − 6)(a + 6)(e) (g − 1)(g + 1) (f) (k − 2)(k + 2)(g) (12 − h)(12 + h) (h) (7 − x)(7 + x)(i) (3m − p)(3m + p) (j) (c − 2e)(c + 2e)(k) (5a − b)(5a + b) (l) (8f − 7g)(8f + 7g)

2 (a) 2(x − 3)(x + 3) (b) 6(x − 2)(x + 2)(c) 5(4 − y)(4 + y) (d) 3(5 − y)(5 + y)(e) 7(a − b)(a + b) (f) 10(m − n)(m + n)(g) 8(x − 2)(x + 2) (h) 11(x − 3)(x + 3)(i) 4(a − 3b)(a + 3b)

3 (a) (4a − 3)(4a + 3) (b) (5b − 1)(5b + 1)(c) (4 − 3p)(4 + 3p) (d) (5 − 8y)(5 + 8y)(e) (x − 7y)(x + 7y) (f) (n − 9p)(n + 9p)(g) (2p − 9q)(2p + 9q) (h) (3a − 7b)(3a + 7b)(i) (2x − 7w)(2x + 7w) (j) (9y − 11k)(9y + 11k)(k) (10m − 3)(10m + 3) (l) (10a − 13b)(10a + 13b)

4 (a) 3(3a − 7b)(3a + 7b) (b) 2(9c − 8d )(9c + 8d )(c) 7(5x − 2)(5x + 2) (d) 5(10y − 3)(10y + 3)(e) 6(6 − 7m)(6 + 7m) (f) 8(5 − 4p)(5 + 4p)(g) 10(4p − 11q)(4p + 11q) (h) 3(2k − 9n)(2k + 9n)(i) 5(3y − 4p)(3y + 4p)

5 Two terms, both squares, separated by a minus sign.6 C 7 B 8 B 9 (x − 9)(x + 9)

10 10(10 − 3x)(10 + 3x) 11 (8x − 3y)(8x + 3y)12 a = b + 1. For example: b = 2, a = 3

32--- 1

4--- 3

2--- 1

4---

94--- 15

4------ 25

16------

12--- 1

2--- 1

2---

12b2

12--- 25b2×------------------- 100 96%=×


answers 521

13 (a) (a − b − c)(a + b + c)(b) a − b − c = 10k, k = 1,2,3,... Sample answers: a = 19, b = 7, c = 2; a = 10, b = −1, c = 1

14 (a) (T2 − T1)(T2 + T1)

(b) (T2 − T1)(T2 + T1) = (T2 + T1) = (T2 + T1)

Exercise 4.8 (p. 183)1 (a) (y + 8)2 (b) (b + 7)2 (c) (k − 6)2

(d) (p − 2)2 (e) (x + 5)2 (f) (y + 4)2

(g) (a − 9)2 (h) (d − 10)2 (i) (c − 12)2

2 (a) (3f + 4)2 (b) (4d + 5)2 (c) (2x − 3)2

(d) (5y − 2)2 (e) (4k + 1)2 (f) (3p + 7)2

(g) (8m − 5)2 (h) (6n − 1)2 (i) (3x + 10)2

(j) (2w + 9)2 (k) (11y − 2)2 (l) (7c − 4)2

3 (a) (k + 3m)2 (b) (x + 6y)2 (c) (p − 4q)2

(d) (c − 5d )2 (e) (5a + b)2 (f) (w + 10z)2

(g) (3m − q)2 (h) (x − 9y)2 (i) (7m − 2n)2

(j) (3a + 4b)2 (k) (3c + 11d)2 (l) (6m − 7p)2

4 Three terms that follow the pattern a2 ± 2ab + b2

5 C 6 D 7 C 8 x + 12 9 −510 (a) (2x + 5)2 (b) −1 or −411 (a) (3a − 6b)2 (b) a = 2b

(c) b = 1, a = 2; b = 3, a = 612 (a) 4x2 − 5x + 1 (b) 5 must be less than 2x

(c) (4x − 1)(x − 1)(d) x − 1 = 0, x = 1; 4x − 1 = 0, x =

Exercise 4.9 (p. 186)1 (a) 3, 2 (b) 10, 2 (c) 4, 7 (d) 2, 8

(e) 2, 24 (f) 1, 7 (g) −5, −3 (h) −2, −12(i) −2, 4 (j) −9, 5 (k) −5, −5 (l) −3, 4

2 (a) (x + 1)(x + 4) (b) (x + 3)(x + 5)(c) (x + 2)(x + 7) (d) (x + 1)(x + 6)(e) (x + 5)(x + 8) (f) (x + 4)(x + 9)(g) (x + 6)2 (h) (x + 11)2 (i) (x + 1)(x + 3)(j) (x + 7)(x + 8) (k) (x + 6)(x + 10)(l) (x + 2)(x + 9)

3 (a) (x − 6)(x − 2) (b) (x − 3)(x − 1)(c) (x + 7)(x + 5) (d) (x − 5)(x − 4)(e) (x − 4)(x + 1) (f) (x − 2)(x + 6)(g) (x − 4)(x + 5) (h) (x − 7)(x + 6)(i) (x − 9)(x + 2) (j) (x − 4)(x + 8)(k) (x − 6)(x + 8) (l) (x − 12)(x + 2)

4 (a) 3(x + 2)(x + 4) (b) 2(x + 2)(x + 5)(c) 6(x − 1)(x − 3) (d) 4(x − 1)(x − 6)(e) 2(x − 3)(x + 5) (f) 5(x − 2)(x + 6)(g) 4(x − 2)(x + 1) (h) 3(x − 8)(x + 2)(i) 6(x − 4)(x − 3)

5 C 6 E 7 B 8 length x + 5; width x + 29 x − 2, x − 7

10 (x + 8)(x − 6); for x = 6 the expression is equal to 0.11 (a) 20, 18, 8

(b) (x + 4)(x + 5), (x + 6)(x + 3), (x + 8)(x + 1)12 (a) x2 + 11x + 24 (b) (x + 8)(x + 3)

(c) x = 97 (d) x = 97 in x(x + 11) + 24

Chapter review (p. 189)1 (a) −3 (b) −5 (c) 122 (a) −7 (b) −34 3 E 4 A5 (a) 4x + 28 (b) x2 − 3x (c) −10x2 + 5x6 (a) (i) 13x − 7 (ii) 18x2 + 19x − 6

(b) (i) 45 (iii) 3587 (a) x2 + 10x + 16 (b) 6a2 + 7a − 208 (a) x2 + 24x + 144 (b) 25c2 − 20cd + 4d2

9 (a) 4(2a + 3) (b) −5k(3 + 4k)(c) pq(5p − 3 + 2q − r) (d) −6(4a + ab + 12)

10 (a)

(b) (50 + 2x) cm (c) 2(25 + x)(d) 20(5 + x) cm2 (e) 100 + 20x

11 (m − 2)(k + 8); m = 5, k = 812 2x + 6 13 5y − 314 (a) 10 + 2x (b) x2 + 5x

(c) (i) x2 + 5x − 14 (ii) (x + 7)(x − 2)(iii) There are no sheep

15 (a) L21H (b) L2

2H (c) H(L1 − L2)(L1 + L2)

(d) (i) 20L22 (ii) 1, 2

Replay (p. 192)1 (a) trapezium (b) rhombus

(c) isosceles triangle2 (a) −11 (b) 27 (c) 103 (a) 0.26 (b) 10.700 (c) 8.6004 (a) 47h (b) −3bc − 5b (c) 2k5 (a) 6m − m2 (b) 15p + 10p2 − 5pq

(c) 10a + 3 − a2

6 (a) $0 (b) $1200 (c) $12 0607 9 months8 (a) 0.3 m (b) 124 500 cm (c) 268.7 mm9 (a) 23.5 cm2 (b) 201.1 m2 (c) 65.4 cm2

10 (a) 102 cm2 (b) 40 cm2 (c) 80 cm2

11 (a) 3.61 (b) 8.49 (c) 17.2912 (a) 10 cm (b) 5.4 cm (c) 3.5 cm


1 (a) 14 (b) 13 (c) (d) 12 (e) 5.34(f) 62.7221

2 (a) equilateral (b) scalene and right angled(c) scalene (d) isosceles(e) isosceles and right angled (f) scalene

3 (a) 42 (b) 40 (c) 54 (d) 44 (a) 64° (b) 25° (c) 53°5 (a) 4 : 5 (b) 3 : 2 (c) 5 : 4 (d) 4 : 3

(e) 3 : 4 (f) 4 : 5

12---g12---g 1

2---g(1

g---) 1

2---

14---

20 cm

(5 + x) cm

13--- 1

3--- 1

3---

1212---



Exercise 5.1 (p. 199)1 (a) (b)

(c) (d)

(e) (f)

2 (a) a (b) f (c) g (d) k (e) n (f) p3 Students’ own answers4 (a) C (b) E (c) E (d) D

5 (b) (c) (d) (e) (f)

6 (a) 13 (b)

7 (a) (b) (c) 10 km

Exercise 5.2 (p. 203)1 (c) 0.71 (e) 0.71 (g) 1

2 (a) (i) (ii) (iii) 1.05

(b) (i) (ii) (iii) or 0.72

(c) (i) or 0.6 (ii) or 0.47 (iii) or 0.22

3 (a) (i) x = 10 km (ii) p = 39 cm (iii) n = 0.7 cm(b) (i) x = 13 cm (ii) y = 6 m (iii) r = 20.8 cm(c) (i) n = 48 cm (ii) s = 12 km (iii) r = 20.8 m

4 (a) (i) p = 4.33 m (ii) b = 24.01 cm(iii) e = 7.81 m (b) (i) u = 4.7 m(ii) q = 72.4 cm (iii) c = 15.4 cm

(c) (i) t = 42.13 cm (ii) b = 51.68 cm(iii) m = 12.47 m

5 (a) D (b) D (c) E6 Any, as long as the ratio between b and a is 7 : 10.

Sample answers: a = 10, b = 7; a = 20, b = 14; a = 100, b = 70

7 160 metres 8 2.95 metres 9 87.53 cm10 5.66 m11 (a) 2.87 m (b) Angle from the ground could be

reduced to 30° or less

Exercise 5.3 (p. 210)

1 (a) (b)

(c) (d)

(e) (f)

2 (a) 0.59 (b) 0.81 (c) 0.733 (a) (i) 0.58 (ii) 0.87 (iii) 0.5 (iv) 0.87

(v) 1.73 (vi) 0.5 (b) same (c) same4 (a) (i) 0.54 (ii) 1.54 (iii) 0.84 (iv) 0.54

(v) 0.84 (vi) 0.65 (b) same (c) same5 (a) (i) 0.74 (ii) 0.67 (iii) 1.11

(b) (i) 0.74 (ii) 0.676 B 7 C 8 A9 (a) A (b) A (c) B (d) C (e) C (f) B

10 (a) (b) sine

11 tan ratio 12 sine ratio

13 (a) (b) 5 (c)

14 sin 42° = 0.669

45

adjacent, hypotenuse

20°xA

OH

H

15A

12Oθ

opposite, adjacent

3.3

7.5 HA

O

θ

opposite, hypotenuse

10541°

yH A

Oadjacent, hypotenuse

32°

x 5.8 AO

Hopposite, adjacent

1035

θ

H

O

Aopposite, hypotenuse

ed--- i

g-- k

j-- o

n--- p

q--

135

A

B C12

M 3 km T

7 km

3 km

H

T

7 km

M

724------

43--- or 11

3---

725------ 3

5--- 21

29------

35--- 8

17------ 9

41------

45

20°xA

OH

cosine

H

15A

12Oθ

tangent

3.3

7.5 HA

O

θ

sine

10541°

yH A

Ocosine

32°

x5.8 AO

Htangent

1035

θ

H

O

Asine

0.5 mramp

25°

13

12

θ513------


answers 523

Exercise 5.4 (p. 214)1 (a) 26.63 (b) 7.51 (c) 18.87 (d) 33.27

(e) 4.04 (f) 58.11 (g) 35.08 (h) 0.922 (a) 313.49 (b) 137.73 (c) 34.31 (d) 13.62

(e) 229.40 (f) 89.71 (g) 8.32 (h) 150.133 (a) C (b) D4 (a) D (b) E5 The adjacent side divided by the hypotenuse must

be approximately equal to 0.45.6 2.40 m 7 1.39 m 8 7.60 m 9 7.01 m

10 10.72 m 11 3.70 m 12 47.57 cm13 5.52 mm

Exercise 5.5 (p. 219)1 (a) 39° (b) 15° (c) 35° (d) 62° (e) 10°

(f) 41° (g) 11° (h) 78°2 (a) C (b) D (c) D3 54° 4 15° 5 24° 6 44° 7 8°8 (a) 31° (b) 4121 m9 Students’ own answers

Exercise 5.6 (p. 229)1 122.06 m 2 16° 3 62.50°4 D 5 B 6 9.58 m 7 24°8 height of tree ÷ distance from car ≈ 0.519 76 m 10 26.17 m


1 (a) (b) (c)

2 (a) x = 11.05 cm (b) t = 3.94 cm(c) p = 10.24 m

3 (a) (b) (c)

4 (a) (b) (c)

5 (a) 0.47 (b) 0.88 (c) 0.53 (d) 0.88(e) 0.47 (f) 1.88

6 (a) 2.19 cm (b) 15 cm (c) 55°(d) 111.9 m (e) 1767 m (f) 68°

7 A 8 22.84 cm 9 33.58 m 10 48°11 1.33 m 12 76.9 km 13 215.44 m 14 46°15 (a) 2.23 cm (b) 15.6 cm2 16 63.4°

Replay (p. 236)1 (a) 1 (b) −1 (c)2 (a) $62.00 (b) $136.403 (a) $13.50 (b) $9924 (a) (i) $12 (ii) 5 weeks

(b) (i) $33 (ii) 5 weeks5 (a) 53.1 cm2 (b) 87.0 cm2 (c) 120 cm2

6 (a) 46 m2 (b) 288 cm2 (c) 50.1 cm2

7 (a) yes (b) no (c) yes (d) no8 4.9 m9 (a) 3 (b) −4 (c) −6

10 (a) 20x + 16 (b) x2 + 5x (c) 6x2 − 18x11 (a) 6(2g + 3) (b) wx(1 − 16x) (c) (2 + p)(5j − 7)12 (a) (x + 5)(x + 2) (b) (x + 5)(x − 3)

(c) (x − 6)(x − 3)

Mixed revision two (p. 238)

1 (a) (g − 12)(g + 12) (b) 4(3 − f)(3 + f)(c) 5(2q − 5)(2q + 5)

2 (a) 30y2 + 72y − 5 (b) 13x − 9 (c) r2 + 33r3 (a) 8.60 (b) 7.96 (c) 7.314 (a) 30° (b) 55° (c) 33°5 (a) (y − 7)2 (b) (3y − 4)2 (c) (2x − 5y)2

6 14.8 m 7 (a) −3 (b) −16 (c) −268 16.89 cm9 (a) xk + 3x − 6k − 18 (b) k2 − 13k + 42

(c) 2h2 + h − 10 10 (a) x = 20.9 m (b) y = 12.6 cm (c) g = 23.5 cm11 9.8 cm 12 14.89 cm13 (a) 56 − 8c (b) 12x + x2 (c) 6p2 − 21p14 (a) g2 − 16g + 64 (b) 36y2 + 84y + 49

(c) 49d2 − 42dw + 9w2 15 (a) (x + 5)(x − 3) (b) (x − 5)(x − 4)

(c) 4(x + 3)(x − 2)16 (a) 7(x − 7) (b) 11r(r + 4) (c) 4a(3b − 8a)17 16.0 cm 18 (a) (y + 2)(x + 7) (b) (z − 3)(z − 5) 19 (x + 7) and (x − 6)20 (a) 2x(3x + 1) (b) 6x2 + 2x21 4.1 m 22 61°23 (a) (y + 3)(x − 8) (b) (j − 7)(5j + 12)24 (a) tan; 2.5 m (b) sin; 3.05 m25 90.14 m 26 12.6 cm27 A → B → C → D → E → F → A (or its reverse);

181.26 m28 (a) x2 + 4x − 21 (b) (x + 7)(x − 3) (c) x = 103

(d) Students to show the equality of the expressions29 29.4 m


1 (a) P = 5 (b) P = 11 (c) P = 3 (d) P = −13(e) C = 5 (f) C = 17 (g) C = 9 (h) C = −7

2

3 (a)

43--- 9

40------ 60

11------

35--- 15

17------ 20

29------

ca-- e

d--- h

g---

34--- 1

15------ 5

12------

x −2 −1 0 1 2

y 2 3 4 5 6

X

Y

1 2 3−1−2

−3

321

−1−2−3−4

−4

A BC

D

E F

G

H



(b)

(c)

4 (a) x = 6 (b) y = 15 (c) a = −10(d) b = 21 (e) c = 12 (f) d = −14

5 (a) g = 19 (b) x = 42 (c) y = 6(d) x = 35 (e) b = −12 (f) k = 36

6 (a) −15x − 6 (b) 20 − 6x (c) 15x + 437 (a) True (b) False (c) False


1 (a)

(b)

(c)

(d)

(e)

(f)

2 (a) Linear

(b) Linear (c) Not linear

(d) Not linear (e) Linear

(f) Linear

3 (a) D (b) B (c) C

4 (a)

x −2 −1 0 1 2

y −4 −3 −2 −1 0

x −2 −1 0 1 2

y −4 −2 0 2 4

c 0 10 20 30

A 0 400 800 1200

P 0 2 4 6

Q 0 $7 $14 $21

G 0 4 8 12

J −20 28 76 124

0 X

Yy = x + 4

1 2 3 4−2−3 −1

654321

−1

0 X

Y y = x − 21

2 3 4−2−3 −1

1

−1−2−3−4−5

y = 2x

0 X

Y

1 2 3 4 5 6−2−3−4 −1

4321

−2−3−4−5

−1

e 0 3 6 9

D 5 −13 −31 −49

B 0 200 400 600

R 0 12 24 36

F 0 6 12 18

C −4 1 6 11

Number of litres 0 1 2 3 4 5 6 7

Cost (dollars) 0 0.95 1.90 2.85 3.80 4.75 5.70 6.65

1 2 3 4 50

8

6

4

2

b

a

0 c

d

3

6 9

3

−3−6−9

0 e

f

1 2 3

108642

0 g

h

1 2 3 4 5

2015105

0 j

k

1 2 3 4−2−3−4 −1

12108642

0 f

q

2

4

6−4−6 −2

6

2

−2−4

4


answers 525

(c) Yes, as the graph is a straight line(d) (i) $2.85 (ii) $2.28 (iii) $5.42(e) (i) 4 L (ii) 2.6 L (iii) 5.5 L (f) c = 0.95d

5 (a)

(c) Yes (d) W = 80 + 100n (e) $880

6 (a)

(c) 230 m (d) 3.5 min (e) 11.8 min(f) d = 85t (g) 3.4 km

7 (a)

(b) $US3.70 (c) $US9.20 (d) $A10.50(e) $A18.30 8 Students’ own answers.

Exercise 6.2 (p. 251)1 (a) 1 (b) (c) (d) 0 (e) −2 (f) undefined2 (a) positive (b) negative (c) zero

(d) undefined3 (a) B (b) A (c) A (d) C (e) B4 (i) (a) −1 (b) 3 (c) (d) 0 (e) −

(ii) Graph b (iii) Graph a5 (a) C (b) B (c) A (d) E6 (a) 2 (b) 3 (c) −4 (d) −1 (e) 2 (f) 1

(g) 2 (h) −1 (i) − (j) − (k) 0 (l) 0

(m) 5 (n) 5 (o) −

7 (a) 1.2 km (b) 20 min (c) 60 m(d) 60 m/min (e) 60 (f) (i) 360 m(ii) 720 m (iii) 1080 m (iv) 60t m (g) D = 60t

8 (a)

(b) 15 m/s (c) 15 (d) D = 15t (e) 795 m

9 Sample answers: A(1, 4) and B(4, 2), A(7, 12) and B(13, 8), A(0, 0) and B(2, −3)

10 (a) 320 L (b) 8 min (c) −40 (d) 40 L/min(e) decreasing volume of water(f) (i) 160 L (ii) 80 L (iii) 240 L(iv) (320 − 40t) L (g) V = 320 − 40t


1 (a) (i)

(ii)

(iii)

(iv)

(v)

Number of sets of books sold 0 1 2 3 4 5

Weekly wage (dollars) 80 180 280 380 480 580

Time (minutes) 0 1 2 3 4 5 6 7

Distance cycled (metres) 0 85 170 255 340 425 510 595

4 8 12 16 20

12

10

8

6

4

2

$US

$A

25--- −1

3---

13--- 2

5---

15--- 5

9---

314------

200

Time (s)

Distance (m)

10 20

100

300400500

30

x

y

1 2 3−1−2

−3

642

−2

y = x + 2

x = 3

0

X

Y

1

2

3−1−2−3

42

−2−4−6

y = x − 3

0

2 X

Y

1 3−1−2−3

54321

−1

−3−4−5−6−7

y = 2x − 1

0

−2

X

Y

1 2 3−1−2

−3

1512963

−3−6

y = 3x + 6

0

Y

X1

2

3−1−2−3

12963

−3−6−9

y = −3x + 3

0



(vi)

(vii)

(viii)

(b) (i) −2, 2 (ii) 3, −3 (iii) −1 (iv) −2, 6(v) 1, 3 (vi) − −2 (vii) 4, 4 (viii) 5, 5

2 (a)

(b) The x-coordinate is 3. (c) vertical

3 (a)

(b) The y-coordinate is −2. (c) horizontal

4 (a) (b)

(c) (d)

5 (a) All points must have 0 as the y-coordinate.(b) The y-coordinate is 0. (c) y = 0

6 (a) All points must have 0 as the x-coordinate.(b) The x-coordinate is 0. (c) x = 0

7 (a) (i) 1 (ii) 1 (iii) −1(b) (i) 2 (ii) − (iii) 3

(c) (i) 3 (ii) (iii) −4

(d) (i) −2 (ii) (iii) 1

(e) (i) 4 (ii) (iii) −2

(f) (i) −3 (ii) 2 (iii) 6(g) (i) −1 (ii) −5 (iii) −5(h) (i) 5 (ii) − (iii) 2

8 (i) (b) 2, 3 (c) 3, −4 (d) −2, 1 (e) 4, −2(f) −3, 6 (g) −1, −5 (h) 5, 2(ii) gradient (iii) y-intercept (iv) 2, 5

9 (a) Sample answers: y = 5x, y = 5x + 2, y = 5x − 1(b) Sample answers: y = −2, y = 2x − 2, y = 5x − 2

10 (a) D (b) C11 (a) Steepness or slope or gradient changes

(b) y-intercept changes

Exercise 6.4 (p. 265)1 (i) (a) y-intercept 1, gradient 2

(b) y-intercept −2, gradient 3

Y

X1 2 3−1−2−3

y = −4x − 2

108642

−2−4−6−8

−10−12−14

0

X

Y

2 4

6

−2−4−6

y = 4 − x

108642

−20

Y

X2 4

6

−2−4−6

y = 5 − x

12108

42

−2−4

6

0

12---,

12---,

Y

X1 2 3−1−2

2

1

−1

−2

0

Y

X1 20−1−2

1

−1

−2

Y

X0

4

Y

X0−2

Y

X0

−1

Y

X0 5

32---

43---

12---

12---

25---


answers 527

(c) y-intercept 3, gradient 1(d) y-intercept 3, gradient 7(e) y-intercept −4, gradient 1(f) y-intercept 3, gradient −4(g) y-intercept 4, gradient −1(h) y-intercept 6, gradient −2

(ii) (a) (b)

(c) (d)

(e) (f)

(g) (h)

2 (i) (a) y-intercept 4, gradient −2(b) y-intercept −3, gradient 1(c) y-intercept −2, gradient 3(d) y-intercept −1, gradient 4(e) y-intercept 3, gradient 2(f) y-intercept 2, gradient −

(g) y-intercept 1, gradient −

(h) y-intercept −2, gradient

(ii) (a) (b)

(c) (d)

(e) (f)

(g) (h)

3 (a) (b)

3Y

X1

1

y = 2x + 1

Y

X1

1

−2

y = 3x − 2

X

Y 10

3

1

y = 7x + 3

X

Y

4

1

3

y = x + 3

X

Y

−4

−3

1

y = x − 43

Y

X1

1

−1y = −4x + 3

4

Y

3

X1

y = −x + 4

y = 6 − 2xX

Y

6

4

1

32---

23---

25---

4

Y

2

X1

2x + y = 4

Y

X1

−2

−3

−x + y = −3

Y

X1

−2

1−3x + y = −2 3

Y

−1X1

4x − y = 1

Y

5

3

X1

2x − y = −3

Y

2

−1X2

3x + 2y = 4

Y

−1

1

X3

2x + 3y = 3

Y

−2X5

2x − 5y = 10

Y

2

X1

y = 2x3Y

X1

y = 3x



(c) (d)

(e) (f)

(g) (h)

4 (a) y = 3x + 4 (b) y = x + 5 (c) y = 2x(d) y = −4x (e) y = −5x + 1 (f) y = 3x − 4

5 (a) D (b) C6 (a) B (b) E (c) A (d) B7 (a) D (b) A (c) C8 Sample answers: (a) (0, −4) (1, −3) (2, −2)

(b) (0, 2) (1, 2.4) (−5, 0) (c) (0, −0.5) (2, 0) (4, 0.5)9 (a) 50 (b) 25 (c) d = 25t + 50 (d) 25 m/min

(e) 550 m10 (a) 30 (b) 30 km/h (c) d = 100t + 90

11 (a)

(b) 12 000 (c) m = 12 000t + 10 000

(d)

(e) m = 12 000t + 10 000 (f) 16 000 tonnes(g) 12 hours

Exercise 6.5 (p. 269)1 (i) (a) 4, 2 (b) 2, 6 (c) 2, −6 (d) 3, −3

(e) 3, −6 (f) 10, −4 (g) 5, 2 (h) 3, 4(i)

(ii) (a) (b)

(c) (d)

(e) (f)

(g) (h)

−1

Y

X1y = −x

Y

X1

−2 y = −2x

2

Y

X3

y = x23 y = x

Y

4

X5

45

Y

X1

−4 4x + y = 0

Y

X1

−6 6x + y = 0

0

20 000

40 000

60 000

80 000

100 000

120 000

1 2 3 4 5 6 7 8

(0, 10 000)

(8, 106 000)

time(hours)

mass ofcrude oil(tonnes)

0

10 000

20 000

30 000

40 000

50 000

1 2 3 4 5 6 7 8

(0, 48 000)

(8, 16 000)

time(hours)

mass ofcrude oil(tonnes)

23---, 1

2---

Y

2

X4

x + 2y = 4

6

Y

X2

3x + y = 6

Y

X2

−6

3x − y = 6

Y

X3

−3x − y = 3

Y

X

−6

3

4x − 2y = 12

Y

X10−4 2x − 5y = 20

Y

2

X5

2x + 5y = 10Y

4

X3

4x + 3y = 12


answers 529

(i)

2 (i) (a) 4, −8 (b) 3, −9 (c) −5, 5 (d) −2, 2(e) 2, 6 (f) 2 (g) − 2 (h) −1

(ii) (a) (b)

(c) (d)

(e) (f)

(g) (h)

3 (a) C (b) B4 (a) (i) $150 (ii) $100 (iii) $(175 − 25n)

(b) A = 175 − 25n (c) $175 (d) 7

(e)

5 (a) 555 L (b) 630 L (c) 42 min

(d)

6 Possible solutions (−1, 0) and (0, 3), (1, 0) and (0, −3), (−2, 0) and (0, 6)

7 (a) $7500 (b) 25 months

(c)

(d) $A = −$300t + $7500 (e) $5700 (f) $4200


1 (a) (b)

(c) (d)

Y

X

3x + 4y = 2

23

12

12---, 4

3---, 5

2---,

4

Y

X

−8

y = 2x − 8

Y

X3

−9

y = 3x − 9

Y

5

X−5

y = x + 5

Y

2

X−2

y = x + 2

6

Y

X2

y = 6 − 3x

2

Y

Xy = 2 − 4x

12

Y

2

X−

2y = 3x + 4

43

−1 X

Y5y = 2x − 5

52

7

175

n

A

42

630

t

V

0

1000

2000

3000

4000

5000

6000

7000

8000

4 8 12 16 20 24

(25, 0)

(0, 7500)

t (months)

Amountowing ($A)

2

Y

X

y = 2 4

Y

X

y = 4

Y

X−3

x = −3Y

X−1

x = −1



(e) (f)

2 (a) y = −6 (b) y = 2 (c) y = (d) y = 3 (a) D (b) B (c) E

4 (a) (b)

(c) (d)

(e) (f)

5 (a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

(k) (l)

(m) (n)

Y

X

y = − 34− 3

4

Y

X

x =

52

52

23---x 3

4---

Y

8

X2

(2, 8) y = 8

x = 2 Y

4

X−3

(−3, 4)

y = 4

x = −3

Y

X−5

(−5, 0) y = 0

x = −5 Y

X3

(3, 6)6

x = 3y = 2x

Y

X−2

(−2, 10)10 y = 10

y = −5x

Y

X1

(0, 0)

7

y = 7x

x = 0

Y

X

−1

2

1

y = 3x − 1

13

Y

1

X

y = 1

Y

−6

X

y = −6

Y

X

1

−4

1

y = 5x − 445

Y

X1

5y = 5x

Y

X1

−2 y = −2x

Y

X8

x = 8 Y

X−4

x = −4

Y

1 X

4

x + 4y = 4

Y

−2X6

x − 3y = 6

Y

−9

X6

3x − 2y = 18

Y

2

X4

2x + 4y = 8

Y

X

x = 0

Y

X

y = 0


answers 531

(o) (p)

(q) (r)

(s) (t)


7 (a)

(b) (0, 0), (3, 6), (3, 10), (−2, 10), (−2, 3)

(c)

(d) Yes, the shed will be on the new road.

Exercise 6.7 (p. 275)1 (a) a = 3 (b) x = 5 (c) b = 4 (d) f = −4

(e) h = −2 (f) x = −1 (g) k = (h) p = (i) r = (j) x = 4 (k) x = −9 (l) x = 6(m) y = 0 (n) x = (o) x =

2 (a) a = −2 (b) b = 6 (c) b = −3 (d) d = −1(e) r = 5 (f) e = 2 (g) e = 4 (h) g = 8(i) h = −2 (j) p = 5 (k) x = −7 (l) p = −15(m) k = 13 (n) y = (o) p =

3 (a) x = 6 (b) x = 8 (c) x = −27 (d) x = −36(e) x = −42 (f) x = 12 (g) x = −36 (h) x = (i) x = 10 (j) x = 0 (k) x = −14 (l) x = 15(m) x = 8 (n) x = 55 (o) x = 57

4 (a) D (b) B (c) E (d) C5 (a) B (b) C (c) E (d) A (e) D

(f) C6 (a) x + 7 = 19, x = 12 (b) y − 5 = 3, y = 8

(c) 3x = 14, x = (d) = −5, x = −20

(e) 2x + 3 = 13, x = 5 (f) 4x − 7 = −12, x = −

7 Sample answers: 5, 3, 1, −1, −3, −58 (a) x = 5 (b) x = −2 (c) x = 2 (d) x = −1

(e) x = −6 (f) x = 4 (g) x = 5 (h) x = 1(i) x = −2 (j) x = 0 (k) x = 6 (l) x = −2

9 (a) 63, 65, 67 (b) −48, −50, −52, −54(c) 84, 91, 98, 105, 112, 119

Exercise 6.8 (p. 279)1 (a) x = 9 (b) x = 6 (c) x = 7 (d) x = −14

(e) x = −9 (f) x = 12 (g) x = 8 (h) x = 4(i) x = 6

2 (a) x = 4 (b) x = −2 (c) x = 2 (d) x = (e) x = −1 (f) x = 6 (g) x = − (h) x = −5(i) −2

3 (a) E (b) B

4 (a) x = − (b) x = − (c) x =

(d) x = (e) x = − (f) x = − (g) x = −

(h) x = (i) 2

5 Sample answer: = 6

6 (a) 24 (b) 36 (c) 88

Exercise 6.9 (p. 285)1 (a) c = −7 (b) b = −8 (c) a = 6 (d) d = 7

(e) e = 4 (f) f = −2 (g) g = −7 (h) h = −6(i) x = 2 (j) j = 2 (k) k = (l) y = 3

2 (a) m = 4 (b) n = 2 (c) x = 1 (d) p = −3(e) y = 1 (f) x = 3 (g) a = 0 (h) x = 9(i) p = 4

3 (a) x = 8 (b) x = −10 (c) x = 4 (d) x = −2(e) x = − (f) x = (g) x =

(h) x = − (i) x = −

4 (a) b = −22 (b) a = 21 (c) c = 3 (d) d = −8(e) x = (f) y = 10 (g) g = 1 (h) k = 1

(i) m = −10 (j) j = (k) x = −

(l) p = −19 (m) x = − (n) y =

5 Students’ own answers6 (a) B (b) D (c) E (d) A7 3 8 24 9 −1 10 12

5

Y

3

X1

y = 5 − 2x

52

−3

−7

Y

X1

y = −3 − 4x

34

−

Y

2

X2

x + y − 2 = 0

Y

1

X−1

x − y + 1 = 0

Y

3

X4

4y = 3xY

1

X2

2y = x

X

Y

1 2 3−2−3 −1

8

6

4

2

10

0

X

Y

1 2 3−2−3 −1

8

6

4

2

0

10

25--- 21

4---

56---

318--- 6

7---

235--- 23

4---

334---

423---

x4---

114---

17---

112---

17---

58--- 111

12------ 81

2---

14--- 1

6--- 8

15------ 11

14------

23--- 5

6---

2(4x 1)–5

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

32---

314--- 55

6--- 1

11------

427------ 212

3---

1612---

112--- 51

2---

213--- 26

41------



Exercise 6.10 (p. 288)1 (a) k + 4 (b) 3k (c) 3(k + 4) (d) 152 (a) x − 5 (b) x + x − 5 = 17; x = 11

(c) Andrew: 11; Lori: 63 length 13 m, width 10 m4 Mark: 600 m; Annette: 300 m; Sue: 1200 m5 $1.65 6 16 7 49°, 55°, 76°8 15 9 11 cm 10 21

11 Any number between 23 and 3212 Gabby 30, Kate 15, Joe 12, Brett 48.


1 (a) k = (b) c = y − mx (c) h =

(d) x = (e) p = (f) w = u(v + xy)

2 (a) x = z − y (b) x = 3a + 2b (c) x =

(d) x = (e) x = rt − p (f) x = vy + w

(g) x = (h) x = (i) x =

(j) x = (k) x = (l) x =

3 (a) t = (b) (i) t = 4 (ii) t = 2.8

4 (a) r = (b) (i) r = 100 (ii) r = 2.61

5 h = h = 2 6 w = w = 19

7 (a) M = DV; M = 84 (b) V = V = 1.9

8 b = b = 13

9 (a) d =

(b) a = or a =


1 (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

2 (a)

(b)

(c)

(d)

(e)

(f)

3 Number line must pass over zero and have a closed circle on the left and an open circle on the right.

4 (a) B (b) D (c) A (d) E

5 (a)

(b) p � 270 0006 0 � s � 100 7 n � 58 7c � 380 or c � 54.299 (a) 50 � x � 120; 0 � y � 40

(b) x + y � 120(c) When x = 80 and y = 40 profit is a maximum of $64.

Exercise 6.13 (p. 298)1 (a) x � −10 (b) x � −5 (c) x � −10

(d) x � 35 (e) x � −9 (f) x � −28(g) x � − (h) x � − (i) x � −9(j) x � 8 (k) x � −2 (l) x � −8 (m) x � 4(n) x � 11 (o) x � 4 (p) x � −8 (q) x � 11(r) x � 10

2 (a) y � −5 (b) y � −6 (c) y � −5(d) y � 12 (e) y � 21 (f) y � 12(g) y � −8 (h) y � 2 (i) y � −4 (j) y � −

(k) y � (l) y � (m) y �

(n) y � (o) y � 4

3 (a) B (b) D (c) B (d) E4 (a) x � (b) x � − (c) x � 0 (d) x � 0

(e) x � 4 (f) x � 12 (g) x � −25(h) x �

5 (a) y � −1 (b) y � 3 (c) y � −

(d) y � (e) y � 30 (f) y � 36

(g) y � −12 (h) y � (i) y �

Pm---- C g+

a------------

a c–b

----------- kn 2+m

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

m n+k

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

f c–d

---------

kp y–2

-------------- mw t–r

---------------- mn k+ap

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

gh e–cd

-------------- n(t kp)–m

--------------------- y(f b)–d

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

v u–a

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

C2π------

Vπr2-------- ; P 2l–

2-------------- ;

MD----- ;

2A ah–h

------------------- ;

2(S na)–n(n 1)–

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

Sn--- (n 1)– d

2--------------------– 2S n(n 1)– d–

2n------------------------------------

3 4 7 86521

987653 102 4

10−1−2−3−5 2 3−4

−4 −3 0 1−1−2−5−6

−4 −3 0 1−1−2−5−6

1098764 11 125

−4 −3 0 1 2 3−1−2

−1 0 1 2 3 4 5 6−2

−1−2−3−5 −4−6−7−9 −8

−3 0 1 2 3 4−1−2

−3 0 1 2 3 4−1−2

−1 0 1 2−2−3−5 −4−6

−1 0 1 2 3 4 5−2−3

−1 0 1 2 3 4 5 6 7

0 1 2 3 4 5 6−1

−4 −3 0 1 2−1−2−5

−4 −3 0 1 2−1−2−5

10−1−2−3−5 2−6 −4

280 000270 000 290 000250 000 260 000

513--- 52

5---

115------

12--- 31

6--- 41

3---

356---

23--- 3

11------

467---

213---

13---

67--- 4 9

13------


answers 533

6 20C � 428; C � $21.407 0.40n + 3.45 � 5; n � 8.75 so n = 1, 2, 38 Sample answer: 2x − 5 � 12 + 3x

Chapter review (p. 301)1 (a)

(b)

(c) $1490 (d) 15 weeks (e) A = 500 + 90n(f) $1850

2 5 3 (a) B (b) D

4

x-intercept −2y-intercept 4m = 2

5 (a) (b)

(c) (d)

6 (a) −4, 2 (b) −2,

(c) 5, −1 (d) 2, −

(e) 0, 3 (f) 0, −5

7 (a) (b)

(c) (d)

Number of weeks 0 1 2 3 4 5 6

Amount paid ($) 500 590 680 770 860 950 1040

680500

86010401220140015801760194021202300

02 4 6 8 10 12 14 16 18 20

Number of weeks

Amountpaid ($)

Y

X1 2 3−1−2

−3

642

−2−4−6

y = 2x + 4

Y

X0 y = 0

Y

X0−2

Y

X0

4

Y

X0

x = 0

32---

X

Y

−4

−2

1

y = 2x − 4

Y

1

X2

−22y = 3x − 4

32---

X

Y

45

1

x + y = 5 X

Y

−1

2

2

3x + 2y = 4

X

Y

3

10

y = 3x

X

Y

−5

10

y = −5x

Y

X1

−44x − y = 4 X

Y

4

10

2x + 5y = 20

X

Y

6

−2

y = 3x + 6

X

Y

5y = 5 − 2x

212



8

9 (a) B (b) D (c) A10 (a) x = −5 (b) x = −1 (c) x = −45 (d) x = 72

(e) x = 0 (f) x = 11 (a) x = 9 (b) x = 19 (c) x = (d) x = 3

12 (a) x = (b) x = −19 (c) x = −9 (d) x = 1

(e) x = (f) x =

13 (a) B (b) C

14 (a) a = (b) x =

15 (a) a = (b) a = 4

16 (a)

(b)

(c)

17 (a)

(b) S � 818 (a) d � 1 (b) x � 1 (c) y � − (d) a � 519 (a) (0, 0) and (5, 350) (b) 70 (c) 70 m/min

(d) d = 70t (e) 560 m20 (a) 21, 22, 23 (b) 22, 24, 26, 2821 length 17 m, width 12 m

22 (a) V = IR; V = 150 (b) R = R = 13.04

23 2 × 89 + 16.50n � 250; n � 4.4 so at least 5 towels24 (b) 80 km/h (c) 15 min (d) 100 km/h

(f) 80 km/h (g) D = 80t (h)(i) 50 km

25 = x = 6

Replay (p. 306)1 $447.50 2 (a) $4920 (b) $19 9203 (a) $6.42 (b) $8.854 (a) 675 cm2 (b) 67.5 cm2 (c) 30 cm2

5 (a) 184 cm3 (b) 1007.4 cm3 (c) 310.8 cm3

6 (a) 35 (b) 1447 (a) 9.8 m (b) 4.7 m

8 (a) x2 + 2x − 15 (b) 2x2 − 13x + 15(c) 12x2 + 2x − 30

9 (a) 3(x + 2) (b) 5x(x − 2) (c) (g − 5)(3 + k)10 (a) b (b) c (c) a11 (a) x = 6.8 cm (b) y = 176.7 m (c) a = 7.0 cm12 (a) 59° (b) 60° (c) 57°


1 (a)

(b)

2

3 STEM | LEAF3 | 94 | 7 85 | 2 5 76 | 4 6 6 77 | 0 1 1 4 48 | 1 2 3 4 8 89 | 0 6 9

4 median = 20.5; interquartile range = 8

Y

3

X1−2

−5

(b)

(a)

(c)

y = 3

y = −5xx = −2

212---

129---

216---

112--- 81

5---

t r+xy

---------- ks w–a

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

v u–t

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

−1 0 1 2 3 4 5 6−2

−4 −3 0 1−1−2−5−6

−4 −3 0 1 2 3−1−2

121110983 132 74 5 6

313---

VI--- ;

2212--- min

4(2x 3)–3

---------------------- 3(3x 2)+5

----------------------- ,

Day Tally Frequency

MTWThF

|||| |||| |||| |||||||| |||||||||||||||| |||| ||

20954

12

Total 50

Frequency

0

Days of the weekM T W Th F

2468

101214161820

400

80120160200240

Distance from home (km)

Timepmnoonam8 9 10 11 12 1 2 53 64


answers 535

Exercise 7.1 (p. 312)1 (a) nominal (b) nominal (c) quantitative

(d) quantitative (e) quantitative(f) quantitative (g) nominal (h) nominal

2 (i) (c) discrete (d) discrete(e) continuous (f) discrete(ii) (a) categorical (b) categorical(g) ordinal (h) categorical

3 (a) discrete (b) continuous (c) continuous(d) discrete (e) continuous (f) continuous(g) discrete (h) continuous

4 Students’ own answers5 (a) B (b) A (c) E6 The results are discrete because there is a fixed,

countable number of values possible. There is no doubt in the measuring process and no rounding off is necessary.

7 The height recorded was an approximation that was forced upon the measurer because of the limited accuracy of the measuring device.

Exercise 7.2 (p. 316)1 (a) = 3, median = 3, mode = 1

(b) = 3.64, median = 4, mode = 4(c) = 14, median = 14, mode = 13(d) = 35.25, median = 35.5, mode = 36(e) = 4.67, median = 4, mode = 4(f) = 4, median = 3, mode = 1(g) = 15.4, median = 14, mode = 13(h) = 37, median = 36, mode = 36

2 (a) C (b) B (c) C3 Julia should tell Sara that the cheapest house in her

sample is $194 000, the dearest is $365 000, the most common price is $221 000 (although this only represented two houses), the middle value of houses is $255 950 and the mean price is $255 950. In essence, the bulk of the houses in the sample were between about $220 000 and $270 000. With this information Sara should be able to decide if she can afford to live in this area.

4 Students’ own answers5 138 6 35 7 226 mm each month8 (a) (i) 3, 3, or 3, 4 or 3, 5 or 3, 6 or 3, 7 or 3, 8

(ii) 3, 9 (iii) 3, 3(b) No—median cannot be 3

9 (a) = 13.85, median = 14, mode = 14(b) = 13, median = 14, mode = 14(c) median, mode the same, smaller

10 (a) = 476.15, median = 470, mode = 470(b) = 496.92, median = 480, mode = 470(c) Mode the same; mean changed by 21

11 (a) mean = 3.56, median = 3, mode = 2(b) mean = 4.44, median = 3, mode = 2(c) The mean increased by just under 25% while the other two measures stayed the same.(d) (i) mean = 15.6/16.6, median = 15.5, mode = 14 and 16 (ii) mean = 35.22/33.56, median = 35, mode = 33 and 35 (iii) mean = 103.11/99.89, median = 102, mode = 101 (iv) mean = 80.5/78.5,

median = 78.5, mode = 78(e) One value, at either end of the data set, will have an effect on the mean, but will do nothing to either the median or the mode.

Exercise 7.3 (p. 321)1 (a) STEM | LEAF

0 | 5 6 6 71 | 0 1 31 | 5 5 82 | 0 1 2 22 | 6 6

STEM | LEAF0 | 5 6 6 71 | 0 1 3 5 5 82 | 0 1 2 2 6 6

(b) STEM | LEAF2 | 0 0 0 2 42 | 6 8 8 9 93 | 0 1 23 | 6 8

STEM | LEAF2 | 0 0 0 2 4 6 8 8 9 93 | 0 1 2 6 8

2 (a) STEM | LEAF16 | 1 316 | 5 5 5 6 7 7 7 9 917 | 0 1 2 2 317 | 8 918 | 0 3

(b) STEM | LEAF16 | 1 3 5 5 5 6 7 7 7 9 917 | 0 1 2 2 3 8 918 | 0 3

3 (a) 30.5 (b) 58 4 (a) D (b) C5 (a) STEM | LEAF

4 | 1 2 85 | 1 6 7 86 | 2 3 7 7 87 | 4

Median = 58

(b) STEM | LEAF2 | 2 3 83 | 0 1 4 74 | 1 2 85 | 2 7

Median = 35.56 (a) STEM | LEAF

2 | 0 1 2 32 | 7 7 83 | 1 43 | 84 | 2

Median = 27

xxxxxxxx

xx

xxx



(b) STEM | LEAF0 | 5 6 7 91 | 2 31 | 5 7 92 | 0 1 42 | 6 8

Median = 16

7 (a) STEM | LEAF2 | 1 4 83 | 0 2 4 54 | 0 55 | 0 4 9

(b) Stem 3, which represents actual distances of 29 500 to 39 499 km inclusive.(c) Sales representatives in the country will drive more kilometres than the city representatives.

8 (a) 31 (b) 72 (c) 359 (a) STEM | LEAF

0 | 5 6 6 71 | 0 1 31 | 5 5 82 | 0 1 2 22 | 6 6

Median = 15

(b) STEM | LEAF2 | 0 0 0 2 42 | 6 8 8 9 93 | 0 1 23 | 6 8

Median = 28

10 (a) STEM | LEAF8 | 0 3 4 4 6 6 7 99 | 1 1 2 6 6 8 9

10 | 3 3 4 5 7 7 911 | 812 | 6 8

(b) Median = 96

11 (a) STEM | LEAF16 | 1 316 | 5 5 5 6 7 7 7 9 917 | 0 1 2 2 317 | 8 918 | 0 3

(b) Median = 169 cm12 (a) Students’ own answers

(b) You can add from 7 to 13 new values and still have 24 as the median.

13 (a) 87.15(b) STEM | LEAF

8 | 0 0 2 3 48 | 6 6 6 6 6 6 7 7 8 8 9 9 99 | 0 0 0 0 0 1 1 1

(c) 87.5 (d) The approximate value is 0.4% larger than the actual median.(e) Rounding off does not seem to make a lot of difference to the value found but the rounding was not really significant itself. The loss of accuracy is of no concern. There is no real time saving in this case

but the stem-and-leaf plot does make the presentation of the data much neater.

Exercise 7.4 (p. 328)1 (a) (i) 166 (ii) 38 (iii) 14

(b) (i) 156 (ii) 31 (iii) 12(c) (i) 167 (ii) 41 (iii) 15

2 (a) B (b) D (c) E (d) B (e) E

3

Punter is a much more consistent scorer (interquartile range of 35 compared with 55 for Lake). Punter has a higher median (57) than Lake (45).

4 (a)

(b) Danielle sold more shoes (3410); Martina (3342)(c) Danielle has higher median (160) than Martina (148.5) (d) Martina is more consistent (interquartile range = 26) than Danielle (45).

5 (a)

IQR = 12

(b)

IQR = 12

6 (a)

(b) interquartile range = 141 − 128 = 13

7 (a)

IQR = 13

(b)

IQR = 9

1050 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Punter

Lake

runs

116 120 124 128 132 136 140 144 148 152 156 160 164 168 172 176 180 184

Danielle

Martina

number of shoes sold per day

20 22 24 26 28 30 32 34 36 38 40 42 44

4 6 8 10 12 14 16 18 20 22 24 26 28

120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150

number of chocolate bars

4 6 8 10 12 14 16 18 20 22 24 26 28

20 22 24 26 28 30 32 34 36 38 40 42


answers 537

8

Team A has a higher interquartile range (19) than B (17) and a greater median (76 to 74).

9 Students’ own answers10 (a) There is no left whisker, so it must be the same

value as the lower quartile. This indicates a cluster of values at this point. (b) There does not appear to be a median. It must be the same as either the lower quartile or the upper quartile. There will be a cluster of values at this point. (c) There are no whiskers. This means there must be clusters of values at both the lower quartile and the upper quartile.

11 (a)

(b) The following table shows the values calculated for these data sets. (Not all of them were strictly required by the question.)

There is no question—females live longer than males! There is only one figure for females that is less than the maximum value for males. This is for Melton, which also produced a low value for males (less than the lower quartile). The female scores are much more tightly bunched than the males—this is confirmed by the IQR. (c), (d) & (e) Students’ own answers(f) We would not expect every sample to give exactly the same results but given the differences between the data sets it would be surprising if any sample gave the male life expectancy as greater than that of females.

Exercise 7.5 (p. 335)1 (a) Blue cars Red cars

LEAF | STEM | LEAF8 3 2 | 2 |

7 4 1 0 | 3 |8 2 1 | 4 | 1 2 8

7 2 | 5 | 1 6 7 8| 6 | 2 3 7 7 8| 7 | 4

(b) White cars Yellow carsLEAF | STEM | LEAF

| 0 | 2 3 8| 1 | 4 5 8| 2 | 1 5 6 7 9

8 | 3 | 0 3 4 5 79 | 4 | 2 45 | 5 |

4 3 1 1 | 6 |9 6 5 2 2 | 7 |

8 7 2 | 8 |6 0 | 9 |

2 Red lollies Yellow lolliesLEAF | STEM | LEAF

3 2 1 0 | 2 |8 7 7 | 2 |

4 1 | 3 |8 | 3 |2 | 4 | 2

| 4 | 7 7 8| 5 | 1 2 3| 5 | 6 7 8| 6 | 1 4| 6 | 8

3 (a) Day 1 Day 2LEAF | STEM | LEAF

1 | 12 | 1 29 9 8 8 6 6 5 | 12 | 6 6 7 8 9

4 3 3 0 | 13 | 0 3 38 6 | 13 | 6 7 8 9 9

3 2 2 0 | 14 | 0 0 1 1 46 | 14 |0 | 15 |

(b) Day 1 Day 2LEAF | STEM | LEAF

9 9 8 8 6 6 5 1 | 12 | 1 2 6 6 7 8 98 6 4 3 3 0 | 13 | 0 3 3 6 7 8 9 9

6 3 2 2 0 | 14 | 0 0 1 1 40 | 15 |

4 Essendon RichmondLEAF | STEM | LEAF

8 | 6 |9 7 4 | 7 |8 6 2 | 8 | 4 5

4 2 | 9 | 2 5 55 2 | 10 | 3 4 4 7

5 | 11 | 6 80 | 12 | 2 9

5 Kim PaulLEAF | STEM | LEAF

4 4 | 1 | 1 3 48 7 6 | 1 | 6 8

4 2 1 0 | 2 | 1 3 48 5 | 2 | 7 8

2 | 3 | 4| 3 | 6

mean min lowerquartile

median upperquartile

max IQR

Males 76.37 73.97 75.405 76.15 77.205 79.26 1.8

Females 82.00 78.89 81.505 81.9 82.41 83.98 0.905

A

B

9062 64 66 68 70 72 74 76 78 80 82 84 86 88 92 94kg

74 76 78 80 82 84

males

73 75 77 79 81 83

females



6

7

8

9 Group A Group BLEAF | STEM | LEAF

3 1 | 16 | 0 1 49 9 7 7 7 6 5 5 5 | 16 | 7 9 9

3 2 2 1 0 | 17 | 0 0 0 3 3 39 8 | 17 | 7 7 7 9 93 0 | 18 | 0 0 2

10 (a) Rugby players’ height (cm)Eels | |Broncos

| 16 | 84 1 0 | 17 |

5 | 17 | 5 6 8 84 4 3 2 1 0 0 0 | 18 | 0 0 2 2 3 3 3 4 4

9 8 8 7 7 7 7 6 5 5 | 18 | 5 5 5 8 8 8 9 9 92 0 | 19 | 0 0 1 2 2

5 | 19 |

(b) Rugby players’ weight (cm)Eels | |Broncos

7 | 7 | 8 83 1 0 0 | 8 | 0

8 6 5 | 8 | 6 6 7 7 93 1 | 9 | 0 1 2 2 3

7 6 5 | 9 | 5 5 7 7 8 84 4 1 0 0 0 | 10 | 1 1 3 3 4

5 5 5 5 | 10 | 5 7 90 | 11 | 2

| 11 |0 | 12 |

(c) For the EelsHeight: mean = 183.6, lower quartile = 180, median = 185, upper quartile = 187.5Weight: mean = 95.64, lower quartile = 85.5,median = 97, upper quartile = 104.5

For the BroncosHeight: mean = 184.2, lower quartile = 181, median = 184.5, upper quartile = 189Weight: mean = 94.8, lower quartile = 88, median = 95, upper quartile = 102As far as height is concerned the shortest player is a Bronco and the tallest is an Eel. The mean slightly favours the Broncos in height, but the median slightly favours the Eels. However, the Eels are slightly more spread out.As far as weight is concerned both the lightest and the heaviest players are Eels. The stem-and-leaf plot shows the concentration of Broncos players in the mid-weight range. The Broncos are slightly lighter than the Eels.

11

Holden and Toyota have seen the biggest increases in 2002 compared to 2001. Ford is relatively stable while Mitsubishi and Honda sales have fallen, with the drop for Honda being more significant than the drop for Mitsubishi. It would appear that total sales are up—the increases for Holden and Toyota should more than compensate for the relatively small drops seen for a number of manufacturers.

50

10152025303540

Profits ($ dollars × 1000)

computer type 1computer type 2

MonthsJan Feb Mar Apr May Jun

2000 2001 2002 2003 2004 2005 Year

20

468

10121416

Numbers of carssold × 1000

Sterling carsSlick cars

Type of real estateHouses Land Units

50

10152025303540

Number sold

Shrimp Real EstateBlacks Property Developers

Subaru

Mazd

a

Hyund

ai

Nissan

Mitsubishi

Ford

Toyota

Hold

en

Hond

a

5 0000

10 00015 00020 00025 00030 00035 00040 00045 000

Number ofvehicles

New car sales

YTD March 2002 YTD March 2001


answers 539

12 (a)

(b) The small number of fatalities compared to the number of minor injuries makes this difficult to draw. (c) The number of fatalities is on the increase with this pattern repeated for serious injuries. There is a slight decline in the number of minor injuries. The significance of any of these changes is not really shown in the graph because of the scale required to fit in the number of deaths.

13 Students’ own answers, but note it would be easiest to start from the median value and keep adding values either side to get the desired result.

14 (a)

(b) The trend is quite consistent: one bedroom flats are the cheapest, followed by two bedroom flats, then two bedroom houses, with three bedroom houses being the most expensive. Inner Melbourne is clearly the most expensive in each category. The prices at the bottom end of the market are quite close across several regions. The further out from Melbourne, the cheaper the rent is a basic trend coming through. The following table gives the mean and median prices (to the nearest dollar) for each type of dwelling.

Both Western Melbourne and Outer-eastern Melbourne would do a good job of representing the

whole of Victoria. For all types of dwelling they are quite close to both the mean and median rental price.


1 (a)

(b)

(c)

2 (a)

(b)

1br flat

2br flat

2br house

3br house

MeanMedian

$119$113

$167$155

$183$172

$194$189

1999 2000 2001 Year

2000

400600800

100012001400Number Deaths

Serious injuriesMinor injuries

Motorcycle accidents

Southeastern Melbourne

Outer-eastern M

elbourne

Northeastern M

elbourne

Northw

estern Melbourne

Western M

elbourne

Southern Melbourne

Inner-eastern Melbourne

Inner Melbourne

Mornington Peninsula

Ballarat

Geelong

Bend

igo

500

100150200250300350400Rent ($)

1br flat2br flat

2br house3br house

Rental prices Victoria 2001

1234567

Frequency

Number of staff absent0 1 2 3 4 5 6

123456

Frequency

Number of flaws0 1 2 3 4 5 6

78

123456

Frequency

Number of goals0 1 2 3 4 5

123

Frequency

Number of staff absent0 1 2 3 4 5

4567

6

123

Frequency

Number of flaws0 1 2 3 4 5

4567

6

8



3 (a)

(b)

(c)

4 (a)

(b)

5 (a)

(b)

(c)

6 (a)

(b)

510

Frequency

Number of students9–11 12–14 15–17 18–20 21–23 24–26

152025

12

Frequency

Number of patrons0–4 5–9 10–14 15–19 20–24 25–29

345567

12

Frequency

Number in queue0–2 3–5 6–8 9–11 12–14 15–17

3455678

5

10

15

Frequency

Number of students

20

25

9–11 12–14 15–17 18–20 21–23 24–26

123

Frequency

Number of patrons

45

0–4 5–9 10–14 15–19 20–24 25–29

67

123

Frequency

Height of students (cm)140 145 150 155 160 165

456

170 175

123

Frequency

Arm span (cm)140 145 150 155 160 165

456

170 175

2

Frequency

Maximum length jumped (cm)160 170 180 190 200 210

46

220

81012

123

Frequency

Height of students (cm)140 145 150 155 160 165

456

170 175

123

Frequency

Arm span (cm)140 145 150 155 160 165

456

170 175


answers 541

7 (a)

(b)

(c)

(d)

(e)

(f)

8 (a) B (b) A9 (a) A (b) D (c) C

10 (a)

(b) and (c)

1

2

3

Frequency

Number of days absent0 1 2 3 4

4

5

6

5 6

7

8

1

2

3

Frequency

Number of brothers and sisters0 1 2 3 4

4

5

6

5 6

7

4

Frequency

Number of bird species sighted3 8 13 18 23

8

12

28 33

16

4

Frequency

Value of house ($’000)125 175 225 275 325

8

12

375 425

16

20

75

Distance (km) Frequency

0–1.92–3.94–5.96–7.98–9.9

10–11.9

574531

Σf = 25

4

Frequency

Mass of individual oranges (g)167.5 172.5 177.5 182.5 187.5

8

12

192.5 197.5

16

20

162.5

2

Frequency

Maximum temperature (°C)19 21 23 25 27

4

6

29 31

8

17

3

5

7

9

1

1

2

3

4

5

6

7Frequency

Distance (km)0–1.9 2–3.9 4–5.9 6–7.9 8–9.9 10–11.9



(d)

(e) and (f)

(g) You cannot tell if the distances have been rounded off to the nearest tenth of a kilometre or if they are really continuous values. If the question said the data had been rounded off then there would be no confusion.

11 Students’ own answers12 (a) 47 (b) 80–�90

(c) It is somewhere in the range 80–�90; you cannot be more precise than this.(d) It is somewhere in the range 140–�150; you cannot be more precise than this. (e) 19

Exercise 7.7 (p. 350)The answers to this Exercise are based on the equation of the line of best fit given in Excel. If the graphs are hand-drawn then different answers would be expected. They could be some distance from the answers given here.

1 (a) and (b)

(c) There seems to be some variation from the rule for these data.(d) 186 cm; this is quite close to what the rule of thumb would predict.

2 (a) and (b)

(c) (i) 36 cm (ii) 4330 g (iii) 38 cm(d) There seems to be a fair bit of variation from the line of best fit predictions.

3 (a)

The scatter plot shows there is a close connection between the times for these two distances. You could use one to predict the other with some confidence.(b)

This scatter plot indicates that there may be a connection between the times for the two races but

Distance (km) Frequency

0–�22–�44–�66–�88–�10

10–�12

574531

Σf = 25

1

2

3

4

5

6

7

Frequency

Distance (km)0 2 4 6 8 10 12

88 90 92 94 96 98176

178

180

182

184

186

188

190

192Male height predictor

19 yearheight (cm)

30-month height (cm)

y = 1.6128x + 34.61

031

32

33

34

35

36

37

38

1000 2000 3000 4000 5000

Birth weight vs head circumference

Headcircumference(cm)

Birth weight (g)

y = 0.0019x + 28.273

9 1019.5

2020.5

2121.5

2222.5

2323.5

11 12 13

100 m vs 200 m200 m (s)

100 m (s)

9 10101112131415161718

11 12 13

100 m vs 5000 m5000 m (s)

100 m (s)


answers 543

it is not as strong a connection as for the other two distances. Predictions could probably be made about the other time given one of them but not with as much confidence.(c) The 100 m and 200 m are both sprints. The record holder could be the same person, in fact. The 5000 m is a different type of race altogether. Some countries seem to produce sprinters and others produce middle to long distance runners. This effect is being seen in the data.

4 (a)

1988: 2.35 m 1992: 2.37 m1996: 2.39 m 2000: 2.42 m(b) Most of these predictions are quite close, with the 1996 value matching the prediction. The 1992 value is not close to predicted.

(c) 2000: 2.35 m(d) The prediction was exact. The problems come from the fact that the height at the next Olympic Games will not always be higher than the previous games (e.g. as in 1992), but the line of best fit predicts it will rise every time.

5 (a)

(b) A straight line does not seem to do much of a job at all. The data appears to be cyclic with a number of warm years followed by a number of cold years and so on. The straight line just goes through the middle of the data. It doesn’t seem to be able to cope with the annual fluctuation seen in these temperatures.(c) The Excel equation predicts constant temperatures of around 12.5°C.(d) The actual figures are relatively close to the predictions. This perhaps indicates that the long-term mean surface temperature for New Zealand will remain around 12.5°C. However, it does nothing about predicting how far individual years might be from the long-term average.

Chapter review (p. 357)1 (a) continuous (b) discrete2 (a) 10th value (b) 11th and 12th values

(c) 55th value3 (a) (i) 2 (ii) 4 (iii) 4.23

(b) (i) 130 and 149 (ii) 133 (iii) 133.834 (a) 76 (b) 171.55 (a) (i) Median = $1050

(ii) Range = 1450 − 550 = 900 (iii) Interquartile range = 1250 − 900 = 350(b) (i) Median = $950(ii) Range = 1300 − 600 = 700(iii) Interquartile range = 1000 − 700 = 300(c) (i) Median = 205 km(ii) Range = 235 − 170 = 65(iii) Interquartile range = 230 − 180 = 50(d) (i) Median = 165 km(ii) Range = 230 − 140 = 90(iii) Interquartile range = 170 − 150 = 20

6 minimum = 7, lower quartile = 13, median = 17, upper quartile = 20.5, maximum = 25

1892 1908 1924 1940 1956 1972 1988 20040

0.5

1

1.5

2

2.5Olympic High Jump

Height (m)

Year

y = 0.0057x − 8.9838

1892 1908 1924 1940 1956 1972 1988 20040

0.5

1

1.5

2

2.5

3Olympic High JumpHeight (m)

Year

y = 0.0058x − 9.251

196511

11.5

12

12.5

13

13.5

1970 1975 1980 1985 1990 1995 2000 2005

New Zealand 1971–2000 Mean Temp °C

Year

y = 0.00005x + 12.519

9 13 17 21 257 11 15 19 23



7 Cobram FosterLEAF | STEM | LEAF

8 | 1 |9 7 0 | 2 |4 2 2 | 3 | 38 5 2 | 4 |

5 | 5 | 5| 6 | 2 2 4 8| 7 | 4 9| 8 | 5| 9 | 5| 10 || 11 | 7

8 (a) 169, 167, 167, 180, 167, 169, 165, 183, 161, 179, 163, 178, 171, 170, 137, 165, 172, 166, 172, 168

(b)

9 (a)

(b)

10 (a)

(b)

11 (The answers to this have been completed using the rule for the line of best fit generated by Excel. If a hand-drawn line of best fit is used then the answers will be different.)(a) and (b)

(c) $490.9012 (a) (i) 24.6 (ii) 10 (b) (i) 23.1 (ii) 16.5

(c) (i) 26.7 (ii) 18.5 (d) (i) 74.4 (ii) 45.5(e) In each case the mean is quite a bit higher than the median. This is because the top four countries have done significantly better than the other six in the table. Those results drag the mean towards them. The median is not affected by the size of individual results and in these cases probably gives a more meaningful result.

13 (a) STEM | LEAF1 | 92 | 1 9 93 | 3 3 5 54 | 2 3 8 95 | 3

(b) Median = 35 (35 000 km)Interquartile range = 45.5 − 29 = 16.5

(c)

Height Frequency131–140 1141–150 0151–160 0161–170 12171–180 6181–190 1

Class interval Frequency0–3 54–7 78–11 5

12–15 716–19 4

Class interval Frequency20–�25 425–�30 330–�35 3

Height (cm)

420

68

1012

Frequency (heights)

130 140 150 160 170 180 190

1234567

Frequency

Number of cars1.5 5.5 9.5 13.5 17.5

35–�40 640–�45 445–�50 5

123456

Frequency

Weight of oranges (kg)22.5 27.5 32.5 37.5 42.5 47.5

Carats vs CostPrice ($)

Carats

y = 3713.5x − 251.8

0 0.1 0.2 0.3 0.4

1000

200300400500600700800900

1000

15 20 25 30 35 40 45 50km (’000)


answers 545

14 Astros CometsLEAF | STEM | LEAF

6 | 13 | 83 | 14 | 7 0

6 5 4 6 0 | 15 | 2 46 | 16 | 3 80 | 17 | 5 3

Astros CometsLEAF | STEM | LEAF

6 | 13 | 83 | 14 | 0 7

6 6 5 4 0 | 15 | 2 46 | 16 | 3 80 | 17 | 3 5

Median (Astros) = 155; Median (Comets) = 154Astros: QL = 146.5, QU = 161Comets: QL = 143.5, QU = 170.5

Astros have very similar heights in their team; there is greater variation in height in the Comets. Overall the average height is much the same (medians similar). On average Comets are probably slightly taller.

15 (a)

(b)

(c) Employee 1 took off more Mondays and fewer Wednesdays than Employee 2.

16 (a) Wetlands Flood PlainsLEAF | STEM | LEAF

| 1 |9 7 0 | 2 |4 2 2 | 3 | 38 5 2 | 4 |

5 | 5 | 5| 6 | 2 2 4| 7 | 4 9| 8 | 5| 9 | 5| 10 || 11 | 7

(b)

17

The consumption of both types of alcoholic beverage has been relatively stable with a slight decrease evident in the average consumption of beer and a slight increase in the consumption of wine. Beer made a very slight comeback in 1996/97 but then continued its downward trend while wine fell a little in 1993/94 but continued to increase after that.

18 (a) discrete

Employee 1 Employee 2

Mondays 12 10

Tuesdays 6 6

Wednesdays 2 4

Thursdays 3 3

Fridays 7 7

130 140 150 160 170height (cm)

180

Astros

Comets

Days of the weekMon Tue Wed Thu Fri

20

468

1012 Employee 1

Employee 2

Frequency

Past 10 years

20100

30405060708090

100110120

Frequency (rainy days)

WetlandsFlood Plains

1 2 3 4 5 6 7 8 9 10

1999/2000

1998/99

20

0

40

60

80

100

120Amount (litres) Consumption per head

of population

Beer Wine

1997/98

1996/97

1995/96

1994/95

1993/94

1992/93



(b)

(c) and (d)

19 (a)

Predictions: 1988—10.8 s; 1992—10.8 s; 1996—10.7 s; 2000—10.6 s(b) The predictions are not very accurate. The graph points have flattened out towards the end and this makes it difficult to make good predictions.(c)

2000—10.5

(d) The prediction for 2000 is actually worse with the additional data because the 1988 result has dragged the line of best fit down a bit.

20 Juanita is 42, Carlos is 44, Carmelita is 20, Enrico and Mercedes are 10 and Christos is 6.

21 The following table shows the values calculated for these data sets. (Not all of them were strictly required by the question.)

(a)

(b) There is no question—females live longer than males! The male scores are more tightly bunched than the females—this is confirmed by the IQR. The difference between males and females is greater at the top end of the scale. There is little difference between the lower quartile values—less than two years but by the time we look at the upper quartiles the difference is out beyond five years. This is also reflected in the larger measures of spread for the females. From the raw data we saw that the countries that have a low male life expectancy also have a low female life expectancy. However, the differences there are not as great as the differences between the two rates for countries where the values are relatively higher.(c), (d), (e) Student answers.

Replay (p. 364)1 (a) 7 (b) 10 (c) m4

2 $367.20 3 $640.754 (a) 22.02 (b) 15.55 (a) (x + 4)(x − 4) (b) (3x − 10)(3x + 10)

(c) 4(2x + 10) = 8(x + 5)6 (a) 0.8 (b) 53°7 (a) (b) 1

8 (a) d = − (b) t = 2 (c) f = −16

9 (a) x = (b) x = (c) x =

10 (a)

(b)

(c)

Height (cm) Frequency

145–149 8

150–154 4

155–159 3

160–164 5

165–169 3

170–174 2

2

4

6

Frequency

Height (cm)

145–

149

8

150–

154

155–

159

160–

164

165–

169

170–

174

1920 1940 1960 1980 200010.811.011.211.411.611.812.012.212.4

Women's 100 m sprintTime (s)

Year

y = -0.0194x + 49.41

1920 1940 1960 1980 200010.410.610.811.011.211.411.611.812.012.212.4

Women's 100 m sprintTime (s)

Year

y = -0.0188x + 48.143

mean min lowerquartile

median upperquartile

max IQR

Males 59.51 39.42 51.68 58.39 73.19 76.12 21.51

Females 63.98 40.37 53.47 63.38 78.63 82.79 25.16

40 50 60 70 80

males

35 45 55 65 75 85

females

13---

83---

ty k–fgh

------------- erk u–----------- ds

y----- wq+

4 6 83 5 7

−4 −2−5 −3 −1

−1 1−2 0 2


answers 547

Mixed revision three (p. 366)1 (a) y-intercept = −7; gradient = 5

(b) y-intercept = 7; gradient = −2(c) y-intercept = − ; gradient =

2 (a) (b)

(c)

3 (a) 12 (b) 16 (c) 74 (a) 5th (b) 6th and 7th (c) 20th and 21st5 (a) a = − (b) t = 5 (c) r = 6 Christie has $30, Justin has $15 and Andrew has $18

7 (a) x = (b) x = (c) x =

8 (a)

(b)

(c)

9 (a) 3 (b) 2 (c) −2 10 5611 (a) x � 7 (b) x � −3 (c) x � −4

12 (a) discrete (b) continuous (c) discrete13 (a) b = 4 (b) a = 15 (c) m = −414 (a) x-intercept = 12; y-intercept = 4

(b) x-intercept = 10; y-intercept = 15(c) x-intercept = − ; y-intercept =

15 (a)

(b)

(c)

16 (a) x = 12 (b) x = 0.25 (c) x = 0.66

17 (a)

(b)

18 (a) 5 goals (b) 4.5 goals 19 5.2 cm

20 (a)

(b) 26.521 (a) a = −3 (b) x = 12 (c) p = 22 66°, 82° and 32° 23 A24

2002 has certainly been much drier than 1999. Two months, January and April, were almost identical but months such as February and August reveal the stark contrast between the months.

85--- 2

5---

Y

X0−3

3 y = x + 3

Y

X0 5

x = 5

Y

X0

(1, 1)

−1

y = 2x − 1

73--- 8

27------

n m+p

--------------v(u j)–

d------------------ k

r-- gh–

X

Y

2 4−2

48121620

( , 0)25

0

X

Y

4 8 12 16 20 24−4

108642

−20

X

Y

2 4 6 8 10−4−6−8−10 −2

4

2

−2

−4

0

25---

Distance Frequency

0.0–�1.01.0–�2.02.0–�3.03.0–�4.04.0–�5.05.0–�6.0

246343

72--- 7

5---

−3 −2 −1 0 1

1 2 3 4 5 6 70−1

−6 −4 −2 0 2 4−8

6543210

Frequency

Distance (km)0.5 1.5 2.5 3.5 4.5 5.5

40 50 60 70 80 90

21631------

August

July

June

May

April

March

February

January

September

10

0

20

30

40

50

60Rainfall (mm) 1999 vs 2002

1999 (mm)2002 (mm)

Month



25 (a) A scatterplot of the data indicates that there is no real connection between the figures. There are too many points well away from the expected places for a connection to exist. (b) Not all samples would necessarily give the same results. Any particular sample could be biased.

26 (a) P = (b) $87 590


1 Students to draw own angles2 (a) acute (b) obtuse (c) reflex (d) reflex3 (a) 35° (b) 245° 4 D5 a = 46°, b = 46°, c = 46°6 (a) 163° (b) 64° (c) 70°

Exercise 8.1 (p. 374)1 (a) Triangles: AED; ABD; BCD

Quadrilaterals: ABCE; ABCD; ABDE(b) Triangles: CBD; CAGQuadrilaterals: BEFA; BDGA; DEFG(c) Triangles: CBD; BAF; BDF; DFE; CAEQuadrilaterals: CBFD; DBAF; BDEF; CBFE; BDEA; CDFA(d) Triangles: BGA; FEH; DCF; BFA; DEF; BCA; DCE; BGC; DHE; BFD; DHC; BFC; CHF; AGF; CGF; ACF; CEF; ACEQuadrilaterals: ABDE; ABDF; EDBF; ABCF; DCFE; CGFH; ABCE; EDCA

2

3 (a) D (b) A (c) D4 Many answers including traffic signs, coins and

company logos.

Exercise 8.2 (p. 378)1 (a) 65° (b) 121° (c) 35° (d) 22°

(e) a° = 48°; b = 84° (f) m° = 29°; n° = 122°(g) 79.5° (h) 73.5° (i) x° = 60, y° = 60, z° = 60

2 (a) 66° (b) 71.5° (c) 20° (d) 30°(e) 18° (f) 10° (g) 61° (h) 135°(i) 40° (j) 33° (k) 24° (l) 16°

3 B 4 (a) D (b) A5 (a) a° = 115°; b° = 40° (b) x° = 121°; y° = 4°

(c) p° = 134°; q° = 29° (d) m° = 118°; n° = 38°(e) p° = 45°; q° = 90° (f) 31°

6 28° 7 25°8 Pairs of values add to 113°

Exercise 8.3 (p. 382)1 (a) 128° (b) 61° (c) 61° (d) 45°

(e) 100° (f) 36.5°2 D 3 (a) C (b) C (c) D (d) D

4 Pairs must add to 137°5 (a) 120° (b) 100° (c) x° = 75°; y = 30°

(d) x° = 86°; y° = 8° (e) x° = y° = 100°(f) p° = q° = 61°; r = 119°(g) a° = 60°; b° = 70°; c° = 50°; d° = 130°(h) a° = b° = c° = f ° = 60°; e° = d° = 120°(i) x° = q° = 70°; y° = 70°; z° = 40°(j) a° = 55°; b° = 45°; c° = 80°; d° = 45°(k) a° = 120°; b° = 50°; e° = 60°; c° = d° = 70°(l) m° = 105°; n° = 38°; p° = q° = 67°; r° = 75°

6 a° = 89, b° = 80, c° = 55

Exercise 8.4 (p. 386)1 (a) Trapezium ABCD (b) Kite ADCB

(c) Parallelogram ABCD (d) Rhombus ABCD7 (a) B (b) C (c) D

8 (a) (b)

(c)

9 51

Exercise 8.5 (p. 388)1 (a) 120° (b) 140° (c) 220° (d) 44°

(e) 45° (f) 51°2 (a) D (b) C (c) C3 (a) 60° (b) 164° (c) x° = z° = 75°; y° = 105°

(d) a° = 42°; b° = c° = 138° (e) 115° (f) 112.5°(g) x° = 70°; y° = 75° (h) m° = 93°; n° = 119°(i) x° = 23°; y° = 140°; z° = 137°(j) a° = 32°; b° = 50°; c° = 58°(k) a° = 61°; b° = 34° (l) k° = 36°; p° = 29.5°

4 The sum of x° and y° should be 180°.5 (a) 100° (b) y° = 40°; x° = 85°

(c) x° = 70°; y° = 110°; z° = 130°6 Three, because the four angles must add to 360° so

they cannot all be less than 90°.7 A parallelogram contains two pairs of parallel sides.

This definition also covers both a rhombus and a rectangle. A rectangle is not necessarily a rhombus because a rhombus must have all equal sides and a rectangle may have equal sides (a square) but generally doesn’t.

8 (a) no, because it has a curved side (b) no, not a closed figure (c) no, this is actually two triangles(d) yes, a closed straight-sided figure with four sides

Exercise 8.6 (p. 393)1 (a) yes (b) yes (c) yes (d) yes2 (a) yes (b) yes (c) yes (d) yes3 (a) D (b) E4 (a) partial (b) perfect (c) partial

(d) partial6 Yes, depending upon how it is drawn.

3 triangle 8 octagon

4 quadrilateral 9 nonagon

5 pentagon 10 decagon

6 hexagon 11 undecagon

7 heptagon 12 dodecagon

1Rn------ A Q Rn 1–( )

R 1–------------------------+⎝ ⎠

⎛ ⎞


answers 549

7 Not true. Concave, irregular quadrilaterals are examples of quadrilaterals which will not tessellate.

8 All triangles will tessellate.

Exercise 8.7 (p. 397)Students’ own answers.

Exercise 8.8 (p. 398)1 (a) 1 : 1000 (b) 1 : 10 000 (c) 1 : 100 0002 (a) B (b) C (c) B3 (a) C (b) C4 (a) 400 km (b) 4 km (c) 400 m (d) 4 m

(e) 20 cm (f) 16 cm5 (a) 1 : 1 000 000 (b) 1 : 10 000 000

(c) 1 : 4 000 0006 (a) 1 : 4 000 000 (b) (i) 200 km (ii) 80 km

(iii) 24 km (iv) 600 km (c) (i) 2 cm(ii) 5 mm (iii) 0.5 mm (iv) 4 mm

7 A scale factor of 1 : 10 000 is as small as could be used and still be seen, and 1 : 5000 is as large as could fit in the rear seat of a car.

Exercise 8.9 (p. 403)1 (a) 1 : 1 (b) 2 : 1 (c) 1 : 2 (d) 1 : 1.62 (b) 0.5 or 2 : 1 3 (b) 1 : 2

Exercise 8.10 (p. 406)1 (a) SSS (b) ASA (c) RHS (d) SAS2 c–f; a–e; b–d 4 Sides of different length

Exercise 8.11 (p. 409)1 (a) 14 (b) 8 (c) 7.5

(d) 202 (a) 10 (b) 6 (c) (d)3 (a) B (b) A (c) D (d) E5 5.25 m 6 7 7.2 m8 (a) Measure these three distances: from the stick to

the tree, the stick to the place on the ground you look from, and the length of the stick. Use similar triangles to find the height of the tree.(b) The ground must be level, you need a clear view of the tree, scouts may not be old enough to understand this maths.

Chapter review (p. 413)1 C2 (a) x° = 139° (b) x° = 77° (c) x° = 36°

(d) a° = 66.5°, b° = 113.5°, c° = 37.5°3 (a) x° = 30° (b) x° = 34° (c) x° = 16°4 (a) B (b) D (c) A (d) C5 (a) x° = 134° (b) x° = 103° (c) x° = 103°

(d) x° = 43° (e) a° = 53°, b° = 127°, c° = 127°(f) p° = 93°, q° = 130°

6 (a) False (b) True (c) False 8 105 km9 (a) B (b) C 10 (a) 0.4 (b) 2.5

11 (a) SSS (b) SAS 12 B 13 (a) 5 (b) 914 They are all the same distance from the epicentre.17 12.6 m18 (a) yes (b) no (c) yes (d) yes19 triangle, square

Replay (p. 418)1 (a) $705 (b) $90.05

2 (a) A = (b) A = (c) A = (a + b)

3 9.86 m4 (a) (y + 7)(y + 3) (b) (d + 3)(c + 4)

(c) (t − 4)(t − 5)5 (a) 33° (b) 57° (c) 70°6 (a) a = 8.5 cm (b) p = 30.4 cm

(c) y = 39.3 cm7 (a) 2 (b) −1 (c)8 (a) x = (b) x = (c) x = 9 (a) (i) 3.13 (ii) 2 (iii) 2

(b) (i) 15.64 (ii) 16 (iii) 1110 STEM | LEAF

1 | 2 21 | 5 6 7 9 9 92 | 0 2 2 32 | 5 5 6 6 9 93 | 0 0 2 3 4 43 | 5 5 5 5 6 7 7 94 | 1 2 2 3 44 | 5 6 6 6

11

12


1 (a) (i) 4 (ii) 5 (iii) 10(b) (i) 10 (ii) 18 (iii) 0 (iv) 0

2 (a) (i) $16 (ii) $75 (b) (i) 4.5 m (ii) 3.2 m3 (a) 3x2 + 12x (b) x2 + 7x + 10

(c) x2 − 4x − 21 (d) x2 − 254 (a) x(x + 2) (b) (x − 4)(x + 4) (c) (x + 6)2

5 (a) (x + 2)(x + 5) (b) (x − 2)(x − 3)(c) (x − 14)(x + 1)

Exercise 9.1 (p. 425)1 (b) (c) (f)2 (a) Yes

(b)

559--- 262

5---

31623--- cm

r 0 1 2 3 4 5

r2 0 1 4 9 16 25

V = 3r2 0 3 12 27 48 75

xy2----- xy

2----- 1

2---h

12---

553------ 13

4------ 13

3------–

10 15 20 25 30 35 40 45 50

0

1

2

3

4

5

1 2 3 4 5

frequency

score



(c)

(d) (i) 18.8 m3 (ii) 43.3 m3

(e) (i) 3.2 m (ii) 4.7 m (f) 30 m3

3 (a)

(b)

(c) 125 m (d) 5 s (e) 96 m (f) 29 m(g) 3.2 s (h) 4.5 s (i) 35 m(j) fifth second i.e. between t = 4 and t = 5 s

4 (a) B (b) E (c) A5 (a) Any expression like x2 + 2x

(b) Any expression like x + 5

6 (a)

(b) 135 km/h (c) 60 km/h (d) 72 km/h(e) 72 km/h (f) 2.4 min; 7.6 min(g) 0.5 min; 9.5 min(h) 0 � t � 1.35 and 8.65 � t � 10

7 (a)

(b) 6 m (c) 9 m (d) 5 m (e) 5 m(f) 6.75 m (g) 3.6 m (h) (i) Yes (ii) No

8 (a)

(b) 100 cm (c) 40 cm (d) 5027 cm2

9 (a) 0 (b) 64 cm3 (c) 6 min (d) 20 cm3

(e) 0 � t � 6, 0 � V � 132

Exercise 9.2 (p. 430)1 (a) (i) (1, 4) (ii) x = 1 (iii) 3 (iv) −1 and 3

(b) (i) (− −1) (ii) x = −(iii) 0 (iv) −3 and 0

2 (a)

(b)

(c) (0, −4) (d) minimum (e) x = 0 (f) (0, −4)(g) (−2, 0) and (2, 0) (h) 6.2 (i) −1.4; 1.4(j) −3; 3 (k) 5; −3; 3 (l) 0; −2; 2

3 (a)

t 0 1 2 3 4 5

h 125 120 105 80 45 0

V

10

40

0

2030

50607080

r1 42 3 5

V = 3r2

t

h

1 4

20

80

2 3 50

4060

100120140

h = 125 − 5t2

t

S

2 8

20

80

4 6 100

4060

100120140

S = 3t2 − 30t + 135

x -4 -3 -2 -1 0 1 2 3 4

y 12 5 0 -3 -4 -3 0 5 12

(x, y) (-4, 12) (-3, 5) (2, 0) (-1, 3) (0, 4) (1, -3) (2, 0) (3, 5) (4, 12)

x −5 −4 −3 −2 −1 0 1 2

y −20 −8 0 4 4 0 −8 −20

d

h

1 4

1

4

2 3 5 60

23

56789

h = −d2 + 6d

p

h

20

80

40 800

4060

100

32---, 3

2---

X1 2 4−2−3 −1−4 3

68

Y

24

−2−4

1012

y = x2 − 4

0


answers 551

(b)

(c) (− maximum turning point(d) (−3, 0); (0, 0) (e) −2; −1 (f) 4; x = −2, −1(g) x = −4, 1 (h) x = −3, 0

4 (a)

(b)

(c) minimum turning point(d) (−1, 0); (2, 0); (0, −2)(e) (i) x = −1, 2 (ii) x = −2, 3 (iii) x ≈ −1.6, 2.6(iv) x = 0.5 (v) no real x values

5 (a) C (b) C (c) A6 Students’ own answers

7 (a)

(b) (−3, 1) (c) no x-intercepts, (0, 10)(d) (i) x = −3 (ii) x = −6, 0 (iii) no real x values(iv) x ≈ −6.7, 0.7

8 (a) (i)

(ii)

(iii)

(b) (i) x = −5, 2 (ii) x = 0, 4(iii) x = 1 (iv) x = −6, 3 (v) x = 2(vi) x = −1, 3 (vii) x ≈ −5.5, 2.5(viii) x ≈ 0.6, 3.4 (ix) x ≈ −1.4, 3.4

9 (a) x2 + 3x + 2 (b) x ≈ 1.4; the solution x ≈ −4.4 is not feasible for a length measurement.(c) length 3.4 cm, width 2.4 cm

Exercise 9.3 (p. 437)1 (a) (i) narrower (ii) wider (iii) wider

(iv) narrower (b) (iii) and (iv) (c) (i) 4(ii) (iii) 7 (iv) (d) (i) narrower(ii) wider (iii) narrower (iv) wider

2 (a) up 4 units (b) down 7 units(c) down one unit (d) up 2 units(e) down 8 units (f) up 5 units(g) up (h) down

3 (a) 5 units to the right (b) 4 units to the left(c) 1 unit to the left (d) 7 units to the right(e) 6 units to the left (f) 3 units to the right(g) unit to the right (h) units to the left

4 (a) (i) dilation factor 2, moved right 1 up 3 (ii) (1, 3)(b) (i) reflected in x-axis, dilation factor 3, moved left 2 down 1 (ii) (−2, −1)(c) dilation factor 4, moved left 3 down 2 (ii) (−3, −2)(d) (i) dilation factor , moved left 5 up 3 (ii) (−5, 3)(e) (i) moved left 4, down 3 (ii) (−4, −3)(f) (i) dilation factor 2, moved left 3 up (ii) (−3, )

5 (a) C (b) B (c) A (d) D(e) E (f) E (g) D

6 (a) C (b) B (c) E (d) B

x −3 −2 −1 0 1 2 3 4 5

y 10 4 0 −2 −2 0 4 10 18

X-1 1-3-4 -2-5 2

Y

4

-8-4

-16-20

8

-12

y = −2x2 − 6x

0

112---, 41

2---);

X2 3 5−1−2

1216

Y

48

−4−8

1

−3 4

20 y = x2 − x − 2

0

(12---, -21

4---);

−8

X−2 −1 1−5−6 −3−7 −4

Y

1216

48

−4

20

y = x2 + 6x + 10

0

4

12

−1

−3−4

3

−5

Y

−2

X1 2 4−1−2 3 5

y = −x2 + 4x

0

−12

48

−4

−16

12

Y

−8

X2 4−2−4−6

y = x2 + 3x − 10

0

−6

24

−2

6

Y

−4

X2 4−2−4 6

y = −x2 + 2x + 3

0

15--- 2

3---

12--- unit 3

4--- unit

23--- 3

2---

13---

12--- 1

2---



7

8 Students’ own answers9 (a) y = (x + 2)2 + 5 (b) (0, 9)

(c)

10 (a) y = 5(x − 3)2 + 2 (b) y = (x − 4)2 − 2(c) y = −(x + 2)2 + 3

Exercise 9.4 (p. 445)1 (a) x = 0, x = 11 (b) x = 0, x = −8

(c) x = 0, x = −5 (d) x = 0, x = 1(e) x = 4, x = 1 (f) x = 2, x = 6(g) x = 3, x = −7 (h) x = 4, x = −1(i) x = 0, x = 6 (j) x = 0, x = 5(k) x = −7, x = −2 (l) x = −3, x = −10

2 (a) x = −8, x = 8 (b) x = 2, x = −2 (c) x = 4(d) x = −7 (e) x = −1 (f) x = 9(g) x = 5, x = −5 (h) x = −10, x = 10(i) x = 1, x = 3 (j) x = 8, x = 7 (k) x = 0(l) x = 0

3 (a) x = 0, x = 6 (b) x = 0, x = −1 (c) x = 0, x = −2(d) x = 0, x = 5 (e) x = 0, x = (f) x = 0, x = −3

4 (a) x = −5, x = 5 (b) x = −9, x = 9 (c) x = 2, x = −2(d) x = 4, x = −4 (e) x = −6, x = 6 (f) x = −3, x = 3

5 (a) x = 7 (b) x = −4 (c) x = −8(d) x = 2 (e) x = −1 (f) x = 3

6 (a) x = 0, x = −2 (b) (i) x2 + 2x + 1 = 0(ii) (x + 1)2 = 0 (iii) x = −1

7 (a) x = 2 (b) x = 6 (c) x = 3 (d) x = 1(e) x = 0, x = 5 (f) x = 0, x = 3(g) x = 0, x = −1 (h) x = 0, x = −2 (i) x = 4(j) x = 5 (k) x = −7 (l) x = −9

8 (a) D (b) B (c) B (d) A9 (−1, 0), (4, 0)

10 (a) (12, 0) (−12, 0) (b) (0, 0) (−4, 0) (c) (6, 0)11 Students’ own answers

Exercise 9.5 (p. 448)1 (a) x = −2 or x = −1 (b) x = −6 or x = −3

(c) x = 4 or x = 7 (d) x = 1 or x = 9(e) x = −5 or x = 6 (f) x = −4 or x = 2(g) x = −8 or x = −3 (h) x = −7 or x = −1(i) x = 5 or x = 9 (j) x = 4 or x = 8(k) x = −5 or x = 3 (l) x = −2 or x = 8(m) x = −6 or x = 2 (n) x = −1 or x = 2(o) x = 1

2 (a) x = −6 or x = −2 (b) x = −4 or x = −3(c) x = −4 or x = 7 (d) x = 1 or x = 8(e) x = 5 or x = 10 (f) x = −7 or x = 6

3 (a) x = −4 or x = −3 (b) x = −6 or x = −2(c) x = −7 or x = 9 (d) x = −8 or x = 3(e) x = −3 or x = −2 (f) x = −3 or x = 5(g) x = −10 or x = 5 (h) x = −3 or x = 9(i) x = 6 or x = 11 (j) x = 1 or x = 5(k) x = −8 or x = 2 (l) x = −7 or x = 3

4 (a) x = −5 or x = 2 (b) x = −1 or x = 3(c) x = −4 or x = 7 (d) x = −7 or x = −1

DilationReflection in

x-axisTranslation in

x-directionTranslation in

y-direction

(a) y = (x + 1)2 + 2 – – 1 unit left 2 units up

(b) y = (x − 3)2 + 1 – – 3 units right 1 unit up

(c) y = (x − 4)2 − 5 – – 4 units right 5 units down

(d) y = (x + 2)2 − 7 – – 2 units left 7 units down

(e) y = −x2 − 6 – invert – 6 units down

(f) y = −x2 − 2 – invert – 2 units down

(g) y = −(x − 2)2 + 3 – invert 2 units right 3 units up

(h) y = −(x − 5)2 + 2 – invert 5 units right 2 units up

(i) y = 5x2 + 4 by factor of 5 (narrower) – – 4 units up

(j) y = 3x2 − 5 by factor of 3 (narrower) – – 5 units down

(k) y = 2(x + 5)2 − 3 by factor of 2 (narrower) – 5 units left 3 units down

(l) y = 5(x − 6)2 − 4 by factor of 5 (narrower) – 6 units right 4 units down

(m) y = (x − 3)2 + 1 by factor of (wider) – 3 units right 1 unit up

(n) y = (x + 4)2 + 6 by factor of (wider) – 4 units left 6 units up

(o) y = −3(x + 6)2 − 4 by factor of 3 (narrower) invert 6 units left 4 units down

(p) y = −4(x + 1)2 − 3 by factor of 4 (narrower) invert 1 unit left 3 units down

12--- 1

2---

34--- 3

4---

2

(−2, 5)

−3 X

Y

−2 −1 1 2 3

4

6

89

1

3

5

7

10

−2−1

0

13---

12---


answers 553

(e) x = −4 or x = 4 (f) x = −3 or x = 3(g) x = −6 or x = −1 (h) x = −7 or x = 6(i) x = 0 or x = 12

5 (a) A (b) E (c) B (d) B (e) B (f) C6 t = 0, t = 50 seconds8 (a) 5°C (b) t = 2, t = 8 (c) 10 am, 4 pm

Exercise 9.6 (p. 452)1 (a) (i) (ii) (0, 15) (iii) (3, 0), (5, 0)

(iv) (4, −1)

(b) (i) (ii) (0, 8) (iii) (2, 0), (4, 0)(iv) (3, −1)

(c) (i) (ii) (0, 12) (iii) (−2, 0), (6, 0)(iv) (2, 16)

(d) (i) (ii) (0, 3) (iii) (−1, 0), (3, 0)(iv) (1, 4)

(e) (i) (ii) (0, −25) (iii) (−5, 0), (5, 0)(iv) (0, −25)

(f) (i) (ii) (0, −9) (iii) (−3, 0), (3, 0)(iv) (0, −9)

2 (a)

(b)

0 X

Y

15

3(4, −1)

5

y = x2 − 8x + 15

8

Y

X2 3 4–10

y = x2 − 6x + 8

0 X

Y (2, 16)

12

6−2

y = −x2 + 4x + 12

Y

43

X10 3–1

y = −x2 + 2x + 3

Y

−25

X50−5

y = x2 − 25

0 X

Y

−9

3−3

y = x2 − 9

21

Y

X3

50 7−4

y = x2 − 10x + 21

12

Y

X2

4

6−4

y = x2 − 8x + 12

0



(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

Y

−3−4

X1−3 −1 0

y = x2 + 2x − 3

Y

−5

−9

X1−5 −2 0

y = x2 + 4x − 5

Y

89

X1 4−2 0

y = −x2 + 2x + 8

16

Y

15

X−1 3−5 0

y = −x2 − 2x + 15

Y

−4

X2 40y = x2 − 4x

Y

−9

X−3−6 0

y = x2 + 6x

Y

−3

X−1 4−2 0

y = 3x2 + 6x

Y

−8

X2 40

y = 2x2 − 8x

Y

−16

X−4 40

y = x2 − 16

Y

−1

X1−1 0

y = x2 − 1

Y

−9

X−2−5−8

16

0

y = x2 + 10x + 16

Y

−9

X−1−4−7

7

0

y = x2 + 8x + 7


answers 555

(o)

(p)

(q)

(r)

(s)

(t)

(u)

3 (b), (c), (e)4 (a) E (b) B 5 C

6

(a) 10 s (b) 25 m

7 (a)

(b) 23°C (c) 3 h and 5 h (d) 31°C(e) 4 hours

Y

−5

X−1−3−5

4y = −x2 − 6x − 5

0

Y

1

X1 2 3

−3

0

y = −x2 + 4x − 3

Y

X−3

9

0

y = x2 + 6x + 9

Y

X−5

25

0

y = x2 + 10x + 25

Y

2

X3

y = −x2 + 3x

32

14

0

Y

X

6

−2−5

y = −x2 − 5x14

12

0

X

y = −x2 + 7x − 1214

12

3 4

Y

h

25

t5 100

h = −t2 + 10t

T

31

23

h2 4 6 8 10

T = −0.5h2 + 4h + 23(4, 31)

0



8 (a)

(b) The graph does not touch or cross the x-axis(c) Answers can be checked on graphical calculator.

Exercise 9.7 (p. 457)1 length 12 cm, width 7 cm 2 x = 123 4 or −5

4 (a) B (b) B (c) D (d) B5 3 s 6 y = 3 7 after 2 min and after 8 min8 79 (a) 6 cm (b) 14 cm by 10 cm (c) 36 cm2

(d) 104 cm2 (e) 64 cm2

10 10, 1011 Students’ own answers


1

(a) (−2, 0), (4, 0), (0, −8)(b) (1, −9), minimum turning point (c) x = 1(d) −5 (e) −3, 5 (f) −3, 5 (g) −2, 4

2 (a) A (b) E (c) B

3

4 (a) x = 0 or x = −4 (b) x = 7 or x = −1(c) x = −4 or x = 4 (d) x = −3(e) x = 0 or x = 8 (f) x = 6

5 (a) x = −5 or x = −7 (b) x = −3 or x = 2(c) x = −9 or x = 1 (d) x = 1 or x = 8(e) x = −4 or x = 1 (f) x = 1 or x = 3

6 (a) x = −1 or x = 5 (b) x = 6 or x = −1(c) x = −3 or x = −4 (d) x = −3 or x = 3(e) x = −8 or x = 4 (f) x = 4 or x = −3

7 (a)

(b)

(c)

2

X

Y

1 2 3 4 5

4

6

89

1

3

5

7

10

0

Y

−4X2 4−2−4 6

−8

84

y = x2 − 2x − 8

0

DilationReflection in

x-axisTranslation in

x-directionTranslation in

y-direction

(a) y = (x − 1)2 + 3 – – 1 unit right 3 units up

(b) y = −x2 + 4 – invert – 4 units up

(c) y = −(x + 2)2 − 1 – invert 2 units left 1 unit down

(d) y = 3(x − 4)2 + 2 by factor of 3 (narrower) – 4 units right 2 units up

(e) y = (x − 1)2 + 1 by factor of (wider) – 1 unit right 1 unit up

(f) y = −2(x + 2)2 − 2 by factor of 2 (narrower) invert 2 units left 2 units down

12--- 1

2---

Y

−4X−2−4−6

12 y = x2 + 8x + 12

15

Y

16

X1 5−3

y = −x2 + 2x + 15

Y

X–3 −1

y = 3x2 + 9x

12

−634


answers 557

(d)

8 (a) B (b) C

9 (a)

(b)

(c) 9 m (d) 1.3 s (e) t: 2 � t � 4 (f) 10 m(g) 5.9 s

10 (a)

(b) 9 m (c) 6 m11 (a) 10 − x (b) A = x(10 − x)

(c)

(d) length 5 m, width 5 m (e) 25 m2

12 length 12 cm, width 5 cm 13 25, 2514 y = (x − 3)2 + 5

Replay (p. 466)1 (a) 104 cm2 (b) 37.5 m2 (c) 103.5 cm2

2 Students’ own answer3 (a) 35° (b) 52° (c) 61° 4 1.2°5 (a) (b)

(c) (d)

6 (a) m = 6 (b) n = 6 (c) a = −27 (a) x � −12 (b) a � −30 (c) y � −78 (a) (i) 3.4 (ii) 3 (iii) 1

(b) (i) 18.45 (ii) 21 (iii) 21

9

10 (a) a° = 60° (b) x° = 35° (c) p° = 12°


1 (a) (b) (c) (d)

2 (a) (b) (c) (d)

3 (a) (b) 1 (c) (d)

4 (a) 0.71 (b) 0.44 (c) 0.75 (d) 1.255 (a) 12.5% (b) 40% (c) 15% (d) 133.3%6 (a) 1, 2, 3, 4, 5, 6 (b) spade, club, diamond, heart

(c) black, red7 (a) (b) (c)


1 2 Elliot:

3 C 4 E

t 0 1 2 3 4 5 6

h 1 6 9 10 9 6 1

Y

X2

4

y = x2 − 4x + 4

t

h

1 4

2

8

2 3 5 60

46

10

7

h = −t2 + 6t + 1

h

9

d3 60

h = −d2 + 6d

0 x (m)

A (m2)

10

(5, 25)

A = −x2 + 10x

Y

X0 5

x = 5

Y

X0

y = 0

Y

X0−2

x = −2Y

X0

3

y = 3

0

1

2

3

4

5

1 2 3 4 5

frequency

score

45--- 2

3--- 4

7--- 3

4---

910------ 11

12------ 17

30------ 5

8---

45--- 7

8--- 5

6---

12--- 3

8--- 7

8---

1327------

310------; Kris: 19

75------; Austin: 67

150---------



5 (a) B (b) C (c) E

6 (a) (b) (c) (d) 1 (e) 0 (f)

(g) 1, as expected, as these three outcomes cover all possibilities.

7 (a) (b) (c) (d) (e)(f) 0

8 (a) 50 (b) (i) (ii) (iii) (iv)

(v) (vi) (c) (i) 0.20 (ii) 0.24 (iii) 0.02

(iv) 0.92 (v) 0.50 (vi) 0.80 (d) (i) 20%(ii) 24% (iii) 2% (iv) 92% (v) 50%(vi) 80%

9 Students’ own answers10 (a) (i) 72.1 years (ii) 72.8 years (iii) 73.8 years

(iv) 76.7 years (v) 80 years (vi) 84.6 years

(b) As you get older your expected age at death

increases.

(c) (half of a half)

(d) Insurance companies; it helps them set the

premiums for policies.

11 The coach is wrong. Pr(success) = for every throw12 (a)

(b) The dimensions of the cube do not matter, Pr(square face down) = 0.638(c) You could make a cube and roll it a large number of times to check the results.

Exercise 10.2 (p. 475)1 (a) experiment 4; 0.17 (b) experiment 5; 0.06

(c) experiment 1; 0.17 (d) experiment 2; 0.10(e) peach; experiment 2; 0.05(f) pear; experiment 4; 0.25

2 (a) E (b) B3 (a) D (b) B

(c) Die 1, Die 4, Die 2, Die 3, Die 5(d) Die 4, Die 5, Die 3, Die 2, Die 1

4 Students’ own answers5 Students’ own answers6 Students’ own answers


1 (a) (b) (c)

2 (a) (b) (c)

3 (a) (b) (c)

4 5 (a) (b)

6 (a) (b) (c) (d)

7 B 8 B 9 10

11 (a) (b) (c) (d) (e) (f)

12 (a) C (b) A (c) D

13 (a) (b) (c) 1 (d) (e) (f)

14 (a) (b) (c) (d) (e)

(f) (g) (h) 0 (i) (j)

15 (a) 28.3% (b) 20.2% (c) 8.5%(d) 36.2% (e) 24.5% (f) 11.8%(g) 15.9% (h) 5.8% (i) 5.7%

16 Sample answers:(a) (b) (c)

17 Students’ own answers, but: 50–50 = 50%; certain = 100%; impossible = 0%


1 (a) (b) (c) (d)

2 (a) Prawn, Lamb; Prawn, Fish; Prawn, Beef; Prawn, Pork; Prawn, Poultry; Oysters, Lamb; Oysters, Fish; Oysters, Beef; Oysters, Pork; Oysters, Poultry; Pâté, Lamb; Pâté, Fish; Pâté, Beef; Pâté, Pork, Pâté, Poultry; Satay, Lamb; Satay, Fish; Satay, Beef; Satay, Pork; Satay, Poultry(b) (i) (ii) (c)

3 (a) (b) (c) (d)

4 (a) A (b) C (c) D5 (a) FGI,M FMI, FBoI, FDI, FGB, FMB, FBoB, FDB,

FGGr, FMGr, FBoGr, FDGr, etc.: 36 in total(b) (i) (ii) (iii) (iv) (v) (c)

6 (a) 48 (b) (i) (ii) (iii) (c) 12 7 Students’ own answers8 (a) H, T (b) 2 (c) HH, HT, TH, TT (d) 4

(e) HHH, HHT, HTH, HTT, THH, THT, TTH, TTT(f) 8(g) Yes. To find the number of events for a combination you multiply together the number possible for each event within the combination.

9 (a) 38 = 6561 (b)

(c) There is only one way it can happen: GGG (d) ‘What is the probability that all the faces will be blue?’ and ‘What is the probability that all the faces will be red?’(e) The complementary question to the statement in (b) would actually be: What is the probability that not all of the faces are green?


1 (a) (b) (c) (d) (e) (f)

2 (a) (b) (c)

3 (a) (b) (c)

4 (a) (b) (c) (d)

17--- 1

7--- 5

7--- 1

7---

726------ 15

26------ 3

26------ 9

26------ 5

13------

15--- 6

25------ 1

50------ 23

25------

12--- 4

5---

14---

23---

614------ 3

7---=

1523------ 8

23------ 1

23------

49--- 5

18------ 1

18------

513------ 8

13------ 1

13------

78--- 1

1000------------ 999

1000------------

13--- 3

5--- 11

15------ 3

5---

310------ 5

12------

13--- 2

3--- 1

6--- 1

3--- 5

6--- 1

2---

14--- 11

20------ 1

5--- 4

5--- 1

2---

145------ 22

45------ 1

5--- 4

45------ 1

9---

1315------ 1

3--- 4

5--- 2

9---

blue

greenorange

green

brownbrown

brow

nbrow

n

brownred

red

red

yell

ow

green

bluered

red

red

15--- 1

25------ 3

5--- 21

25------

120------ 2

5--- 3

5---

116------ 7

16------ 1

4--- 3

4---

136------ 4

9--- 2

3--- 2

3--- 4

9--- 1

9---

148------ 1

12------ 1

3---

16561------------

38--- 1

8--- 1

2--- 5

8--- 1

2--- 5

8---

45--- 1

2--- 7

10------

79--- 5

9--- 2

3---

13--- 1

2--- 5

6--- 2

3---


answers 559

5 (a) (b) (c) (d) (e) (f)

6 B7 (a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k) (l)

8 (a) (b) (c)

(d) You can write out the sample space or use Pr(either) = Pr(left) + Pr(right) − Pr(both)(e) (f) (g) (h)


10 (a)

(b) (i) (ii) (iii) (iv)

(c) (i) (ii) (iii) (iv) (v) (vi)

(d) Yes, but C and D are the only mutually exclusive pair

Exercise 10.6 (p. 501)1 Answers will vary according to the results of the

simulation but Anil should get approximately 19 sleep-ins.

2 (a) Answers will vary according to the simulation results but the table should approximately be

(b) There should be approximately twice as many families with a boy and a girl as there are families with two boys. Only one outcome produces two boys (a boy then a boy) whereas for a boy and a girl there are two outcomes (girl/boy or boy/girl).

3 (a) (i) 1.1 (ii) 4.4 (iii) 6.6 (iv) 24.24(b) In the long run a 5 occurs once every six rolls. The other five numbers will average out to be 1, 2, 3, 4 and 6 = 16.

4 (a) Students’ own answers(b) 6 (c) no upper limit in theory(d) Probably let each face of a die represent one of the animals (e)–(f) Students’ own answers


1 2 (a) (b)

3 (a) (b) (c) 0 (d) (e) (f)

4 (a) 36 (b) (i) (ii) (iii) (iv)

5 (a) (b) (c) (d) (e)

6 (a) (i) (ii) (iii) (iv)(b) (i) 0.03 (ii) 0.48 (iii) 0.97 (iv) 0.34

7 (a)

(b) (i) (ii) (iii)8 (a) (b) (c)

9 (a) Students’ own answers, but will probably indicate the use of a die to test each egg. A cracked egg could be represented by a 1, for instance.(b)–(d) Students’ own answers

10 (a)

(b) (i) (ii) (iii) (iv)

(v) (vi) (vii) (viii)

(c) No—Pr(5 on green) + Pr(3 on blue) ≠ Pr(5 on green or 3 on blue)(d) and (e) Students’ own answers

Replay (p. 507)1 (a) 415.6 cm2 (b) 266.1 cm2 (c) 9.2 mm2

2 (a) (x + 7 )2 (b) (x − 3)2 (c) (2x + 5)2

3 41.6 m4 Erin is 8 and Joanne is 32

5 (a)

(b)

(c)

6 (a) continuous (b) discrete(c) discrete (d) continuous

7 (a) 120° (b) 160° (c) 118°8 (a) 42° (b) 24°9 (a) x = 0 or 7 (b) x = 0 or −3 (c) x = −4 or 4

10 (a) x = −3 or 5 (b) x = −4 or −2 (c) x = 3 or 511 x = 11 or −12

red die

1 2 3 4 5 6

blue

die

1 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1

2 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2

3 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3

4 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4

5 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5

6 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

Two girls

Two boys

A boy and

a girl

Number of familiesEstimated probability

10 10 20

115------ 8

15------ 3

5--- 7

30------ 1

3--- 7

30------

12--- 1

4--- 3

4--- 7

26------ 3

13------

352------ 15

52------ 12

13------ 3

4--- 11

13------

413------ 15

26------

213------ 5

26------ 4

13------

126------ 11

13------ 21

26------ 9

13------

16--- 1

6--- 5

36------ 5

18------

1136------ 5

18------ 7

18------ 5

18------ 7

18------ 5

12------

14--- 1

4--- 1

2---

1013------ 3

20------ 1

4---

SedanStationWagon Coupe

Panelvan

WhiteBlackRedYellowSilver

✓✓✓✓✓

✓✓✓✓✓

✓✓✓✓✓

✓✓✓✓✓

green die

1 2 3 4 5bl

ue d

ie1 1, 1 2, 1 3, 1 4, 1 5, 1

2 1, 2 2, 2 3, 2 4, 2 5, 2

3 1, 3 2, 3 3, 3 4, 3 5, 3

4 1, 4 2, 4 3, 4 4, 4 5, 4

5 1, 5 2, 5 3, 5 4, 5 5, 5

110------ 3

10------ 2

5--- 7

10------ 1

2---

19--- 11

12------ 3

4--- 1

4---

38--- 1

2--- 5

8--- 1

2--- 7

8---

129------ 14

29------ 28

29------ 10

29------

120------ 4

5--- 2

5---

136------ 1

6--- 1

4---

225------ 19

25------ 2

5--- 21

25------

1925------ 21

25------ 4

25------ 4

5---

0 1 2 3 4

−8 −6 −4 −2 0

−1 0 1 2 3



Mixed revision four (p. 509)

1 Triangles: ABC, AGC, GDF, DFEQuadrilaterals: ABCG, GDEF, FDCA

2 (a) x° = 75° (b) y° = 10° (c) p° = 152°3 (a) (b) (c)

4 (a) (b)

5 (a) 5 (b)

6 (a) (b) (c)

7 (a) x = 0 or 9 (b) x = or − (c) x = ±4

8 (a) x = ±6 (b) y = ±40 (c) t = ±109 (a) RHS (b) SAS

10 (a) (b) (c)

11 (a) 65° (b) 245° (c) 70°12 (a) (b) 0 (c)

13 (a)

(b) (i) (ii) (iii)

14 (a) 1 : 250 000 (b) 1 : 1 000 000

15 (a)

(b)

(c)

16 (a) 12 (b) 1517 It has been flipped/reflected over the x-axis.18 7.15 m19 (a) x = ±4 (b) w = ±1 (c) h = ±220 Students to produce their own construction21 (a) 2.4% (b) 22.7% (c) 26.3% (d) 33.3%22 Students to produce their own construction23 (a) (b) (c) (d)24 (a) 1 : 1 000 000 (b) 1 : 500 000

(c) 1 : 2 000 00025 The number could be 8 or −1026 a = 360 − (f + g + h); b = 360 − (e + g + h);

c = 360 − (f + e + h); d = 360 − (f + g + e)So, a + b + c + d = 1440 − (f + g + h + g + h + e + h + e + f + e + f + g)

= 1440 − 3(e + f + g + h) = 36027 (a) y = 3(x − 4)2 − 2

(b) Dilated by a factor of 2, reflected in the x-axis, and moved 7 units up.

28 Need to draw a spinner with 31 equal pieces: 16 green, eight blue, four brown, two pink and one red.

first die

1 2 3 4 5 6

seco

nd d

ice

2 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2

3 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3

5 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5

7 1, 7 2, 7 3, 7 4, 7 5, 7 6, 7

11 1, 11 2, 11 3, 11 4, 11 5, 11 6, 11

13 1, 13 2, 13 3, 13 4, 13 5, 13 6, 13

619------ 10

19------ 15

19------

Y

X1 20−1−2

5

4

3

2 y = x2 + 1

1

Y

X1 20−1−2

4

3

2

1

y = 2x2

25---

15--- 1

2--- 3

10------

53--- 3

2---

916------ 3

4--- 11

16------

16--- 1

2---

12--- 5

36------ 1

18------

X2−2

6

8

Y

2

4

−2

−4

−6

−8

−10

−4 4

10

0

X−2 2−6−8 −4−10 4 6 8 10

Y

20

−40

−20

−80

−100

−60

0

X−2 2−6−8 −4 4

Y

4

−8

−4

8

12

0

213------ 7

26------ 3

4--- 4

13------


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Heinemann Maths Year 9 VELS Answers