99 NCM 11 NSW SB ANSmathsbooks.net/New Century Year 11/99_set answers.pdf · 2015-08-04 · 99 NCM 11 NSW SB ANS ... f) ×---

ANSWERS 453

Chapter 1

1. (a) 3p2 + 6p (b) 5de + 10df (c) 2m2 + 5

(d) 2ar − 4r (e) 4x2 + 2xy + 3x (f) 4u − 15

(g) −k2 − 2k + 8 (h) y2 + 2y − 15 (i) 8t + z

(j) 6w (k) −10c2 + 13c (l) 18x

2. (a) 16a2km (b) −24cd2 (c)

(d) 25x6 (e) 6n4 (f) 14k5p2

(g) 36mn (h) 2e3 (i) 4x2y4

(j) a2y3 (k) −20a2b2 (l) 18p2q

(m) x6 (n) −n6 (o) 4k4

3. (a) 2m (b) 7x (c) −5

(d) 2ut (e) (f)

(g) (h) (i) m2n2

(j) (k) (l)

(m) −8fg (n) (o)

(p) (q) −3a2 (r)

1. 52.04 cm2

2. (a) 100°C (b) 55°C (c) 28°C

3. (a) US$13.35 (b) US$3.00 (c) US$6.00

4. s = 8 cm, A = 8.94 cm2

5. (a) 360° (b) 720° (c) 1440°

6. 16 m/s 7. proof

8. (a) 17 (b) 81 (c) 301

9. 12 770.05 cm3 10. 3.08 s

11. $6931.49 12. 13.5 m

13. (a) 20.8 (b) increase her weight

14. (a) 25°C (b) 38°C (c) 15°C (d) 37°C

15. 22 m/s 16. 40 km

17. $487.20 18. 21 m

19. 207.35 cm2 20. proof 21. $510

22. (a) 78.54 cm2 (b) 157.08 cm3

23. $154.50

24. (a) 1.52 m (b) 2.53 m (c) 7.62 m(d) 91.44 m (e) 8847.73 m

25. (a) 687 days (b) 89 days (c) 365 days

Exercise 1-01

5t3w2

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

12---

3x2----- 3r–

q---------

3g5

------ 1a---

d5--- 1

4---

13xz---------

14---

2x2

5w--------

3ce

------ 2n2

x--------

Exercise 1-02

1. (a) 3p2 − 3ap2 (b) −8k − 16

(c) −d2e + 5d (d) 7k2m + k3

(e) 9a3b − 9ab3 (f) 6tu − 8t2

(g) −24n + 6n2 (h) 5x4 + 5x2

(i) −2a2 + 4 (j) 5a2b + 15b2 − 35b

(k) −x2 + 4x − 10 (l) 3h2 − 21eh − 12h3

(m) 2y2 + 3y − y3 (n) d3e − 2de + de3

(o) −2av2 − v2 + 2av2. (a) 2, −2 (b) −6

(c) yes; −(b − a) = −b + a = a − b

3. (a) 3x + 14 (b) d − 22(c) 2r + 80 (d) 7f + 9

(e) −9x − 32 (f) 3x2 + 27x

(g) 2b2 + 23b (h) 3w2 − 29w

(i) k2 + 6k + 9 (j) −b2 + 6b + 10

(k) 2v2 − 4v − 16 (l) 3t2 + 14t + 14

(m) 4e2 + 3e (n) a2 + 10a − 21

(o) p2 − q2 (p) 2x2 + 8x + 3

1. d = 6 2. p = 2 3. u = −2

4. k = 13 5. a = −3 6. x = −7. a = 4 8. d = − 9. x = −2

10. f = 12 11. x = 12 12. x = −20

13. x = 13 14. a = 2 15. x = 3

16. b = 2 17. k = −5 18. c = 1

19. k = 5 20. y = −5 21. m = 8

22. u = −17 23. y = 6 24. k = −12

25. f = −5 26. a = −13 27. a = 1

28. u = −2 29. y = − 30. x = 1

1. x = 93 2. m = 26 3. n = 1

4. a = 10 5. t = 5 6. r = 20

7. x = − 8. n = 5 9. x = 1

10. p = − 11. r = − 12. u =

13. b = 4 14. z = 3 15. k = −23

16. r = 7 17. h = 13 18. a = 1

19. m = 7 20. p = 11 21. n = 4

Exercise 1-03

Exercise 1-0412---

13---

12--- 1

2---

310------

59--- 1

5---

Exercise 1-0513--- 1

4--- 13

17------

1011------ 5

11------

617------ 7

20------

49--- 1

5--- 5

7---

25--- 4

5--- 1

2---

15--- 5

7--- 2

7---

45--- 44

45------

Answers

454 NEW CENTURY MATHS GENERAL: PRELIMINARY

22. k = 4 23. d = 6 24. w =

25. y = 6 26. r = 5 27. b = 1

28. u = 29. p = 30. h = 10

1. (a) (i) 13 (ii) 31 (b) (i) 7 (ii) 18

2. 12 cm

3. (a) 300 m (b) 60 s

4. 2 m

5. (a) (i) 180° (ii) 540°(b) (i) octagon (ii) hexagon

6. 21 7. 8 cm 8. $4387.15

9. (a) 2 min (b) 3.6 min

10. (a) 3.11 miles (b) 0.93 miles

11. (a) (i) 12 (ii) 26 (b) (i) 11 (ii) 19

12. 1.61 × 10−28 kg 13. $2320

14. 3.5 cm 15. 19.2 km

16. (a) 18 (b) 27 17. (a) 135° (b) 20

18. 4 h

19. (a) $1.50 (b) $29.96 (c) $11.23

20. (a) (i) 16th floor (ii) 4th floor(b) (i) 7 s (ii) 12 s

21. 5 years 22. 3 m/s2 23. 4.99 cm

24. 64 km 25. 2 26. 1.80 m

1. (a) y = 3x + 7 (b) y = −2x + 1 (c) y = x − 1

(d) y = x − (e) y = − x (f) y = 5

2. (a) y = 2x + 3 (b) y = 3x − 1 (c) y = 4x

(d) y = −2x + 2 (e) y = −x + 1 (f) y = x − 1

(g) y = −x (h) y = x − 2 (i) y = x − 3

(j) y = −3x + 2 (k) y = − x + 5 (l) y = x

3.

213------ 5

8---

34---

13--- 3

5---

Exercise 1-06

Exercise 1-07

13--- 1

2--- 5

4---

12---

34---

23--- 3

2---

(a) (b)

(c) (d)

(e) (f)

321

0

y

−1−4 x

−2

0

1 20

y

−1−2 x

−2

2

21

0

y

−2

−2 x

−3

1−1−2

0

y

−4

−2 x

−5

1 2

21

y

−2

−2 x

−3

−1−2 2

−1

321

−3

2

y = 4x − 3

y = −2xy = x − 2

y = x + 2

y = 2x − 5

12

54

321

0

y

−1−2

y = x − 135

1 2−1 x3

1. (a) E (b) C (c) A(d) D (e) F (f) B

2. (a) y = 2x + 4 (b) y = 5x − 2 (c) y = x − 3(d) y = 7x + 10 (e) y = −2x − 2 (f) y = 4x

(g) y = −x + 9 (h) y = x − 1

3.

4. (a) m = 6, 11, 16, 21, 26, 31 (b) m = 5h + 1(c) (i) 101 (ii) 201 (iii) 501(d) gradient 5, y-intercept 1

5.

6.

(g) (h)

(i)

1 2

321

0

y

−1 x1 2

321

0

y

−1 x3

4

4 5

45

3

1 2

21

0

y

−1 x3

4

4 5

3

y = −x + 4

y = x + 143

y = − x + 314

Exercise 1-08

12---

17m =

m = 7 is steeper y

x

y = −3

y

x

y

x

y

x

y

x

y

x

y

x

y = 1

x = 4 x = −3

y = 0x = −

12

−3

12

112

4 −3

12

−

(a) (b)

(c) (d)

(e) (f)

12m =

y

x

12m = −

slopes upwards

slopes downwards

ANSWERS 455

1. A, D, F, H

2. (a) y = 9x + 7 (b) y = −5x + 200 (c) y = x + 163. (a) C, cost of a call (b) C

(c)

(d) 80, cost per minute (e) 22c, starting cost(f) C = 80t + 22 (g) $3.42, formula(h) $14.62 (i) 7 min

4. (a) t, time (b) V = −420t + 1900(c) depreciation per year(d) original value of computer(e) value of computer cannot be negative(f) $850 (g) 4.5 years(h) 0.75 years or 9 months

5. (a) n, number of overs (b) S

(c)

(d) m = 4.5, b = 0 runs (e) number of runs per over(f) runs/over (g) 225 runs(h) Weaker batters bat last, with lower run rate.(i) (i) 9 runs (ii) 90 runs(j) (i) 40th over (ii) 12th over

6. (a) 0, 0 km = 0 miles (b) K (c) 1.6(d) K = 1.6M (i) 160 km (ii) 62.5 miles(e) (i) 19 km (ii) 12 miles

7. (a) C (b) C = 235p + 8400(c) (i) $30 490 (ii) $18 975(d) (i) 34 (ii) 58(e) $8400, the cost even when no printers are made

8. (a) T = −0.006h + 15(b) (i) 12.6°C (ii) 15°C(c) 2500 m (d) drop in °C per rise in metres(e) (i) T on vertical axis, h on horizontal axis

(ii) gradient flat but negative, sloping downwards(iii) vertical intercept is 15°C

9. (a) C (b) C = 0.7n + 4.2(c) starting cost of taxi trip(d) (i) $18.20 (ii) 48 km

10. (a) T (b) T = n + 3

(c) 21°C (d) 184 chirps/min(e) 3°C, temperature too cold for summer

1. (a) 9ut + t2 (b) 15k3 (c) −6d2

(d) 32p5 (e) 7 − 6b (f) 8r2

(g) −27d6 (h) (i) −

(j) 8x2 + 8x (k) (l) −

Exercise 1-09

34---

0

800

1200

400

5Duration, t (min)

10 15

C = 80t + 22

Cos

t of

calls

, C (

c)

0

100

150

50

20Overs, n

30 40

C = 4.5n

Run

s, S

10

18---

Chapter assignment

35---

vw7

-------

3cb

------ 1a2-----

2. 204.20 cm2 3. $540

4. (a) 2n2 − n − 1 (b) 4m2 + 11m − 6

(c) −6d2 + 2d + 12 (d) −4p

(e) −2k2 + 4k − bk (f) 6xy + 2xy2 − 4y2

(g) x + 43 (h) 11d + 8

(i) 7h2 + 26h (j) gr2 + 2gr − 15r + 6r2

5. (a) 108° (b) 9

6. $5674.27 7. 110.5 m

8. (a) p = 5 (b) r = 4 (c) b = −3(d) a = −7 (e) n = −4 (f) k = −12(g) g = −1 (h) z = −2.6 (i) t = −7

9. (a) y = − x + 1 (b) y = 3x − 3

10. 28 years 11. 80 chirps/min

12. (a) r = 20 (b) p = −3 (c) t = 1

(d) u = 2.6 (e) k = 57 (f) y = −7.5

(g) a = 3 (h) x = 5 (i) w =

13. (a) y = 3x + 4 (b) y = −x + 4

14.

15. (a) S (b)

(c) , increase in inches per shoe size

(d) 8 inches, the vertical intercept

(e) L = S + 8

(f) (i) 10 inches (ii) 10 inches

(g) (i) size 1 (ii) size 14

16. (a) t (b) A = −275t + 4950(c) the reduction in the loan amount per month(d) the original amount of the loan(e) (i) $3300 (ii) $1100(f) after 18 months, the horizontal intercept (where the

graph crosses the t-axis)

Chapter 2

1. (a) 6.4 (b) 58 (c) 106.8 (d) 42.7(e) $20.79 (f) $6.60 (g) $280 (h) $69.60(i) 75.6 (j) $108 (k) 48.375 (l) $445

2. (a) (b) (c) (d)

(e) (f)

3. (a) 66 % (b) 25% (c) 12 % (d) 20%

(e) 5% (f) 83 %

12---

12---

13---

2335------ 7

13------ 5

6---

(a) (b)

20

y

−1−2 x

−2

321 y = −2x + 1

2

21

0

y

−2

−2 x

−3

−1

y = − 2

1

0

8

12

4

4Size, S

8 12

L = S + 8

Len

gth,

L (

inch

es)

13---1

3---

13---

13---

13--- 1

3---

13--- 5

6---

Exercise 2-01

34--- 1

3--- 1

10------ 1

2---

2225------ 3

8---

23--- 1

2---

13---


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

(e) (f)

5. (a) 66% (b) 80% (c) 37.5% (d) 8 %

(e) 14.5% (f) 48%

6.

7. (a) $25.92 (b) $146.88 8. Bing’s

9. (a) 4.5 (b) 7200 (c) 6.3 (d) 0.08(e) 6.9 (f) 6900 (g) 0.0135 (h) 32.1(i) 0.28 (j) 0.04 (k) 2170 (l) 0.002 17

10. 29% 11. $57.60 12. 30%

13. (a) 0.375 (b) 0.42 (c) 0.06(d) 0.7025 (e) 0. (f) 0.8

14. 91% 15.

16. 26 games 17. 32.7%

18. (a) 62 % (b) 70% (c) 3.4%

(d) 20% (e) 41 % (f) 10.5%

19. (a) $53 (b) 10.2% 20. Jason

1. (a) 2.717 (b) 28.303 (c) 0.050(d) 9829.920 (e) 6.325 (f) 3.142

2. (a) 2.72 (b) 28.3 (c) 0.0496(d) 9830 (e) 6.32 (f) 3.14

3. (a) 12.25 (b) 22.33 (c) $154.80(d) $11.25 (e) 0.14 (f) $320.57

4. (a) 2.7 (b) 20 (c) 0.040(d) 750 (e) 0.35 (f) 1900(g) 0.064 (h) 50 000 (i) 0.0039(j) 0.82 (k) 0.0022 (l) 180

5. (a) 3000 (b) 3 (c) 30 000(d) 0.005 (e) 20 (f) 0.2(g) 0.08 (h) 0.3 (i) 300

6. (a) 0.67 (b) 0.0055 (c) 1.3(d) 0.14 (e) 0.087 (f) 790 000(g) 7.7 (h) 7.5 (i) 0.75(j) 0.029 (k) 34 (l) 0.0072

7. 6 420 000 8. 750 000

9. (a) 6370 km (b) 352 000 kg(c) 4190 m (d) 67.1 km/h(e) 14.8 mL (f) 150 000 000 km

1. (a) 0.08 (b) 0.226 (c) 0.3 (d) 0.7

(e) 0.8 (f) 0.85 (g) 0.145 (h) 0.91

(i) 0.0975 (j) 0. (k) 0.9045 (l) 0.42. (a) 6 (b) $9.04 (c) 1.44

(d) $53.34 (e) 169.05 (f) $88(g) 31.2 (h) $10.46 (i) $28.86

3. (a) $53.87 (b) $155.15 (c) $29.57(d) $353.76 (e) $904.75 (f) $75.51

4. $2565 5. 211 people 6. $497.34

7. $437.50 8. $391

9. (a) 4% decrease (b) 4% decrease(c) 16.64% increase (d) 6.5% decrease(e) 9.76% decrease (f) 3.1% decrease

10. 7.4% 11. 68

12. 18 742 544 13. $41.25

14. $54.47 15. $42 208.11

125------ 7

20------ 11

20------ 1

6---

38--- 1

13------

13---

916------

1.

320------

12---

23---

Exercise 2-02

Exercise 2-03

6.

1.

16. 13.5 g 17. $610.60 18. $877.50

19. 6480 children 20. $2193.10

1. (a) 900 (b) $243 (c) $1650(d) $186 (e) $68.75 (f) 400

2. $207 3. 950 students 4. $25

5. 1.8 L 6. 3120 people

7. (a) $235 (b) $21.15

8. $230.71 9. 81 kg

10. (a) $9550 (b) $10 314

11. $145 200 12. $481

13. $42.80 14. 60 questions

15. (a) $234 200 (b) $25 762

16. $456, $114, $171 17. $6000

18. $550 19. 6 677 900 dwellings

20. 146 21. $12 954

1. (a) 4.213 × 107 (b) 1.81 × 10−2 (c) 3.4 × 103

(d) 2 × 104 (e) 3.5 × 10−3 (f) 2 × 10−4

(g) 3.3 × 10−1 (h) 4 × 10−3 (i) 2.3 × 102

(j) 7.23 × 10−5 (k) 6.1 × 108 (l) 8 × 10−8

2. (a) 740 000 (b) 0.312 (c) 1850(d) 0.000 66 (e) 0.002 54 (f) 475 100 000(g) 0.078 (h) 300 (i) 0.054 87(j) 32 160 (k) 0.802 (l) 6020

3. 1.2 × 1010 years 4. 4 500 000 000 years

5. 0.000 000 03 mm 6. 152 600 000 km

7. 1.27 × 104 km 8. 0.000 001 m

9. 9 461 000 000 m 10. 7.8 × 10−7 m

11. 0.000 000 141

1. (a) 4.7 × 10−4 (b) 6.211 × 1012

(c) 3.94 × 109 (d) 2 × 10−5

(e) 7.035 × 10−10 (f) 8.6 × 1016

2. (a) 24 000 000 (b) 0.000 000 03(c) 7510 (d) 0.000 064 2(e) 0.000 000 000 915 (f) 81 620

3. (a) 2.144 × 107 (b) 3.2 × 105

(c) 3.5 × 104 (d) 2.304 × 10−5

(e) 5.31 441 × 1014 (f) 3.76 × 101

(g) 1.26 × 104 (h) 2.3 × 105

4. (a) 3.0 × 104 (b) −3.6 × 10−3

(c) 3.9 × 1012 (d) 3.3 × 10−8

(e) 5.9 × 104 (f) 3.4 × 10−2

(g) 9.2 × 102 (h) 1.2 × 10−4

5. (a) 0.0048 (b) 4 368 000 000(c) 0.000 025 (d) 0.0094(e) 338 560 000 (f) 13 640 000(g) 49 033 000 (h) 1 680 000(i) 0.000 052 (j) 246 200(k) 350 000 (l) 56 250 000

6. (a) 6.81 × 105 (b) 4 × 101

(c) 2.5 × 10−1 (d) 1 × 10−2

(e) 4.216 × 101 (f) 9.3 × 104

(g) 3.1 × 10−1 (h) 8 × 10−3

(i) 7.73 × 104 (j) 4 × 103

Exercise 2-04

Exercise 2-05

Exercise 2-06

ANSWERS 457

1. the column

2. (a) subtracts 4 from the value in B5(b) multiplies the value in B5 by 4(c) divides the value in B5 by the value in B4

3. A label is a word; a value is a number.

4. the column

5. The keyboard doesn’t have keys for × and ÷; × might be confused with the letter x.

6. (a) Benny and Bjorn (b) Maths(c) Bjorn (d) 323, 412, 350, 336(e) 80.75, 82.4, 70, 84 (f) Bjorn(g) 3, 3, 4, 4 (h) 78.75, 88, 81.67, 73.25, 76(i) Maths (j) History(k) row 9: 89, 91, 87, 81, 80; row 10: 61, 86, 73, 59, 70

9. (a) H5, I5, C7, C8, C10 (b) decrease

10. (e) 20 people

3. (a) 168 (b) sleep (c) TV(d) meals and transport (e) job(f) 2 hours (g) 7.1 hours (h) 11.5 hours(i) sleep (j) 6.5%

6. (a) eraser (b) folder (c) pen(d) exercise book (e) 26c

2. $5753.84

3. (a) $5612.71 (b) $2056.75 (c) $7046.78

2. (a) There are more expenses than income.(c) home loan (d) driver’s licence

1. (a) 3850 (b) 0.016 (c) 0.72 (d) 82.3(e) 0.98 (f) 0.341

2. (a) 38.54 (b) $5.28 (c) 49.4 (d) $55

(e) 167 (f) 406

3. (a) 80% (b) 33 % (c) 12.5% (d) 20%

(e) 5% (f) 75%

4. (a) 0.15 (b) 0.119 (c) 0.0875

5. (a) (b) 16 %

6. $33.65 7. $45.10

8. (a) 2100 (b) 65 (c) 0.18(d) 78000 (e) 0.091 (d) 9.8

9. $213 579

10. (a) No (b) $307

11. 12. 43.2%

13. (a) 3.5 × 104 (b) 8.1 × 10−2 (c) 2.9 × 107

14. (a) 890 000 (b) 0.0007 (c) 0.0401

15. $448.35 16. 25%

17. $16 550 18. $748

19. (a) $30.82 (b) $24.50

20. (a) 85 184 000000 (b) 70 000 (c) 3 721 000

21. (a) 9 756 000 0000 (b) 3360 (c) 108

22. (a) 11.24% increase (b) 16% decrease

Exercise 2-07

Exercise 2-08

Exercise 2-09

Exercise 2-10

Chapter assignment

13---

13---

16--- 2

3---

225------

23. (a) value in A3 multiplied by value in B3(b) minimum value of cells from B4 to E4(c) number of values in cells from G3 to G11

24. (a) =B5/B4 (b) =AVERAGE (C3:C8)(c) =E1-G1

25. (a) =SUM(B4:E4)(b) =AVERAGE (B4:E4) or =F5/4(c) =MAX (D2:D5)

Chapter 3

1. (a) 63 mm (b) 436 cm (c) 4 m(d) 0.285 kg (e) 6900 m (f) 58 L(g) 35 mg (h) 6320 mL (i) 2300 kg(j) 5320 g (k) 3.4 t (l) 5.82 kL(m) 0.006 kg (n) 172 800 s (o) 400 000 cm(p) 23 400 s (q) 0.0025 kL (r) 1 × 1010 g(s) 525 600 min (t) 14.6 L

2. 8.56 kL 3. 169 cm

4. 57 500 g 5. 10 km

6. 97 min 7. 59 000 L

8. 4.9 Mt 9. 18 100 m; 1.8 h

10. 1421 steps 11. 833.4 km

12. (a) 2.8 × 108 m (b) 0.46 mm (c) 5.6 L(d) 6.7 × 10−9 Mt (e) 3.62 × 104 t(f) 9.5 × 104 kg (g) 1.32 × 1010 h

13. 1.16 × 10−5 days 14. 135 nautical miles

15. 3.6 × 104 km

1. (a) B (b) B (c) C(d) B (e) C (f) A(g) B (h) C (i) B

2. (a) kg (b) m or cm (c) m(d) km (e) L (f) mg(g) mm (h) L or kL (i) t(j) μm

3. (a) ≈ 3 cm (b) ≈ 30 cm (c) ≈ 200 m(d) ≈ 2 kg (e) ≈ 300 m (f) ≈ 100 L–150 L(g) ≈ 5 g (h) ≈ 30 cm (i) ≈ 5 mL(j) ≈ 0–2 km (varies)

1. (a) 1 m; 4 m (b) 0.1 cm or 1 mm; 1.8 cm(c) 10 km/h; 50 km/h (d) 0.5°C; 38°C(e) 5 m/s; 45 m/s (f) 500 rpm; 7000 rpm

2. The difference between the measured value and the true value, caused by:• faults in measuring device• human error• precision of measuring device too large

3. (a) not look directly at a tape; not start at zero(b) not set properly; tape stretched

4. (a) 0.1 m (b) 1 km (c) 1 min(d) 1 s (e) 1 mL (f) 10 t(g) 1 kg (h) 1 day(i) 1 m (j) 100 s

Exercise 3-01

Exercise 3-02

Exercise 3-03


5. (a) T (b) F (c) F (d) T(e) F (f) F

6. (a) 5.04 mL (b) 0.72 kg (c) 0.25 mL (d) 86.2 cm

7. (a) 32°, 145°, 170°

(b) 64 ° has a precision of °, 103.5° has a precision of 0.1°

Both are ‘more exact’ than the protractor allows.

8. It has a precision of 1 cm, not 1 mm.

9. 44.8 cm 10. 1 cm

11. 38.0 L 12. 150 cm (to nearest cm)

1. (a) (i) 1 mL (ii) 0.5 mL (iii) 24.5 to 25.5 mL(b) (i) 1 mm (ii) 0.5 mm (iii) 5559.5 to 5560.5 mm(c) (i) 0.1 g (ii) 0.05 g (iii) 6.45 to 6.55 g(d) (i) 0.1 s (ii) 0.05 s (iii) 78.05 to 78.15 s(e) (i) 0.1 ha (ii) 0.05 ha (iii) 0.05 to 0.15 ha(f) (i) 1 m (ii) 0.5 m (iii) 23.5 to 24.5 m(g) (i) 1 kg (ii) 0.5 kg (iii) 34.5 to 35.5 kg(h) (i) 1 mL (ii) 0.5 mL (iii) 599.5 to 600.5 mL(i) (i) 0.1 cm (ii) 0.05 cm (iii) 8.55 to 8.65 cm(j) (i) 10 g (ii) 5 g (iii) 495 to 505 g(k) (i) 0.1 t (ii) 0.05 t (iii) 3.55 to 3.65 t(l) (i) 1000 L (ii) 500 L

(iii) 14 999 500 to 15 000 500 L

2. 20.5 cm to 21.5 cm

3. (a) (i) 1 mL (ii) 0.5 mL (iii) 374.5 to 375.5 mL(b) (i) 0.1 t (ii) 0.05 t (iii) 2.25 to 2.35 t(c) (i) 1 km (ii) 0.5 km (iii) 12 682.5 to 12 683.5 km

4. (a) (i) 1 × 10−5 times (ii) 5 × 10−6 times(iii) 1.75 × 10−4 to 1.85 × 10−4 times

(b) (i) 1 × 105 km/s (ii) 5 × 104 km/s

(iii) 2.5 × 105 to 3.5 × 105 km/s

(c) (i) 100 km/h (ii) 50 km/h(iii) 1.0705 × 105 to 1.0715 × 105 km/h

(d) (i) 1 × 1018 t (ii) 5 × 1017 t(iii) 5.9735 × 1021 to 5.9745 × 1021 t

(e) (i) 1 × 107 km (ii) 5 × 106 km

(iii) 3.55 × 108 to 3.65 × 108 km

1. (a) 0.588% (b) 0.2% (c) 0.0196%(d) 0.323% (e) 0.197% (f) 0.0585%(g) 0.0833% (h) 5% (i) 0.37%(j) 3.33% (k) 25% (l) 1.43%(m) 0.676% (n) 0.0735% (o) 0.1%(p) 0.137% (q) 10% (r) 1.11%(s) 0.588% (t) 2.17%

2. (a) 0.15 g (b) 0.15 g (c) 800 g

3. (a) 1 mm; 1 mm (b) 2%; 0.667%Both have the same precision and the same absolute error but 75 mm is more accurate as it has a smaller % error.

4. Both have the same % error of 2% so the same accuracy, though 25 mm has smaller absolute error.

5. (a) 1% (b) 0.5%

6. We don’t know the precision or the absolute error.

1. (a) 50 000 cm2 (b) 250 000 mm2 (c) 7.5 ha(d) 3 200 000 m2 (e) 0.68 m2 (f) 24.95 cm2

(g) 53 450 000 m2 (h) 600 ha(i) 3 490 000 mm2 (j) 5.4 km2

12--- 1

2---

Exercise 3-04

Exercise 3-05

Exercise 3-06

2. 80 160 000 ha or 8.016 × 107 ha

3. 2 ha by 1 ha 4. 1.1 × 1014 ha

5. 4.255 m2 6. 6000 m2

1. (a) 64 m2 (b) 34.9 m2 (c) 314.2 cm2

(d) 4322.5 m2 (e) 24 m2 (f) 40 m2

(g) 375 m2 (h) 4 523 8934 km2 (i) 300 m2

(j) 6 m2 (k) 88.4 m2 (l) 197.9 cm2

(m) 11.0 m2 (n) 42.4 m2

(o) 40.8 m2 (p) 189 m2

2. 113 cm2 3. 100 m × 100 m 4. 42.3 m2

5. 5.8 m2 6. 90 ha 7. $211.30

8. (a) 314.2 cm2 (b) 85.8 cm2

9. 418 mm2 10. 653 mm2

11. 6.9 m 12. 14 827 m2

13. (a) 0.4096 m2 (b) $55.30

14. (a) area is 4 times as big (b) area is 9 times as big(c) 10 times the side of the first square

15. 16 A4 sheets

1. (a) 428 m2 (b) 962 m2 (c) 6195 m2

(d) 3755 m2 (e) 2352 m2

2.

1. Student’s work

2.

Exercise 3-07

Exercise 3-08

(a) 264. 5 m2 (b) 1871 m2

(c) 1214 m2 (d) 1574.5 m2

(e) 1747.5 m2

8

10

5

1816

7

36

1415

84012

12

6

20

28

36

26

18

18

24 5 25

21

15 1218

24

47

25

15

1518

10

22

Exercise 3-09

ANSWERS 459

3.

4. Student’s work.

1.

2.

3.

4. (a) The greater the height of the observer, the more of the top of the solid is seen.

(b) The further away the observer, the longer the solid looks.

5. (a) 2.5 m (b) 1 m (c) 0.5 m

T

TT

TT

T

F F

F

F

FF

SS

SS

S

S

(a) (b) (c)

(d) (e) (f)

Exercise 3-10(a) (b)

(c)

V

(a) (b)

(c) (d)

(e)

V V

V

V

V

6.

1. Student’s work

2. 3.

4.

5. (a) pentagonal pyramid (b)

6. A, the rectangle must be wider. This will not fold into a cylinder.

7. (a) hexagonal prism

8.

(a)

(b)

variations possible

Exercise 3-11

(a) (b)

(c) (d)


10.

11. triangular prism

12.

1. (a) 7 × 106 cm3 (b) 5 × 104 mm3 (c) 5.5 × 108 cm3

(d) 2.4 × 105 mm3 (e) 2 × 10−3 m3 (f) 7.648 × 109

(g) 8.5 × 104 mm3 (h) 6 cm3 (i) 8.5 × 10−3 m3

(j) 0.0045 m3 (k) 4 × 1012 cm3 (l) 5 × 105 cm3

(m) 0.063 m3 (n) 87 m3 (o) 5.4 × 104 cm3

1. (a) prism; 250 cm3 (b) prism; 1.70 m3

(c) prism; 30 800 cm3 (d) prism; 3040 cm3

(e) pyramid; 31 000 mm3 (f) prism; 20.2 m3

(g) pyramid; 150 cm3 (h) pyramid; 6570 cm3

2. 4.93 m3 3. 350 cm3, 1 cm3 = 1 mL

4. 1320 cm3

5. 16.1 m3 or 16 100 L 6. 2450 cm3

7. 4 m3; $104 8. 576 m3

9. 30 000 m3 10. 2 420 000 m3

11. (a) 10.7 m3 (b) 10 700 L

12. 8495 L 13. 1.8 m3

1. (a) 1392 cm2 (b) 1950 cm2

(c) 5400 cm2 (d) 39.36 m2

(e) 10.6 m2 (f) 2225 cm2

(g) 36 153 mm2 (h) 1670 m2

(i) 385 cm2 (j) 810 m2

(k) 564 m2 (l) 337 m2

(m) 223 cm2

2. Ph gives the sum of the faces other than the two A.

(e) alternatives possible

Exercise 3-12

Exercise 3-13

Exercise 3-14

1. (a) 16 965 cm3 (b) 2262 cm2

2. 135 240 m2 3. 249 L

4. (a) 9.776 m3 (b) 20.83 m2

5. (a) 5.9 m3 (b) 36 m2

6. 90.72 m3

7. (a) 9048 cm3 (b) 3242 cm2

8. (a) 11 cm (b) 408 cm2; 406 cm2

9. 9 cm

10. 2.44 × 1010 km2 11. 1.6 L

12. (a) 11.76 m3 (b) $697.48

13. 4188.8 cm3

14. (a) 3.289 m2 (b) 16.98 m2

15. (a) Volume is 8 times as large.(b) Volume would be 27 times as large.

1. (a) 680 mL (b) 8.5 L(c) 22 000 or 2.2 × 104 L (d) 8 m3

(e) 3.5 × 109 mL (f) 3.6 × 106 cm3

(g) 650 mL (h) 5.9 × 106 L(h) 4300 kL (j) 9.5 m3

(k) 7850 m3 (l) 8.5 × 104 mL(m) 9.5 × 1010 L (n) 4.3 × 10−10 m3

(o) 1 × 109 m3

2. (a) 0.864 m3 (b) 864 L

3. (a) 27 cm3 (b) 27 mL

4. (a) 75.4 m3 (b) 75 400 L (c) 75 400 kg

5. (a) 4021 mL (b) 101 mL

6. (a) 8000 m3 (b) 6400 t(c) 0.64 m or 64 cm

1. (a) m or km (b) L (c) km2 or ha

2. (a) 28 500 m (b) 6400 kg (c) 84 cm2

(d) 0.34 L (e) 56 000 m2

(f) 89.4 mL (g) 6.5 × 106 cm3

3.

4. (a) Precision is the smallest ‘mark’ on a measuring device.(b) Accuracy is the ‘exactness’ of a measurement.(c) Error is the difference between the measured value and

the true value.

5. (a) 44 m2 (b) 1040 m2 (c) 228 cm2

6. (a) (i) 1 cm (ii) 0.5 cm (iii) 31.5 and 32.5 (iv) 1.6%(b) (i) 0.1 m (ii) 0.05 m (iii) 43.45 and 43.55 (iv) 0.11%(c) (i) 1 mL (ii) 0.5 mL (iii) 599.5 and 600.5 (iv) 0.08%

Exercise 3-15

Exercise 3-16

Chapter assignment

(a) i

(b) i

ii

ii

ANSWERS 461

7.

8. (a) 11 994 cm3 (b) 210 000 cm3 or 0.21 m3

(c) 411 470 mm3 or 411.47 cm3

9. (a) 8004 mm2 (b) 789.6 cm2 (c) 17 418 cm2

10. 8143 L 11. 1204 cm3

12. (a) (i) 6283 cm3 (ii) 4189 cm3 (iii) 2094 cm3

(b) The cone is the volume of the cylinder and the

sphere volume. The sphere is the cylinder volume.

13. 16.6 cm

14. (a) 27 L (b) 4.2 L

15.

Chapter 4

2. (a) any information to do with roads, road accidents, drivers, vehicles, etc.

(b) any information on car, home, boat, life and other insurance

(c) weather statistics(d) stocks and shares(e) land ownership (past and present)(f) law(g) anything to do with people, habits, products(h) people: immigrants, emigrants(i) imports, exports(j) gambling

4. (a) (i) best tasting food(ii) restuarant customers surveyed

(b) (i) best tasting chocolate(ii) sample of people asked

(c) (i) most pools sold(ii) sales statistics

(d) (i) most-watched programs(ii) TV poll

(d) (i) best-tasting coffee(ii) coffee shop customers surveyed

Advertisers want customers to believe that they should buy/use the product as it is the best there is.

1. (a) electricity, gas, rates, mortgage, insurance, phone, cleaning

(b) (i) $3.20 (ii) $5.60(c) $6000 (d) $400(e) shows proportions of expenses

(a) 1600 m2 (b) 1284 m2

35

13

32

16

24

24

8

20

28

16

10

16

13--- 1

2---

23---

(a) (b)V1 V2V

Exercise 4-01

Exercise 4-02

2. (a) 500 000 CDs(b) January sales, post-Christmas, holidays(c) November (d) March (e) Jan. to Feb.(f) 1 750 000 CDs (g) 5.7%

(h)

3. (a) sector graph showing primary voting intentions; table showing two-party preferences (breakdown by gender and age); map of Kogarah district in relation to neighbouring districts

(b) Labor (c) Coalition(d) Labor (e) 44 837 votes(f) Not necessarily; 44% of the people polled said they

intended to vote for ALP but we don’t know the actual number who took part in the poll or whether these people will vote ALP in the actual election.

4. (a) Bruce Willis’s films, budget for films, money made at US cinemas, Bruce’s wage

(b) about $A30 million budget, $A85 million box office(c) Yes, continuous movie roles over many years.(d) Die Hard II(e) 30% of the film’s budget on one actor does not seem

justified, but it was the third movie in a series so without Bruce the movie might flop.

(f) Blind Date

5. (a) UAC (b) uni preferences for 1995(c) 13.7% fewer students want to study at Western Sydney

in 1995 than in 1994(d) 23.4% less students want to go there in 1995(e) only uni where more want to go in 1995 than in 1994(f) shows results on a mortar board (graduate’s hat); shows

both column graph and percentages

6. (a) no; becoming overweight.(b) 18 to 27 kg/m2 (c) no; height(d) Increase his weight to a healthy level.(e) Keep at her healthy level.(f) 17 to 27 kg/m2

7. (a) November (b) February

(c) (i) 9 mm (ii) 14 mm (d) (i) 5 days (ii) 5 days(e) September; least rain.(f) shows number of rainy days each month.(g) a bit hard to read with two scales and two different

graphs

8. (a) about 4200 t(b) 1993–95(c) 1983, 1985, 1986, 1988, 1990(d) 1 500 000 kg (e) scale too small

9. (a) Both spend the same; sector angle is 30° for each, circle size is unimportant

(b) 8 % (c) Kara $54.17; Shelley $75

(d) divided bar graph

Labour35%

Ingredients25%

O’heads20%

Profit15% A

5%

(f)

100 mm

0

200

300

100

Oct Nov DecMonth

Jan Feb Mar

400

500

No.

CD

s so

ld (

× 10

00)

13---


10. (a) about 35 000 databases (b) 14 million records(c) January to February 1998, March to April 1998(d) February to March 1998, April to June 1998(e) about 400 000 databases (f) about 20 million hits(g) very suitable(h) yes; both graphs have shown steady increases so assume

usage will increase (with some peaks and troughs).

1. A categorical variable yields data that is a category, e.g. brand of car owned. A quantitative variable yields data that is numerical, e.g. number of children in a family.

2. (a) C (b) N (c) C (d) N (e) N(f) C (g) C (h) N (i) N (j) N

3. (a) C (b) C (c) D (d) D (e) C(f) C (g) D (h) C (i) D (j) C

2. (a) Sy (b) St (c) Sy (d) St (e) Sy(f) Sy, St (g) St (h) St

3. (a) Sy (b) No (c) R (d) St (e) R, Sy(f) Sy, St (g) R, St (h) No (i) R (j) R(k) St (l) Sy (m) Sy

4. random, stratified

5. × 150 ≈ 67 drivers; 39 passengers; 19 pedestrians;

17 motorbikers; 8 cyclists

1. Sample too small; sample is selected for convenience (e.g. close to home, all objects in one area); sample selected from one section of a population (e.g. city dwellers, males, over 50s).

2. (a) Use a systematic sample (e.g. choose 1 person every 60th page as there are about 6000 pages).

(b) Choose first 50 and last 50 people in the book; choose all ‘Smiths’.

3. Sample size is too small; only students in Chicago surveyed.

4. (e) is best. Other methods either involve bias or include people who are not library users.

5. 79 83 55 89 71 60 52 85 72 8990 74 96 60 52 80 79 81 57 68

6. 18 750 black fish

7. 29 167 trout

8. Using all digits 4, 4, 5, 5, 3, 5, … no aged 4 = = 27%

1. (a) 85 302 confinements(b) 88 133 births (c) 1.3%

Exercise 4-03

Exercise 4-04

975821 935----------------

Exercise 4-05

830------

Exercise 4-07

(d)

Singleton (842 mm)

Twins (21 mm)Triplets (0.7 mm)Quads (0.04 mm)

864 mm

NSW births, 1996

(f) It is too difficult to show small segments for triplets and quads.

2. (a) a disease caused by lack of vitamin B1 due to a bad diet.

(c) change in diet

(d) 40.5% (e) =

3. (a)

(b) second clinic; better hygiene, more doctors or nurses(c) (i) 1842 (ii) 1845(d)

4. (a)

(c) all people 18–44 years as this is the largest percentage of smokers

(e)

Singleton

Twins, triplets, quads

355°

(b)

Dea

ths

from

ber

iber

i

0

1000

1500

500

1880 1882Year

1884 1886 1888

2000

7185638------------ 359

2819------------

Dea

ths

of m

othe

rs

0

200

300

100

1841 1842 1843Year

1844 1845 1846

400

500

First clinic

Second clinic600

Bir

ths

0

3000

2000

1941 1942 1943Year

1944 1945 1946

4000First clinic

Second clinic

(b)

Never smoked

Ex-smoker

Smoker138°

181°

Never smokedEx-smokerSmoker

100 mm

41°

20.37% 22.5% 57.1%

Smoking by females, 1995

ANSWERS 463

5. (a)

(b)

(c) (i) 65.8% (ii) 42%

6. (a) 1993, 1996, 1997 (b) $1 748 300 000(c) $1 979 100 000(d)

7. (a) 12.9% (b)

(c)

8. (a) 1 458 000 people(b) 23.4%(c)

(d) sample; not whole population of Sydney(e) no; sample is large enough but includes only Sydney

viewers

9. (a)

(b) Amount of cannabis is too large compared with the other amounts.

(c) 43.3 kg (d) cannabis; 45 483%

Ave

rage

dai

ly in

take

(m

L)

20

40

18–44 45–65Age (years)

�65

60

Consume Do not consume

Female alcohol consumption, 1995

100 mm

alcohol54.6% 45.4%

alcohol

Val

ue (

A$m

)

0

350

250

1993 1994 1995Year

1996 1997

450

Exports

Imports500

400

300

5193------

ChinaMiddle

20 mm 35 mm

93 mm

East Indi

a

Afg

hani

stan

Tur

key

Iraq

Oth

er

7 10 3 12 6 mm

Immigrants to Sydney

Channel

49 mm 34 mm

146 mm

9

32 mm 31 mm

Channel 2

Channel 7

Channel 10

TV news watching

Am

ount

(kg

)

0

40

50

30

Cannabis CocaineDrug type

Heroin Ecstasy

60

70

10. (a)

(b)

(c) Either graph; sector graph is more visually appealing to some but bar graph is easier to draw.

1. (a) sales figures over a number of months(b) New company director was responsible for the fall in

sales.(c) scale on each axis(c) no; because we don’t know the time or amount of sales

2. (a) Second diagram is actually 4 times the area of the first and should be twice the area.

(b)

3. (a) Price of oil doubled.(b) Second barrel is actually 8 times the volume of the first

since both base diameter and height have been doubled.(c)

Only the height has been doubled.(Note: Doubling the base diameter makes the second barrel 4 times the volume.)

4. (a) Small cars are the best buy.

(b)

(c) The lines look flatter in the second graph and don’t give the first graph’s impression of a steep rise in small car sales along with a drop in big car sales.

storage

Warehouse/

63%

Hi-tech14%Transport/

9%

Manufacturing14%

50°

32°50°

227°

office

Man

ufac

t.

Warehouse/

63 mm 14

100 mm

14 mm9

office

Tra

nspo

rt

Hi-

tech

Exercise 4-08

$400

$800

$50

$25

THE BIG AND SMALL OF IT

40%

35%

30%

25%

1995 1996 1997 1998 1999

SMALLCARSALES

20%

15%

10%

5%

BIG CARSALES


5. (a) no, unless you consider 1.6% a leap(b)

(c) The graph drawn this way does not mislead the viewer but also does not have as much impact as the first, which is designed to show a ‘leap’.

1. (a)

(b) There are two peaks (around ages 25 and 75).(c) The males only had one peak (around age 25) and the

females had 2; the males had a much higher number of deaths around 25 years.

(b)

(c) Most employees are young.

3. (a) 43 students(b) 6 students

(c) 16.3%

(d) no; these are included in the ‘more than 30 calls’ column; could be any number from 0 to 6

2. (a) Age group Frequency

15–1920–2425–2930–3435–3940–4445–49

39309

10444

Total 100

10-year bonds

December 11 June 11

YIELD %

7.006.00

5.00

4.00

3.00

2.00

1.00

0.00

Exercise 4-09

Fem

ale

deat

hs

0

300

100

0 10 20Age (years)

30 40 50

600

400

500

200

60 70 80 90

Freq

uenc

y

0

20

30

10

15 20Age (years)

30 45 50

40

25 35 40 55

(b)

(c) Program seems effective as most men lost some weight.

(d) $2350

(b)

6. (a) discrete

(c)

Note: Discrete data is treated as continuous when using classes.

4. (a) Class Frequency

0–�22–�44–� 66–� 88–�10

10–� 1212–�14

510106432

Total 40

5. (a) Age (years) Frequency

56789

101112

73658542

Total 40

(b) No. of words Frequency

0–910–1920–29

101610

Total 36

Freq

uenc

y

0

4

6

2

2Weight lost (kg)

6 12 14

8

4 8 10

10

Freq

uenc

y

0

4

6

2

5 6Age (years)

8 11 12

8

7 9 10

No.

of

sent

ence

s

0

10

15

5

0 10No. of words

30

20

20

ANSWERS 465

(b)

(c) yes, as about half the eggs were less than 60 g

8. (a) 6 new models

(c)

1. (a)

(b) 0 and 18 hours(c) Cluster around 6– 9; gap at 1–2 and 11–17 hours.

2. (a) 10 students(b) Yes; 12 because it is away from the cluster on its own.

3. (a)

(b) Team is not consistent.

4. (a)

7. (a) Mass (g) Frequency

565758596061626364

27

11675406

Total 48

(b) Height (cm) Frequency

155–<160160–<165165–<170170–<175175–<180180–<185185–<190

15

1086

108

Total 48

Freq

uenc

y

0

4

6

2

56 58Mass of egg (g)

62

8

60 64

10

12

Freq

uenc

y

0

4

6

2

155 160Height (cm)

170 185 190

8

165 175 180

10

12

Exercise 4-10

0 2 4 6 8 10 12 14 16 18 Hours

0 1 2 3 4 5 6 7 Goals

0 2 4 6 8 10 12 14 16 Hours

(b) One person spent significantly more hours than others (15 hours); others were fairly evenly spreadover 0–9 hours.

5. (a) 34 students(b) 26 students(c) They were quite good spellers or the words were easy.

6. (a) Machine B around 8.00–8.01 cm.(b) 12 pins (Machine A) and 2 pins (Machine B)(c) Machine B is more accurate as all but 2 pins are around

the correct diameter.

4. (a) 48 skiers (b) 90 seconds(c) 15 racers

(b) 10 Patients(c) The patient is possibly dead.(d) 4 fit patients

(b) 7 students (c) 43 %

(d) 187 s

1. (a) Stem Leaf

45678

3 5 90 2 7 81 2 4 5 7 80 2 3 92 4 9

2. (a) Stem Leaf

6 *7 *8 *9 *

3 4 5 5 60 2 30 1 5 5 7 82 3 7 9

3. (a) Stem Leaf

23456789

1011

84 8 17 3 23 9 1 76 8 32 8 9 94 2 1 33 43 4 00 7 2

5. (a) Stem Leaf

056789

02 5 6 80 0 3 3 4 4 4 5 8 8 9 92 2 2 4 4 6 6 8 90 1 1 3 3 4 4 5 90 0 3 4 7

6. (a) Stem Leaf

1112131415161718

6 80 1 1 41 90 3 3 5 6 6 6 70 4 4 6 6 73 5 82 4 71 7

Exercise 4-11

(b) 20 matches(c) 89(d) 43

(b) 18 students(c) 99, 63

(b) 13 %

(c) more people, coldweather

13---

13---


(b) 6% (c) $975 000(d) easier to read in an ordered display

(b) 28 (c) 19

1. (a)

(b)

2. (a)

7. (a) Stem Leaf

123456789

02 18 8504 10 17 17 23 26 35 37 74 76 7717 26 42 54 66 75 85 85 9853 62 65 73 75 7610 2414 29 32 34 35 35 5452 63 8512 23 46 72 9303 38 65 75

8. (a) Stem Leaf

1 *2 *3 *4 *5 *6 *7 *8 *9 *

93 9521 28 61 68 68 75 88 9618 36 38 52 52 75 8627 48 71 78 8326 27 32 43 54 83 9212 38 45 84 93 94 9528 36 68 74 75 83 8635 37 56 9703 26 46

Exercise 4-12

7 am9 am

11 am

1 pm

3 pm

5 pm7 pm

9 pm

11 pm

1 am

3 am

5 am42

40

38

36

34

Miss Loh’s temperature chart (°C)

Tem

pera

ture

(°C

)

0

3738

36

7 am

11am

Time

7 pm

39

3 pm

3 am

404142

11 p

m

Miss Loh’s temperature chart (°C)

7 am

JanFeb

Mar

Apr

May

JunJul

Aug

Sep

Oct

Nov

Dec1000

500

Bill’s sales in $Ben’s sales in $

0

Bill and Ben

(b)

4.

3. (a) N; D (b) Ca (c) N; Co(d) N; Co (e) N; D (f) Ca

4. (a) 11 869 (b) prostate (c) 589(d) 10% (e) 4.6%

3. Month Jan Feb Mar Apr May Jun

Broome (°C) 19 18 20 17 14 11

Tumut (°C) 18 17 16 8 5 2

Month Jul Aug Sep Oct Nov Dec

Broome (°C) 9 8 11 13 16 18

Tumut (°C) 0 1 6 7 15 17

5. (a) Stem Leaf

89

1011121314151617181920

0 2 4 63 4 5 8600 4 4 8 936 83 80 703 5 50 4 85

6. (a) Weight (kg) Frequency

50–5960–6970–7980–8990–99

100–109

4127836

Total 40

Sale

s ($

)

0

400

200

Jan Mar MayMonth

Jul Sep Nov

1200Bill and Ben Bill

Ben

600

800

1000

6 am

10 am

2 pm

6 pm

10 pm

2 am

37.5

Miss Shand’s temperature chart (°C)

38

37

36

36.5

Chapter assignment

(b) 8 days(c) 11 days

ANSWERS 467

(b)

7. (a) Percentages of males, females in different types of schools continuing on to Year 11.

(b) Australian Bureau of Statistics(c) census, Department of Education(d) Males in government schools had lowest retention rate.

Males in non-government schools had a higher retention rate than females in government schools.

(e) Females had higher retention rates than males in same type of school. Females in non-government schools had the highest retention rate.

8. (a)

(b) No; sample is too small.

9. Use a systematic sampling process; for example choose any bottle then test each 10th bottle on the production line.

10. • Capture a large quantity (males and females) tag and release.

• Recapture a fairly large quantity and find percentage of tagged males and females.

• =

11. (a) increased Earth’s temperature caused by pollution in atmosphere

(b)

(b)

(c) Females have a much higher incidence of fraud while men have a much higher incidence of sex offences.

12. (a) Offence H A S R B F O D

Male (%) 10 13 14 13 14 4 7 7

Female (%) 9 10 2 10 11 17 10 11

Freq

uenc

y

0

4

6

2

50 60Weight (kg)

80 110 120

8

70 90 100

10

12N

umbe

r (%

)

0

40

10

15–1

9

20–2

4

25–2

9

Age (years)

30–3

4

35–3

9

40–4

4

60Males

Females

20

30

50

50+

45–4

9

Male populationTagged males

--------------------------------------- Recaptured malesRecaptured tagged males------------------------------------------------------------

CO2

100 mm

49% NO

6%

CFCs

14%

CH4

18%

Others

13%

Freq

uenc

y

0

10

15

5

H AOffence

R O D

20

S B F

FemalesMales

13. (a) real data on a number of accidents, crimes(b) did not consider less cars, cheaper houses, smaller

population than some other states

14. (a) Three-quarters of those surveyed had no pimples after using the cream.

(b) unknown; could be only 4 people or 4000.(c) This is a ‘miracle’ cream for getting rid of pimples.

15. (a)

(b) 6 children

16. (a)

(b) column graph

17. (a) 30(b)

18. (a) different scales on the vertical axis(b) the graph exaggerates the differences in popularity of

brand names

19. (a) percentage of radio listeners in the second week of May 1999 who listened to specific radio stations in Sydney.

(b) A. C. Neilsen (c) 2UE (d) 19.4%(e) 3 stations (f) 18.1%(g) too many other radio stations with small percentages

20. (b) 100 students(c) Choose percentage of boys and girls in sample to equal

the percentage of boys and girls in the population.

21. spreadsheet to construct graphs, charts; use graphics calculator to plot graphs; Internet to find information

Practice Paper One1. D 2. D 3. C 4. A 5. B

6. B 7. C 8. A 9. B 10. D

11. (a) h = −95 (b) 800 deer (c) 7.88%

(d) (i)

(ii) 9562.5 m2

0 1 2 3 4 5 6 7 8 9 Age

JanFeb

Mar

Apr

May

JunJul

Aug

Sep

Oct

Nov

Dec10 000

5000

0

Scaffolding earnings ($)

Freq

uenc

y

0

8

10

4

10 20Class

40

12

30 50

16

60

A

R

K

P55

55

30

25

50


12. (a) A sample in which the proportions of items accurately represent the proportions of items in the population, e.g. if 21% of Australians are from non-English-speaking backgrounds (NESB), then a stratified sample of Australians should have 21% of its subjects from NESB.

(b) (i) 16, 17 or 18 minutes(ii) 19 (iii) 21.1% (iv) 2 minutes

(c) (i) Gradient is − , y-intercept is 4(ii)

13. (a) (i) 1634 cm2 (ii) 5.0 L (b) =E2*5−8(c) (i) about 900 (ii) 1999 (iii) 1999

(iv) increasing rapidly over the 4 years (also more rapidly than paper); increasing in a linear pattern

Chapter 5

1. (a) 1 : 3 (b) 2 : 1 : 5 (c) 1 : 1

(d) (e) (f) 4 : 12 : 3

(g) 10 : 1 (h) 1 : 2 (i) 6 : 5

2. (a) 1 : 8 (b) 3 : 28 (c) 1 : 500(d) 3 : 20 (e) 84 : 19 (f) 5 : 2(g) 1 : 5 (h) 2 : 3 : 52 (i) 1 : 10(j) 200 : 1

3. (a) 1 : 4 (b) different units

4. (a) 1 : 10 (b) 1 : 9 (c) 10 : 9

5. 10 : 2 : 1

6. (a) 1 : 40 (b) 1 : 0.6 (c) 1 : 6 (d) 1 : 3

7. (a) 1. : 1 or : 1 (b) 0.25 : 1 or : 1

(c) 4 : 1 (d) 3 : 1

8. (a) 2 : 3 (b) 1 : 6 (c) 3 : 1

9. male 1 : 4.5, female 1 : 8. or 1 : 8.

10. D

1. (a) 15 cm, 45 cm (b) 135 cm

2. (a) 529 boys (b) 621 girls

3. (a) 400 mL (b) 3.9 L

4. 11.25 m 5. carbon 533 g, hydrogen 978 g, oxygen 489 g

6. 80 teachers 7. Heath $33 500, Joy $20100

8. petrol 4.5 L, oil 3 L 9. 13 rams

10. $105 000 11. Trent $1500, Keiran $900

12. 15 losses 13. 3470 books

14. (a) 1 : 125 lobsters (b) 1.25 × 106 lobsters

15. (a) copha 400 g, coconut 400 g, rice bubbles 1 kg, cocoa 200 g

(b) copha 2 kg, coconut 2 kg, rice bubbles 5 kg, cocoa 1 kg

16. (a) 12 shovels (b) 1333 kg

17. (a) 5 : 10 : 8(b) copha 583 g, coconut 1167 g, sugar 933 g

12---

y

x−2

6

4

2 4−4 −2

2

6 8

Exercise 5-01

75--- 1

4---

3. 4

3--- 1

4---

23--- 6

.

Exercise 5-02

18. (a) 550 : 7 (b) 53 : 168 : 24

19. (a) 38 250 males (b) 5 : 4 (c) 1600 females

20. (a) 1 : 3 : 5 (b) 2 : 5 : 8 (c) 1 : 2 : 4(d) 17 animals

1. (a) $3125, $1875 (b) 325 kg, 50 kg(c) 1.2 × 106 L, 1.8 × 106 L (d) 44 444 m2, 55 556 m2

(e) 13 462 kg, 11 538 kg (f) cup, 2 cups

2. (a) $10 080 (b) $15 120

3. $75 000, $50 000, $50 000, $25 000

4. oil 400 mL, petrol 19.6 L

5. cement 50 kg, sand 200 kg, aggregate 300 kg

6. (a) fruit juice 2400 mL, lemonade 2400 mL, ginger ale 1200 mL

(b) 6000 cm3

7. $37 500 8. 200 mL

9. (a) 6 : 1 : 19 (b) 808 g (c) 520 g (d) 365 g

10. 842 mL 11. 470 girls

12. copper 318 kg, nickel 182 kg

13. (a) 16 : 13 : 21 (b) $5281.25, $8531.25(c) $20 312.50

14. (a) N: 444 kg, K: 444 kg, P: 111 kg (makes 999 kg fertiliser)(b) Make 1008 kg, then remove 8 kg.

(1008 kg is first amount >1 t divisible by 9.)

1. scale drawings

2. (a) (b) 3 (c)

3. (a)

(b)

(c)

Exercise 5-03

12---

Exercise 5-04

14--- 1

2---

O

O

O

ANSWERS 469

1. (a) E → F, or F → E, 2 (b) A → B, or B → A, 1.4

(c) R → T, or T → R, (d) A, B, T, 10:6:5

(e) G → H, or H → G, 2

2. (a) 1.3, x = 4.42 (b) ; x = 14, y = 3, z = 5

(c) 1; x = 8, y = 4, z = 3 (d) ; x = 11

(e) 1.5; α = 120°, θ = 30°, x = 6, y = 8, z = 9

3. (a) 1.5 (b) Yes; matching sides in same ratio. (c) 9:4

1. 18.7 m 2. 1.9 m 3. 18.3 m

4. 4.9 m 5. 15.6 m

6. (a) Sun is lower. (b) 3.75 m

7. 5.76 m 8. 13.125 m 9. 1.16 m

10. 93.75 m 11. 4.7 m 12. 13.7 m

1. (a) 1 cm : 1 km = 1 : 100 000 (b) 1 : 5(c) 8 cm : 10 km = 1 : 1250 (d) 1 : 10(e) 250 : 1

2. (a) 1 cm : 40 km = 1 : 4 000 000(b) 84 km (c) 244 km (d) 216 km(e) 120 km (f) Mittagong(g) Katoomba and Penrith; Mittagong and Wollongong

3. (a) 4 m (b) 66 cm (c) 270 m (d) 5 mm

4. (a) Actual house is 100 times larger than the drawing.(b) 1.8 m (c) (i) 5.8 m (ii) 1.2 m(d) (i) 3.2 m (ii) 5.6 m

5. (a) 20 km (b) 13.2 km (c) 11.6 km

6. (b) 55 m (c) 92 m

7. (b) 30 m (c) 2.7 m (d) 22.5 m

8. (a) 50 m (b) 1000 m (c) 1250 m

9. 27.5 mm 10. (c) 8.41 m2 (d) 12 L

1. drawings

2. (b) skillion (c) 2 m (d) 6 m (e) 36 m2

3. (b) gable (c) 6 m (d) 8 m (e) 48 m2

4. (b) 80 m2 (c) 880 m3

5. (a) 2.0 m (b) 2.6 m (c) 164 m2

(d) Number of windows optional

1. (a) toilet (water closet) (b) 9 windows(c) G.L., F.L., C.L. (d) concrete support for piers(e) south (f) hip(g) dotted lines (h) cross-section from A to A on plan

2. (a) 42 m2 (b) skillion (c) 10°(d) No, diagrams are similar.(e) 8.8 m2 (f) 4.4 m × 5 m (g) 1.0 m each(h) 2.4 m (i) 3.8 m

3. (a) skillion (b) 2° (c) west(d) 100 mm (e) 2150 mm (f) 1200 mm


7---

32--- 2

3---

12---

12---

53--- 2

3---

Exercise 5-06

Exercise 5-07

Exercise 5-08

Exercise 5-09

(g) 21 m2 (h) north-east corner(i) 15 piers (j) 1 m3

4. (a) 6 or 7 steps(b) (i) (ii) (iii)

(iv) (v) (vi)

(vii) (viii)

(c) 15.5 m2 (d) 168 tiles (6 rows of 28)(e) 11.3 m laid front to back costs $1751.50; 10.7 m laid

side to side costs $1658.50.

5. (a) 1 : 100 (b) 13.5 m (c) 12 windows(d) 2 doors (e) hip(f)

(g) 20° (h) 5.7 m × 2.7 m(i) 8 m2 (to nearest m2)(j) 2400 mm (k) rectangle(l) 60 tiles (9.6 m2) laid costs $510 + $96 = $606.(m) $1300 (n) 4° (o) 5 supports

6. (a) 104 m2 (b) 3.6 m × 3.6 m(c) (i) 3.6 m (door) (ii) 10.8 m2

(d) 17 m2 (e) $63 180(f) (i) 14 tiles (ii) 14 tiles (iii) 196 tiles

7. (a) 4.5 m (b) 1.8 m(c)

(d)

(e) 5 m2 (f) 45 m2 (g) 200 boards(h) 192 × 3.2 m × $2.30 = $1472

(i) 128 m2 (j) × 100% = 70%

1. (a) 1 : 7 (b) 1 : 10 (c) 8 : 3 : 24 (d) 27 : 16

2. (a) 20 years (b) $150

3. (a) 160 mL (b) 560 mL

4. (a) 3 : 4 (b) Sylvia $8000, Shannon $6000

5. 20 cm × 15 cm 6. 16.4 m

7. (a) 500 g strawberries, 190 g castor sugar, 15 egg whites(b) 150 g strawberries, 60 g castor sugar, 5 egg whites(c) need to ‘round’ some quantities

8. (a) 8 lengths (c) 1 : 10 000

HWS

Linen M/OWO

North elevation

560800---------

Chapter assignment


9. (a) 1 : 200 (b) 35 m2

(c) 2.56 m2 (d) 63 m2

10. (a) y = 6.75 (b) θ = 75°, α = 67°, β = 75°

(c) x = 9, y = 4 (d) x = 11 , y = 9.6 (e) x = 20

11. (a) 110 kg (b) 72.5 g

12. $3555.56, $7111.11, $5333.33

13. (a) 15 (b) 300 mm

14. 12.86 m 15. enlargement

16. (a) 9 : 10 (b) 1 : 9 (c) 11 %

17. 4 cups 18. 17 m2

Chapter 6

1. $910.85 2. $541.80 3. $738.68

4. (a) $32 248.58 (b) $620.17 (c) $16.32

5. $10.77 6. $1034.52 7. $481.44

8. (a) $20 456.80 (b) $1704.73

9. $395.01

10. (a) $3228.78 (b) $7019.92

11. $606.30

12. (a) $2277.08 (b) $1047.34 (c) $104.73

13. 35 normal hours, 20 overtime hours, $789.10

14. (a) $31.14 (b) $2615.75 (c) $5687.08

15. (a) $617.27 (b) $704.56

16. $562.56

17. (a) $163.21 (b) $816.05 (c) $3536.22

18. C 19. $598.90

20. (a) $11.32 (b) $577.32 (c) $30 020.64

21. $733.95 22. $8.40

1. $102.30

2. (a) 168 envelopes (b) $20.16

3. $27.90

4. (a) $4085 (b) $6800

5. $7240 6. $9.10

7. $203.98 8. $1353.24

9. (a) $29 880 000 (b) $4 332 600

10. $1073.70

11. (a) $146.19 (b) 821 brochures

12. $88.56 13. $784 14. $58 417.45

15. $277.50 16. $438 17. 8.8%

18. 2520 newspapers 19. $807.65

20. (a) $215 730.00 (b) $23 730.30

21. (a) $64.98 (b) 97 gifts

22. (a) $532 (b) 24 days

23. 60 tastings 24. $530.85

25. (a) $825 (b) $780

26. $461.38

1. (a) e.g. roof tiler (b) e.g. stockman(c) e.g. submarine sailor (d) e.g. steel-worker(e) e.g. Antarctic scientist (f) e.g. window cleaner(g) e.g. construction worker (h) e.g. coal miner

2. $835.50 3. $634.45 4. $671.52

23---

19---

Exercise 6-01

Exercise 6-02

Exercise 6-03

5. (a) $1064.63 (b) $55 360.50

6. $2049.22 7. $550.44 8. $663

9. (a) $668.16 (b) $367.50

10. $714.88

11. (a) $267.40 (b) $350.20 (c) $293.60 (d) $176(e) more allowance for single people, living away, with

children(f) less, because partners can combine incomes(g) more, because older youths have more expenses

12. $30.81 13. $459.60 14. $475.65

15. (a) $325.70 (b) $3819.40(c) less, because partners can combine incomes

16. $2053.70 17. $1527.45

18. (a) $326.80(b) Growing children have growing needs (e.g. food,

clothes), but older children stop growing and have more responsibilities/jobs.

(c) $494.90

19. $231.04 20. $383.40 21. $2273.73

22. (a) Age Pension, $361.40(b) Carer Allowance, $75.60(c) Austudy, $267.40(d) Sickness Allowance, $293.80(e) Disability Support Pension, $301.60(f) Austudy, $350.20

1. $498.86

2. (a) $615.10 (b) $172.23 (c) $326

3. (a) $129.39 (b) $37.64 (c) $188.97 (d) $281.53

4. (a) $616.00 (b) $61.60 (c) $414.18

5. (a) $1159.49 (b) $689.49 (c) 26.5%

6. (a) $521.82 (b) $130.46 (c) $373.96

7. (a) $100.09 (b) 23.00% (c) 6.00%

8. (a) $4022.92, $2590.49 (b) 26.02% (c) 64.39%

9. (a) $426.80 (b) $102.43, $29.88(c) $144.35

10. (a) $384.25 (b) 61%

11. (a) $821 (b) $265.29 (c) 32.31%

12. (a) pay $401.80, $68.88, $22.96, gross wage $493.64, total deductions $178.01, net wage $315.63, tax $123.41

(b) total deductions $142.20, gross pay $1802.45, tax $558.76, net pay $1101.49

1. (a) quarterly (b) 12 May 2000 (c) 21 days(d) water and sewerage services, $90.10(e) 1 April to 30 June 2000 (3 months)(f) kilolitres(g) No. Last bill covered summer period, when more water

was used.(h) similar season(j) 10 February 2000, 681 kL; 8 May 2000, 699 kL(k) 80 c/kL (m) $32

2. (a) kWh (b) bimonthly (c) 14.5 kWh(d) July/August, middle of winter, more heating/lighting(e) 813 kWh (f) 56 days(g) Commonwealth Bank, post office, Target(h) $5 off next bill. It’s more convenient for company; they

don’t have to chase up money owing; automated processing

Exercise 6-04

Exercise 6-05

ANSWERS 471

(i) 21 April 2002, 72 822 kWh(j) $9.00 (k) 3 May 2002(l) Pensioners are needy; life support machines use a lot of

electricity.(m) 13.49c for the first 185 kWh, 10.25c for the remainder,

c/kWh

3. (a) $93.70, more (b) 7 April 2003 (c) 21 days(d) 7 ways (f) $50.43 (g) yes(h) $52.58 (i) 25c (j) yes

4. (a) There are no usage charges because nothing is used.(b) 31 Aug 2004 (c) $117.29 (d) $465.29(e) Yearly amount is divided by 4, with 3 instalments

showing whole dollars only and the first instalment containing the remainder.

(f) quarterly (g) $29 310(h) 0.71% (i) $187.72(j) $3.60 or $3.61 (k) Interest is charged.

5. (a) megajoules (MJ) (b) quarterly (c) $56.35(d) 22 April to 23 July 2001, 92 days(e) 200 units (f) 8025 MJ (g) 87 MJ(h) 22 April 2001, 23 July 2001 (i) 3176, 3376 units(j) 1.0274 c/MJ, 1.0595 c/MJ; price increased on

1 July 2001.(k) supply fee $22.80 (l) gas usage $83.06

2. (a) $68.40 (b) yes

4. (a) $364.60 (b) $152.60

1. (a) $8533.60 (b) $1424.26 (c) $413.10(d) $26 986.90 (e) $13 568.62 (f) nil

2. (a) $607.68 (b) $197.80 (c) nil(d) $1264.05 (e) $828.17 (f) nil

3. (a) $40 451 (b) $8515.30, $606.77(c) $780.81 refund

4. (a) $46 124 (b) $10 217.20, $691.86(c) $10 909.06 (d) 23.7%

5. (a) $27 739.40 (b) $7212.40(c) $27 673 (d) $4681.90, $415.10(e) $2115.40 refund

6. (a) $22 728.70 (b) $1128.15 (c) $23 856.85(d) 32% (e) $21 812.64 (f) $2044.21 debt

7. (a) $24 772.80 (b) $27 336(c) $4580.80, $410.04 (d) $4990.84(e) 18.26%

8. (a) $11 155 (b) $52 796, $12 554.32(c) $1399.32 (d) 39.5%(e) She moved into a higher tax bracket.

9. (a) $36 316.80 (b) $36 474.00(c) $7322.20, $547.11, $7869.31(d) $7833.28 (e) $36.03 debt

10. A. 9183 B. 5189.60 C. 18 480D. 75 E. 27 738 F. 241G. 95 H. 54 I. 390J. 27 348 K. 20 001–50 000L. 4584.40 M. 410.22 N. 4994.62O. 5189.60 P. 4994.62 Q. 194.98

1. $2.57 2. $18.15 3. 130.88 francs

4. 90.75 Euro 5. £52 6. $5.50

Exercise 6-06

Exercise 6-07

Exercise 6-08

7. 46.50 rand 8. 17.5%

9. (a) 1852 drachma (b) 11.5%

10. $30.80, $34.65

11. (a) 14 290 won (b) 10%

12. (a) 58 098 lira (b) 19%

13. 9% 14. 16%

15. 238.97 Euro 16. $118.08

17. 8% 18. $31.13

19. 4125.45 baht 20. 12%

21. 632.82 francs 22. $34.29, $36.69

23. $472.73 24. 21%

25. $60.92

1. (a) $3.10 (b) $9 (c) $11.25(d) $2 (e) $5.80 (f) $8.50

2. (a) $56 (b) $24 (c) $13(d) $90 (e) $32 (f) $76

3. line through (40, 2.8), (100, 7), (150, 10.5)

4. line through (5, 1.05), (25, 5.25), (50, 10.5)

5. (a) $6000 (b) $1900 (c) $13 400(d) $500 (e) $0 (f) $7100

6. (a) $47 000 (b) $35 500 (c) $20 000(d) $26 500 (e) $56 500 (f) $15 500

7. (a) (i) $11 952 (ii) $9880 (b) 17.3%(c) Piecewise linear graph through (0, 0), (5400, 0),

(20700, 3060), (38000, 8942), (50000, 14102), (60000, 18802)

1. B 2. $177.84

3. (a) $1695.09 (b) $7370.83

4. (a) $468.86 (b) $290.44

5. $547.30 6. $398.13

7. (a) $1040.15 (b) $728.10

8. $358.30

9. (a) $147.27, $64.03 (b) $407.37 (c) 63.6%

10. $12 461.53 11. $747.23

12. $598 13. 88 questions

14. $4245.73

15. (a) 1 July–30 June(b) holiday pay—17.5% of 4 weeks’ normal pay(c) rate of tax increasing as taxable income increases(d) goods and services tax added to price of items or services(e) amount of taxable income below which no income tax is

payable

16. (a) $666.08 (using 1 year = 52.18 weeks)

17. (a) 25% (b) $6621.68(c) $26 487.50 (d) $26 316(e) $4274.80, $394.74 (f) $1952.14 refund

18. A tax deduction is an amount deducted from your income that is not taxed, such as a work-related expense or donation to charity. PAYE tax is regular tax payments made every payday—the employer deducts these amounts from the employees’ pays.

19. line through (30, 5.25), (60, 10.5)

20. $476.00 21. 16% 22. 26.25 krona

23. (a) $6200 (b) $52 000

24. Piecewise linear graph through (0, 0), (8000, 0), (25000, 3400), (40000, 8650), (50000, 13050)

Exercise 6-09

Chapter assignment


Chapter 7

1. (a) n2 = m2 + p2 (b) j2 = i2 + k2

(c) c2 = d2 + e2 (d) y2 = x2 + z2

(e) t2 = r2 + s2 (f) w2 = u2 + v2

2. (a) no (b) no (c) yes(d) yes (e) yes (f) yes

3. (a) 6.8 cm (b) 4.2 cm (c) 12 m(d) 7.8 m (e) 40 cm (f) 3 m

4. (a) 5.39 m (b) 7.30 m (c) 12.21 cm(d) 18.73 cm (e) 5.66 cm (f) 7.62 m

5. (a) 9.17 cm (b) 11.0 cm (c) 30.0 cm(d) 98.6 m (e) 57.8 cm (f) 33.0 m

1. 4.20 m 2. 461 m

3. (a) 34 cm (b) 51 cm (c) 66 cm

4. 5.66 m 5. 120 nautical miles 6. 1100 m

7. (a) 3.35 m (b) 6.02 m

8. 2.1 m

9. (a) no (b) no (c) no (d) yes

10. 19.4 m 11. 43.27 cm 12. 21.4 cm

13. 3.96 m 14. 110.99 m

15. (a) 337 km (b) 337 km

16. (a) 0.9 m (b) 198.0 m

17. (a) 6.5 cm (b) Sides could be 4 cm and 2 cm.

18. 1.3 m 19. 15 m 20. 2.46 m

21. 40 cm × 31 cm

1. (a) (b) (c)

(d) (e) (f)

2. (a) 2.1429 (b) 0.4493 (c) 0.4167(d) 0.4 (e) 1.3333 (f) 2.4

3. 0.5774 approx. 4. 1.4281 approx.

5. 0.9004

7. (a) 5.6713 (b) 0.4040 (c) 0.1228(d) 4.1653 (e) 0.2126 (f) 1.0355(g) 0.6494 (h) 0.1566 (i) 1.9643

1. (a) 0.47 (b) 3.01 (c) 1.14 (d) 3.72(e) 0.45 (f) 43.46 (g) 3.57 (h) 7.36(i) 24.16 (j) 10.00 (k) 1.25 (l) 2.57

2. (a) 20.71 cm (b) 2.70 m (c) 2.00 m(d) 29.20 m (e) 11.09 m (f) 8.51 cm(g) 40.49 m (h) 104.49 mm (i) 5.50 m(j) 8.70 m (k) 25.50 m (l) 54.88 mm

3. 30.02 cm 4. 95 m 5. 42.9 m

6. 28.1 m 7. 132.8 m 8. 327 m

9. 182 m 10. 2.27 m 11. 2.06 m

1. (a) 37°45′ (b) 18°29′ (c) 50°42′(d) 63°9′ (e) 24°40′ (f) 28°6′

2. (a) 37° (b) 21° (c) 83°(d) 14° (e) 22° (f) 75°

Exercise 7-01

Exercise 7-02

Exercise 7-034.52.8------- m

p---- 4

3---

ab--- 4.8

2------- r

t--

Exercise 7-04

Exercise 7-05

3. (a) 73°0′ (b) 25°54′ (c) 38°40′(d) 77°28′ (e) 67°8′ (f) 78°41′

4. (a) 60° (b) 21° (c) 38°(d) 45° (e) 19° (f) 70°

5. (a) 41°59′ (b) 69°27′ (c) 59°35′(d) 42°43′ (e) 78°50′ (f) 77°28′

6. 53° 7. 25° 8. 87°43′9. 12° 10. 7°36′

11. (a) 29°21′ (b) (i) 1.69 m (ii) 1.69 m

12. 20°

1. (a) 12.04 (b) 143.97 (c) 3.04

2. (a) 25° (b) 79° (c) 30°

3. (a) (b) (c)

(d) (e) (f)

4. (a) 12.47 m (b) 8.50 m (c) 74.89 mm(d) 22.24 cm (e) 7.36 m (f) 4.81 m

5. (a) 42° (b) 34° (c) 39°

6. (a) 24°13′ (b) 27°49′ (c) 43°40′7. 4.81 m 8. 12 m 9. 8.18 m

10. 20° 11. 26° 12. 2.5 m

13. 3418 km

1. (a) 9.38 (b) 3.69 (c) 11.28

2. (a) 71° (b) 70° (c) 60°

3. (a) (b) (c)

(d) (e) (f)

4. (a) 7.07 m (b) 46.02 mm (c) 11.01 cm(d) 14.83 m (e) 7.63 m (f) 15.77 cm

5. (a) 64° (b) 29° (c) 84°

6. (a) 41°6′ (b) 66°48′ (c) 78°28′7. 54.70 m 8. 25°0′9. (a) 41 m (b) 55°

10. 25°22′ 11. 9.1 m 12. 49.6 m 13. 34.0 m

1. (a) tan (b) sin (c) cos

2. (a) (b) (c) (d)

(e) (f)

3. (a) 26.59 cm (b) 9.73 m (c) 6.83 m(d) 20.88 mm (e) 13.76 m (f) 23.42 m(g) 7.72 cm (h) 75.77 mm (i) 14.42 m

4. (a) 29° (b) 32° (c) 56°(d) 24° (e) 73° (f) 53°

5. (a) 16°16′ (b) 24°1′ (c) 54°54′6. 62°

7. (a) 73°44′ (b) 5.00 cm (c) 5 cm

8. d = 6 m, ∠D = 65°, ∠E = 25°9. 43° 10. 10° 11. ,

12. , 13. 51°3′ 14. 41.4 m

15. 50° 16. 44.2 cm 17. 4.04 m

18. 26.8 m 19. 4.33 cm, 10.83 cm2

Exercise 7-06

kp--- 24

25------ t

w----

66.8------- d

e--- 24

26------

Exercise 7-07

mp---- 7

25------ y

w----

3.26.8------- f

e--- 10

26------

Exercise 7-08

jl-- k

l-- j

k-- k

l--

jl-- k

j--

1237------ 35

37------

2025------ 20

15------

ANSWERS 473

1. (a) SW (b) SE (c) NE(d) SE (e) NW (f) SW

2. (a) 043° (b) 262° (c) 135° (d) 113°(e) 345° (f) 083° (g) 308° (h) 026°(i) 206° (j) 233°40′ (k) 157°25′ (l) 322°45′

3. (a) NW (b) SW (c) SE

6. (a)

1. (a) 55 km (b) 95 km

2. (a) 24°12′ (b) 335°48′ (c) 2930 m

3. 131° 4. 11.59 km 5. 31 km

6. 4.24 km 7. 097° 8. 21.282 km

9. (a) 25° (b) 275°

10. 9.216 km 11. 4.141 km

12. (a) 155 km (b) 174 km

13. (a) 179.98 km (b) 129.64 km

14. 1013.89 km, 506.95 km/h

15. (a) 19 km (b) 020°

16. 28.3 km 17. 51.2 km

18. (a) (b) 32.5 km (c) 141°1′(d) 321°1′

1. 156 m 2. 109 m 3. 49.5 m

4. 624 m 5. 137 m

6. (a) 2.97 m (b) 3.20 m 7. 1.63 m

8. (a) 9.05 cm (b) 9.05 cm

9. 1232 m 10. 14° 11. 136 m

12. 252 m 13. 57°

14. (a) 2241 m (b) 2165 m

15. 21.7 km 16. 3864 m 17. 64°37′18. 57 m 19. 164 m 20. 139 m

1. (a) yes (b) yes (c) no

2. (a) 6.23 cm (b) 6.3 cm (c) 12.49 m(d) 47.89 cm (e) 17 m (f) 9.69 m

3. 42 cm 4. no

5. (a) 182.06 mm (b) 17.63 cm 6. 130 m

7. (a) 6.43 cm (b) 9.37 cm (c) 8.00 m(d) 10.46 cm (e) 11.01 cm (f) 7.30 cm

Exercise 7-09

4. N

S

EW

(a) (i)

(d)

(g)(c)(e)

(b)

(f)

(h)

5. A

A C

B

45°

38°

8 km

(b) ∠A = 38°,∠B = 97°, ∠C = 45°

Exercise 7-10

A B

C

10.5 km

8.5 km

Exercise 7-11

Chapter assignment

8. (a) 68° (b) 68° (c) 40°

9. (a) 44°25′ (b) 16°16′ (c) 78°28′10. 117 cm 11. 27°13′12. (a) 12.6 m (b) 76°39′13. 5.69 cm 14. 255°

16. 68° 17. 254.76 nautical miles 18. 1082 m

19. (a) 18.68 km (b) 106° 20. 776 m

Chapter 8

1. (a) c/min (b) $/hour (c) words/minute(d) $/kg (e) $/kg (f) m/s

2. (a) population density (b) cost of classified ad(c) fuel consumption (d) data download speed(e) birthrate (f) cost of carpet

3. 2.4 cm/week 4. 5.25 runs/over

5. 2750 persons/year 6. $24.85

7. (a) $4.75/kg (b) $4.18

8. $25.80 9. 4.8 kb/s 10. 69 beats/min

11. B 12. 5.2 L/min 13. 13.2 c/kWh

14. 0.425 c/$ 15. $16.45

16. (a) kg/m2 (b) or 0.25 kg

17. 2.50 persons/km2 18. (a) 77.35 kL (b) $61.88

1. 23 min 2. 12 h 40 min

3. (a) 0.05 mg/g (b) 5 mg

4. (a) 336 km (b) 5 h 5. 147 runs

6. 4 kg 7. (a) 288 510 (b) 130 791

8. 252 km 9. 74.88 L 10. $3.24

11. (a) 65c (b) $307.69 12. 2.4 g

13. (a) 4.1 kg (b) 6 times

14. (a) 165 m3 (b) 123.75 g (c) 31 s

15. (a) 600 mL/L (b) 60% v/v

16. 1.8 mL 17. 4.8 mL 18. 130 mL

19. (a) 2.5% v/v (b) 60 mL 20. 0.15 mL

21. (a) 1.5% w/v (b) 0.5 or mL

22. (a) 2 mg/mL (b) 0.2% w/v

23. (a) 5 g (b) 6.25 mL

24. (a) 3.36 g (b) 33.6 mL (c) 246.4 mL

1. (a) 16 km/h (b) 50 km (c) 1 h 22.5 min

2. (a) 6 h 30 min (b) 5 h 38 min (c) 2 h 3 min

3. 29.7 knots

4. (a) 43 200 km (b) 75.52 days 5. 4 min 39 s

6. (a) highway; more efficient use of petrol at higher speeds(b) Fuel consumption increases, larger engine size uses

more petrol to move higher mass.

15. N

157°

Exercise 8-01

1240--------- 1

4---

Exercise 8-02

3.

815------

Exercise 8-0323---


7. 43.2 L 8. 381 km 9. 324 km

10. (a) 3 h (b) 13.71 km/h

11. 1.6 km 12. 12.5 min

13. (a) 15 L/100 km (b) 37.5 L

14. (a) 40.54 L (b) 394 km

15. (a) 1.8868 m/s (b) 566 m

16. (a) 15 m (b) 21 m (c) 26.25 m

17. 4 h 23 min

18. (a) 44 924.77 km (b) 1 h 48 min

19. (a) 110 mL (b) 22 drops/min

20. 3h 30 min 21. 6 h 40 min 22. 31.25 drops/min

1. (a) $2708.33/month (b) 120 L/day(c) 1.25 km/min (d) 180 m/min(e) $35 620/year (f) 48 cm/h(g) 1.3 words/s (h) 4680 words/h(i) 0.082 L/km (j) 105 000 mL/min(k) 1.75 L/s (l) 1.4 beats/s

2. (a) 464.3 km/h (b) (i) 7738 m (ii) 129 m

3. 340 m/s 4. 1800 L/h

5. (a) $14.40/h (b) 28.8 km/h (c) 54 km/h

(d) 54 L/h (e) 18 c/min (f) 1.8 c/g (g) 16 m/s

(h) 30 m/s (i) 2 or 2.08 kg/min

6. (a) 2 g/cm2 (b) 12.61 kL/year (c) 12.66 km/L

7. 43.4 km/h 8. 25.54 km/h

9. (a) 45 m/s (b) 161 km/h 10. 104 m

1.

12---

Exercise 8-04

23---

112------ 3

.

Exercise 8-05(a) (b)

(c) (d)

(e) (f)

y

x−2

y = −2x − 1

−4

4

2

2 4−4 −2

(g) (h)

y

x−2

6;

4

2 4−4 −2

y

x−2

−4

4

2

2 4−4 −2

y

x−2

y = 3x − 2

−4

4

2

2 4−4 −2

y

x−2

y = − x

−4

4

2

2 4−4 −2

y

x−2

−4

4

2

2 4−4 −2

y

x−2

−4

4

2

2 4−4 −2

y

x−2

y = x

−4

4

2

2 4−4 −2

12---

y = 4

y = x + 123---

y = x + 214---

2

y = x + 4

2. (a) y = −3x + 5 (b) h = 4b − 3 (c) v = u + 8

(d) p = −m + 10 (e) r = k − 1 (f) c = 4

3. (a) y = x + 1, y = − x + 6, (2,3)

(b) y = 2x − 3, y = x − 2, (1, −1)

(c) y = x, y = 2x + 6, (−4, −2)

(d) y = 3x + 3, y = −x − 1, (−1, 0)

4. (a) x = 3, y = −2 (b) x = −2, y = −3 (c) x = 1, y = 1

1. (a) d = 2.75 , d = 2.75r (b) 90.75 m (c) 36

2. k = 3.5; 3.5, 35, 38.5

3. (a) 5.88 (b) 235.2 kPa (c) 141 m

4. (a) 2.4, F = 2.4d (b) 7800 kg

5. (a) 1.6 (b) 96 km/h (c) 75 miles/h

6. 6.25 min

7. (a) 64 (b) volume of water pumped per minute(c) 512 L (d) 15 min

8. 2 h

9. (a) 22.8 kg (b) 84.1 kg 10. 8 h 53 min

11. (a) 2 min 30 s (b) 120 min 12. 40 cm

13. (a) 1.3 (b) 317.2 cm (c) 92 cm

14. (a) 117.6 m/s (b) 18 s

1. (a) 108 cm (b) 5.9 ft(c) (i) 61 cm (ii) 76 cm (iii) 182 cm

2. (a) $48 (b) $88 (c) $105(d) $13 (e) $20

3. (a) $1.24 (b) $0.65 (c) $0.90

4. (a) E14 (b) E48 (c) E22(d) E81 (e) E59 (f) E2.10

5. 1.61, the number of $A/E; number of $A per Euro

6. (a) (i) 71.5 kg (ii) 55.5 kg (iii) 79.5 kg(b) (i) 180 cm (ii) 159 cm (iii) 193 cm(c) 0.65, rate of change of weight per height (in kg/cm)

7. (a) (i) $51 (ii) $24 (iii) $70(b) (i) $29 (ii) $94 (iii) $64(c) 0.85, ratio of discount price to marked price(d) 15%

8. (a) (i) 41 kg (ii) 62 kg (iii) 73 kg(b) (i) 88 lb (ii) 140 lb (iii) 198 lb(c) 0.46 kg/lb

Note: Values for lines of best fit will vary between individuals, but should be close to the answers provided here.

1. (a) t, time (b) T = 38t + 22(c) increase in temperature per minute(d) initial temperature (e) 269°C (f) 7 min 19 s

2. (a) t (b) C = t + 20

(c) Gradient is the increase in cost in dollars per minute, vertical intercept is the initial cost.

(d) $100 (e) 150 min

3. (a) C = 73.3a − 73(b) 75.5 mm/year, increase in circumference per year(c) (i) 660 mm (ii) 1393 mm (d) 9 years 10 months

4. (b) V = −2560y + 25 880 (c) $2560/year(d) $25 880 (e) $7960(f) 5th year (g) 10th year

12---

23---

32---

12---

Exercise 8-06

23---

Exercise 8-07

Exercise 8-08

23---

ANSWERS 475

5. (a) s (b) s = 9.8t − 2(c) 9.8, increase in speed (m/s) per second(d) (i) 7.8 m/s (ii) 96 m/s (e) 9.4 s

6. (a) A = 2n − 12 (b) 2, increase in allowance/year(c) $14 (d) 11 years(e) (i) Values of A are negative

(ii) Children are old enough to earn own money

7. (a) E = 9.6w + 468 (b) 1188 kJ (c) 86 kg(d) Underweight women use moderate amounts of energy.

8. (a) C (b) C = 0.045n + 8(c) 4.5 cents (d) initial cost (before any cards are printed)(e) (i) $41.75 (ii) $75.50 (f) 650 cards

9. (b) D = −0.27p + 111 (c) 38% (d) $410(e) 111, which implies that the demand will be 111% when

the price is $0. Demand cannot be more than 100%, and a price of $0 is impractical.

1. (b) Megan (c) less than $1600 (d) $1600

2. (b) $150 (c) $100 (d) $5 (e) 45 yo-yos(f) the manufacturing cost is more than the revenue

received, so the business would lose money

3. (a) yes, after 25 minutes at about 7.5 km from Brian’s house(b) Brian, by 10 minutes

4. (a) MegaPhone(b) QuickFix $51, MegaPhone $43.50 (c) 20 min(d) (i) infrequent callers, less than 20 min use per month

(ii) caller who uses mobile phone for more than 20 min per month

5. (b) d = 260 km, C = $239. The cost is the same with both companies for a distance of 260 km.

(c) Megahertz, $244.50

1. (a) payment to family in the event of the death of a person(b) (i) $203 (ii) $334 (iii) $179(c) Chance of a person dying in this age range is fairly

constant.(d) increases; greater chance of person dying at higher ages

— greater risk to insurance company(e) (i) 40 years (ii) 50 years

2. (a) decreases, cheaper to buy in bulk(b) (i) $4 (ii) $5.50 (iii) $3.50 (iv) $6(c) 49 boxes

4. (a) (i) $7.35 (ii) $2.80 (iii) $6.90(c) (i) 1 kg (ii) 250 g (iii) 3 kg

5. (a) (i) $510 (ii) $270 (iii) $870(c) Gradient increases; the lines become steeper.

6. (a) 2 rates (b) 14 c/kWh (c) lower(d) (i) $19.50 (ii) $42 (iii) $50(e) (i) 240 kWh (ii) 86 kWh (iii) 370 kWh

7. (a) C = $0, $2700, $3900, $4550(c) decreases; commission rate decreases(d) (i) $3330 (ii) $4075

8. (b) 45 min(c) Patty started her journey 2 km from her home.(d) 4 km (e) 3 km/h, 2 km/h, 0 km/h, 8 km/h

1. $952 2. 48 000 L

3. $3122.10 4. 27 h 47 min

5. (a) (i) 9.264 m/s (ii) 33.35 km/h (b) 18 min

Exercise 8-09

Exercise 8-10

Chapter assignment

6. (a) 5 mL (b) 16 g, 24 mL

7. 428 km 8. 17 c/min

9. (a) r (b) t = −5r + 11

10. x = −3, y = −3 11. 1759 m

12. (a) (i) $30 (ii) $76 (iii) $93(b) (i) 1700 baht (ii) 2150 baht (iii) 2650 baht(c) 0.04, number of $A per baht

13. (a) L = −13 063t + 313 500(b) −13 063, the decrease in the loan per year(c) $313 500(d) (i) $235 122 (ii) $104 492(e) (i) 20 years (ii) 24 years

14. (a) (i) $4.10 (ii) $0.20 (iii) $2.15(b) For each interval of 30 s, the cost jumps by 65 cents.(c) call with duration of more than 3 min but less than or

equal to 3.5 min

15. (b) h = 2l + 95(c) (i) 151 cm (ii) 171 cm(d) (i) 50 cm (ii) 40.5 cm

16. (b) C = $210, R = $175(c) Cost is more than revenue — you would lose money.(d) n = 36 guests (e) When n � 36, you make a loss. When n � 36, you make

a profit. When n = 36, you come out ‘even’ — neither profit nor loss.

Practice Paper Two1. A 2. C 3. A 4. A 5. A

6. D 7. A 8. C 9. C 10. A

11. (a) (i) 4.39 m/s (ii) 877 m (b) 31 Euros(c) 7.95 m (d) (i) $553.50

(ii) = C3*B3+D3*1.5*B3 or =(C3+1.5*D3)*B3(iii) $15.00

12. (a) 53 m(b) (ii) 15.81 m2 (iii) $4023(c) (i) $41 813.20 (ii) $41 327 (iii) $9398.01

13. (a) (i) V = −5.5t + 84(ii) the rate at which water is drained, i.e. 5.5 kL/h

(iii) 84 kL (iv) 15.3 hours

(b) (i) 12 mL/L (ii) 1.2% v/v

(c) (i) 25 cm (ii) 18.4 cm(iii) $594 (iv) 3 windows

Chapter 9

1. (a) L (b) AC (c) VU (d) VU (e) VU(f) VU (g) VU (h) U (i) AC

2. (a) VU (b) AC (c) VU (d) VL (e) I(f) VU (female) or I (male) (g) AC (h) L(i) C

3. (a) VU (b) L or AC (c) L (d) VU(e) VU (f) VU (g) VU (h) AC (i) VU(j) VU (k) AC (l) U

1. (a) (i) 26 outcomes (ii) {A, B, C, …, Z}(iii) yes; one of each letter

(b) (i) 8 outcomes (ii) {M, A, T, H, E, I, C, S}(iii) no; M, A, T occur more often

Exercise 9-01

Exercise 9-02


(c) (i) 1 outcome (ii) {white sock}(iii) yes; only one possible result

(d) (i) 10 outcomes (ii) {1, 2, 3, …, 9}(iii) yes; one of each numeral

(e) (i) 52 outcomes (ii) {A, K, Q, J, 10, …, 2 of ♥♦♣♠}(iii) yes; one of each card

(f) (i) 4 outcomes (ii) {1, 2, 3, 4}(iii) yes; each side identical

(g) (i) 3 outcomes (ii) {red, blue, green}(iii) no; different numbers of each

2. (a) 2, 4, 6 (b) 1, 2, 3, 4 (c) 3(d) 1, 4 (e) no outcome

3. (a) 26 outcomes (b) 4 outcomes (c) 20 outcomes(d) 2 outcomes (e) 12 outcomes(f) 2 outcomes (g) 2 outcomes

4. (a) K♥ K♦ K♣ K♠ (b) 8♣ 8♠

(c) A♥ A♦ A♣ A♠ (d) 6♦

(e) no outcome (f) 5♣ 5♠ 6♥ 6♦

(g) 2♥ 2♦ 2♣ 2♠ J♥ J♦ J♣ J♠(h) 5♣ 5♠ 5♥ 5♦ 9♥ 9♦

5. (a) W, O, L, M (b) 2, 4, 6, 8 (c) no outcome(d) black jellybean (e) no outcome

1. (a) 2 × 2 × 2 = 8 outcomes(b) HHH THH HHTTHT

HTH TTH HTTTTT(c) HTT THT TTH TTT (d) HHT HTH THH(e) HTT THT TTH TTT (f) HHH HHT HTH THH

2. (a) 2 × 2 × 2 × 2 = 16 outcomes(b) 210 = 1024 outcomes

3. (a) 6 outcomes (b) 6 × 6 = 36 outcomes(c) 6 × 6 × 6 = 216 outcomes

4. 26 × 26 = 676 stations

5. (a) 60 meals (b) 3 combinations(c) 40 choices (d) 12 meals (e) 20 meals

6. (a) 96 combinations (b) 24 combinations(c) 48 combinations (d) 4 combinations(e) 24 combinations

7. (a) 1000 suburbs(b) Use letters and numbers or more numbers.

8. 1000 combinations

9. (a) 160 000 combinations (b) 1 way

10. (a) 9 × 106 = 9 000 000 (b) 10000 numbers(c) 10000 numbers (d) 900000 numbers

11. (a) (i) 3 homes (ii) 3 homes (iii) 3 homes(iv) 6 homes (v) 27 homes

(b) 333, 335, 338, 353, 355, 388, 533, 588, 833, 855, 383, 358, 385, 555, 553, 558, 535, 585, 538, 583, 888, 883, 885, 838, 858, 835, 853(i) 19 outcomes (ii) 12 outcomes

(iii) 6 outcomes

12. (a) 2, 3, …, 12 (b) 1 way (c) 36 outcomes

(d) + 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

Exercise 9-03

(e) (i) 7 (ii) 2 or 12

13. (a) 52 × 6 × 2 = 624 outcomes(b) (i) 48 outcomes (ii) 104 outcomes

(iii) 312 outcomes (iv) 4 outcomes(v) 24 outcomes (vi) 78 outcomes

(vii) 78 outcomes (viii) 156 outcomes(ix) 78 outcomes (x) 12 outcomes(xi) 0 outcomes (xii) 208 outcomes

14. (a) 7 pieces (b) 28 pieces(c) 00 01 02 03 04 05 06

11 12 13 14 15 1622 23 24 25 26

33 34 35 3644 45 46

55 5666

(d) 7 pieces (e) 12 pieces

1–12. experimental results

1. (a) 10 tails (e) 50 tails

2. (a) (i) 1 six (ii) 10 sixes

3. experimental results

1. (a) (b) (c) 1 (d) 0

2. (a) (b) (c) (d)

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

4. (a) (b) (c) (d) 0

5. (a) (i) (ii) (iii)

(b) (i) (ii) (iii)

6. (a) (b) (c) (d)

(e) (f)

7. (a) (b) (c) (d)

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

8. (a) (b) (c) = (d)

9. (a) (b) (c) (d) =

10. (a) (b)

11. (a) (b) (c) (d)

12. (a) (b) (c) (d) (e)

13. (a) (b) (c) (d)

14. (a) (b) (c) (d)

15. (a) 1, 2, 3, 4, 5, 6, 6

(b) (i) (ii) (iii)

(iv) (v) (vi)

Exercise 9-04

Exercise 9-05


3---

715------ 8

15------ 1

15------ 2

15------

15--- 2

5--- 2

5--- 11

15------

613------ 9

13------ 9

13------

138------ 9

19------ 1

38------

3738------ 10

19------ 18

19------

120------ 9

20------ 1

2--- 3

20------

12--- 1

10------

12--- 3

26------ 1

13------ 1

13------

126------ 1

52------ 1

26------ 1

4---

512------ 7

12------ 3

12------ 1

4--- 5

12------

15--- 3

10------ 7

10------ 2

10------ 1

5---

14--- 1

3---

59--- 1

9--- 1

9--- 4

9---

14--- 1

32------ 1

8--- 1

8--- 1

8---

13--- 1

6--- 1

3--- 1

2---

16--- 1

3--- 5

6--- 1

3---

27--- 5

7--- 4

7---

17--- 5

7--- 2

7---

ANSWERS 477

1. (a) 50 people

(c) 1 (d) = (e) (f)

2. (a) (i) (ii) (iii) =

(b) (i) (ii) (iii)

(c) = (d) = (e)

3. (a) 34 students (b) (i) = (ii) 0 (iii)

(c) = (d) =

4. (a) 0.72 (b) 0.15 (c) 0.13

5. (a) = (b) = (c) = (d)

6. (a) 0.38 (b) 0.18 (c) 0.44 (d) 0.19 (e) 0.18

7. 8. 60 children 9. 90% 10.

1. (a) head (b) A, 2, …, 10 (c) 1, 3, 5(d) white sock (e) 2, 3, …, 9(f) blue or green marble

2. (a) (b) (c) 1 (d) 0 (e)

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

4. (a) (b) (c) (d) (e) 0

5. (a) (b) (c) (d)

6. (a) (b) (c) (d)

7. (a) (b) (c) (d) (e) (f)

8. (a) (b)

9. (a) (b) (c) (d) (e)

10. (a) (i) (ii) 1, 3, 5, 7, 9, 11

(b) (i) (ii) 1, 2, 4, 5, 7, 8, 10, 11

(c) + = 1 (d) + = 1

1. (a) L (b) L (c) VU (d) C (e) AC(f) VU (g) E

2. (a) VU (b) C (c) C (d) I (e) VU(f) I (g) E

(b) No. of games No. of people Relative frequency

0

1

2

3

4

5

6

6

7

8

10

9

5

5

Exercise 9-07

650------

750------

850------

1050------

950------

550------

550------

1050------ 1

5--- 19

50------ 21

50------

1150------ 1

50------ 4

50------ 2

25------

16--- 1

36------ 5

36------

1450------ 7

25------ 10

36------ 5

18------ 1

225---------

834------ 4

17------ 3

34------

834------ 4

17------ 26

34------ 13

17------

210------ 1

5--- 8

10------ 4

5--- 8

10------ 4

5--- 3

10------

1328------ 1

4---

Exercise 9-08

12--- 1

2--- 1

2---

16--- 5

6--- 1

2--- 1

2---

512------ 3

4--- 1

3--- 2

3---

23--- 1

3--- 1

3--- 2

3---

111------ 9

11------ 7

11------ 9

11------

12--- 1

2--- 3

5--- 7

10------ 11

20------ 9

20------

1200--------- 199

200---------

127------ 2

27------ 25

27------ 26

27------ 53

54------

12---

13---

12--- 6

12------ 1

3--- 8

12------

Chapter assignment

3. (a) (b) (c) 1 (d) (e)

4. (a) 390 tosses (b) 0.25, 0.48, 0.27(c) (i) 0.25 (ii) 0.48 (iii) 0.75

5. (a) = (b) = (c)

(d) (e) (f)

6. (a) (b) (c) 1 (d)

7. same probability of occurring; (b), (d), (e)

8. (a) (b) (c) (d) (e)

(f) (g) (h)

9.

(c) (i) 0.3 (ii) 0.35 (iii) 0.1

11. (a) (b) (c) (d)

12. (a) (b) = (c) (d) (e)

13. (a) BBB GGB BBGGBGBGB GBB BGGGGG

(b) (c) (d) (e) (f) 20 families

Chapter 10

1. (a) $1480 (b) $320.40 (c) $3717.90(d) $246 (e) $471.18 (f) $1027.46(g) $42.08 (h) $440.78 (i) $625.50(j) $569.58

2. $1620 3. 11% 4. 2 years

5. 12% 6. $7400

7. (a) $1984.50 (b) $847.91 (c) $4680(d) $207.66 (e) $2400

8. 0.035% 9. 15 months 10. 0.8%

11. $8250 12. 2.25%

1. (a) $8994.74, $1594.74 (b) $3891.04, $1051.04(c) $4951.80, $451.80 (d) $17 869.38, $869.38(e) $9714.53, $464.53 (f) $9516.52, $516.52(g) $14 364.27, $1464.27 (h) $15 989.37, $2189.37(i) $16 011.05, $2211.05 (j) $7341.81, $421.81

2. $18 363.23

3. (a) (i) $2975 (ii) $3421.68(b) compound; by $446.68(c) Compound interest is greater because you get interest on

your interest.

4. (a) $23 152.50 (b) $23 180.07 (c) $23 194.20(d) $23 203.76 (e) $23 208.43

10. (a), (b) Class (hours) No. of globes Rel. freq.

50–<6060–<7070–<8080–<9090–<100

41210104

0.10.30.250.250.1

40 1

1118------ 2

3--- 1

9--- 2

9---

452------ 1

13------ 36

52------ 9

13------ 2

13------

1013------ 1

13------ 8

13------

13--- 5

12------ 1

6---

2126------ 1

4--- 2

7--- 1

6--- 1

6---

12--- 1

2--- 1

36------

124243---------

110------ 3

5--- 9

10------ 7

20------

12--- 18

20------ 9

10------ 3

10------ 4

5--- 1

2---

18--- 1

2--- 1

4--- 7

8---

Exercise 10-01

Exercise 10-02


5. Interest increases as frequency increases because you get interest on your interest more often.

6. 18 years 7. 4 years 8. $3200

9. $7993.54 10. C

11. (a) $4484.07, 8.3% (b) no

1. (a) $1080 (b) $300 (c) $780 (d) $540

3. (a) (i) $960 (ii) $2880(b) Higher rate of interest has steeper graph.

4. (a) $4000 (b) $2400 (c) $3300 (d) $2800

5. (a) 3 years (b) 7 years

7. (a) (i) $6580 (ii) $11 000(b) Higher rate of interest has steeper graph.

8. (a) $23 424 (b) $13 695.50 (c) $4.04(d) $10 249.14 (e) $12 159.90 (f) $9137.52(g) $24 388 (h) $62 368 (i) $4548.60(j) $7208

9. 5 years

1. 50c

2. (a) Phone/Internet banking; fully automatic/computerised and costs bank less money

(b) Withdrawal at bank; tellers cost bank more money.

3. (a) $5 (b) Yes; balance is below $500(c) $1.50 (d) 50c + 30c = 80c (e) $346.38

4. (a) dormancy fee, $10(b) Discourage customers from leaving their account

unchecked.

5. (a) cheque dishonour fee (b) $25

6. (a) $7 (b) $4702.10

7. (a) Excessive use of services; to discourage withdrawals.(b) Discourage low balances; to encourage higher balances.(c) Bad cheques create more work for the bank.

8. (a) Counts as one withdrawal; minimises number of monthly withdrawals.

(b) Minimises number of withdrawals.(c) Credit and direct debit are free.(d) Balance has more chance of staying above $500; avoids

monthly account-keeping fee.(e) cheaper fee

9. (a) automated/computerised, cheaper than employing tellers

(b) Bank has to pay another bank if withdrawal is made at other bank’s ATM.

1. (a) $8850 (b) $197 (c) $53.40 (d) 17.94%

2. (a) $2.23 (b) $960 (c) 10.76%

3. (a) $1192 + $29.80 = $1221.80(b) $3.60 (c) $88, 9.17%

4. (a) $3.90 (b) 24c

5. (a) $23706.10 (b) $7007.50

6. (a) $10 200 (b) $24 800.45 (c) $1596(d) 10.37%

7. (a) $1020 (b) $75 (c) 7.4%

8. (a) $20 522 (b) $1041.06

9. (a) $1050 (b) 5.0% (c) 125 shares

10. 6.73%

11. (a) $7750 (b) $1135

Exercise 10-03

Exercise 10-04

Exercise 10-05

(c) (i) $27 725 (ii) 5%

12. (a) $23 224.13 (b) $3355.92

1. (a) 5.26% (b) $3.80 (c) blank entry for ‘move’(d) $2.35 (e) $3.21 (f) 20c

2. (a) Westpac (b) 0.2c decrease

3. (a) Qantas (b) 19c increase

4. (a) Westpac (b) Just Jeans

5. (a) AGL, Westpac (b) Just Jeans (c) TAB

6. Sydney Gas

7. (a) $1.468 (b) $1.45 (c) $0.04

8. (a) Westpac (b) Westpac (c) AGL(d) Just Jeans (e) AGL

9. (a) $8.25 (b) $7.95 (c) 6 months(d) 3 times (e) $8.42 (f) $8.40

10. (a) $2.80 (b) $2.15 (c) 4 times (d) $2.40(e) Price dropped slowly, then sharply, then rose gradually.(f) Price was stable, then rose sharply, then dropped

gradually, then rose and dropped sharply.(g) remain stable or drop more(h) no, because the price is low

11. (a) Price remains stable or rises; doesn’t fall.(b) Price rises sharply once in first 3 months, but remains

fairly stable; rises gradually in next 3 months.

(c) (i) $6.00 (ii) $7.50 (iii) $12.00(d) August (e) May(f) Sell, as price is high or buy, as price may get higher.

1. $2.52 2. $2589.16 3. $29.23

4. $716 per ounce 5. $18 909.20

6. antiques, rare cars, collectibles 7. 6.5%

8. $62 816.89 9. $31.90 10. $44.41

11. $821.19 12. $115.98 13. $3093.93

14. (a) $4080.75 (b) $5646.03

15. $20 400.44 16. $15.50 17. $130000

18. $121 095 19. 18 years 20. $86.17

1. (a) $1350 (b) $162 (c) $1854

2. (a) 4.5% 3. 9 years

4. (a) $8636.13, $1436.13 (b) $4215.07, $165.07(c) $12 323.05, $2023.05

5. (a) $1102.50 (b) $1103.81 (c) $1104.48

6. If interest is compounded more often, the total interest increases

7. (a) $10 245.91 (b) $9554.46

8. (a) A (b) D (c) C (d) B

9. $9.90 10. $194.40

11. (a) $15 519.20 (b) $4668.80

12. (a) $2243.50 (b) $98 (c) 4.37%

13. (a) 2 months or 78 days or 11 weeks

(b) $3.18, October(c) Price rose sharply at first, then dropped slowly and

remained stable; dropped and rose sharply in October.(d) 3 times (e) $3.54(f) Sell, as price is high, or buy as price could get higher.

14. (a) $669 (b) $450

15. $15 027 16. $417.90

Exercise 10-06

Exercise 10-07

Chapter assignment

12---

ANSWERS 479

Chapter 11

1. (a) 6, 7; mean; no outlier (b) 6, 6; mean; no outlier(c) 6, 1; median; there is an outlier(d) 6, 6; mean; no outlier

2. (a) (i) 15 (ii) 4.7 (iii) 5 (iv) 5(b) (i) 12 (ii) 5.9 (iii) 6.5 (iv) 7(c) (i) 15 (ii) 47.3 (iii) 44 (iv) 41 and 64(d) (i) 10 (ii) 5 (iii) 5.5 (iv) 7

3. (a) 5, 5, l and 5 (b) 34.4, 34.5, 31, 32 and 35(c) 36, 38, no mode (d) 9.4, 8.5, 7 and 8

4. (a) blue (b) categorical data(c) can only find them for numerical data

5. (a) 25.5 min (b) 26 min (c) bad weather, sickness6. (a) 1700 hours (b) have more staff at peak times

(c) other peak times (1200 and 1600 hours)7. (a) 50 students (b) 3 CDs (c) 2.88 CDs8. (a) 1980 mL (b) 165 mL/h9. 7840 persons

10. (a) 52.5 events(b) (i) 12.20 points (ii) 8.90 points(c) 497 points

1. (a) 24.7°C (b) 24.5°C (c) 24°C2. (a) 40 items (b) $2784 (c) $69.60 (d) $68.503. (a) 10 patients (b) 38.2°C (c) 38°C

(d) median; there is an outlier4. (a) 50 matches (b) 50 matches

(c) 50.04 matches (d) valid claim since mean, median and mode are all 50 (to nearest unit)

5. (a) 48 skiers (b) 90 s (c) 129 s (d) 125.5 s6. (a) 7.5 days (b) 9.25 days

(c) median; there are 2 outliers7. (a) 14 households (b) 17 households (c) 10 households

(d) pensioners 4.2 ML, non-pensioners 3.7 ML(e) no; they use more water than non-pensioners

8. (a) B+ (b) B (c) 12 ratings(d) Put D− = 1, D = 2, D+ = 3, …, A+ = 12, find the

numerical mean, then the nearest rating.(e) B− (f) A Civil Action

9. (a) 88.52 (b) 84 (c) median; there are outliers(d) There is a wide range of abilities in the class, most

scoring around 50%.10. (a) 40 employees (b) $262.50

(c) casual workers working part-time11. (a) 180 motorists (b) 48.6 km/h

(c) 155 vehicles (d) $725212. (a) 20–29 (b) 38.7 years

(c) mode, so this age group can be taught better road safety13. (a) 234 trees (b) 40–49 cm (c) 44.9 cm14. (a) 20 packets (b) 4 packets

(c) 1 biscuit (d) 1.6 biscuits15. (a) 172 cm (b) 170–<180 cm (c) 180–<190 cm

1. (a) mode (b) median (c) mean (d) all(e) mean (f) mean (g) median (h) mode(i) mean (j) mode

2. median; does not consider the $98 300 outlier

Exercise 11-01

Exercise 11-02

Exercise 11-03

3. (a) 35 batteries (b) median; skewed(e) 28 hours (18th score)

4. (a) mean, median or mode; symmetrical (averages equal)(b) median; skewed(c) mean, median or mode; symmetrical (averages equal)(d) mean; fairly symmetrical

5. (a) (i) median (ii) mean (iii) median(b) median

6. $2.40 (mean), takes into account all prices

1. (a) 18.8% (b) 6 students (c) 23 students(d) 9.4% (e) 7 students

2. (a) 28 students (b) 16 students (c) 126 students(d) 8th, 9th, 10th (e) 9.3%

3. (a) 2 deciles (b) 10% (c) 30%

4. (a) 20% (b) 1.2 months (c) 40%

5. (a) 25 063 students (b) 2523 students (c) 10.2%(d) 7503 students (e) 29.9%

1. (a) 6, 4 (b) 9, 6.5 (c) 8, 5 (d) 17, 12 (e) 10, 5

2. (a) 46 s (b) 12 s(c) e.g. more expertise, more training

3. (a) 6°C (b) 2°C 4. (a) 104 (b) 16.5

5. (a) 4 matches (b) 2 matches

6. (a) $1.35 (b) 50c

1. (a) 2 (b) 3.3 (c) 1.5

2. (a) 2 accidents (b) 1.3 accidents

3. (a) 2 min (b) 3.4 min

1. (a) 5, σn − 1 = 3.5 (b) 5.4, σn − 1 = 2.1(c) 34.4, σn − 1 = 2.9 (d) 36, σn − 1 = 6.5(e) 9.4, σn − 1 = 3.2

2. (a) Jane 30 shirts, σn − 1 = 3.3 shirts;Tony 30 shirts, σn − 1 = 9.3 shirts

(b) Jane; more consistent since standard deviation is smaller(c) e.g. sickness, inattention, dropped some

3. (a) $820 (b) σn = $267

4. (a) 5.99 peas (b) σn − 1 = 1.02 peas(c) yes; a small standard deviation in the number of peas per

pod

5. (a) 90.5, σn − 1 = 1.4 (b) 83, σn − 1 = 3(c) $5578, σn − 1 = $1416 (d) 8.00, σn − 1 = 0.03(e) 125, σn − 1 = 20

6. (a) $24.60 (b) σn = $21.95

7. (a) 88 s (b) 129 s (c) σn = 22.4 s

(b) 170.5 cm, σn − 1 = 8.6 cm

8. (a) Class Centre Frequency

150–154155–159160–164165–169170–174175–179180–184

152157162167172177182

1336746

Total 30

Exercise 11-04

Exercise 11-05

Exercise 11-06

Exercise 11-07


4. (a) 20 cigarettes (b) 12 cigarettes(c) 36 cigarettes, 3 cigarettes (d) 25% × 60 = 15 people(e) 50%

(b) Dotplot shows the spread better but not the summary statistics.

6. (a) $75 000 (b) $42 000(c) $41 000 (d) $28 000 and $51 000(e) $57 000 (f) be higher (g) be higher

(b) 4 pairs (c) 5 − 3 = 2 pairs

Exercise 11-08

34323028 36 38 40 42 44 46

1. (a)

(b)

(c)

(d)

(e)

87654321 9 10

87654321 9 10

36343230 38

11975 13 15

8.5

29.5 41.5 45

34.5

1.5

31 39

2.

9753 11Golf score

6.5

3.

40302010 50 60 70

14 28.5 36 44.5 68

5. (a)

6420 8

6420 8No. of children

OR

Lower quartile = median

Excluding the outlier 8

Exercise 11-09

1. (a)

0

10

15

5

2 3Pairs of shoes

5

20

4 6

25

30

35

Cum

ulat

ive

freq

uenc

y

40 100%

75%

50%

25%

4 53

(b) 30 nails (c) 31 − 29 = 2 nails(d) 118 packets

(c) 5, 6, 7 peas (d) 6 peas(e) 7 − 5 = 2 peas

4. (a) 25 motorists (b) 45 km/h(c) 56 − 28 = 28 km/h (d) 15 motorists

(b) $260 (c) $330 − $210 = $120(d) $277 (e) σn = $109

(c) 15 words (d) 28 − 5 = 23 words(e) 21 − 9 = 12 words (f) 15 words, σn − 1 = 7.6 words

3. (a) No. of peas 3 4 5 6 7 8

No. of pods 1 3 29 38 21 8

Cum. freq. 1 4 33 71 92 100

6. (a) Class (words) Frequency Cum. freq.

0–910–1920–29

101610

102636

2. (a)

0

40

60

20

28 29Nails per packet

31

80

30 32

100

120

140

Cum

ulat

ive

freq

uenc

y

100%

75%

50%

25%

30

33

3129

(b)

0

40

60

20

3 4Peas in a pod

6

80

5 7

100

Cum

ulat

ive

freq

uenc

y

100%

75%

50%

25%

6

8

5 7

5. (a)

0

10

15

5

100 200Wages per week ($)

400

20

300 500

25

30

Cum

ulat

ive

freq

uenc

y 100%

75%

50%

25%

600

210 330260

(b)

0

10

20

10 20

Words per sentence

30

30

40

Cum

ulat

ive

freq

uenc

y

100%

75%

50%

25%

15 219

ANSWERS 481

(c) 6 kg (d) 3 kg and 8 kg(e) 5.8 kg (f) σn − 1 = 3.3 kg

(c) 34 years (d) 60 − 22 = 38 years(e) e.g. more drivers in this age group, inexperienced drivers

1. (a) 4.6, 4.5, 3 (b) 34.3, 32, no mode(c) 173.6, 176, 165 and 178

2. (a) 172.6 cm (b) 170 cm(c) mean; no outliers, small data set

3. (a) middle 50% of scores (b) 25 − 21 = 4

4. (a) 6.8, 7, 7 (b) median or mode; skewed(c) no (d) 8 − 5.5 = 2.5(e) σn − 1 = 2.48

5. (a) 1.998 cm, 2.00 cm (b) σn − 1 = 0.018 cm(c) σn − 1; is a sample

6. (a) 50.3 g (b) σn − 1 = 1.3 g

7. (a) Class (kg) Frequency Cum. freq.

0–1.92–3.94–5.96–7.98–9.9

10–11.9

686

1046

61420303440

8. (a) Age group (years) Cum. freq.

0–<1010–<2020–<3030–<4040–<5050–<6060–<7070–<80

157544108414201645184121272464

(b)

0

10

20

2 4Weight loss (kg)

8

30

6 10

40

Cum

ulat

ive

freq

uenc

y 100%

75%

50%

25%

12

6 83

(b)

0

1000

1500

500

10 20Age (years)

40

2000

30 60

2500

Cum

ulat

ive

freq

uenc

y

100%

75%

50%

25%

60

7050 80

3422

Chapter assignment

(c)

25232119 27

(d) no; is the median weight

7. (a) 39.85, σn − 1 = 23.44 (b) 12, 18.5, 38.5, 51, 81

8. (a) 8 goals (b) 12, 0 goals (c) 12 goals(d) 5 goals (e) no outliers shown

9. (a) $15 000 (b) $6500 (c) $32 329 (d) σn − 1 = $4487 (e) 40 hours

10. (a) mode (b) all (c) mean(d) median, mean (e) mode (f) median, mean

(b) 81 km/h, σn − 1 = 9.04 km/h

(d) 82 km/h, 88 − 74 = 14 km/h

12. (a) (i) $50 180 (ii) $24 960 (iii) $54 080(b) (i) $980 (ii) $995(c) mean(d) 55.1% of nation’s full-time workers earn between $500

and $600 a week.66.4% of nation’s full-time workers earn less than $600 to $700 a week.

(e) $1210 (f) $100 000 (g) $34 060

Practice Paper Three1. B 2. D 3. B 4. C 5. B

6. A 7. D 8. D 9. B 10. B

11. (a) (i) 6, 7, 8, 8, 10, 11; 7, 8, 9, 9, 11, 12

(ii) 36 outcomes (iii) (iv)(b) 7.5% p.a.(c) (i) 70 years (ii) 15

(iii) median (iv) 31 members

12. (a) HHH, HHT, HTH, HTT, THH, THT, TTH, TTT(b) (i) $17 940.00 (ii) $18 467.51 (iii) $18 586.59(c) (i) ≈ 2.5 kg, σn − 1 ≈ σn ≈ 0.6 (ii) 0.9 kg

13. (a) (i) C6 (ii) =SUM(B2:B7)(b) (i) $5883.90 (ii) $351.36

(c) (i) (ii) (iii)

(d) $547 740

11. (a) Class (km/h) Frequency Cum. freq.

60–6970–7980–8990–99

713237

7204350

(c)

51504948 52 53Weight of packet (g)

(c)

40302010 50 60 70 80 90

18.5 38.5 5112 81

(c)

0

20

30

10

60 70Speed (km/h)

90

40

80 100

50C

umul

ativ

e fr

eque

ncy

100%

75%

50%

25%

888274

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