Chapter 1
1. (a) 6x2− 4x + 3, C (b) −2x+ 10, L (c) x2−x+ 5, Q (d) x+ 8, L (e) −x3+x2+ 7x, C (f) 20x+ 1, L (g) 5x2+ 7, Q (h) − x+ 2, L (i) − x2 + x+ 1, Q (j) −x3 +7x2 + x, C (k) x3− 5x2 + 14, C (l) −x+ 4, L
2. (a) 7x2 (b) 22m+ 2 (c) d2−d+ 3bd (d) 5c+ 14 (e) 2r2+ 2r (f) −7t2 + 8tu (g) e2 − 2e + 9 (h) −2p2 + 9p (i) 6xy − 5yz (j) 10k+ 11y− 26 (k) −7jk+ 11j (l) 3u2− 4 3. (a) 6m3n (b) 30p2 (c) 4r2t4
(d) 2w4y (e) 15u3 (f)
(g) (h) −18r3 (i) 27x6
(j) 5u2 (k) 5 (l)
4. (a) 7k + 28 (b) 4 (c) 9r+ 55 (d) 5m+ 55 (e) 11a+ 11 (f) 2t− 5 (g) x2+ 2x+ 15 (h) u2 + 13u (i) πr2+ 2πrh (j) −2x3+ 15x2−x (k) 7m+ 10 (l) 3r2− 15r+ 40 (m) 14d− 21 (n) 5f2+ 10 f + 25 (o) 15x2− 6x (p) 2c2 + 22c
5. (a) −2b3d (b) 16a2b2 (c) 4xz + x + 6 (d) 2y2− 12y − w (e) (f) 20d3e2
(g) (h) 2jr− 3r (i) 15w3
(j) 8tu + 3u2− 8t (k) (l) 25f6 (m) 4a2y3 (n) 3ay + 2y (o m2+ 2mn
(p) 12h k3 (q) (r)
1. (a) 2.3 × 105 (b) 8.95 × 106 (c) 1.7 × 10−4 (d) 6 × 10−3 (e) 2 × 107 (f) 3.08 × 10−2 (g) 1.73 × 104 (h) 9.02 × 102 (i) 2.4 × 10−1 (j) 3.6 × 10−5 (k) 4.8 × 106 (l) 7 × 108 2. (a) 720 000 (b) 0.0072 (c) 60 000
(d) 81 900 000 (e) 0.000 002 (f) 0.000 032 (g) 960 000 000 (h) 4 000 000 (i) 0.0175 (j) 2800 (k) 0.000 308 7 (l) 51 290 000
Exercise 1-01
1 2
---3 4
---1 3
---6k2 y ---2 p
5
---3 7d
---2 p2 3 ---5u
– 2t
---9 u
---3d 4
--- 3a
2
---Exercise 1-02
3. (a) 361 100 (b) 7.29 × 10−8 (c) 5.4682 × 107 (d) 75 (e) 3.3 × 10−5 (f) 1.25 × 10−7 (g) 4.565 33 × 1014 (h) 5.789 × 10−4
4. (a) 7.1 × 1011 (b) 3.9 × 107 (c) 2.4 × 104 (d) 6.6 × 102 (e) 8.1 × 106 (f) 6.3 × 1010 (g) 1.9 × 108 (h) 1.8 × 104
1. 16 m2 2. 20 J 3. $1634
4. (a) 26.3 (b) yes; by reducing his weight 5. (a) $NZ51.32 (b) $NZ109.00 (c) $NZ15.65 6. (a) 1 days (b) 1 day (c) 6 days 7. (a) 140° (b) 144° 8. 1.8 × 1014 9. (a) 152 chirps/min (b) increase
10. 51 cm2 11. 11 200 m/s
12. (a) 1.92 mL (b) 1.71 mL 13. (a) 6.75 mL (b) 0.0243 14. (a) 10.2°C (b) 9.2°C 15. 894 m2 16. 2.50 persons/km2
17. 21.76 cm2 18. 64 km 19. 290 cm3
20. $14 664.82 21. 172.79 cm2 22. $24 500
23. (a) 300 101.96 cm3 (b) 0.3 m3
1. p =−5 2. x =−5 3. d = 2 4. h = 12 5. c = 6. r = 17 7. k =− 8. c =−28 9. t =−30 10. k =−2 11. b =− 12. w = 2 13. h = 1 14. y = 5 15. a = 23 16. k =−14 17. c =−4 18. q = 1 19. m = 90 20. c = 3 21. d =−2 22. x = 6 23. z =− 24. y = 4 25. e = 3 26. r =−4 27. d = 11 28. n =−3 29. g =−4 30. b = 15
1. (a) y = 9 (b) m = 65 (c) u =−2 (d) a = 13 (e) y = 144 (f) d = 612 (g) e =−108 (h) k = 4 (i) x = 4 2. (a) d ≈69.80 (b) y ≈ 62.19 (c) c ≈ 1.88
(d) n ≈65.29 (e) p ≈−1.82 (f) w ≈ 61.20 (g) h ≈ 1.55 (h) r ≈66.40 (i) p ≈ 2.88 3. (a) r = 12 (b) x = 7 (c) p = 4
Exercise 1-03
1 2
---Exercise 1-04
1 3
--- 1
2
---1 2
---1 6
---2 7
--- 4
7
---1 2
--- 13
18
---1 2
---1 5
--- 5
6
--- 1
2
---1 5
---9 11
--- 7
8
---Exercise 1-05
(d) d =15 (e) y = 9 (f) a = 5 (g) t ≈ 11.0 (h) c ≈ 6.9 (i) w ≈ 6.2 (j) n ≈ 3.0 (k) h ≈ 4.9 (l) h ≈ 23.8 4. (a) h = 16 (b) k = 11 (c) u = 7
(d) n =5 (e) p ≈ 4.4 (f) r ≈ 6.5 (g) x ≈ 10.2 (h) t ≈ 2.7 (i) a ≈ 8.3
1. (a) y = 10 − 2p (b) y = w − 3 (c) y = 4x + 4 (d) y =−2m + 5 (e) y = or − n (f) y = (g) y =6 (h) y = (i) y = 15k − 1 (j) y =6 (k) y = (l) y =
2. (a) P = (b) m = (c) t = (d) D = (e) v =6 (f) x = 6 (g) s = (h) u = 6
(i) h = (j) m = (k) c = 6
(l) x = (m) A = (n) a =
(o) v = 6 (p) a = (q) x = sz + M (r) n = 8T − 24 (s) r = 6 (t) m = Bh2
(u) k = (v) l = g or
(w) a = 2S − b − c (x) r = (y) k = (z) y = 2P − 220 3. (a) F = + 32 (b) r =
(c) R = 6 or 6
(d) n = + 2 or (e) h =
(f) t = 6 (g) h = 6
(h) T = − 1 or (i) h =
1. Q 2. G 3. N 4. D 5. C
6. B 7. H 8. K 9. V 10. A
11. E 12. X 13. R 14. J 15. T
16. L 17. H 18. S 19. M 20. D
21. U 22. F 23. O 24. I 25. W
26. P
1. 100.4°F 2. 0.5°C 3. 6 cm 4. (a) $2599.73 (b) 11 years 5. (a) 4 sides (b) 10 sides 6. 43.2 km/h 7. 781 m 8. 8 years
Exercise 1-06
u–2n 2 --- u
2 ---x2–3
6
--- z2–x2 2ar 5 ---r
14 x
--- 5d2 64 ---c–b
2a
---I rn
--- y–b
x
--- d S ---V–S
n
--- dg 3V
h ---v2–u2
2a
--- v2–2as 2 A
b
--- E
c2
--- E
m ----h
θ tan
--- 150d m
--- 2s–2ut t2 ---2K
m
--- v–u t
---A π ---8m
5
--- T
2π --- 2 gT2
4π2 ---v2
2g ---C–60
2.7
---9C 5
--- 3V
4π ---3
A π
---+r2 A+πr2 π ---S
180
--- S+360 180
--- S 2πr 2 –
2πr ---2d
g
--- m
B ----6
D
---- 6–D D
--- C–4 8
---Group activity
Exercise 1-07
9. (a) 270.6 km (b) 14 h 17 min
10. 8.8 cm 11. 11 cm 12. year (6 months) 13. (a) 64% (b) A = 51.2% (c) 14 washes 14. (a) $A15.59 (b) $A29.62 (c) $A77.94 15. 21°C 16. 6 cm 17. 15.9 m/s 18. (a) 75 kg (b) 1.81 m or 181 cm
19. 3 × 108 20. 2.49 m 21. 14.2 years 22. 5.70 cm 23. (a) 16.5 mL (b) 11% 24. 2.37 × 109 persons 25. $54 100
1. (a) B, E, J, L (b) A, C, G (c) D, F, K (d) H, I 2. (a) y = 7x − 18 (b) C =−8k + 200
3. (a) C = 0.85v + 92
(b) increase in cost in dollars for each kL of water used (c) initial or fixed cost of water usage
(d) v; volume of water used
4. (b) A = 0.24P − 1.08 (answers may differ) (c) 0.24 accidents (d) 4.68 accidents (e) 88000 persons
5. (a) F = + 32 (b) C
(c) 32; Fahrenheit temperature equivalent to 0°C (d) (i) 53.6°F (ii) 30°C
(e) (i) 55°F (ii) 30°C
6. (a) V =−81.74m + 3760 (answers may differ) (b) $3760
(c) −81.74; decrease in value per month (d) (i) $2125.20 (ii) $326.92 (e) 3 years 10 months (46 months) 7. (a) S (b) L = + 8 or
(c) increase in shoe length per shoe size (d) length of a shoe size of 0
(e) (i) 10 inches (ii) 10 inches (f) (i) size 1 (ii) size 14 8. (a) C (b) C = 270p + 8400
(c) increase in costs for each new computer produced (d) initial or fixed costs
(e) $62 400 (f) 191 units 9. (b) d = 10.5V − 8 (answers may differ)
(c) (i) 464.5 km (ii) 34 L
(d) 10.5; increase in distance travelled per litre of petrol (e) 9.5 L/100 km
1. (a) y = 2x + 4, y =−3x − 1, (−1, 2) (b) y = 3, y = − 3, (4, 3) 2. x = 2, y = 3
3. (a) CopyCat (b) CopyCat $650, own $1450 (c) purchase price/initial cost of owning photocopier (d) 15 000 copies
(e) Own photocopier is cheaper than CopyCat. 4. (a) break-even point at n = 18, C = I = $864
(b) lose money, because income is less than cost (c) cost = $1136, income = $1680 (d) $48 (e) $576 is a fixed (constant) cost of hiring; $16 is the cost
per video.
5. (b) 10°C (c) above 10°C (d) 35°C and below
(e) yes; good approximation for values below 35°C 1 2
---Exercise 1-08
9C 5
---S 3 --- 1
3
--- S+25
3
---1 3
--- 5
6
---Exercise 1-09
---6. (a) break-even point at t = 20, C = 20
(b) Optnet (c) Optnet $22.40, OzExpress $24.00 (d) OzExpress is cheaper if Internet use is less than 20 hours
per month; Optnet is cheaper if use is more than 20 hours per month.
(e) student’s choice 7. (a) k = 7, C = 10.90
(b) At 7 km, cost is the same for both companies ($10.90). (c) Whiteknuckle Cabs is cheaper for shorter journeys of
less than 7 km; Burntrubber Taxis is cheaper for longer journeys of more than 7 km.
(d) Burntrubber: $1.20
1. (a) (b) 16b6 (c) 2y
(d) (e) 3f2+ 5f (f) 24g2h2 2. (a) 3d2+ 20d − 8 (b) 2yz − 4y + 4z
(c) 2πr2+πrs (d) 2m2− 3my
3. (a) 8.3 × 105 (b) 4.71 × 104 (c) 1.62 × 10−7 4. (a) 0.000 29 (b) 654 000 000 (c) 3 000 5. (a) 8.15 × 104 (b) 6.62 × 10−3
6. 30.2 m
7. (a) 119 mm Hg (b) 124.5 mm Hg (c) 130 mm Hg 8. y = 2P − 220 9. 7.8 × 107 km
10. (a) x =−9 (b) k =−2 (c) p =−8 (d) d =63 (e) m = 3 (f) r =−29 11. (a) h ≈64.5 (b) a ≈ 1.7 (c) x ≈60.7
(d) d ≈−2.2 (e) k ≈ 4.2 (f) p ≈ 9.6
12. d =6 13. 27 squares
14. (a) 6 years (b) 16 years (c) 18 years 15. 7 years
16. (a) B, E, I (b) D, F, H (c) A, C, G 17. (a) L (b) L = 4.8M + 36 (answers may differ)
(c) 36 cm; the length of the spring when there is no mass (d) 4.8 cm (e) 93.6 cm (f) 24 kg 18. y = + 12
19. (b) B = 9.5d + 3.5
(c) increase in the amount of bacteria (in thousands /mL) per day
(d) 70 000 bacteria (e) after the 10th day (on the 11th) 20. (b) below; company would lose money as revenue is less
than cost
(c) C = $21 900, R = $20 500 (d) p = 60, C = R = $24 600 (e) $8400; initial or fixed cost of producing computers (f) $410
Chapter 2
1. (a) 39.1 m2 (b) 6 881345 km2
Chapter assignment
2 f3 5 ---mn
2
---1 3
--- 22
29
--- 2
5
---2V–19.8 h
---x 4
---Exercise 2-01
4.6 m
8.5 m
1480 km
(c) 66.08 cm2 (d) 55.5 m2
(e) 1462 mm2
2. (a) 384 m2 (b) 25.1 m2 (c) 103 cm2 (d) 662 m2 (e) 1.54 × 106 km2 (f) 217 m2 (g) 54 cm2
3. (a) A = 840 m2 (b) A = 6879 m2
4. (a) 93 m2 (b) 56 m2 (c) 36 cm2 (d) 7747 mm2 (e) 134 m2 (f) 127 m2 (g) 30 m2 (h) 124 m2 (i) 55 cm2 (j) 89 m2
5. (a) 52 m2 (b) 65 m2 (c) 165 m2 (d) 105 m2 (e) 33 m2 (f) 644 m2 (g) 168 m2 (h) 189 m2 (i) 66 m2 6. (a) (i) 60.7 cm2 (ii) 256 cm2
(b) Area of toy is equal to area of square 16 cm by 16 cm. 7. 98 m2
8. (a)
(b) 6.3 m2 (c) 217 m2 (d) $5900 9. (a) 3.45 m2 (b) 28 circles (7 across and 4 down)
(c) 3.45 − 28 ×π× 0.162≈ 1.2 m2 10. (a) 1000 cm2
(b)
Length needed is 205 cm or 2.05 m.
11. (a) 430.4 ha (b) $96 000 (c) $4620 (d) $240 (e) $18 750 (f) $119 610 12. (a) (i) 113.1 cm2 (ii) 30.9 cm2
(b) 30.9 cm2 (c) 30.9 cm2 (d) Background area is always 30.9 cm2.
5.9 cm
11·2 cm
7.4 m
10 m 5 m
68 mm Other diagonal is 43 mm.
12
21
15 21 14
46
30 22 37
16
58 42
24 m
10 m 2.3 m
2.7 m
1. (a) 16.8 m (b) 45.2 m (c) 202.6 mm (d) 188.5 m (e) 65.4 cm (f) 55.7 cm 2. (a) 314 cm2 (b) 26 m2 (c) 150 954 km2
(d) 7088 mm2 (e) 1 325 359 m2 (f) 883 573 m2 3. (a) 7 m2 (b) 8482 cm2 (c) 88 m2
(d) 150 796 km2 (e) 982 cm2 (f) 1608 m2 4. (a) 198 cm2 (b) 225 m2 (c) 612 mm2
(d) 531 000 km2
5. (a) 98.3 m2 (b) 970 m2 (c) 38.8 m2 6. (a) 78.5 cm2 (b) (i) semicircle (ii) 1608 mm2 7. (a) sector (b) 88 cm2 (c) 12 cm 8. (a) annulus (b) 7.9 m2
9. (a) 43 m2 (b) 47 m2 @ $58/m2= $2726
10. (a) 98 m2 (b) 4 tins @ $152 = $608 11. (a) 424 cm2 (b) 47 cm
12. (a) major segment (b) A = ×πr2
(c) 2 (d)
(e) proof (f) proof
1. (a) 62.0 cm2 (b) 137.2 m2 (c) 50.3 mm2 (d) 21.6 km2 2. (a) 47.1 m2
(b) 11 435 mm2
(c) 1 940 000 ha
3. 7.02 × 1016 km2 4. 35 343 ha 5. Tsar 75 mm2, Anastasia 35 mm2
6. (a) 6130 m2 (b) 6130 × $2.80 = $17 164 7. 3336 m2 8. 217 mm2
9. (a) 3.5 m2 (b) 21 m3 or 21 000 L 10. (a) 45.9 m3 (b) 45 900 L 11. 11 m
1. 666 m2 2. 700 m2
3. area ≈ 60.83 m2, cost ≈ $127
4. 398 m2 5. volume ≈ 6580 m3 or 549 truckloads 6. (a) 115.8 m2 (b) 324 m3 (c) 324 kL 7. 5928 m3
8. (a) 26 m2, 23 m2, 28 m2 (b) 487 m3 9. 146 m2
1. (a) 236 m2 (b) 347 m2 (c) 703 m2 (d) 205 m2 (e) 317 m2 (f) 736 m2
Exercise 2-02
2.4 m
4.4 m
θ 360 ---r2–d2 d r2–d2
Exercise 2-03
6 m
10 m
56 mm
65 mm
112 km
220 km
Exercise 2-04
Exercise 2-05
2. (a) 319 m2 (b) 244 m2 (c) 1022 m2 (d) 1113 m2 (e) 843 m2 (f) 255 m2 3. (a) 406 cm2 (b) 9600 cm2
(c) 1300 cm2
4. 1.7 m2 5. 6.0 m2 6. 4200 cm2
7. (a) 24 cm2 (b) 216 cm2 (c) 1000 small cubes
8. surface area ≈ 168 cm2; 297 wedges
9. (a) 3.6 m2 (b) 0 < length < 1.8 m
1. (a) 836 m2 (b) 6 m2 (c) 1131 cm2 (d) 3 m2
(e) 72 m2 (f) 11 m2
2. (a) 1005 cm2 (b) 4524 cm2
(c) 18 m2 (d) 648 cm2
(e) 1885 cm2
3. (a) 4 m2 (b) 31 m2 (c) 6912 cm2 (d) 1478 cm2
4. (a) 658 cm2 (b) 812 cm2 5. 13.4 m2 6. 5451 cm2
1. (a) 2463 m2 (b) 1963 cm2 (c) 4986 cm2 (d) 193 221 km2 (e) 68 094 mm2
2. (a) 310 000 km3 (b) 224 000 m3 (c) 9.05 × 108 m3 (d) 994 cm3 (e) 2.44 m3
3. (a) 2100 m2 (b) 13 m2 (c) 620 cm2 4. (a) 1.011 × 1010 ha (b) 1.068 × 1012 km3
(c) 5.594 × 109 t
5. (a) 19.40 m3 (b) 19 396 L (c) 30.5 m2 6. (a) 113 cm3 (b) 216 cm3
(c) (i) 6912 cm3= 0.006 912 m3
(ii) You can only fit 32.The bauble in or out of the box takes up the same ‘airspace’.
7. (a) 0.0115 m3 (b) 2463 mirror tiles 8. Light is actually a whole sphere but split in half.
(a) 2.9 m2 (b) 1.4 m2 (c) 0.46 m3 11 cm
7 cm
40 cm
15 cm
10 cm
20 cm
Exercise 2-06
12 m
8 m
30 m
24 m
1.8 m
2.4 m 16 cm
5.5 cm
10 cm
60 cm
1. (a) 4620 cm3 (b) 212 058 cm3 (c) 1646 cm3 (d) 864 cm3 (e) 1386 cm3 (f) 458 cm3 2. (a) 214 L (b) 61 days 2 h 3. 121 cm3 4. 8400 cm3
5. (a) two square pyramids (b) 96 mm3 6. (a) 37 400 m2 (b) 16.7 m 7. (a) 180 cm3 (b) 57 cm2
8. (a) 994 020 mm3 (b) 33.3% (c) 1 265 625 mm3 (d) most appropriate package; less wasted space
9. 571 cm3
10. (a) 1.72 × 106 mm3 (b) 1.59 × 106 mm3 11. 120 cm3
12. (a) pool A 42 m3, pool B 48 m3
(b) pool B (c) 48 000 L (d) 73 m2 13. (a) 0.31 m3 (b) 33 414 cm2 14. (a) 174 cm3 (b) 1390 cm3 (c) 1.4 L
1. (a) (i) 0.5 km, 7.750 × 10−3%
(ii) 0.05 ha, 0.72% (iii) 50 m, 0.63% (iv) 0.005 mg 0.012 55% (v) 0.5 ML, 0.204% (vi) 0.5 m3, 8.333 × 10−3%
(b) (i) is most accurate: has the smallest percentage error 2. (a) 14.5 < 15 , 15.5 cm (b) 240.25 cm2, 210.25 cm2
(c) 230 cm2; valid to 2 s.f.
3. (a) 68.1625 < A (69.01) , 69.8625 m2 (b) 69 m2; valid to 2 s.f.
4. No; it should be recored as 7.8 m2 as it is valid only to 2 s.f. 5. (a) 39.081 25 cm2, 38.201 25 cm2
(b) 39 cm2; valid to 2 s.f.
6. (a) 1 s.f. (b) 45 < 50 , 55 mm (c) 437.5 < A (600) , 787.5 mm2 (d) 600 mm2; valid to 1 s.f. 7. (a) 3 s.f. (b) 50 km
(c) 9.16 × 1011 km3, 8.94 × 1011 km3 (d) 9.05 × 1011 km3; valid to 3 s.f. 8. 332 000 mm3; valid to 3 s.f. 9. (a) 15.625 < V (27) , 42.875 cm3
(b) 37.5 < A (54) , 73.5 cm2
(c) (i) 30 cm3 (ii) 50 cm2 10. (a) 3.78 × 107 km2, 3.83 × 107 km2
(b) 3.80 × 107 km2
(c) 2.19 × 1010< V , 2.23 × 1010 km3 (d) 2.21 × 1010 km3
11. (a) 92 800 < A (93 100) , 93 400 m2 (3 s.f.) (b) 93 100 m2; valid to 3 s.f.
(c) (i) 130 000 m3
(ii) correct for 3 s.f. and there are 3 s.f. in question 12. (a) 60 000 cm2 (3 s.f.) (b) 60 000 cm2 (2 s.f.)
(c) 60 000 cm2 (1 s.f.)
1. (a) (i) 25 m2 (ii) 24 m2 (iii) 7.1 m2 (iv) 25.1 m2 (v) 15.9 m2 (vi) 18.8 m2 (b) semicircle
Exercise 2-08
Exercise 2-09
Chapter assignment
(c) has a variety of water spray patterns
(d) to water different-shaped areas and not waste water 2. (a) 100 cm2 (b) 5400 m2
3. (a) 33.0625 < A , 34.2225 m2
(b) Record volume as 1.7 m3; valid to 2 s.f.
(c) the largest possible value 34 m2 (to 2 s.f.) to be sure to have enough paint
4. 45 cm2
5. (a) 1072 cm3, 2788 cm3 (b) 1716 cm3 (c) 1341 cm2 (d) 1072 cm3≈ 1.1 L 6. (a) 34 000 cm3 (b) 5000 cm2 7. 57 000 bottles 8. 204 m3 9. 1.4 m3 10. 2618 m3 11. (a) 213 m2 (b) 290 m2 12. 3900 m3
13. (a) $1178 (b) (i) 4712 m2 (ii) $53 010 14. (a) 154 cm2 (b) 6404 kg 15. (a) 3.96 m3 (b) 10.5 m 16. (a) 169 cm3 (b) 52 cm 17. (a) 126 m2
(b) width needed = 14 m (4 widths), length = 13.82 m 56 whole metres
18. (a) 13.2 m2 (b) 304 m3 (c) 4 loads (d) 15 tins (not quite enough in 14)
Chapter 3
1. (a) $13 500 (b) $225 2. (a) $5075 (b) $65.06 3. $64.31
4. (a) $403.20 (b) $44.53 5. $29.82
6. (a) $1922.50 (b) $534.94
(c) $31.51 (d) $20.18
7. (a) $8552.50 (b) $3463.76 (c) $333.79
8. (a) $230 (b) $11 040
(c) $3040 (d) 9.5%
9. (a) $109.08 (b) $2617.92
(c) $417.92 (d) 9.5%
10. (a) $154.85 (b) $2991
11. A (a) 9.4% (b) $10 575 (c) $551.25 B (a) 10.75% (b) $2902.50 (c) $330.63 C (a) 10.49% (b) $11 329.20 (c) $654.24 12. A (a) 10.99% (b) $1648.50 (c) $381.19 B (a) 10.99% (b) $4483.92 (c) $305.92 C (a) 11.49% (b) $2815.05 (c) $420.50 13. (a) $71.39 (b) $267.69
(c) $37.07 (d) $340.94
1. (a) $26 160 (b) $6660 (c) 12 % 2. (a) $7460 (b) $9200 (c) $16 524
(d) Toyota 11.9%; Holden 8.2%; Kombi 10.5% (e) lower rates for cars he wanted to sell quickly; higher
rates for more popular cars
Exercise 3-01
Exercise 3-02
---3. (a) $23 200 (b) 24.6% 4. (a) $24 537.80 (b) 18.1% 5. (a) $3600 (b) $750 (c) 19.5%
6. (a) $1460 (b) 20.9%
7. (a) $1780 (b) 17.5%
8. (a) $1560 (b) $410 (c) 23.8% 9. (a) Advantage: No interest paid.
Disadvantage: Need to save up.
(b) Advantage: Pay in amounts you can afford. Disadvantage: High interest.
(c) Advantage: Time to save for purchase but have goods now.
Disadvantage: Interest charged if goods not paid before the interest-free period.
(b) $995.99 (c) $1164.01 (d) $35.99
(b) $941.31 (c) (i) $1152.06 (ii) $1146.63 (d) getting less
(b) $134.65 (c) $134.65 (d) 1 years (e) $115.35
(a) 18 weeks (b) $131.97 (c) $31.97 (d) $60.58 1. (a) n $P $I $(P + I) $(P + I − R)
6 7 8 9 10 11 12
14 594.64 14 511.94 14 428.69 14 344.88 14 260.51 14 175.58 14 090.08
97.30 96.75 96.19 95.63 95.07 94.50 93.93
14 691.94 14 608.69 14 524.88 14 440.51 14 355.58 14 270.08 14 184.01
14 511.94 14 428.69 14 344.88 14 260.51 14 175.58 14 090.08 14 004.01
2. (a) n $P $I $(P + I) $(P + I − R) 2
3 4 5 6
99 844.62 99 688.64 99 532.06 99 374.88 99 217.09
384.02 383.42 382.82 382.21 381.60
100 228.64 100 072.06 99 914.88 99 757.09 99 598.69
99 688.64 99 532.06 99 374.88 99 217.09 99 058.69
3. (a) n $P $I $(P + I) $(P + I − R) 1
2 3 4 5
2000 1550 1088.75
615.97 131.37
50 38.75 27.22 15.40 3.28
2050 1588.75 1115.97 631.37 134.65
1550 1088.75
615.97 131.37
0
4. n $P $I $(P + I) $(P + I − R) 1
2 3 4 5 6 7 8 9
2500 2206.73 1912.67 1617.82 1322.18 1025.74 728.50 430.46 131.62
6.73 5.94 5.15 4.36 3.56 2.76 1.96 1.16 0.35
2506.73 2212.67 1917.82 1622.18 1325.74 1028.50 730.46 431.62 131.97
2206.73 1912.67 1617.82 1322.18 1025.74 728.50 430.46 131.62
0
Exercise 3-03
1 4
---1. (a) $1012 (b) $1048.75 (c) $1646.80 (d) $1335.69
2. (a) (i) $2527 (ii) $909 720 (iii) $529 720 (b) (i) $517.24 (ii) $155 172 (iii) $88 172 (c) (i) $3687.60 (ii) $1 327 536 (iii) $907 536 (d) (i) $3285 (ii) $788 400 (iii) $423 400 3. (a) (i) $29 119.20 (ii) $9119.20
(b) (i) $133 225.20 (ii) $33 225.20 (c) (i) $6967.20 (ii) $1967.20 (d) (i) $79 291.20 (ii) $29 291.20 (e) (i) $145 593.60 (ii) $45 593.60 (f) (i) $34 833.60 (ii) $9833.60 4. (a) (i) $531.27 (ii) $61 129.56
(b) (i) $603.93 (ii) $106 179.00 (c) (i) $768.92 (ii) $176 811.20 (d) (i) $742.64 (ii) $71 498.56 (e) (i) $860.19 (ii) $90 801.04 (f) (i) $492.37 (ii) $38 626.60 (g) (i) $1408.16 (ii) $247 448.00 (h) (i) $2855.75 (ii) $224 035.00 5. (a) (i) 11% (ii) 8%
(b) (i) 20 years (ii) 25 years
1. (a) $1876 (b) $216
2. (a) $206 (b) $1245
3. (a) $644 912 (b) $99 370
4. (a) 9.3% (b) 7.3%
5. (a) 10 years 3 months; $107.26 (b) 11 years 6 months; $345.34
6. (a) $3650; $1789.04 (b) $2520; $691.14 7. (a) $1933
(b) The term increases by 1 to 4 periods, depending if the payment is missed towards the end or towards the start. (c) (i) Principal remains the same; repayment only pays off
the interest.
(ii) Loan will never be paid off; principal keeps increasing as repayment doesn’t even cover the interest.
(d) $1501 8. (a) $386
(b) (i) repayment $193 (half) (ii) repayment $772 (double)
(iii) repayment $719 (not quite double—about 1.9 times as large)
(iv) repayment $222 (more than half—about 60%) (c) (i) 53 periods not 60 (7 periods less)
(ii) 28 periods not 60 (less than half the term) (iii) 55 periods not 60 (5 periods less) (iv) 62 periods not 60 (2 periods more)
1. (a) $391 (b) $393.39 2. (a) $750 (b) $5.72 3. (a) $1156 (b) $13.61
4. (a) $538 (b) $558.21 (in a non-leap year)
Exercise 3-04
Exercise 3-05
(b) 70c (c) $20; 10 March (in a non-leap year)
1. (a) $4440 (b) $92.50
2. (a) $15 705 (b) $9423 (c) $523.50 3. (a) $1399.90 (b) 35.7%
4. (a) $38 880 (b) $2880 (c) 6%
(b) $186.41 (c) $413.59 (d) $3.08 6. (a) $1528
(b) nil as 15 December is last day of interest-free period (c) $30.76
7. (a) $636 (b) $90 000 (c) 9%
(d) $707 (e) $90 000 (f) 8.5%
8. (a) (i) $513 (ii) $18 468 (iii) $3468 (iv) $6300 (b) (i) $1238 (ii) $22 284 (iii) $2284 (iv) $4200 (c) (i) $930 (ii) $55 800 (iii) $15 800 (iv) $28 000 (d) (i) $1680 (ii) $40 320
(iii) $5320 (iv) $9800
9. (a) (i) $10 400 (ii) $866.67
(b) No; this would need a monthly repayment of $1729. (c) $75 176
10. (a) about 260 repayments (b) about $290 000 (c) about 175 months
11. (a) loan paid off sooner; less interest paid (b) (i) about $85 000 (ii) about $75 000 (c) (i) about 21 years (ii) about 15 years
Practice Paper One
1. C 2. B 3. D 4. A 5. B
6. C 7. B 8. A 9. D 10. D
11. (a) (i) T = 11.1 (ii) x = 3.9 (b) (i) $5850 (ii) $68.65 (c) 331 733 m2
12. (a) (i)
5. (a) Date Details Amount
18 Jan 28 Jan 28 Jan 1 Feb 6 Feb 10 Feb
Elio Restaurant Cash advance Cash advance fee Big M Groceries Payment—thank you Robert’s Roses
$95.60 $100.00 $1.00 $138.50 $1595.12 CR
$55.00 Balance from previous
Payment and credits Purchases, cash advances Interest and other charges Closing balance
$1595.12 $1595.12 CR
$389.10 $1.00 $390.10
5. (a) n $P $I $(P + I) $(P + I − R) 1
2 3 4 5
10 000 9 963.33 9 926.36 9 889.08 9 851.49
83.33 83.03 82.72 82.41 82.10
10 083.33 10 046.36 10 009.08 9 971.49 9 933.59
9963.33 9926.36 9889.08 9851.49 9813.59
Chapter assignment
No. of yo-yos, n
10 20 30 40 50
300 $
200
100 90
(30, 180)
R = 6n
C = 3n + 90
(ii) (30, 180) (iii) $165
(iv) Below. The factory would make a loss producing 25 yo-yos because the cost would be more than the revenue.
(b) 150 m3
(c) (i) $69 195.69 (ii) $2555.69 (iii) =D10−$B$4 or =B10+C10−$B$4
13. (a) b = (b) (i) 47.5 m to 48.5 m (ii) 1236.75 m2 (c) $222.15 (d) (i) $27 866.40 (ii) $7866.40
Chapter 4
1. (a) quantitative continuous (b) quantitative discrete (c) quantitative continuous (d) categorical
(e) categorical (f) quantitative continuous (g) quantitative discrete (h) quantitative continuous 2. population too large; population too difficult to survey 3. Biased sample is not truly representative of the population.
Unbiased sample is representative of the whole population. 4. (a) systematic (b) stratified (c) simple 5. (a) (i) column graph showing percentages of different
drugs used by Australians (ii) qualitative (or categorical)
(iii) Display gives clear comparison of drugs most/least used.
(b) (i) clustered column graph showing the numbers of people in different age groups who get a Newstart Allowance
(ii) quantitative (or numerical) and continuous (iii) Display should have a title on each axis; shows a
good comparison within age groups.
(c) (i) line graph showing road fatalities from March 1995 to March 1999
(ii) qualitative (or categorical)
(iii) Display shows peaks, troughs and steady decline in deaths; exact values not easy to read off.
1. (a) mean ≈ 5.1; median = 5; mean better as it takes into account all scores and data set is evenly spread (b) mean ≈ 23.9; median = 23.5; mean better as data set is
evenly spread and all scores are included
(c) mean ≈ 33.8; median = 38; median better as there is an outlier of 8
(d) mean = 8.8; median = 8.5; mean better as there are no outliers and all scores are included
2. (a) range = 7; IQR = 5; evenly spread distribution so either measure is suitable
(b) range = 8; IQR = 3; evenly spread distribution so either measure is suitable
(c) range = 37; IQR = 12; IQR better due to the outlier of 8. (d) range = 6; IQR = 4; either measure suitable as data set
has no outliers 3. (a) ≈ 65.1; σn − 1≈ 19.7
(b) ≈ $425.6; σn − 1≈ $165.9 (c) ≈ 38.2°F; σn − 1≈ 1.2°F (d) ≈ 164.0 kg; σn − 1≈ 17.4 kg (e) ≈ 19.3; σn − 1≈ 3.2
2 A h
---Exercise 4-01
Exercise 4-02
4. (a) blonde
(b) We are interested in ‘most popular’ colour.
(c) categorical data; can’t find an ‘average’ hair colour as it has no meaning
5. (a) 24.5 min (b) 25 min (c) 6 min (d) 2 min (e) σn − 1≈ 1.8 min
(f) mean and standard deviation as the data set is fairly evenly spread with no outliers
(b) agree with statement as Ted has a smaller standard deviation which means he has less variation each day 7. (a) 4 accidents (b) 4 accidents
(c) either as the data is fairly evenly spread; mean is usually used in this case
(d) 9 accidents (e) 3 accidents (f) σn − 1≈ 2.5 accidents
(g) disagree with statement as spread is quite large 8. (a) ≈ 35.8 min (b) σn − 1≈ 14.0 min 9. (a) = $785 (b) σn≈ $111.9 10. (a) 65 (b) σn≈ 24.4
(c) Many students scored between 71 and 100 but scores ranged from below 20 to the 90s.
1. (a) (b)
(c) (d)
(e)
2. (a) (i) negatively skewed (ii) cluster around 6–8
(iii) no (iv) 1 peak
(b) (i) symmetrical (ii) no
(iii) yes (iv) none
(c) (i) slight positive skew (ii) no
(iii) no (iv) 2 peaks
(d) (i) symmetrical (ii) no
(iii) no (iv) 4 peaks
(e) (i) symmetrical (ii) no
(iii) no (iv) none
(f) (i) symmetrical (ii) no
(iii) no (iv) 2 peaks
6. (a) Ted Julie
(i) (ii) (iii) (iv)
168 shirts 6 shirts 21 shirts σn − 1≈ 3.9 shirts
160 shirts 6.5 shirts 20 shirts σn − 1≈ 5.2 shirts
x x
Exercise 4-03
3.
Display shows a negative skew and peak time around 1700– 2000. This is the early evening timeslot and shows the most popular time for Internet use.
4. (a)
(b) Display is fairly uniform with a peak around 8–9; no real clustering or outliers.
(b) Display shows clustering in the 10s and 20s and is positively skewed.
(c) ages of people at, say, a dance party since most scores are 15–23
6. (a) ≈ 2.9 accidents (b) σn − 1≈ 2.5 accidents (c) faulty equipment; inexperienced workers (d) ≈ 2.4 accidents; σn − 1≈ 1.7 accidents
(e) Including the outlier 9 gives a larger mean and a greater spread since both and σn − 1 are larger.
1. (a) (i) A: = 15.0; median = 15 B: ≈ 18.3; median = 15 (ii) Set B has an outlier of 40.
(iii) Median is not affected by outlier; mean is raised. (b) (i) A: = 38.4; median = 41
B: = 44.6; median = 41 (ii) Set A has an outlier of 5.
(iii) Median is not affected by outlier; mean is lowered. (c) (i) A: = 8. ; median = 8.5
B: = 10. ; median = 8.5 (ii) Set B has an outlier of 25.
(iii) Medians are the same but mean of B is higher. (d) (i) A: = 130.0; median = 135
B: ≈ 126.4; median = 140 (ii) Set B has an outlier of 55.
(iii) Medians are about the same and so are the means; outlier has little effect.
2. (a) (i) ≈ 10.3; median = 8; mode = 8
(ii) 26 (iii) median
(iv)
(b) (i) = 13; median = 14; mode = 4, 16 (ii) no outliers (iii) mean 5. (a) Stem Leaf
1 2 3 4 5
5 5 5 5 5 5 5 5 6 6 7 7 7 8 9 9 9 0 0 1 1 2 2 2 3 3 4 4 4 4 5 6
0 3 9 0 4 5 8 9
1200 1400 1600 1800 2000 2200
Time 0
1 2 3 4 5 6
Hits (
×
1000)
Website hits
3 5 8 10 11 12
2 4 6 7 9 13 14
x
x
x
Exercise 4-04
x x
x x
x 3.
x 6.
x x
x
(iv)
(c) (i) ≈ 82.8 g; median = 80 g; mode = 80 g
(ii) 120 g (iii) median
(iv)
(d) (i) ≈ 38.1°C; median = 38°C; mode = 37°C (ii) no outliers (iii) mean
(iv)
3. (a) ≈ $403.57 (b) $420
(c) median as $635 is an outlier and mean is affected by this score
(d) new ≈ $443.93; new median = $462 (e) 10%
(f) = $365; median = $385
4. (a) Wombats: = 16.8 points; median = 18 points Possums: = 16 points; median = 16 points Koalas: = 17.2 points; median = 14 points (b) Possums as mean and median are the same (c) = 18.8 points; median = 18 points
(d) still the Possums with the Wombats a close second 5. (a) Pam 3 copiers; Percy 3 copiers
(b) They are equally good salespeople. (c) Pam 5.5 copiers; Percy 17 copiers (d) Pam 7.2 copiers; Percy 16.6 copiers (e) median as Pam has an outlier of 25
(f) Percy as his median sales are much higher than Pam’s. 6. The mean and median will move towards 100.
7. (a) $46 500 as 10 people have this wage
(b) $46 500 (c) $40 138 (d) median (e) median because of the outliers $13 500 and $64 300
1. (a) Boys: $14, $17, $29, $41, $52 Girls: $12, $20, $25, $31, $42 (b) Boys: IQR = $24; Girls: IQR = $11 (c)
(d) The larger spread of data for boys; the middle 50% of the amount spent by girls ranged over only $11 whereas for boys it ranged over $24.
2. (a) 12 cm (b) 26 cm
(c) Estimates: range = 34 cm, IQR= 17.5 cm Actual: range= 11 cm, IQR = 3.5 cm
(d) Definitely agree; the box plot for estimates has a much greater spread as well as a much lower median, even though some people did overestimate.
3. (a) A: range= 90, IQR= 58.5; B: range= 91, IQR = 18 (b) A: median = 56.5; B: median = 53
x
g x
°C x
x
x x x x
x
Exercise 4-05
10 20 30 40 50
Boys
Girls
0
Amount spent at Easter show ($)
(c)
(d) Stem-and-leaf plot: set B is clustered in the 50s. Box plots: ranges are about same but IQR of set B is much smaller.
(b) X: ≈ 75.4 beats/min; Y: = 73.5 beats/min (c) X: 76 beats/min; Y: 76.5 beats/min (d) Both are suitable as there are no outliers and
distributions are fairly symmetrical.
(e) Group X shows clustering in the 70s; group Y shows clustering in the 70s and 80s.
5. (a) 6 beats/min
(b) Those with the lowest pulse did not exercise hard enough and pulse stayed the same; or someone who had a higher pulse due to rushing to class could have reduced their pulse rate by not working hard in the class. (c) Two people exercised very hard and got their pulse rates
up very high.
(d) 5 people (e) 22 beats/min
6. (a) Before: IQR = 18 cigarettes; Later: IQR = 15 cigarettes (b)
(c) Although upper and lower extremes have both gone down, the median of the ‘later’ has increased. The program would need to go for longer to see if it was really going to work.
(b)
(c) Stem-and-leaf plot: Sydney values cluster around 12 days.
Box plots: Sydney has a much smaller spread than Melbourne; median and upper quartile for Sydney are equal.
(d) Disagree with ‘much’; the median number of rainy days per month is only 1 day greater for Melbourne (13) than for Sydney (12).
4. (a) Group X Group Y
8 9 7 6 2 9 7 7 5 2 2 2 1 0 8 1
5 6 7 8 9
2 3 2 4 4 3 4 5 8 9 0 1 1 2 6 2
7. (a) Sydney Melbourne
3 2 2 2 2 2 2 2 1 0 0 0 0 1
7 8 9 1 2 2 4 4 4 5 5 6
20 40 60 80 100
Set A
Set B
0
x x
10 20 30 40 50
Before
6 weeks later
0
Cigarettes smoked per day
5 10 15 20
Sydney
Melbourne
0
8. (a) 50 globes (b) ≈ 129.5 hours (c) = 131.5 hours (d) Oso Bright: σn − 1≈ 14.7 hours
Brighta Longa: σn − 1≈ 13.9 hours (e)
(f) Brighta Longa; it has less spread and a higher average.
1. (a) 4 days (b) 9 days at Perisher; April (c) 23 days (d) Perisher; highest number of clear days
(e) Not necessarily; although Perisher has the greater number of clear days, more information (such as snow conditions, temperature) needed before deciding this. 2. (a) about 1 400 000 wage earners
(b) about 5 800 000 wage earners (c) about 4 600 000 wage earners
(d) Wage earners in the public sector were fairly constant over the 6-years. There was a fall in those employed in the private sector in 1992–93 with a steady rise after that. (e) Private sector has about 4 times more wage earners as
the public sector.
3. (a) about 110 mm (b) about 90 mm (c) about 350 mm (d) The widest ‘band’; it could contain rainforest. (e) Rainfall is highest in autumn and winter; the greatest
seasonal change is from summer to autumn.
(f) Rainfall in SW region is similar each season; rainfall in SE and N regions increase in autumn and winter. 4. (a)
(b) similar, but intake larger
(c) Output peaks after input; no periods of 0 input or output. 5. (a)
x x
110 120 130 140 150
Oso Bright
Brighta Longa
100 160
Lifetime of globe (hours)
Exercise 4-06
Mr Pappadopoulos’s fluids (mL)
6 am
8 am
10 am
12 noon
4 pm 6 pm 8 pm
12 pm 2 am
4 am
2 pm 10 pm
0 50 100 200 150 250
Intake Output
Clark and Lois’s earnings from writing ($)
Jan
Feb
Mar
Apr
Jun
Jul Aug Oct
Nov Dec
May Sep
0 200 400 800 600 1000 1200 1400
Lois Clark
(b)
(c) earnings over the 12-month period; contribution of each to their holiday fund by relative sizes of enclosed areas (d) highest earnings in June
6. (a) percentage of Australia’s population by age group from 1921 to 2041
(b) estimated (or projected)
(c) largest group; declining in proportion in 21st century (d) (i) 30% (ii) 55%
(e) 25%
(f) two peaks for 0–14 age group in 1961 and 2001 (see ‘Baby boomers’ on page 139); increasing percentage of 65+ group; decreasing percentage of 0–14 group (g) Age 60+ will increase from 2001 to 2041 as the ‘baby
boomers’ age; percentage of 0–14-year-olds will keep getting smaller (fewer babies are expected to be born).
1. (a) 10 140 (b) 12 650 (c) 45% (d) 32% (e) increased costs; better public facilities locally
(b) 57%
(c) The trend over the 85 years has been towards city living. 3. (a) (i) 524 860 people (ii) 821 690 people
(b) 51% (c) 37%
(d) (i) 24% (ii) 14%
(e) increased: 39% to 51% then 49% (f) stayed fairly steady: 37% to 35% then 37% (g) The number of users doubled by 1997 but so did the
population, so market share increased only about 10%. 4. (a) (i) 2020 people (ii) 3650 people
(b) 64% (c) 39%
(d) The 55–69 group as 82% voted to keep the flag. Perhaps the older you are the less you like change or the stronger your ties to Britain.
2. (a) 1911 1996
Rural areas 43% 13%
Urban (city) areas 57% 87%
1. (a) Group A Group B
4 5 3 0 9 8 6 5 5 4 2 5 1 0 1
3 4 5 6 7 8
2 6 8 8 9 0 5 8 0 1 2 4 5 8 0
Clark and Lois’s earnings from writing
2400
2000
1600
1200
800
400
0
Earnings ($)
J F M A M J J A S O N D
Clark Lois
Exercise 4-07
(b)
(c)
(d) Stem-and-leaf plot: clustering in the 60s for group A; less range for group B.
Clustered column graph: both groups’ mode in the 60s; group B nearly bimodal; group B more symmetrical. Box plots: larger range and higher median for group A. (e) A: ≈ 61.9 seconds; σn − 1= 13.0 seconds
B: ≈ 56.4 seconds; σn − 1= 8.8 seconds
(f) Group A data tended to be closer to the 60-second value but estimates were spread out. Group B tended to under-estimate the minute but under-estimates were less spread out.
(b) Birds: have a higher average and cluster in the 50s. Bees: have a smaller range and are more evenly spread. (c) Birds: = 52.6; σn − 1≈ 15.0
Bees: = 36.7; σn − 1≈ 13.0
The Birds have a higher mean and a slightly higher standard deviation.
The Bees have a smaller mean but a smaller standard deviation so are less spread out.
2. (a) The Birds The Bees
3 5 8 6 5 2 1 4 2 0
1 2 3 4 5 6 7
8 3 4 7 6 1 6 8 8 6 6
5 4 3 2 1 0
Group A Group B
30–39 40–49 7
50–59 60–69 70–79 80–89
Frequency
Estimated time (s) Estimation of 60 seconds
40 50 60 70 80
Group A
Group B
30 90
Estimated time (s)
x x
4
3
2
1
0
The Birds The Bees
10–19 20–29 30–39 40–49 50–59 60–69
Frequency
Score Netball scores
60–69
20 30 40 50 60
The Birds
The Bees
70 Netball scores
x x
Neither team stands out as being more consistent than the other, but due to the lower standard deviation the Bees are a little more consistent.
3. (a) The number of persons belonging to a workers’ union increases with age but drops off at 65+ as most people have retired from work by then.
(b) The eastern region consistently has a higher percentage of people belonging to a union than the western region. However, only those aged 35–64 are more likely to belong than not belong, as these are the only age groups with 50% or more belonging.
4. (a) clustering; location (average) (b) spread
(c) Men: median = 175 cm; IQR = 10 cm Women: median = 164.5 cm; IQR = 10 cm (d) Men: ≈ 175.0 cm; σn − 1≈ 8.4 cm
Women: ≈ 164.0 cm; σn − 1≈ 7.4 cm
(e) same IQR; mean and median for each group about the same (≈175 cm for men and ≈164 cm for women) (f) Men’s heights have higher mean and median; men have
greater range of heights.
5. (a) Suggested displays: column graphs, radar charts, line graphs.
(d) (i) Canberra (ii) Hobart (iii) Sydney (iv) Darwin 6. (a) Suggested displays: area charts, column graphs.
(c) (i) winter (ii) summer
(d) Rainfall does vary between seasons, especially in winter where the average is higher.
1. (a) quantitative discrete (b) quantitative discrete (c) quantitative continuous (d) quantitative discrete (e) quantitative continuous (f) categorical
2. (a) = 11.75; median = 12; mode = 12; ages of students in Year 7
(b) = 4; median = 4; no mode; number of teeth that a 1-year-old child has
(c) = 80.1; mean = 79.5; mode = 72; ages of a group of senior citizens or HSC university entrance scores 3. (a) 9.9 (b) 8.5
(c) (i) Mean and median both increase. (ii) Mean and median both increase.
(b) (c) City Mean Median Range σn
Adelaide 10.3 10 13 4.2
Brisbane 10.2 10 8 2.6
Canberra 9 9 5 1.6
Darwin 9.1 7.5 21 7.8
Hobart 13.3 14 6 1.8
Melbourne 12.3 13 9 2.8
Perth 9.7 9 15 5.4
Sydney 11.4 12 3 1.0
(b) Season Mean Median Range σn
Summer 10.0 10.5 18 4.7
Autumn 10.5 11 17 3.7
Winter 11.4 12.5 18 5.1
Spring 10.7 11 14 3.2
x x
Chapter assignment
x x
(iii) Mean and median both decrease. (iv) No effect on mean; median decreases. (d) (i) Mean and median both increase.
(ii) Mean and median both decrease. 4. (a) (i) ≈ $126.45; σn − 1≈ $42.3
(ii) fairly symmetrical
(b) (i) = 6.6 trips; σn − 1≈ 1.9 trips (ii) bimodal (c) (i) ≈ 3.3 hours; σn − 1≈ 1.5 hours
(ii) positively skewed
5. (a) C (b) A (c) B (d) D
6. (a) A: = 52.7 g; σn − 1≈ 3.64 g B: ≈ 53.9 g; σn − 1≈ 5.01 g (b) median = 51.5 g; IQR = 6.5 g (c) median = 53 g; IQR = 7 g (d)
(e) Disagree; machine B data is clustered in the 50s but has a bigger spread, thus is not as consistent as machine A. 7. (a) 30°C
(b) Goulburn: range = 16°C; Grafton: range = 10°C (c) Goulburn: median = 19.5°C; Grafton: median = 25°C (d) median temperature; range of temperatures; highest and
lowest scores 8. (a)
(b) Not uniform; most of combined total comes from area 1. (c) Area 2 has much lower rainfall; range is much greater in area 1; distribution more uniform in area 2 (positively skewed).
9. (a) clustered (horizontal) column graph; male and female occupations in Australia in 1996
(b) Categorical data; occupations are categories.
(c) Elementary and Intermediate clerical, sales and service. Advanced clerical and service persons. Professionals (d) Tradespersons and related
(e) good visual comparison but difficult to read off actual values.
10. (a) about 1 350 000 (b) about 1 600 000 (c) about 2 500 000
(d) Yes; number of females in 70+ age group was about 700 000 compared with about 400 000 males. 11. (a) Class A Class B
8 3 9 5 4 0 0 9 8 8 6 5 4 4 3 3 5 3 3 2 1 0
3 4 5 6 7 8 9
2 5 2 4 5 6 3 3 3 4 6 1 9 9 2 9 0 2 x
x x
x x
60 50
Machine A
Machine B
40
Mass of rod (g)
65
45 55
180 160 140 120 100 80 60 40 20 0
Area 1 Area 2
Rainfall (mm)
Jul Aug Sep Oct Nov Dec
Monthly rainfall, Australia, 1999
(b) Class A: cluster in 60s; slight negative skew Class B: bimodal; slight positive skew (c) Class A: range = 32; IQR = 15
Class B: range = 60; IQR = 34
(d) Class A: σn − 1≈ 9.2 Class B: σn − 1≈ 19.5 (e) Range, IQR and standard deviation all are appropriate as
all show the much greater spread of class B. (f) mean since the data sets have no outlier scores
(mean of both sets ≈ 63)
12. (a) about 14% (b) about 17% (c) 1992–93 (d) Households have saved a smaller percentage of national
income, and corporates a larger percentage; but total savings have decreased over the years.
(e) Saving remained fairly steady for both households and companies until about 1986–87; then company saving increased and household saving decreased. Household and corporate savings fluctuate similarly with minor peaks and troughs.
13. (a) 606 people (b) 290 people (c) 47%
(d) 6% (e) 50%
Chapter 5
1. (a) x = 8.30 m (b) t = 25.74 cm (c) y = 3.35 m (d) p = 90.46 mm (e) d = 0.74 m (f) h = 21.36 cm (g) w = 6.53 mm (h) k = 2.05 m (i) p = 49.20 cm
2. (a) 36° (b) 42° (c) 66° (d) 56° (e) 35° (f) 8°
3. (a) 74°53′ (b) 32°22′ (c) 48°1′ 4. 53° 5. (a) 5.5 m (b) 1.8 m 6. 78°11′ 7. 31.4 m 8. 31.5 m 9. 21.7 km 10. 18°58′ 11. 88.9 m 12. 142.15 m 13. 17.5 m 14. 3.3 m 15. 223 m 16. 2.3 m 17. 24.8 m
18. 208 m 19. 11° 20. proof
1. (a) NW (b) SW (c) SE (d) NE (e) SW (f) SE
2. (a) 237° (b) 059° (c) 294° (d) 130° (e) 196°46′ (f) 317°45′
3.
Exercise 5-01
Exercise 5-02
(a) (b)
(c) (d)
81° N
247° N
300° N
4. (a) 315° (b) 225° (c) 045° 5. (a) (i) Nowra (ii) Mt Kosciuszko
(iii) Moruya (iv) Jenolan Caves
(v) Tumut (vi) Cooma
(b) (i) 344°; 49 km (ii) 151°; 306 km (iii) 210°; 182 km (iv) 225°; 127 km (v) 110°; 143 km (vi) 050°; 163 km
6. (a) pool (b) NW (c) SE
(d) school (e) cemetery (f) Daniela Way (g) (i) S (ii) NE (iii) SE
(h) Coopers Lane; E 7. C
8. (a) 2.9 km (b) 6.6 km (c) 024° 9. 125°
10. (a)
(b) 77 km, by Pythagoras’ theorem (c) 074° 11. (a) 14.45 km (b) 18 min 12. 18.3 km 13. (a) 2122 km (b) 330° 14. 186°
1. (a) positive (b) positive (c) negative (d) negative (e) positive (f) positive
2. (a) 47° (b) 85° (c) 22°
(d) 79° (e) 56° (f) 18°
3. (a) −0.8290 (b) −1.7321 (c) 0.2807 (d) −0.0875 (e) −0.2653 (f) 0.8973 (g) 0.9976 (h) −0.6963 (i) −0.5589 (j) −0.6421 (k) 0.9839 (l) −0.7364 4. (a) acute (b) obtuse (c) both
(d) acute (e) obtuse
5. (a) 61°07′ (b) 72°54′ (c) 63°49′ (d) 73°0′ (e) 75°4′ (f) 41°49′ (g) 38°48′ (h) 72°33′ (i) 8°13′ 6. (a) 105° (b) 151° (c) 128° (d) 127°
(e) 166° (f) 105° (g) 110° (h) 114° (i) 153° (j) 125° (k) 120° (l) 135° 7. (a) 19.06 (b) 61.84 (c) 196.07 (d) 0.27 (e) 7.27 (f) 4.04 (g) −1.38 (h) 0.45 (i) 20.91 (j) 0.64
1. (a) x = 11.39 m (b) y = 7.47 cm (c) d = 4.07 m (d) w = 9.58 cm (e) c = 18.69 m (f) b = 78.46 mm 2. (a) 15.9 km (b) 3.4 km
3. 13.9 cm B
A 35°
35°
S N
55° 48 km
60 km
Exercise 5-03
Exercise 5-04
4. (a)
(b) By drawing a perpendicular from AC to B, two right-angled triangles are created. ∠ABC = 73° + 75° = 148° (c) 63 M
5. AP = 8.0 m, AQ = 6.5 m
6. (a) 357 m (b) 383 m (c) 350 m 7. (b) A = 38°, B = 97°, C = 45° (c) 11.2 km 8. 2.4 m 9. 7.2 km 10. 20.1 km 11. 5.62 × 107 km
12. (c) 942 m (d) 208 m (e) 128 m
1. (a) 41°50′ (b) 9°28′ (c) 77°34′ (d) 28°43′ (e) 32°05′ (f) 64°21′ (g) 35°6′ (h) 63°29′ (i) 20°57′ 2. (a) 120° (b) 111° (c) 131° 3. (a) 47°22′ (b) 132°38′
4. 50° 5. 281° 6. 64°
7. 234°37′ 8. 125° 9. 239° 10. (a) 30° (b) 30° (c) isosceles (d) 4.5 m
1. (a) d = 5.57 m (b) r = 6.02 cm (c) k = 7.59 m (d) h = 8.65 m (e) w = 5.17 cm (f) y = 27.21 mm 2. 35.3 km 3. 0.6 m 4. 22.4 km 5. 20.4 cm 6. 9300 m 7. 3.3 m 8. 7.2 m 9. (c) 4.4 km
10. (a) 360° (b) 72° (c) 47.02 cm 11. (b) 32° (c) 46 km
12. (a) 3.14 cm (b) 3.13 cm (c) arc AB by 0.01 cm
1. (a) 26°3′ (b) 52°11′ (c) 123°12′ (d) 36°11′ (e) 91°26′ (f) 48°15′
2. (a) 98° (b) 41° (c) isosceles (d) 41°
3. 21° 4. 9°
5. (a) 25° (b) 78° 6. proofs 7. 8°28′
8. (a) 56° (b) 124° (c) 24.2 m
9. 29° 10. 125°
11. 11° 12. proof
1. (a) 8.04 m2 (b) 24.07 cm2 (c) 19.86 m2 (d) 13.02 m2 (e) 24.20 cm2 (f) 85.88 mm2 2. 269 mm2 3. 27.9 cm2 4. 1207 m2 5. 26.1 cm2 6. 6 cm2
7. (a) 60° (b) 64.95 cm2 (c) 5 cm 8. 21.22 cm2 9. 21.22 cm2 10. 7.2 m2
11. (a) 55.85 m2 (b) 31.51 m2 (c) 24.34 m2 12. 41.6 cm2
N
N
195° 31 M 163° A
C B
Exercise 5-05
Exercise 5-06
Exercise 5-07
Exercise 5-08
(e) (f)
180° N
1. (a) x = 7.11 m (b) p = 17.85 cm (c) r = 44.30 mm (d) a = 11.38 cm (e) y = 11.71 m (f) k = 50.67 mm
2. (a) 40° (b) 51° (c) 92°
(d) 43° (e) 47° (f) 89°
3. 133° 4. (b) 180 m 5. 15 m 6. 8.5 m 7. 153°51′ 8. 1420 km 9. (a) 20.5 m (b) 69.0 m2 10. (c) 216 m 11. (a) 87°16′; 20.98 cm2 (b) 50°59′; 20.98 cm2 12. 1287 m 13. (b) 190 m 14. 11.1 cm; 5.4 cm
1. (a) 1608 m2 (b) via B; 4.6 m
2. (a) 94° (b) 1876 m2 (c) 320 m 3. 9055 m2
4. (a) 147° (b) 1200 m2 (c) 77° (d) 74 m 5. AC = 50 m; CB = 74.31 m
6. 15.73 m 7. 201 m
8. (a) ∠JOK = 77°; ∠KOL = 96°; ∠LOM = 103°; ∠MOJ = 84° (b) 5256 m2
9. 102 m 10. 2700 m2
11. (a) 90 m (b) 66.06 m (c) 76.45 m
(d) 89 m (e) yes
12. (a) 121° (b) 5424 m2 13. (a) 120 m (b) 5400 m2 14. 5300 m2
15. (a) difference in accuracy of surveying methods and measurement of areas
(b) radial or offset survey; greater number of measurements taken
(c) Simpson’s rule; is an approximation method
1. (a) d = 11.39 cm (b) x = 18.92 m (c) p = 8.78 m 2. (a) 153°17′ (b) 57°7′ (c) 61°36′ 3. (a) acute (b) obtuse (c) both
4. (a) 18° (b) 55° (c) 73°
5. (a) 151° (b) 166° (c) 136°
6. 384 m 7. A
8. 104° 9. A
10. 63° 11. 15.7 km
12. 35°32′ 13. 3.95 km
14. 252 m 15. 170 m
16. 72.1 m
17. (a) 78° (b) 38 m (c) 129° (d) 354 m2
Exercise 5-09
Exercise 5-10
21 m
6 m 35 m 38 m
36 m 27 m
3 m K
L
M N
P
Chapter assignment
18. (a) (b) 2588 m2
19. (a) 340 km (b) 13 949 km2
20. (a) ∠QPR = 47°; ∠PRQ = 68° (b) 63 m
Chapter 6
1. (a) (b) (c) (d)
(e) (f) 0
2. (a) 0.0064 (b) 0.64%
3. (a) 0.020 (b) 0.137 (c) 0.252 (d) 0.803
4. (a) (b) (c) (d)
5. 55.6%
6. (a) (b) (c) (d)
7.
8. (a) (i) (ii) (iii) (b)
9.
10. (a) (b) (c) (d)
11. (a) 6.25% (b) 29.2% (c) 85.4% (d) 37.5% 12. 13. 14. (a) a drawn game (b) 7%
15. (a) (b) (c) 1 (d)
(e) 0 (f)
16. (a) any certain event (b) any impossible event 17. (a) 83.75% (b) 7.5% (c) 8.75% (d) 98.125%
18. (a) (b) (c) 0 (d)
19. 20. (a)
(b) The first digit in a phone number is not random but depends on the area covered by the phone book.
21. (a) (b) (c) (d)
22. (a) (b)
1. (a) BBBB, BBBG, BBGB, BGBB, BBGG, BGBG, BGGB, BGGG, GBBB, GBBG, GBGB, GGBB, GBGG, GGBG, GGGB, GGGG
(b) (i) (ii)
2. (a) (b) (c)
20 m
19 m 25 m
16 m
28 m 21 m 35 m
E C
B D F
Exercise 6-01
1 5
--- 1
10
--- 7
10
--- 3
10
---9 10
---1 3
--- 4
9
--- 1
9
--- 7
9
---2 7
--- 4
7
--- 17
21
--- 5
7
---7 32
---1 4
--- 1
26
--- 1
2
--- 25
51
---6 7
---4 7
--- 5
7
--- 2
7
--- 6
7
---2 11
--- 2
3
---19 50
--- 7
10
--- 3
10
---31 50
---3 4
--- 1
2
--- 1
4
---1 73
--- 1
10
---2 7
--- 3
7
--- 3
7
--- 5
7
---w r+w+b
--- w+b r+w+b
--- or 1 r r+w+b ---–
Exercise 6-02
1 4
--- 3
8
---2 9
--- 1
18
--- 1
---3.
(a) (b) (c) (d)
4. (a) (b) (c) (d)
5. (a) 20 pairings
(b) (i) (ii) (iii)
6. (a) 16 possibilities
(b) (c)
7. (a) (b)
8. (a) 6 possibilities
(b) (i) (ii) (iii)
9. (a) similar to the tree diagram for question 6(a) 5 6 9 2 6 9 2 5 9 2 5 6 25 26 29 52 56 59 62 65 69 92 95 96 2 5 6 9 1 12 --- 1 2 --- 5 12 --- 1 4 ---3 8 --- 1 8 --- 3 8 --- 1 8 ---K S A B E S A B E K A B E K S B E K S A E K S A B EK ES EA EB KE KS KA KB SE SK SA SB AE AK AS AB BE BK BS BA 1 10 --- 1 20 --- 1 5
---R ---R ---R ---R R R R
R R R
R R
R R R
R R
R R
R R R R R R R R R R R R R R˜ R˜
R˜ R˜
R˜
R˜ R˜
R˜ R˜
R˜ R˜ R˜
R˜
R˜ R˜
R˜ R˜
R˜ R˜ R˜
R˜ R˜
R˜ R˜ R˜
R˜ R˜ R˜
R˜ R˜ R˜ R˜
R R R˜ R˜ R R R R R R R R R˜ R˜ R˜ R˜ R˜ R˜ R˜ R˜ R R R R R˜ R˜ R˜ R˜ R R˜ 3 8 --- 15 16 ---1 4 --- 1 3 ---C T A T A C A C T ACT ATC CAT CTA TAC TCA T C T A C A 1 6 --- 1 3 --- 2 3
---(b) (i) (ii) (iii) (iv)
(a) (b) (c) 1
11. (a) 24 (b) (i) (ii) (iii)
1. 240 2. 248 832 3. (a) 15
(b) CL, CV, CR, DL, DV, DR, JL, JV, JR, ML, MV, MR, PL, PV, PR
4. 128 5. 1 000 000 6. 144
7. 7776 8. 17 576 9. 120
10. (a) 10 000 (b) 456 976
11. 1024 12. 360 000 13. 300 14. (a) 24
(b) RG, RJ, RN, RC, RL, RI, AG, AJ, AN, AC, AL, AI, HG, HJ, HN, HC, HL, HI, WG, WJ, WN, WC, WL, WI
15. 64 16. 63 17. 45 697 600
18. (a) to create more phone numbers (b) 90 000 000
19. 30 20. 128 21. 2n
1. (a) 120 (b) 60
2. (a) 9; 11, 13, 18, 31, 33, 38, 81, 83, 88 (b) 6; 13, 18, 31, 38, 81, 83
3. 24
4. (a) 342 (b) 6; JM, JB, MJ, MB, BJ, BM
5. 15 600 6. 16 777 216
7. 479 001 600
8. 24; AFEM, AFME, AEFM, AEMF, AMFE, AMEF, FAEM, FAME, FEAM, FEMA, FMAE, FMEA, EAFM, EAMF, EFAM, EFMA, EMAF, EMFA, MAFE, MAEF, MFAE, MFEA, MEAF, MEFA
9. 5040 10. 42
11. (a) 12 144 (b) 96 909 120 12. (a) 64 (b) 24
13. 6; BMR, BRM, MBR, MRB, RBM, RMB
14. 1716 15. 336
16. (a) 6; MJC, MCJ, JMC, JCM, CJM, CMJ (b) 6; MJ, MC, JM, JC, CJ, CM (c) 3; M, J, C
17. (a) 24; KJGE, KJEG, KGJE, KGEJ, KEJG, KEGJ, JKGE, JKEG, JGKE, JGEK, JEKG, JEGK, GEKJ, GEJK, GKJE, GKEJ, GJKE, GJEK, EGKJ, EGJK, EKJG, EKGJ, EJKG, EJGK
(b) 6; JG, JE, GJ, GE, EJ, EG
18. 15; 1, 4, 6, 14, 16, 41, 46, 61, 64, 146, 164, 416, 461, 614, 641
19. (a) 120 (b) 12
20. (a) 30 (b) 25 (c) 21
10. − 1 2 3 4 5 6
1 0 1 2 3 4 5
2 1 0 1 2 3 4
3 2 1 0 1 2 3
4 3 2 1 0 1 2
5 4 3 2 1 0 1
6 5 4 3 2 1 0
1. (a) 10 (b) CF, CS, CV, CP, FS, FV, FP, SV, SP, VP 2. 1 961 256 3. 2024 4. 231
5. 5 586 853 480 6. 3 838 380 7. 1.58 × 1010 8. (a) 10
(b) ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE
9. 70 10. 4; ABC, ABD, ACD, BCD 11. 3003 12. 56
13. (a) 15 (b) 360
14. (a) 120 (b) 28 (c) 3360
15. 2 760 681
16. (a) 10 (b) 5 (c) 10 (d) 1 17. (a) 2660 (b) 5984
18. 38 760 19. 1287 20. (a) 15 (b) 15
(c) They are the same, as the number of ways of choosing 2 children for the front is the same as the number of ways of choosing 4 children for the back.
1. (a) ordered (b) ordered (c) unordered (d) ordered (e) unordered (f) unordered (g) unordered
2. (a) 120 (b) (c) 24 3. (a) 120 (b) 2
4. (a) 210 (b) 80 (c) 5.
6. (a) 1680 (b) 7. (a) 24 (b) 8. (a) 36 (b) 10 (c)
9. (a) 24 (b)
(c) = 4; CVM, CVS, CMS, VMS (d) 10.
11. (a) (b) (c)
(d) (e) (f)
12. (a) 7 059 052 (b) 3 258 024 (c) Lotto 13.
14. (a) (b) (c)
15. proof 16. (a) 30 (b) 17. (a) 84 (b) (c) 60 480
18. (a) (b) (c)
19. (a) 625 (b) (c)
20. (a) JK, JL, JM, JN, KL, KM, KN, LM, LN, MN
(b) (c) (d)
1. (a) (b) (c)
2. (a) (b)
Exercise 6-05
Exercise 6-06
1 120 ---8 21 ---1 35 ---1 8 --- 1 4 ---5 18 ---1 4---4×3×2 3×2×1
--- 1 4 ---2 3 ---1 270 725 --- 256 270 725 --- 1 270 725 ---69 184 270 725 --- 16 270 725 --- 325 833 ---1 66 ---6 203 --- 75 406 --- 45 116 ---4 15 ---10 21 ---1 120 --- 1 20 --- 2 5 ---1 625 --- 16 625 ---2 5 --- 3 10 --- 1 6
---Exercise 6-07
1 7 --- 2 7 --- 4 7 ---1 45 --- 16 45 ---3. (a)(b) (i) 38.4% (ii) 51.2% (iii) 48.8%
4. (a) (b) (c) (d)
5. (a) (b) (c) (d) 6.
7. (a)
(b) 0.0132 (c) 0.9868
8. (a) (b) (c)
9. (a) 0.250 (b) 0.441
10. (a) (b) 11. (a) (b)
12. (a)
(b) (i) (ii) (iii) (iv) 1 13. 0.0579%
14. (a) 0.8% (b) 7.2% (c) 9.2%
15. (a) p3 (b) (1 − p)3 (c) p2(1 − p) (d) 3p2(1 − p)
1. 210 2. 58 3. 47
4. (a) $0.75 (b) no
5. (a) 3 (b) 10 (c) 12
6. (a) 15c (b) no; 15c 7. (a) 0.0011 (b) 2048
8. (a) $22.50 (b) loss, because he bet $25 9. (a) $1.71 (b) (i) $400 (ii) $342 10. (a) 8 145 060 (b)
(c) (i) $4 500 000 (ii) 2 (iii) $1 500 000 11. (a) 98.4 cents (b) yes (close enough) 12. B, with a financial expectation of $290
13. 13
14. (a) 20 (b) 60 (c) 140
R R R
R R R R R R R R R R˜ R˜
R˜ R˜
R˜
R˜ R˜
R˜ R˜
R˜ R˜ R˜
---(b) 9 (c) lose 33c per game 16. (a) $1250 (b) $620.30
17. (a) 7 (b) 20 (c) 47 18. 14
1. (a) 0.3125 (b) yes 2. (a) 31.25% (b) 6.25% 3. 0.69 4. 0.62
5. (a) $1.61 (b) and (c) $128.80 6. P(stick = win) = , P(switch = win) =
7. 3 8. boys 9. 14
10. 23 11. 0.52 12. 0.57
1. (a) across: 28, 212, 240 (b) 212 (c) 1 (d) ≈ 0.393 (e) ≈ 0.995 (f) 5% 2. (a) down: 37, 363; across: 34, 366, 400
(b) 400 (c) 9.25% (d) 8.5% (e) 1.25%
(f) ≈ 2.94% (g) ≈ 1.09%
3. (a) 92 (b) 12% (c) 3 (d) (e) (f) no rain
4. (a) 5 (b) 60 (c) 355 (d) ≈ 0.98 (e) non-anaemic (0.98 vs 0.96)
5. (a) 240 (b) 116 (c) 10.8% (d)
(e) (f) females
6. (a) (i) 2001 (ii) 19 (iii) 2020 (b) 2020 (c) 87 (d) 99% (e) = 0.075 (f) ≈ 0.007
1. (a) (b) (c) (d)
(e) (f)
2. 12.2% 3. (a) (b)
4. (a) (b) (c)
(d) (e)
5. 4536 6. 12
7. (a) (b) (c) (d)
8. 9. 17 576 000 10. 39 916 800
11. 20 12. 21 13. 1330
14. (a) 231 (b) 253
15. 58 16. 17. 252 18. 133 784 560
19. (a) 0.012% (b) 82% (c) 18% (d) 17%
20. 28 21. B 22.
15. (a) + 1 1 3 4 5 6
1 2 2 4 5 6 7
2 3 3 5 6 7 8
3 4 4 6 7 8 9
4 5 5 7 8 9 10
6 7 7 9 10 11 12
6 7 7 9 10 11 12
Exercise 6-09
1 3
--- 2
3
---Exercise 6-10
11 28
--- 211
212
---1 34
--- 4
366
---7 10
---39 41
---295 298
---115 132
---99 108
---6 80
--- 13
1940
---Chapter assignment
1 26
--- 2
13
--- 3
4
--- 5
13
---5 26
--- 11
13
---1 6
--- 11
36
---1 120 000
--- 1
8
--- 13 073
15 000
---13 6000
--- 799
800
---1 2
--- 1
4
--- 1
2
--- 3
4
---3 4000
---33 95
---1 15 625
---23. (a) 90c (b) Expectation does not equal cost of game. (c) 90c
24. (a) (b) (c) (d)
25. (a) 200 (b) 95% (c) 28 (d) 26. $2460
Practice Paper Two
1. C 2. A 3. D 4. B 5. B
6. A 7. D 8. D 9. B 10. C
11. (a) 22° (b) (iii) 285 m (c) (i) 39 s
(ii) The processing times of the automated checkouts were generally shorter and slightly less spread out than those of the manual checkouts.
(iii) The manual checkouts are not more consistent; they are slightly more spread out. It is better to use automated checkouts because they are more consistent and their average processing time is lower.
12. (a) (i) (ii) (iii)
(b) (i) (ii) 31.1 km
(c) (i) 61.7% (ii) 2.5% (d) 266= 308 915 776 13. (a) (i) 2.01 − 1.98 = 0.03 cm (ii) σn − 1= 0.018 cm
(b) $352 gain
(c) (i) 145° (ii) 878 m2 (iii) 106 m
Chapter 7
1. (a) D (b) G (c) A (d) C
(e) F (f) B (g) E (h) H
2. (a) G (b) C (c) D (d) E
