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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---
456 NEW CENTURY MATHS GENERAL: PRELIMINARY
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
458 NEW CENTURY MATHS GENERAL: PRELIMINARY
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)
460 NEW CENTURY MATHS GENERAL: PRELIMINARY
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---
462 NEW CENTURY MATHS GENERAL: PRELIMINARY
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
464 NEW CENTURY MATHS GENERAL: PRELIMINARY
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---
466 NEW CENTURY MATHS GENERAL: PRELIMINARY
(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
468 NEW CENTURY MATHS GENERAL: PRELIMINARY
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
Exercise 5-0512--- 5
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
470 NEW CENTURY MATHS GENERAL: PRELIMINARY
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
472 NEW CENTURY MATHS GENERAL: PRELIMINARY
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---
474 NEW CENTURY MATHS GENERAL: PRELIMINARY
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
476 NEW CENTURY MATHS GENERAL: PRELIMINARY
(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
Exercise 9-0623--- 1
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
478 NEW CENTURY MATHS GENERAL: PRELIMINARY
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
480 NEW CENTURY MATHS GENERAL: PRELIMINARY
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
16--- 5
9---
x
16--- 1
2--- 11
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