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
---1 2
---3
x2
--- –3r
q
---3g 5
--- 1
a
---d
5
--- 1
4
--- 1
3 xz
---1 4
--- 2 x
2
5w
---3c
e
--- 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+ 2av
2. (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 1-04
1 2
---1 3 ---1
2
--- 1
2
---3 10
---5 9
--- 1
5
---Exercise 1-05
1 3--- 1
4
--- 13
17
---10 11
--- 5
11
---6 17
--- 7
20
---4 9
--- 1
5
--- 5
7
---2 5
--- 4
5
--- 1
2
---1 5
--- 5
7
--- 2
7
---4 5
--- 44
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. 2 13
--- 5
8
---3 4
---1 3
--- 3
5
---Exercise 1-06
Exercise 1-07
1 3 --- 1
2
--- 5
4
---1 2 ---3
4
---2 3
--- 3
2
---(a) (b)
(c) (d)
(e) (f)
3 2 1
0 y
−1
−4 x
−2
0
1 2
0 y
−1
−2 x
−2
2 2 1
0 y
−2
−2 x
−3
1
−1
−2
0 y
−4
−2 x
−5
1 2
2 1 y
−2
−2 x
−3
−1
−2 2
−1
3 2 1
−3
2
y = 4x − 3
y =−2x
y = x − 2
y = x + 2
y = 2x − 5
1 2
5 4 3
2 1
0 y
−1
−2
y = x 3 − 1
5
1 2
−1 3 x
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
3 2 1
0 y
−1 x
1 2 3 2 1
0 y
−1 3 x
4
4 5
4 5
3
1 2 2 1
0 y
−1 3 x
4
4 5 3
y =−x + 4
y = x 4 + 1
3
y =−1x + 3
4
Exercise 1-08
1 2
---1 7
m =
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 = 0
x = −
1 2
−3
1 2
1 12
4 −3
1 2 −
(a) (b)
(c) (d)
(e) (f)
1 2
m = y
x
1 2
m = −
slopes upwards
1. A, D, F, H
2. (a) y = 9x + 7 (b) y =−5x + 200 (c) y = x + 16
3. (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
3 4
---0 800 1200
400
5
Duration, t (min)
10 15
C = 80t + 22
Cost of calls,
C
(c)
0 100 150
50
20
Overs, n30 40
C = 4.5n
Runs,
S
10
1 8
---Chapter assignment
3 5
--- vw
7
---3c
b
--- 1
a2
---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 %
1 2
---1 2
---1 3
---23 35
--- 7
13
--- 5
6
---(a) (b)
2 0 y
−1
−2 x
−2
3 2
1 y =−2x + 1
2 2 1
0 y
−2
−2 x
−3
−1
y =− 2 1
0 8 12
4
4 Size, S
8 12
L = S + 8
Length,
L
(inches) 1
3 ---1 3
---1 3
---1 3
---1 3 --- 1
3
---1 3
--- 5
6
---Exercise 2-01
3 4
--- 1
3
--- 1
10
--- 1
2
---22 25
--- 3
8
---2 3
--- 1
2
---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) 0.4
2. (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
1 25
--- 7
20
--- 11
20
--- 1
6
---3 8
--- 1
13
---1 3
---9 16
---1.
3 20
---1 2
---2 3
---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 × 104km 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
Exercise 2-04
Exercise 2-05
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
1 3
---1 3
---1 6
--- 2
3
---2 25
---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 × 10−5days 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
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) 100km/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
1 2
--- 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
18 16
7
36
14 15
8 40
12
12
6
20 28
36
26
18
18
24 5 25
21
15 12
18
24
4 7
25
15 15 18
10
22
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
T
T
T T
T
F F
F
F
F F
S
S
S S
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)
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) 87m3 (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
7.
8. (a) 11 994 cm3 (b) 210 000 cm3 or 0.21 m3
(c) 411 470 mm3 or411.47 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
1 3
--- 1
2 ---2
3
---(a) (b)
V1 V2
V
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
Labour 35%
Ingredients 25%
O’heads 20%
Profit
15% A 5%
(f)
100 mm
0 200 300
100
Oct Nov Dec
Month
Jan Feb Mar
400 500
No. CDs sold (
×
1000)
---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 89
90 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
9758 21 935
---Exercise 4-05
8 30
---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)
Deaths from beriberi
0 1000 1500
500
1880 1882
Year
1884 1886 1888
2000
718 5638 --- 359
2819
---Deaths of mothers
0 200 300
100
1841 1842 1843 Year
1844 1845 1846 400
500
First clinic Second clinic 600
Births
0 3000
2000
1941 1942 1943 Year
1944 1945 1946 4000
First clinic Second clinic
(b)
Never smoked Ex-smoker
Smoker 138°
181°
Never smoked Ex-smoker
Smoker
100 mm 41°
20.37% 22.5% 57.1%
5. (a)
(b)
(c) (i) 65.8% (ii) 42%
6. (a) 1993, 1996, 1997 (b) $1 748 300 000
(c) $1 979 100 000 (d)
7. (a) 12.9% (b)
(c)
8. (a) 1 458 000 people
(b) 23.4% (c)
(d) sample; not whole population of Sydney
(e) no; sample is large enough but includes only Sydney viewers
9. (a)
(b) Amount of cannabis is too large compared with the other amounts.
(c) 43.3 kg (d) cannabis; 45 483%
A
v
erage daily intak
e (mL)
20 40
18–44 45–65
Age (years)
65 60
Consume Do not consume
Female alcohol consumption, 1995
100 mm alcohol
54.6% 45.4%
alcohol
V
alue (A$m)
0 350
250
1993 1994 1995
Year
1996 1997
450
Exports Imports 500
400
300
51 93
---China Middle
20 mm 35 mm
93 mm
East India
Afghanistan
T
urk
ey
Iraq Other
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
Amount (kg)
0 40 50
30
Cannabis Cocaine Drug 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-tech
14% Transport/
9%
Manufacturing 14%
50°
32°50°
227°
office
Manuf
act.
Warehouse/
63 mm 14
100 mm
14 mm 9
office
T
ransport Hi-tech
Exercise 4-08
$400
$800
$50 $25
THE BIG AND SMALL OF IT
40%
35%
30% 25%
1995 1996 1997 1998 1999
SMALL CAR SALES
20%
15%
10% 5%
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
15–19 20–24 25–29 30–34 35–39 40–44 45–49
39 30 9 10 4 4 4
Total 100
10-year bonds
December 11 June 11 YIELD %
7.00 6.00
5.00
4.00
3.00
2.00
1.00
0.00
Exercise 4-09
Female deaths
0 300
100
0 10 20
Age (years) 30 40 50 600
400 500
200
60 70 80 90
Frequenc
y
0 20 30
10
15 20
Age (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
0–2 2–4 4–6 6–8 8–10 10–12 12–14
5 10 10 6 4 3 2
Total 40
5. (a) Age (years) Frequency
5 6 7 8 9 10 11 12
7 3 6 5 8 5 4 2
Total 40
(b) No. of words Frequency
0–9 10–19 20–29
10 16 10
Total 36
Frequenc
y
0 4 6
2
2
Weight lost (kg)
6 12 14
8
4 8 10
10
Frequenc
y
0 4 6
2
5 6
Age (years)
8 11 12
8
7 9 10
No. of sentences
0 10 15
5
0 10
No. of words 30 20
(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
56 57 58 59 60 61 62 63 64
2 7 11 6 7 5 4 0 6
Total 48
(b) Height (cm) Frequency
155–<160 160–<165 165–<170 170–<175 175–<180 180–<185 185–<190
1 5 10 8 6 10 8
Total 48
Frequenc
y
0 4 6
2
56 58
Mass of egg (g) 62 8
60 64
10 12
Frequenc
y
0 4 6
2
155 160
Height (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
4 5 6 7 8
3 5 9 0 2 7 8 1 2 4 5 7 8 0 2 3 9 2 4 9
2. (a) Stem Leaf
6 * 7 * 8 * 9 *
3 4 5 5 6 0 2 3 0 1 5 5 7 8 2 3 7 9
3. (a) Stem Leaf
2 3 4 5 6 7 8 9 10 11
8 4 8 1 7 3 2 3 9 1 7 6 8 3 2 8 9 9 4 2 1 3 3 4 3 4 0 0 7 2
5. (a) Stem Leaf
0 5 6 7 8 9
0 2 5 6 8
0 0 3 3 4 4 4 5 8 8 9 9 2 2 2 4 4 6 6 8 9 0 1 1 3 3 4 4 5 9 0 0 3 4 7
6. (a) Stem Leaf
11 12 13 14 15 16 17 18
6 8 0 1 1 4 1 9
0 3 3 5 6 6 6 7 0 4 4 6 6 7 3 5 8 2 4 7 1 7
Exercise 4-11
(b) 20 matches (c) 89 (d) 43
(b) 18 students (c) 99, 63
(b) 13 %
(c) more people, cold weather
1 3
---(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
1 2 3 4 5 6 7 8 9
0 2 1 8 8 5
0 4 1 0 1 7 1 7 2 3 2 6 3 5 3 7 7 4 7 6 7 7 1 7 2 6 4 2 5 4 6 6 7 5 8 5 8 5 9 8 5 3 6 2 6 5 7 3 7 5 7 6
1 0 2 4
1 4 2 9 3 2 3 4 3 5 3 5 5 4 5 2 6 3 8 5
1 2 2 3 4 6 7 2 9 3 0 3 3 8 6 5 7 5
8. (a) Stem Leaf
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 *
9 3 9 5
2 1 2 8 6 1 6 8 6 8 7 5 8 8 9 6 1 8 3 6 3 8 5 2 5 2 7 5 8 6 2 7 4 8 7 1 7 8 8 3 2 6 2 7 3 2 4 3 5 4 8 3 9 2 1 2 3 8 4 5 8 4 9 3 9 4 9 5 2 8 3 6 6 8 7 4 7 5 8 3 8 6 3 5 3 7 5 6 9 7
0 3 2 6 4 6
Exercise 4-12
7 am
9 am
11 am
1 pm
3 pm
5 pm 7 pm 9 pm 11 pm 1 am
3 am
5 am 42
40
38
36 34
Miss Loh’s temperature chart (°C)
T
emperature (°C)
0 37 38
36
7 am 11am Time
7 pm
39
3 pm 3 am 40
41 42
11 pm
Miss Loh’s temperature chart (°C)
7 am
Jan Feb
Mar
Apr
May
Jun Aug
Sep Oct
Nov
Dec 1000
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
8 9 10 11 12 13 14 15 16 17 18 19 20
0 2 4 6 3 4 5 8 6 0 0 4 4 8 9 3 6 8 3 8 0 7 0 3 5 5 0 4 8 5
6. (a) Weight (kg) Frequency
50–59 60–69 70–79 80–89 90–99 100–109
4 12 7 8 3 6
Total 40
Sales ($)
0 400 200
Jan Mar May
Month
Jul Sep Nov
1200
Bill 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)
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
Frequenc
y
0 4 6
2
50 60
Weight (kg)
80 110 120
8
70 90 100
10 12
Number (%)
0 40
10
15–19 20–24 25–29
Age (years)30–34 35–39 40–44
60 Males
Females
20 30 50
50
+
45–49
Male population Tagged males
--- Recaptured males Recaptured tagged males
---CO2
100 mm 49% NO 6%
CFCs 14%
CH4
18% Others
13%
Frequenc
y
0 10 15
5
H A
Offence
R O D
20
S B F
Females Males
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 One
1. 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
Jan Feb
Mar
Apr
May
Jun Jul Aug Sep Oct
Nov
Dec 10 000
5000
0
Scaffolding earnings ($)
Frequenc
y
0 8 10
4
10 20 Class
40 12
30 50
16
60
A
R
K
P 55
55
30 25
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
1 2 ---y
x
−2
6 4
2 4
−4 −2
2
6 8
Exercise 5-01
7 5
--- 1
4
---3. 4
3
--- 1
4
---2 3 --- 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
1 2
---Exercise 5-04
1 4
--- 1
2
---O
O
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 5-05
1 2--- 5
7
---3 2
--- 2
3
---1 2
---1 2
---5 3
--- 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/O
WO
North elevation
560 800
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 3
---1 9
---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
Exercise 6-04
(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. 18 480
D. 75 E. 27 738 F. 241
G. 95 H. 54 I. 390
J. 27 348 K. 20 001–50 000
L. 4584.40 M. 410.22 N. 4994.62 O. 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