answers
CHAPTER 1 Earning money
Skills check
1 75 2 12.6 3 3825
4 11.4% 5 400 km 6 20.8 days
Exercise 1A — Calculating salary
payments
1 $1700 2 $960 3 $4500
4 a $745 b $1490 c $3228.33
5 $1653.84
6
7 $23 920 8 $32 500 9 $69 600
10 C 11 $14.28
12 a $634.62 b $17.63
13 a $688 b Karina ($16.38 per hour)
14 45 hours
Exercise 1B — Calculating wages
1 $518
2
3 a $424.80 b $566.40 c $501.50
4 a $432 b $499.50 c $600.75
5 a $17.34 b $225.42
6 D 7 $9.68 8 39
9
10 $12.54 11 C 12 D
13 $422.62 14 $548.80
15 a $349.65 b 43 hours
16 $11.78
10 Quick Questions 1
1 $344.16 2 $518.70 3 $218.40
4 $95.04 5 $12.87 6 $903.85
7 $2692.31 8 $4706.67 9 $846.15
10 $24.18
Exercise 1C — Commission and
royalties
1 $ 2000
2 a $260 b $327 c $568.79
3 a $400 b $1200 c $1360
4 $1425 5 $4140 6 B
7 C 8 $8125 9 $800
10 a $4125 b $5375 c $16 875
11 $950
12 a $390 b $490 c $649
13 B
14 a $400 b $500 c $8000 d $8125
15 $625
16 a $300 b $345 c $406.80
17 D
18 $15 500 19 $510 20 $810
Exercise 1D — Payment by piece
1 $75.95
2 a $103.50 b $94.50 c $85.50 d $81
3 $175 4 $135 5 $325.50 6 $327
7 a $92 b $138 c $87.40 d $114.08
8 a $57.75 b $125.13 c $103.95
9 $22.80
10 a $11 b $27.80 c $19.32
11 a $134.40 b $16.80
12 a $174 b $21.75/h c $29.00/h
13 24
10 Quick Questions 2
1 $455.84 2 $346.15 3 $740.38
4 $3307.69 5 $32 406.40 6 $487.20
7 $570 8 $208.55 9 $60.30
10 $1840
Exercise 1E — Working overtime
1 $16.95 2 $22.84 3 $28.70
4 $142.56 5 $157.20
6
Answers
Annual
salary Weekly pay
Fortnightly pay
Monthly pay
$30 000 $576.92 $1153.84 $2500.00
$39 500 $759.62 $1519.23 $3291.67
$42 250 $812.50 $1625.00 $3520.83
$54 350 $1045.19 $2090.38 $4529.17
$86 475 $1662.98 $3325.96 $7206.25
Name
Hourly rate
Hours
worked Wage
A. Smith $14.52 40.5 $580.80
B. Brown $16.45 38.5 $625.10
N. Tran $15.95 37.5 $598.13
A. Milo $20.10 41.5 $824.10
L. McTavish $18.04 36.5 $649.44
Name Wage
Hours worked
Hourly rate
A. White $416.16 36 $11.56
B. Black $538.80 40 $13.47
C. Green $369.63 37 $9.99
D. Brown $813.96 42 $19.38
E. Scarlet $231.30 15 $15.42
F. Grey $776.72 38 $20.44
Name
Ordinary rate
Overtime rate
Hours worked Pay A. Nguyen $8.90 Time and
a half
4.5 $53.40
M. McDonnell $9.35 Double time
6.5 $112.20
F. Milosevic $11.56 Time and a half
7.5 $121.38
J. Carides $13.86 Time and a half
6.5 $135.14
Y. Robinson $22.60 Double time
answers
➔
10 $543.52 11 $721.60 12 $596.25
13
14 C 15 A 16 $595.20
17 a $705.28 b $788.80 c $928
18 $455.78 19 $492
Exercise 1F — Additions to and
deductions from gross pay
1 $385.20
2
3 $389.80
4 a $2519.23 b $1585.23
5 $7.58
6 $56.02
7 a $511.10 b $5.11 c $407.26
8 a $2153.85 b $44.84 c $1448.41
9 $18.71
10 $106.44
11 a $422.56 b $23.24 c $331.14
12 a $2884.62 b $137.02 c $69.60
d $1668.78
13 a $516.80 b $2428.96
14 a $880.77 b $4139.62
15 a $466.20 b $81.59 c $464.55
16 a $5269.23 b $922.12 c $96.15
d $4315.28
Chapter review
1 $761.54 2 $2592.31 3 $15 912 4 $22.29
5 a $522 b $594.70 c $588.24
6 a $442.80 b $220.80
7 $11.40 8 43 hours 9 $395.20
10 $798.50 11 $534 12 $340.75
13 $98
14 a $21.30 b $28.40
15 a $98.10 b $109
16 a $368.60 b $426.80 c $426.80
d $485
20 a $1855.77 b $83.51
21 a $631.55 b $13.26
c $22.10 d $455.89
CHAPTER 2 Taxation
Skills check
1 20.4 2 15% 3 $110
4 17.8 litres 5 4.05 hrs
Exercise 2A — Calculating allowable
deductions
1 $1153.90 2 $1624.55
3 $1070.10 4 $1540.36
5 a $914 b $1208.77 c $811.72
d $1560.20
6 a $1000 b $600 c $360
7 $3087.50
8 a i $30 000 ii $18 000 iii $10 800
b 2005–06
9 $960 10 $18 760
11 $712.27 12 $40 074.50
Exercise 2B — Taxable income
1 $43 754.25
2 a $16 879.20 b $15 736.50
3 $43 568.34
4 a $24 219.40 b $22 262.60
5 a $20 503.60 b $20 075.20
6 a $42 500 b $2600 c $39 900
7 a $34 262.30 b $498.24 c $32 204.06
8 a $74 280 b $8737.46 c $65 542.54
9 a $25 649 b $1470 c $1540
d $1349.40 e $21 289.60
10 A
10 Quick Questions 1
1 $2260 2 $1581.22 3 $1650
4 $1105.50 5 6 years 6 $36 520
7 $41 771 8 $22 660 9 $37 525.80
10 $24 570
Exercise 2C — Medicare levy
1 $598.05
2 a $648.75 b $851.18 c $1410
3 a $23 491 b $352.37
Exercise 2D — Calculating tax
1 $7015
2 a Nil b $2154.75 c $5755
d $9676 e $14 677 f $23 303.04
3 a $17 039.36 b $1876.63
4 $3897.40
5 a $7060 b $534.00 c $7594
6 a $2402.50 b $8646.10 c $18 662.50
7 $81.14
8 $230.69
9 B 10 B 11 D
12 a $38 674.10 b $8562.31 c $291.69 refund
13 a $38 942.80 b $166.28 c $8252.67
d $393.89 refund
Name
Ord. rate
Normal hours
Time and a half hours
Double time
hours Total pay
W. Clark $8.60 38 4 $378.40
A. Hurst $9.85 37 .5 6 $482.65
S. Gannon $14.50 38 5 2 $717.75
G. Dymock $16.23 37.5 4 1.5 $754.70
D. Colley $24.90 36 6 8 $1518.90
Gross pay Deductions Net pay
$345.00 $89.45 $255.55
$563.68 $165.40 $398.28
$765.90 $231.85 $534.05
$1175.60 $429.56 $746.04
$2500.00 $765.40 $1734.60
answers
14 a Gross annual pay = $44 650, PAYG tax = $11 940.50
b $41 513.40 c $9456.72 d $2483.78
15 a $392.05 b $4751.14 debt
16 1590 17 Pay $180
10 Quick Questions 2
1 $600 2 $360 3 $442.01
4 $385.05 5 $502.62 6 Nil
7 $2305.20 8 $6130.00 9 $14 603.80
10 $25 920
Investigation — Tax offsets
1 The amount appears correct ($52.50)2 $1115
Exercise 2E — Calculating GST and VAT
1 $3.562 a 23c b $6.89 c $9.85
d 13c e $8.99
3 a 80c b 48c c 9c
d 63c e 34c
4 $123.75
5 a $126.39 b $32.89 c $16.17
d $5.45 e $6.47
6 a $30 b 94 cents c $47
d $2.94 e $9.86
7 $98.50
8 a $1.90 b 19c
9 $348.10
10 a $1.08 b $80.63 c $193.29
d $49.21 e $6.95
11 a $33 550 b $36 630 c $34 705
d $38 885
Chapter review
1 $28652 $2148.43
3 a $12 600 b $9072 c $6531.84
4 6 years
5 $27 057.35
6 $43 883
7 $70 420
8 a $28 483.60 b $26 465.60
9 a $34 409.30 b $32 366.15
10 $585
11 a $232.50 b $375 c $412.50
d $502.60 e $570
12 $9730
13 a Nil b $2270.69 c $7081
d $15 160 e $24 040
14 a $33 987.20 b $6576.16 c $509.81
d $7085.97 e $136.27
15 $291.66
16 a $40 255 b $9060.33 c $1100.93
17 $99
18 a $1.13 b $36.90 c 12c
d $3.75 e $1.25
19 $22 20 $112.50
CHAPTER 3 Spending money
Skills check
1 33.75 2 237.6 3 306
4 $360 5 $53.45
Exercise 3A — Discount
12
3
One item is discounted by just over 30% but the others range from a 10.00% to a 28.59% discount.
4
5
6
9
10
11 No, as the 12.5% is calculated from different amounts. For example, a $60.00 item reduced by 12.5% ($7.50) is $52.50. A $52.50 item increased by 12.5% ($6.56) is $59.06.
Exercise 3B — Profit and loss
12
5 Children’s $14.40; Adults’ $20.40; Extra large $22.80
a 25% b 49.3% c 27.7% d 28.8%
e 11.5% f 26.5% g 25.2% h 28%
i 10% j 20%
a i $10.05 ii 25.16%
b i $7.05 ii 23.54%
c i $17.05 ii 42.68%
d i $7.95 ii 19.90%
a 25.02% b 11.12% c 10.00% d 28.59%
e 22.23% f 20.01% g 30.78%
a i $4.98 ii 19.88%
b i $10.57 ii 9.46%
c i $5.91 ii 7.78%
d i $4.65 ii 14.19%
e i $16.99 ii 11.77%
f i $8.35 ii 10.30%
Item
Original price
($)
% dis-count
Discount ($)
Sale price ($)
a Microwave 300 10% 30 270
b Furniture set 2030 5% 101.50 1928.50
c Mirror 40 30% 12 28
d Necklace 1560 12.5% 195 1365
e Fridge 760 20% 152 608
f Stereo system
480 33 % 160 320
g Washing
machine
564 25% 141 423
h Car 7500 50% 3750 3750
a $119 b $101.15 c $17.85
7 A 8 D
a $11.94 b $1.79
a $175 b $8.75
a 74.94% b 40.63% c 80.08% d 50%
e 55.26% f 197.5% g 45% h 63.64%
a 80% b 78% c 85.71% d 92.48%
e 85.71% f 70% g 75% h 95.83%
3 $70, 140% 4 $79.75; 53.26%
6 4 years 7 $150 8 $25 each
1 3
answers
➔
10 Quick Questions 1
1 25% 2 $105 3 12.5% 4 $23.80
5 50% 6 $21.60 7 $40 8 236%
9 $780 10 $180 000
Investigation — Dealing in diaries
1 $2.40 2 $30 3 25%
4 58.3% 5 $50 6 41.7%
7 $130 8 $80 9 61.54%
Exercise 3C — Budgeting
1
2 Answers will vary.
3 a
b $34.83
4
5 a $320.83
b Income = $809.50 per month; New expenses = $677 per month, so she can afford to move out.
6 Answers will vary.
7 a
b $600 c 2.36%
Exercise 3D — Cost of services
1 a $348.50 b 1/3/01
c Previous $375.55, down $27.05
d 7/11/00, 7/02/01
e $3.79 f $26.60
g Tariff 11 up, Tariff 33 down
2 a 2253 b 52 964 c $24.13
d $241.31 e 10.7 cents
3 a 1904 b 1352 c $319.35
4 a $100.70 b $9.40 lower
c Approx. samed $1.12 e $408.40
f $34.03
5 a 134 b × by MJ factor
c $9.16 d 2.397c/MJ
e $101.48
6 a 6370 b $106.26 c $10.63
d $116.89
7 $138.66
8 a $166.09 b $181.09 c Pensioner
d $367.27 e $664.36 f $55.36
9 a 62 kL b $0.80 c 248 kL
10 $138.60
11 a $10 000 b 15%
12 a Call charges + Service and equipment charges − Flexi-Plan
b 28.2% c Flexi-Plan d $144.15
13 a 404 @ 25c b 17.7% c 35.6
d 22.8c e 7 pm
Exercise 3E — Credit cards
1
4 a53 days, 48, 40, 34 and 26 days bVery beginning
5 $17.70
6 a 28 days b $22.10
c No, since it was paid on 29/4, which was less than 25 days from the end of the statement
d The balance is over $25, but under $1000, so the minimum amount due is $25.
e Credit limit − Closing balance: $1000 − $650 = $350
7
Exercise 3F — The exchange rate
1 a 58.29 b 38.27 c 119 900 d 406
2 a $373.83 b $821.14 c $630.32 d $74.57
3 a 50 504 yen b $784.59 c $15.41
4 a 800 b 320 c $257.82
5 $15.41
10 Quick Questions 2
1 Fixed, variable 2 $8.46
3 $46 800 4 3110 kWh
5 0.0493% 6 4th May
7 The total amount owing is $540.65.
8 Selling 9 7.81 Pounds 10 $150.28
a $1565 b $785 c $1450 d 2.07 months
Monthly income ($) Monthly expenses ($) Austudy
Birthday money 502.67
20.83
Board and food Transport Books and
stationery Insurance Entertainment Enrolment fee Clothes
216.67 63
40 24 55 25 65
Total: 523.50 Total: 488.67
Item
Cost ($ per week)
Rent 138.46
Food 90
Electricity 32.31
Gas 4.62
Phone 27.69
Car registration 8.27
Car insurance 9.62
Health insurance 13.46
Contents insurance 2.40
Clothes 23.08
Entertainment 18.46
Total: 368.37
Income ($) Expenses ($)
Government subsidy Membership
fee Profit from
auction Profit from
stalls Profit from
concerts
4 200
16 250
400
920
3 600 Rent Newsletter Sunday School Bills
Public liability and insurance Advertising Stationery Computer Unexpected
6 000 960 7 200 2 640
1 860 360 250 3 500 2 000
Total: 25 370 Total: 24 770
a $17.50 b $25 c $25 d $25
e $33 f $57 g $87 h $54
i $58 j $80
2 $4.95 3 $0.75
a $19.89 b $29.08
answers
Chapter review
1 $35 2 16.7% 3 $250
4
5 $256.20 6 $200
7
8 a Rent $100; Electricity $10; Gas $7; Phone $23; Car registration $8; Car insurance $9; Contents insurance $3; Health insurance $9; Food $100; Sport $30; Entertainment $20; Clothes $28; Holidays $23; Total $370 b $5200
9 $45.42 10 $400.97 11 $40
12
13 65.03 pounds
CHAPTER 4 Length, area and
volume
Skills check
1 The shortest measured distance between two points.
2 mm, cm, m, km.
3 The distance around the boundary of an object.
4 a 24 cm b 28 m c 15 m d 18.85 m
5 The amount of space within the boundary of a two-dimensional closed figure.
6 mm2, cm2, m2, km2, ha
7 a 36 cm2 b 40 m2 c 10.83 m2 d 28.27 m2
8 a Square b Rectangle c Triangle
d Trapezium/trapezoid e Parallelogram
f Kite
9 a 2.13 b 1.75 c 79.51 d 3.06
10 ‘Volume’ is the amount of space within, or occupied by, a 3-D object. ‘Capacity’ is the quantity of liquid or gas which a 3-D container could hold.
11 a mm3, cm3, m3
b mL, L, kL, ML
12 a 0.6 cm b 250 mm
c 0.004 m2 d 450 m
e 0.3 L f 0.005 m3
g 0.025 kL h 5000 mm3
l 0.1 L j 25 m3
Exercise 4A — Changing units and
calculating perimeters
1 a 7 cm b 6 m c 5 km d 90 mm
e 1200 cm f 9000 m g 8.6 cm h 9200 m
i 2.4 km j 64 mm k 1125 cm l 22 mm
2 5200 mm long 2400 mm wide 2500 mm high
d 42 mm e 24 m f 510 m
4 a 108 m b 12.1 m c 71.7 m
d 334.3 mm e 79 cm f 139 m
5 E
6 C
Exercise 4B — Calculating areas
1 a 0.7 cm2 b 0.6 m2 c 30 000 cm2
d 2 500 000 m2 e 45 000 m2 f 300 ha
2 a 64 cm2 b 841 mm2 c 12.96 km2
d 27 m2 e 1026 mm2 f 2914 cm2
g 20.37 m2 h 26.46 km2 i 6.845 m2
j 216.32 km2 k 3306 mm2 l 6.4 m2
m 60 m2 n 5.84 m2 o 26.82 cm2
p 161.2 cm2 q 26.9 mm2 r 438.7 m2
s 14.14 cm2 t 4.19 m2 u 65.45 mm2
3 a 140 m2 b 36 m2 c 104 m2
4 a 144 m2 b 68.5 cm2 c 10 m2
d 80 m2
5 B 6A 7B
8 a 34.56 m2 b $960.77
9 a b 180 m2
c 18 m long and 15 m wide d 90 m2
10 a C b E
11 107 cm2
12 30.6 cm2
13 a 2474 cm2 b 34.4%
10 Quick Questions 1
1 452.4 cm2 2 31.2 m2
3 184.3 cm2 4 13 939.2 mm2
5 306 cm2 6 625 cm2
7 1428.3 m2 8 1147.6 cm2
9 17 121.8 mm2 10 670.9 cm2
Investigation — Effect of scale factors
on perimeter and area
1 Pentagon
2 All angles 108°. Figure is regular pentagon.
3 Larger knot has twice the side length of smaller knot
4 S = 2
5 Larger knot has twice perimeter of smaller knot
6 Area of larger knot is four times area of smaller knot
7 Perimeter is 3 times as long; area 9 times as large
8 Perimeter is ‘S’ times as long; area is ‘S2’ times as large
9 a Parallelogram
b 4 trapeziums
c Perimeter of larger knot twice as long and area 4 times as large as smaller knot. Supports conclusion in 8.
Exercise 4C — Total surface area
1 a iii Triangular prism
b iii Square-based pyramid
c iii Triangle-based pyramid Item
Cost price ($)
Per-centage discount
Discount ($)
Selling price
($)
a 200 12% 24 176
b 150 5% 7.50 142.50
c 98 10% 9.80 88.20
d 130 12.5% 16.25 113.75
e 416 20% 83.20 332.80
f 228 33 % 76 152
a 80% profit b 124.14% profit
c 37.5% loss d 44.44% loss
a $35 b $39.89
1 3
---1.5 m
15 m 12 m
answers
➔
b
c
3 a Square pyramid
b Triangular prism
c Cone
4 a 150 cm2 b 486 cm2 c 6144 cm2
d 95.98 cm2 e 1444 cm2 f 1274 mm2
5 11.92 m2 6 28 125 cm2
7 a 17.5 m2 b 70 c 42.5 m2
d 17.5 m2 e 5 L
8 a 4.9 m2 b 9148.3 mm2c 2945 cm2
9 360 cm2 10 28 cm2 11 B
12 36 cm2
13 a 15.5 cm2
b 3267.3 cm2
c 879.6 cm2
14 a 58.1 cm2
b 39.3 m2
c 374 mm2
15 2 cm
16 No. If the side length was doubled, the area would be four times as large.
17 95.6 m2
18 50 m2
19 99 m2
20 C 21 B 22 E 23 A
24 a Cylindrical loaf
b 108.7 cm2
10 Quick Questions 2
1 0.44 m2 2 29.52 m2
3 4224 m2 4 Triangular prism
5 Square pyramid 6 Triangular pyramid
7 486 cm2 8 236 cm2
9 568 cm2 10 160 cm2
Exercise 4D — Volume and capacity
1 a 350 mm3 b 0.0048 m3 c 56 litres
d 1500 cm3 e 1600 litresf 2.3 mm3
g 570 cm3 h 0.14 litres i 250 cm3
e 6 000 000 cm3→ 6 000 000 mL → 6000 L
f 12 000 L g 4.2 kL h 7.5 kL → 7500 L
i 5.2 cm3 j 6000 cm3
k 20 000 mL = 20 000 cm3 l 5.3 m3
3 a 125 cm3, 125 mL b 13.824 m3, 13.8 kL
c 2197 m3, 2197 kL d 56.448 m3, 56.4 kL
e 4050 mm3, 4.1 mL f 4228.125 m3, 4228.1 kL
g 1357.2 cm3, 1357.2 mL or 1.4 L
h 339.3 m3, 339.3 kL i 29 772.9 cm3, 29.8 L
4 a i 12 cm2 ii 60 cm3
b i 24 cm2 ii 288 cm3
c i 4.59 m2 ii 6.885 m3
d i 12.48 m2 ii 156 m3
5 B 6 D 7 D
8 a 504 000 cm3 b 504 L 9 101.25 kL
10 a 150.796 m3 b 150 800 L
11 a 175 m2 b 17.5 m3 c $2546.25
12 a 2.8 m3 b 2800 L c 24 429 L
d 27.5 cm
13 a 96 cm3 b 560 cm3 c 120 m3
d 100 cm3
14 a 262 cm3 b 1810 cm3 c 2212 mm3
d 77 585 cm3
15 254.5 cm3
16 a 904.8 cm3 b 2144.7 cm3c 8181.2 m3
d 137.3 m3
17 6.37 cm3 18 A 19 C 20 D
21 a i 200 cm2 ii 2000 cm3
b i 99 m2 ii 792 m3
c i 204 cm2 ii 1224 cm3
d i 153 m2 ii 1836 m3
22 335.1 cm3
23 a 7 cm b 2144.7 cm3c 1436.8 cm3
d 707.9 cm3
24 a 565.5 cm3 b 84.8 cm3 c 480.7 cm3
25 14.3 cm3
26 a 52.4 cm3 b 65.4 cm3 c 85.1 cm3
Chapter review
1 a 19 cm b 1.9 cm2 c 0.19 cm3
d 0.5 L e 0.0005 kL f 50 000 L
g 200 000 cm3 h 2000 cm2 i 20 cm
j 120 mL k 0.12 L l 300 000 cm3
2
3
4
5 a b c
a i 97.98 mm2 ii 48 mm
b i 8.55 cm2 ii 16.44 cm
c i 168 cm2 ii 54 cm
d i 32 cm2 ii 49.3 cm
e i 8.8 m2 ii 13.4 m
a i 540 cm2 ii 106 cm
b i 60.7 m2 ii 45.7 m
c i 29.7 cm2 ii 21.4 cm
a C b E
answers
7 a 105.84 cm2b 25.98 m2 c 19.44 m2
d 18.18 m2
8 a 54 m2 b 352 cm2 c 340 m2
9 a 301.6 cm2 b 23.1 m2 c 2670.4 cm2
10 a 247 m2 b 2463 mm2 c 879.6 cm2
11 a 452 cm2 b 763 mm2 c 157 cm2
12 a 75 m2 b 1650 m3 c 1 650 000 L
d 1316.2 m2
13 37.5 m2
14 a 274.625 cm3, 274.6 mL
b 24 389 mm3, 24.4 mL
c 202.768 m3, 202.8 kL
d 984 cm3, 984 mL
e 368 cm3, 368 mL
f 57 906 mm3, 57.9 mL
15 585 cm3
16 a 48 cm3, 48 mL b 798 mm3, 0.8 mL
c 5.29 m3, 5.29 kL
17 a 10 800 m3 b 10.95 m3 c 19 658 mm3
d 2339 mm3 e 50 965 mm3 f 179 594 cm3
18 a 6.1 m3, 6.1 kL
b 123 717.1 cm3, 123.7 L
c 2356.2 cm3, 2.4 L
19 a 179.6 cm3
b 808.2 cm3
c 269.4 cm3
20 58.1 cm2 21 226.19 cm2
22 129.2 cm2 23 452 cm2
24 77.47 cm2 25 5.37 cm2
26 2073 cm2 27 21.237 cm2
28 2100.6895 cm3 29 536 cm3
CHAPTER 5 Right-angled
triangles and trigonometry
History of mathematics
1 Samos Island
2 Egypt and Babylonia
3 c2=a2+b2 or hypotenuse2= base2+ height2
4 Patterns in music
5 Plimpton 322
6 A set of numbers that obeys Pythagoras’ theorem
Skills check
1 a AB b DF c GI
d No hypotenuse (as the triangle is not right-angled)
2 In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides
hypotenuse2= base2+ height2
3 a a= 10 m b b = 4.47 m c c= 14.14 cm
4 a 15 b 2 c 0.75
d 12.5
5
6 a a= 56° b b = 63°
′ ′ ″ ′ ″
8 a 45.45° b 84.59° c 64.01°
9 In a right-angled triangle
a sine =
b cosine =
c tangent =
10 a b
c
11 a 0.7071 b 0.8660 c 0.4142
d 0.9222 e 0.7871
12 a
b
c
13 a x= 2.08 b x= 1.56
Exercise 5A — Pythagoras’ theorem
1 a PR b YZ c AB
2 a 13 cm b 170 mm c 61 m
3 a 10.82 cm b 6.93 m c 14.20 km
4 a 10.4 cm b 1.9 m c 3.9 m
5 a 8.9 cm b 22.1 cm c 47.4 mm
d 37.3 m
6 a Right b Right c Obtuse
Angle of ele vation
Shadow
opposite side length length of hypotenuse
---adjacent side length length of hypotenuse
---opposite side length adjacent side length
---Opposite
Adjacent
Hypotenuse
Opposite
Adjacent
Hypotenuse
Opposite
Hypotenuse
Adjacent
Angle of ele
vation
Angle of depression
Angle of elevation
answers
➔
9 a Yes b No c Yes
d No e Yes f Yes
g No h No i Yes
j Yes k Yes l No
10 a 9, 12, 15 b 7, 24, 25 c 1.5, 2.0, 2.5
d 3, 4, 5 e 11, 60, 61 f 10, 24, 26
g 9, 40, 41 h 0.7, 2.4, 2.5
11 a 15 c 50 e 1.0 f 25
i 61 j 26 k 20
12 E
13 B
14 13 m
15 3.23 m
16 3.73 m
17 2.2 m
18 7.5 m
19 7.07 cm
Exercise 5B — Shadow sticks
1 a 5.7 m b 15.6 m c 5.3 m d 7.8 m
2 5.4 m 3 6.4 m 4 8.1 m
5 16 m 6 B 7 D
Exercise 5C — Calculating
trigonometric ratios
1 a 1.540 b 17.663 c 40.460
d 0.657
2 a 0.602 b 2.092 c 15.246
d 51.893
3 a 0.707 b 0.247 c 6.568
d 5.896
4 a 0.500 b 0.966 c 1
d 548.643 e 64 f 1.301
g 5.306 h 1.374 i 15.772
5 a 0.42 b 1.56 c 0.09
d 5.10 e 2.87 f 0.38
g 7.77 h 73.30 i 0.87
6 10°
7 a 44° b 80° c 57°
8 86°40′
9 a 42°57′ b 31°21′ c 16°5′
Exercise 5D — Finding an unknown
side
1 a
b
c
2 148.1 mm
3 5.08 m
4 30 cm
5 a 12.1 cm b 55.2 m c 9.4 km
7 a 5.4 m b 1.4 km c 2.1 km
d 18.4 mm e 3.2 cm f 66.5 m
g 5.4 m h 5.4 km i 0.2 m
j 41.6 km k 84.4 m l 13.2 cm
8 D 9 A 10 A 11 C
12 6 m 13 4.2 m 14 20 km
15 a b 6 m
16 a b 1.6 m
17 9.65 m
18 a b 58 m
c 15.5 m
10 Quick Questions 1
1 17 cm 2 22.4 m 3 26.5 km
4 21.5 m 5 32.9 cm 6 25.3 m
7 12.5 mm 8 177.8 mm 9 97.5 m
10 17 m
Exercise 5E — Finding angles
1 a 30° b 75° c 81°
2 a 32°48′ b 45°3′ c 35°16′
3 a 53°8′ b 55°35′ c 45°27′
4 a 50° b 32° c 33°
d 21° e 81° f 34°
5 a 39°48′ b 80°59′ c 13°30′
d 79°6′ e 63°1′ f 19°28′
6 A 7 B 8 C 9 37°
10 75°31′ 11 8°38′ 12 13° 13 4°35′
10 Quick Questions 2
1 13 cm 2 17.0 cm 3 22.4 cm
4 6.409 m 5 0.8290 6 10.96
7 133.55 8 30° 9 73°
10 63°26′
Exercise 5F — Angles of elevation and
depression
1 26.8 m 2 3984 m 3 190 m 4 39.2 m
5 42.1 m 6 100 m 7 15 km
8 Yes, the ladder needs to be only 28 m long.
9 a 914 m b 868 m
10 39° 11 21°
12 a b 85 m
c 40°
Chapter review
1 a 13.01 m b 18.65 cm c 3.58 m
d 15.65 cm e 2.30 km f 2.47 m
hyp opp
adj θ
hyp
opp adj
α
hyp opp adj
γ
24°
13.5 m
60° 1.4 m
15° 60 m
12° 400 m
answers
4 a Right-angled b Right-angled
c Obtuse d Acute
5 b and c 6 11.25 metres
7 a 0.7193 b 4.2303 c 2.7400
d 8.1955 e 21.9845 f 14.2998
8 a 54° b 51° c 53°
9 a 78°31′ b 26°34′ c 14°54′
10 a 37.9 cm b 3.8 m c 13.6 cm
d 11.7 cm e 14.7 cm f 14.6 m
g 1.5 m h 4.9 cm i 15.6 mm
j 7.5 m k 10.7 m l 5.3 km
11 8.5 m 12 2.5 km 13 63.9 m
14 a 57° b 27° c 68°
15 a 23°4′ b 61°37′ c 59°35′
16 39° 17 24° 18 23 m 19 57°
CHAPTER 6 Earth geometry
Skills check
1 Latitude — imaginary lines which circle the Earth in an east–west direction parallel to the equator. Longitude — imaginary lines circling the Earth joining the North and South Poles and running perpendicular to the equator.
2
3
4
sphere is represented by the length of an arc of a circle.
6 40 030 km
7 a Greenwich Mean Time (GMT) — the standard time in Greenwich (England) which is used as the basis for calculating the time in all other parts of the world.
b The meridian of longitude 180° from the Greenwich Meridian. When we cross the International Date Line, the date will be different.
c Eastern Standard Time — the time adopted by the eastern States of Australia (Qld, NSW, Vic and Tas) and the ACT.
8 Three — EST (Eastern Standard Time), CST (Central Standard Time), WST (Western Standard Time).
9 Clocks are put forward 1 hour during summer.
10 EST is 10 hours ahead of GMT.
Exercise 6A — Latitude and longitude
1 a Cairo b Shanghai c Darwin
d Montreal e London f Auckland
g Tokyo h Beijing i Rio de Janeiro
j Oslo
2 a (38°S, 145°E) b (40°N, 75°W)
c (18°N, 76°W) d (26°S, 28°E)
e (42°N, 12°E) f (35°S, 57°W)
g (33°N, 44°E) h (55°N, 40°E)
i (2°N, 104°E) j (18°S, 178°E)
Exercise 6B — Distances on the Earth’s
surface
1 50°
2 a 40° b 40° c 71° d 21° e 80°
3 60°
4 3336 km
5 a 3892 km b 15 012 km
c 4337 km d 10 675 km
6 6672 km
7 5226 km
8 6600 km
9 a 4337 km b 4003 km c 3781 km
10 D 11 A
12 a 110° b 12 200 km
13 20 016 km
14 a 28° b 3114 km
15 3892 km
16 17 792 km
17 a 6894 km to South Pole
b 4559 km to North Pole
c 4893 km to North Pole
d 8896 km to South Pole
18 a 2470 km b 3233 km
c 2859 km d 425 km
e 16 301 km f 6452 km
Exercise 6C — Time zones
1 10 h
2 a 14 h b 7 h c 11 h d 22 h
3 11:00 pm Monday 1
– 2
North Pole (90° N)
South Pole (90° S)
Tropic of Cancer (23 ° N)
1 – 2
Tropic of Capricorn (23 ° S) Equator (0°)
S N
50°W 0° 20° E
Equator
Tropic of Capricorn N
S
answers
➔
c 5:00 pm Wednesday d 11:00 pm Tuesday
e 3:45 pm Monday
5 5:00 am Saturday
6 11:00 pm Tuesday
7 10:00 am Monday
8 a 10:00 pm b GMT+11
c i 3:00 pm Monday ii 8:00 am Friday
9 a 18 h b 19 h c 17 h
10 7 h
11 a 10 h 20 min b 24 min c 2 h 48 min
12 C 13 D
14 2:00 pm Tuesday LAX local time
15 a 4:00 pm Wednesday b 8:00 am Sunday
16 a 1:00 am Wednesday b 3:00 am Wednesday
Chapter review
1 a 207.3 cm b 44.0 cm c 57.8 m
2 56.5 km
3 71 cm
4 a Manila b Lima c Santiago
5 a (41°N, 3°W) b (1°N, 104°E)
c (43°S, 147°E)
6 58°
7 a 16° b 1779 km
8 5671 km
9 a 14 481 km b 18 425 km
10 a 8 h b 11 h c 17 h
11 3:00 am Thursday 12 3:30 am Tuesday
13 a 11:00 am the same day
b 11:00 am the same day
14 7:00 pm the same day
CHAPTER 7 Basics of construction
Skills check
1 a 1 : 0.75 b 1 : 4 c 1 : 25 d 1 : 40
2 a Enlargement b Reduction
c Reduction d Reduction
3 a 1 m b 2.5 cm
4 a P= 40 m, A= 80 m2 b P= 56 m, A= 128 m2
5 a 0.6 m3 b 1 m3
6 a 3394 mm b 1.8 m
7 a 34.4° b 43.3°
8 a 3.46 m b 11.22 m
9 a 7.18 m b 2784 mm
10 a 76 m2 b 18.97 m2
Exercise 7A — Scale drawings
1 a 8.215 m b 3.5 m c 89 000 m
d 0.026 m e 0.04 m f 6400 m
2 a 45 mm b 67 mm c 58 mm
3 a Reduction b Reduction c Enlargement
d Reduction e Enlargement f Reduction
4 a 1 : 5000 b 1 : 200 000 c 10 : 1
5 a 1.8 m b 6.75 m c 22.5 m d 3.375 m
6 a 2.4 cm long × 1.4 cm wide
b 3 cm × 1.8 cm c 4.4 cm × 2 cm
7 1 : 550
8 a 4.75 m b $3034 c 18.75 m
9 a Approx. 70 m b Approx. 1000 m
c Approx. 2 km2
Exercise 7B — Building plans
1 a 630 m2 b 30 m, 21 m
c Approx. 1 : 1750 e 632 m2
f i 1063 m2, $58/m2 ii 850 m2 is larger
g i Lot 110
ii Does it front a main road? Is it low lying? Slope of land, views, aspect.
2 a 2100 m2, 83 perches b 104 m2
c Approx. 1 : 1000 d i Rising ii 1.4°
3 a 77.8 m2 b Approx. $265
c in order, 10.85 m2, 11.25 m2, 6.84 m2, 5.04 m2
Exercise 7C — Floor plans and
elevations
1 a No doors and 1 window
b 9 (D4–D12)
c Kitchen and dining room
d 2400 mm (2.4 m)
e At 4 corners of house, downpipes
f 1490 mm (1.49 m)
g 290 mm, 90 mm
h Shower, bath, vanity unit, toilet
i Refrigerator, pantry, oven, broom cupboard, hot plates, sink, benches
j i No doors and 1 window, window is 310 mm wide
ii 8990 mm, 7790 mm
k
10 Quick questions 1
1 1 : 250 2 NE 3 20 m × 25 m
4 10 m × 15 m 5 4.4 m 6 1 :125
7 5.6 m × 3.75 m 8 Bed 1 9 3.75 m square
10 2.5 m
Exercise 7D — Pegging out the
perimeter
1 a 1697 mm b 45°
2 Acute angle
3 12 m square
4 No — it could be a parallelogram.
5 The shed could be rectangular or square.
6 17.7 m
7
The wall at X is 2 cm below horizontal level of wall at Y.
Exercise 7E — Footings and slabs
1 a 8.855 m3 b 5.016 m3 c 20.832 m3
2 7.43 m3
3 a 10 lengths b 5.28 m3
2090 2400 4000
7990 8990
310 w 5
2 cm
Wall Wall Water X
Y
answers
5 a i 12.579 m3 ii 24 lengths iii 12.75 m3
b i 14.679 m3 ii 28 lengths iii 16 m3
Exercise 7F — Bracing
1 a 6.46 m b Angle is 21.8° c 4 m
2 Yes, brace is at 45° to base.
3 a 1697 mm b 45° c Yes
4 3839 mm, 38.7°
5 a 40.6° and 43.8°
b 3688 and 3467 mm = 7155 mm
6 a 34.18 m b 13.8 m
Exercise 7G — The roof
1
2
3 a 13.4° b 16.9° c 36.9° d 36.9°
4 a 1 : 3, 18.4° b 1 : 1.67, 31°
5 a 43.8° b 33.6°
Exercise 7H — Cladding the roof
1
2 a EF = 18 m, FH = 6 m
b ∠CAB = 20°
c AB = 3 m
d AC = 3.2 m BC = 1.1 m
e CD = 12 m
f 48 m2
g 9.6 m2
h 115.2 m2
i $5184 (≈$5200)
= = ∠ = °
b VQ = 3 m
c TV = 1.1 m TQ = 3.2 m
d 57.6 m2, 115.2 m2
e $5184
4
5
6 a
i There is no ridge — all faces meet at a point.
ii 148.8 m2
b 148.8 m2
7 $3577.50
8 a and b
c
Exercise 7I — Brickwork
1 a 1680 b 3000 c 3000 d 1920
2 a 210 b 1955
3 a 50 b 25 c 19
4 a 43 cm b 1.892 m c 4.73 m
5 a 25 b 10 c 120
6 a 15 b 35 c 525
d 542 This is an estimate and allows for breakages.
7 4056
Chapter review
1 a 1 : 140 b 4
c 3.8 m × 3.6 m with ensuite containing shower, handbasin and toilet, walk-in wardrobe with hanging space and shelves
d 5.8 m × 6.09 m
e Living–dining room and hallway near bathroom
f 231.45 m2
g Vanity basin, broom cupboard, washing machine, water closet, walk-in wardrobe, wall oven, range hood, hot plates, drain pipe
Pitch ratio Pitch angle
1 : 22.9 2.5°
1 : 57.3 1°
1: 7.6 7.5°
1: 5.7 10°
1:1 45°
1 : 2.7 20°
1 : 1.43 35°
1 : 1.08 42.8°
Roof pitch
Building width
King post height
Rafter length
10° 8 m 705 mm 4062 mm
12° 10 m 1063 mm 5112 mm
18.4° 12 m 2 m 6325 mm
25° 27.19 m 6339 mm 15 m
10.8° 31.4 m 3 m 16 m
34.6° 14 m 4822 mm 8.5 m
Hip roof Triangles
Trapeziums
Gable roof Rectangles
12 m 4 m
5.8 m
8 m 18°
8 m 4.2 m
18°
12 m
12 m
12 m 15°
15°
12 m 12 m
10 m 10 m 2.7 m 2.7 m 2.7 m
5 m 20° 20°
10 m
20° 20°
10 m 2.7 m
2.7 m
2.7 m
2.7 m 2.7 m 5 m 5 m
2.7 m
answers
➔
c 21.3 m × 28.175 m d Sweetapple Crescent
e 1.5 m f 4.5 m
g 38.6%
5 a Garage b North
c North-west d 1
e Panel lift f 4
g Concrete tiles h 21°
i Gable j Brick
k 1000 mm l 600 mm
m 2400 mm n Standard Type A
o 2.67 m × 3.6 m p 70 mm
q 220 mm
6 a 200 mm b 100 mm c 900 mm
d The floor of the garage falls 50 mm from back to front.
e Internal footings
f No, garage is 1 step down from house.
g 40 mm h
i Down western side of allotment, 600 mm
8 a 6.4 cm × 4 cm b 12.8 cm × 8 cm
9 4.48 m 10 $46.57
11 1.67 m3 12 6
13 $470 14 3988 mm
15 3042 mm 16 1 : 2.6
17 a No b 10.9°
18 1441 mm 19 $2880
20 $907.20 21 1000
22 11 23 28
24 a 308 b 312
Both methods give approximately the same number.
CHAPTER 8 Construction: The
finishing touches
Skills check
1 a b
c
2 a 37.5 m2 b 29.64 m2
3 a
b 96 m2
c
°
g h
4 a 11.847 m2 b 5.79 m2
5 a 471.24 m3 b 21.6 cm
Exercise 8A — Painting and
wallpapering
1
b 150 m2 c 25 L d 7 e $252
2 $243 3 1.3 L
4 3 tins 5 81.6 L
6 a 3.6 L white undercoat; 4.8 L blue enamel
b 3.3 L white undercoat; 5 L acrylic
c $198.40
7 a
b 14 m c 28 d 2.4 m e 67.2 m f 7
8 9
9 Wallpaper $405
Paint $192
10 Wallpaper $4.50/m2 Painting $1.44/m2 So it is cheaper to paint.
Exercise 8B — Tiling, carpeting and
kitchen planning
1 $7380
2 a $234.78 b $123.12
3 a 24 m b 24 m
4 a
b 116 tiles c 22.8 m d 21.6 m
5 $127.80/m
6 a i 1226 mm
ii 820 high, 700 wide, 495 deep
iii 720 high, 595 either side of corner
b i 2135 high, 800 wide, 590 deep
ii 875 mm
iii Cabinet O — Deep corner floor cabinet 900 iii and narrow corner floor cabinet 750
iv 400 wide or 800 wide, 2135 high
c 0.354 m2 d 590 mm e 315 mm
7 Check with your teacher
8 a 1.296 m2 b 1.0206 m2 c 0.567 m2
d 1.6686 m2 e 4.5522 m2 f 910 mL
3 m 6 m
10 m 10 m 6 m
10 m 5 m 5 m
6 m
10 m
6 m 3 m 5 m
10 m
15 m
3.5 m
2.4 m 2.4 m
12 m 11.4 m 5.4 m
6 m
Tiles (30cm × 30cm)
Carpet
answers
10 Quick questions 1
1 30 m × 34 m 2 128 m
3 $416 4 10.8 m × 14 m
5 151.2 m2 6 SW
7 42 m 8 43.2 m
9 85.68 kL 10 75 m2
Exercise 8C — Landscaping
1 a 2.4 m b 3 c 200 mm d 5
e 15 f $44.40 g $666
2 a 1.8 m b 4 c 100 mm d 10
e 40 f $9.45 g $378
3 a 1.8 m b 4 c 150 mm d 7
e 28 f $18.27 g $511.56
5 a i 75 mm wide and 38 mm thick 75 mm wide and 50 mm thick
ii 75 × 50 mm
iii 6 cm
iv 10 m
b i 100 × 38 mm and 100 × 50 mm
ii 75 × 38 mm and 75 × 50 mm
iii 2850 mm2 and 5000 mm2
iv 100 × 38 mm
6 a 20 PRP
b or
or other combinations
c or
or other combinations
d 78.5%
7 a 0.288 m3 b 0.375 m3 c $86.19
d 16 m2 e 1.125 m2 f 3.99 m2
g 21.115 m2 h $253.38 i $339.57
Chapter review
1 a $32.60 b 1 : 25 c $42 d $210
2 a 32 m2 b $1216
c i $456
ii $850 laid horizontally $680 laid vertically
3 a Sink, oven and refrigerator arranged in triangle
b 2 × 800 and 2 × 900
c 0.2 m3
d Approx. 356 mm
5 a 600 b $990 c 450 m2 d No, 574
e 568
f The closer the rectangle approaches a square shape, the smaller the perimeter, and fewer palings would be required.
6 a Sand, clay
b Compete with plants for water and nutrients
c Makes them too thirsty
d Thick grass requires too much water and water has difficulty reaching the roots.
e Couch/kikuyu/buffalo — the broad leaf helps it absorb water.
f Clay soil does not absorb as well, so requires a longer watering time. Once the clay is wet, it retains the water for a longer period of time than sandy soil does.
g They sprinkle a further distance.
h Water runs off surface.
7 a 0.1 m3 b $13 c 5.65 m2 d $84.75
e $97.75 f 1.13 m3 g 1.96 m
CHAPTER 9 Collecting and
entering data
Skills check
1 Qualitative — some quality or feature (not involving numbers or measurements).
Quantitative — involving some quantity or number which can be measured.
2 a −2, −1, 0, 1, 3, 6.5, 8, 12, 25
b −2, 25, 3
3 a
b c
4 a 0.196 c/g b $0.88/L c 0.76 c/g
5 1 L for $2.50
Exercise 9A — Types of data
1 a Numerical b Categorical c Numerical
d Categorical e Numerical f Numerical
2 a Continuous b Discrete c Continuous
d Continuous e Discrete
4 + 6 + 4 + 6
4 + 4 + 4 + 4 + 4
4 + 4 + 4 + 4 + 4
4 + 4 + 3 + 3 + 3 + 3
6 m
6 m
Year Students
8 117
9 102
10 92
11 77
12 62
Year 9 Year 8
Year 12
Year 10
Year 11
No. of students
Year level 8 9 10 11 12 0
10 20 30 40 50 60 70 80 90 100 110 120
answers
➔
b Categorical
c Categorical
d Numerical and continuous
e Numerical and continuous
f Numerical and discrete
4 Categorical, ordinal 5 Categorical, ordinal
6 Numerical and discrete 7 B
8 Categorical 9 Numerical and continuous
Exercise 9B — Collecting data
1 Open questions — no boundaries for response. Closed questions — answer within category.
2 A variety of categorical responses suitable; check with your teacher.
3 A variety of categorical responses is suitable; check with your teacher.
4 a Vague — weekly? yearly? all jobs?
b Vague — define ‘exercise’, ‘regularly’.
c What do abbreviations stand for?
d Emotional language.
e Capable of being answered? What is the PM’s policy?
g Double-barrelled question.
h Leading question suggesting a particular response.
i Emotive language.
5 Check with your teacher.
Exercise 9C — Organising and
displaying data using column and
sector graphs
1
2
3
5
6
7
8
9 Check with your teacher.
10
10 Quick Questions 1
1 Qualitative
2 Quantitative and discrete
3 Quantitative and discrete
4 Quantitative and continuous
5 40 6 Married 7 15 8 11 9 28
10
Make Tally Frequency
Holden |||| ||| 8
Ford |||| ||| 8
Nissan || 2
Mazda ||| 3
Toyota |||| || 7
Mitsubishi || 2
Mark Tally Frequency
4 || 2
5 |||| 4
6 |||| | 6
7 |||| |||| 9
8 |||| 5
9 ||| 3
10 | 1
Mark Tally Frequency
40–49 | 1
50–59 || 2
60–69 |||| |||| 9
70–79 |||| ||| 8
80–89 ||| 3
90–99 || 2
Holden FordNissanMazdaToyota Mitsubishi
Frequenc
y
Make of car 0
1 2 3 4 5 6 7 8 9
Holden Ford Nissan Mazda Toyota Mitsubishi Make of car
0
4 5 6 7 8 9 10 1
2 3 4 5 6 7 8 9
Number of students
Spelling test results 10
0
40–4950–5960–6970–7980–8990–99
1 2 3 4 5 6 7 8 9
Number of students
Maths exam mark
40–49 50–59 60–69 70–79 80–89 90–99 Marks on maths exam Number of students
Married
Widowed Separated Divorced
Never married
answers
Exercise 9D — Graphical methods of
misrepresenting data
1 Check with your teacher.
2 Horizontal axis uses same division for 5 and 7 year periods
3 a Check with your teacher
b No
4 a 20.5
b 18.2, country schools have smaller class sizes
5 Check with your teacher
6 Check with your teacher
7 a 0.2 b 71.5° c 80°
d The perspective appears to magnify some sections of the pie chart and diminish others.
8 a It is a circle viewed on an angle to produce an ellipse.
b No, because it causes some angles to be larger and others to be smaller.
Exercise 9E — Histograms and
freauency polygons
1
2
3
4 a
b
6 a
b
Exercise 9F — Stem-and-leaf plots
1
2
3
4
No. of matches in a box Frequency
47 3
48 5
49 10
50 15
51 7
52 5
53 4
54 1
0 0 2 4 6
1 2 3 4 5 Number of mistakes
(score)
Number of dri
v
ers
(frequenc
y)
8 10 12 14
1 0 1 2 3
2 3 4 5 6 No. of children in family
Frequenc
y
4 5 6 7 8 9
18 0 2 4 6
19 20 21 22 23 Age
No. of members
8 10 12
24 25 14
16
53 54 47
0 2 4 6
48 49 50 51 52 No. of matches in a box
Frequenc
y
8 10 12 14 16
Time taken
(seconds) Class centre Frequency
6 to <8 7 1
8 to <10 9 4
10 to <12 11 15
12 to <14 13 18
14 to <16 15 12
16 to <18 17 8
18 to <20 19 2
304.5314.5324.5334.5344.5354.5 0
5 10 15
Length of fish (mm)
Frequenc
y20
19 7
0 2 4 6
9 11 13 15 17 Time taken (s)
Frequenc
y
8 10 12 14 16 18
Key 0
|
6 = 6 errors Stem0 1 2 3 4
Leaf 6 3 5 7 8
0 0 5 6 6 7 8 9 1 2 2 8
3 6 Key 3
|
6 = 36 minStem 3 4 5 6 7 8
Leaf 6 7 8 8 9 9
0 0 1 2 2 2 2 2 3 5 6 7 7 8 8 8 0 2 2 2 3 4 5 7 8 9
6 8 8 1 2 5 2
Key 10
|
1 = 101 wpm 10*|
6 = 106 wpm Stem8* 9* 9* 10* 10* 11* 11* 12* 12* 13*
Leaf 6 8 2
5 5 5 6 6 6 8 9 2 2 2 3
7 7 7 8 8 0 1 2 5 0 1 1 4
0
Key 14
|
3 = 14.3 V 14*|
8 = 14.8 V Stem13* 14* 14* 15* 15*
Leaf 8 9 0 2 3 3 5 6 6 7 7 8 8 1 2 2
answers
➔
5 1.95 g
6 a 8.4 s
b Lower quartile = 7.8 s, upper quartile = 8.85 s
c 1.05
7 D 8 A 9 D 10 B
11 a
b 22.9 cm
c Lower quartile = 21.75 cm, upper quartile = 24.1 cm
d 2.35 cm
12 a
b 99.5 cm
c Lower quartile = 92 cm, Upper quartile = 110 cm
d 18 cm
Exercise 9G — Five-number summaries
and boxplots
1 8, 15, 16.5, 18, 25 2 a 23, 44, 81.5, 83.5, 92
b 1, 2, 4, 6, 7 c 8, 29, 45, 72, 93
3 a 13 b 5 c 26
4 a 122 b 6 c 27
5
6 a 147 b 56 c 90 d 91 e 28
7 a 58 b 31 c 43 d 27 e 8
8 B 9 C 10 D
11 a 22, 28, 35, 43, 48 b
12 a 10 mm, 13.5 mm, 22 mm, 33.5 mm, 45 mm
b
Chapter review
1 a Categorical b Numerical c Numerical
d Numerical e Categorical
2 a Discrete b Continuous cContinuous
d Discrete e Continuous
3 a Double-barrelled question b Double negative
c Emotional language d Abbreviations e Leading question
4
5
6
7 Key 20
|
6 = 20.6 cmStem 20 21 22 23 24 25
Leaf 2 7 4 6 7 8 2 8 8 8 0 1 2 6 6 6 6 7 8 1
Key 8
|
2 = 82Stem 8 9 10 11 12 13
Leaf 2 4 5 5 8
0 1 2 3 4 6 6 7 8 9 1 1 3 3 7 8
0 0 1 4 5 7 6 6
2
35 40 45 50 55 60
20 25 30 35
Scales40 45 50
10 15 20 25 Rainfall (mm)
30 35 40 45
Score Tally Frequency
1 ||| 3
2 |||| | 6
3 |||| | 6
4 |||| | 6
5 ||| 3
6 ||| 3
Number of CDs Tally
Number of students
0–4 ||| 3
5–9 |||| |||| 9
10–14 |||| |||| 9
15–19 ||| 3
20–24 |||| 4
25–29 | 1
30–34 0
35–39 | 1
0
1 2 3 4 5 6 1
2 3 4 5 6 7
Frequenc
y
Number of people in a household
1 2 3 4 5 6 Number of people
in a household
10
0
0–45–9
10–1415–1920–2425–2930–3435–39
1 2 3 4 5 6 7 8 9
Number of students
Number of CDs purchased
0–4 5–9 10–14 15–19 20–24 25–29 30–34 35–39 Number of CDs
purchased
answers
8 Check with your teacher
9
10 a
b
11
12 a 28 b 38 c 12.5
13 6, 24, 41, 69, 91
14 a 43 b 43 c 14
15
16 20 17 11 18 7.5 19 7
20
21 45 22 15 23 35 24 7
25 Check with your teacher
CHAPTER 10 Describing,
exploring and comparing data
Skills check
1 a 3, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9
b 11 c 6th
d 5 e 3 to 9 or 6
f 5.55 g 6, 5
h 4
i Mean = 5.5, median = 5, mode = 4. The mean takes into account all scores, the median is the middle score (arranged in order), the mode is the most frequently occurring score. These values would only be the same for a symmetrical (or near symmetrical) distribution.
j 4, 7
2 Central tendency is a measure of how the scores tend to be grouped around the centre of the data. The measure represents a typical score in the data set. 3 Range, interquartile range
4 The median is the second or middle quartile. 5 b, d
6 Consult your teacher.
Exercise 10A — Calculating and
interpreting the mean
1 Average, total, number, central, median, mode.
2 a 5 b 26.5 c 74.25
d 7.72 e 376
3 72.6, 3, 2
4 73.4 c/L, yes, 3 above and 4 below 5 1.81 m, 3
6 a Yes, mean mass is 45.035 g.
b Both the same distance from the mean 7 a Mean is 10 greater; that is, 13
b Mean is 10 times as large; that is, 30.
Exercise 10B — Mean, from frequency
distribution tables
1 a
b 131.36 mm
2 a
b 7 c 10
Class Class centre Frequency
5000–9999 7 500 1
10 000–14 999 12 500 5
15 000–19 999 17 500 9
20 000–24 999 22 500 3
25 000–29 999 27 500 2
30 000–34 999 32 500 2
6 0
0 2 4 6
1 2 3 4 5
Number of sales
Frequenc
y
8 10 12
0
7500
12 50017 50022 50027 50032 500
2 4 6
No. of people at a football match
Frequenc
y
8 10
Key 2
|
1 = 21Stem 2 3 4
Leaf
1 1 3 4 8 8 8 9 9 9 0 3 4 5 5 5 6 8 8 8 8 9 0 0 0 1 1 2 2 4 5 5 5 6 8 9
2 6 10 14 18
0 4 8 12 16 20
0 5 10 15 20 25
Score (x) Tally
Frequency
(f) fx
119 | 1 119
124 | 1 124
125 | | 2 250
126 | | 2 252
127 | 1 127
128 | | 2 256
129 | 1 129
130 | 1 130
131 | | | | 5 655
132 | | | 3 396
134 | | | 3 402
135 | | 2 270
136 | 1 136
138 | | 2 276
139 | | 2 278
141 | 1 141
Σf = 30 Σfx = 3941
Score Tally Frequency fx
4 | | 2 8
5 | | | | 4 20
6 | | | | 5 30
7 | | | | | | | | 9 63
8 | | | 3 24
9 | | | | 5 45
10 | | 2 20
Σf = 30 Σfx = 210
answers
➔
b 20.4
4 a
b 2.3
c 31 below, 19 above — could be a better measure 5 a
b 12
c Size 12 not available, perhaps a better measure could be used.
7 B
8 C
Exercise 10C — Mean, from grouped
data
1 a
Mean = 131.6 mm
b Slightly larger — scores not evenly spread around each class centre.
2 a
b 68.17 c 61–70 class
3 a
b 53.1
c 39 — remember faster is lower time 4 Check with your teacher.
5 a 14.1 b 3.4 c 44.4
No. of
televisions sold No. of weeks fx
16 4 64
17 4 68
18 3 54
19 6 114
20 7 140
21 12 252
22 8 176
23 2 46
24 4 96
25 2 50
Σf = 52 Σfx = 1060
Score (x) Frequency (f) fx
0 4 0
1 9 9
2 18 36
3 10 30
4 5 20
5 4 20
Σf = 50 Σfx = 115
Score (x) Frequency (f) fx
8 2 16
10 7 70
12 11 132
14 6 84
16 2 32
18 2 36
Σf = 30 Σfx = 370
1 3
---1 3
---Class
Class
centre (x) Tally
Frequency
(f) fx
119–121 120 | 1 120
122–124 123 | 1 123
125–127 126 | | | | 5 630
128–130 129 | | | | 4 516
131–133 132 | | | | | | | 8 1056
134–136 135 | | | | | 6 810
137–139 138 | | | | 4 552
140–142 141 | 1 141
Σf = 30 Σfx = 3948
Class
Class centre
(x) Tally
Frequency
(f) fx
31–40 35.5 | 1 35.5
41–50 45.5 | | | 3 136.5
51–60 55.5 | | | | 4 222.0
61–70 65.5 | | | | | | 7 458.5
71–80 75.5 | | | | | | | | | 11 830.5
81–90 85.5 | | 2 171.0
91–100 95.5 | | 2 191.0
Σf = 30 Σfx = 2045
Time
Class centre
No. of
swimmers fx
50.01–51.00 50.5 4 202.0
51.01–52.00 51.5 12 618.0
52.01–53.00 52.5 23 1207.5
53.01–54.00 53.5 38 2033.0
54.01–55.00 54.5 15 817.5
55.01–56.00 55.5 3 166.5
Σf = 95 Σfx = 5044.5
answers
7 166.25
8 a 12.5, 13.5, 14.5, 15.5, 16.5 b 14.4 9 a
b 46.4 c 33
Exercise 10D — Median and mode
1 Middle, arranged in order, , average,
cumulative frequency.
2 6
3 81
4 a 5 b 5.4 c 62 d 102
5 a 4 b 5.6
c The median is a better measure because one large score makes the mean larger than what is typical.
6 a
b 20
7 3 8 1 9 C 10 C 11 A
12 a
b 10–14
13 Most frequent, bimodal, modal class.
14 a 5 b 8 c 11
d 0.4 e 110
d 72 e 2.6
16 a 4 b 8 c 42, 44
17 17
18 a 17–20 b 22–28
19 a
b $350–$399
10 Quick Questions 1
1 5.5, 15.5, 25.5, 35.5, 45.5 2 5, 20, 49, 86, 97
3 48 4 86
5 Grouped 6
7 8 29
9 21–30 10 31–40
Exercise 10E — Best summary statistics
1 a $215 000 b $170 000 c $150 000
d The median, as the mean is inflated by one large score and the mode is the lowest price.
2 a 7.1 b 7 c 7
d The mode, as it is the size that sells the most.
3 a 23 550 b 20 000–30 000
c 10 000–20 000 d Median
4 B
5 a
b 6.8 c 0–4 d 0–4
Class Class centre Frequency
1–10 5.5 12
11–20 15.5 6
21–30 25.5 5
31–40 35.5 7
41–50 45.5 9
51–60 55.5 9
61–70 65.5 5
71–80 75.5 5
81–90 85.5 5
91–100 95.5 7
Score Frequency
Cumulative frequency
17 4 4
18 9 13
19 6 19
20 12 31
21 8 39
22 5 44
23 4 48
24 2 50
Days sickness Frequency
Cumulative frequency
0–4 10 10
5–9 12 22
10–14 7 29
15–19 6 35
20–24 5 40
25–29 3 43
30–34 2 45
n+1 2
---Class
Class
centre Frequency
Cumulative frequency
$200–$249 224.5 8 8
$250–$299 274.5 4 12
$300–$349 324.5 6 18
$350–$399 374.5 6 24
$400–$449 424.5 4 28
$450–$499 474.5 2 30
$500–$549 524.5 6 36
$550–$599 574.5 4 40
Class
Class
centre Frequency
Cumulative frequency
0–4 2 16 16
5–9 7 6 22
10–14 12 4 26
15–19 17 2 28
20–24 22 1 29
25–29 27 1 30
5.5 15.525.535.545.5
0 5 10 15
Score
Frequenc
y
20 25 30 35 40
5.515.525.535.545.5
0 5 10 15
Score
Frequenc
y
20 25 30 35 40
answers
➔
groupings used.
7 a
b 42.2 c 16–30 d 16–30
e No
f Check with your teacher. 8 a Player A: 34.3 Player B: 41.8
b Player B
c Player A: 32.5 Player B: 0 d Player A
e Check with your teacher.
9 a The statement is true but misleading as most employees earn $18 000.
b Check with your teacher, but you should quote $18 000 as the median and the mode salary and that only 15 out of 80 (less than 20%) earn more than the mean.
Exercise 10F — Range and
interquartile range
1 Dispersion, spread, lowest, highest, outlying, interquartile, upper, lower, median, quarter, quarter, four, scores.
2 a 5 b 9 c 1
d 6.94 e 89
3 a 4 b 5 c 6
4 a 49 b 30 c 23
5 a Sydney — 120 Collingwood — 40
b Collingwood, because the range is lower.
6 a 9 b 8
c The range for machine A is large, only because of one extreme score.
7 a 5 b 25 c 53
d 15 e 74
8 a 5 b 9 c 2
d 4 e 32
9 A 10 B 11 D 12 B
Exercise 10G — Standard deviation
1 Spread, mean, σn (or σx), σn – 1 or Sn,consistent/reliable, low.
2 a 2.29 b 2.19 c 20.17
d 3.07 e 42.44
3 a 26.94 b 2.14 c 57.51
d 0.26 e 96.04
4 a Sample b Population c Population
d Sample e Population
5 a 616.6 b Sample c 270.97
6 a $1.44 million b Population c $0.48 million 7 a x– = 4.9, σ= 1.0 b x– = 48.3, σ= 1.2
c x– = 78.3, σ= 2.3
– = σ= – = σ=
c x– = 56.02, σ= 14.26 9 a Brianna: x– = 75, σ= 3.69
Katie: x– = 74, σ= 18.28
b Brianna is more consistent because she has a lower standard deviation.
10 B
