Maths A Textbook - Answers

560 A n s w e r s
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
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
5.5 $248.60
1A
1E
MQ Maths A Yr 11 - Ans Page 560 Thursday, July 5, 2001 8:08 AM

A n s w e r s 561
answers
➔
7 C 8 A 9 B
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
17 $590.24 18 $333.25 19 $4.05
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
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
1A
2D

562 A n s w e r s
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
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 $3.56
2 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 $2865
2 $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
1
2
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
1
2
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
---
1F
3B
MQ Maths A Yr 11 - Ans Page 562 Monday, September 24, 2001 7:16 AM

A n s w e r s 563
answers
➔
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. same d $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 a 53 days, 48, 40, 34 and 26 days b Very 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
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
2E
3F

564 A n s w e r s
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
3 a 28 m b 34 m c 84 cm
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 6 A 7 B
8 a 34.56 m2
b $960.77
9 a b 180 m2
c 18 m long and 15 m wide d 90 m2
10 a C b E
11 107 cm2
12 30.6 cm2
13 a 2474 cm2
b 34.4%
1 452.4 cm2
2 31.2 m2
3 184.3 cm2
4 13 939.2 mm2
5 306 cm2
6 625 cm2
7 1428.3 m2
8 1147.6 cm2
9 17 121.8 mm2
10 670.9 cm2
Investigation — Effect of scale factors
on perimeter and area
1 Pentagon
2 All angles 108°. Figure is regular pentagon.
3 Larger knot has twice the side length of smaller knot
4 S = 2
5 Larger knot has twice perimeter of smaller knot
6 Area of larger knot is four times area of smaller knot
7 Perimeter is 3 times as long; area 9 times as large
8 Perimeter is ‘S’ times as long; area is ‘S2
’ times as
large
9 a Parallelogram
b 4 trapeziums
c Perimeter of larger knot twice as long and area 4
times as large as smaller knot. Supports
conclusion in 8.
Exercise 4C — Total surface area
1 a iii Triangular prism
b iii Square-based pyramid
c iii Triangle-based pyramid
Item
Cost price
($)
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
3C
4C

A n s w e r s 565
answers
➔
2 a
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 mm2
c 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
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 litres f 2.3 mm3
g 570 cm3
h 0.14 litres i 250 cm3
2 a 750 mL b 0.8 L c 2500 mL d 40 L
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 cm3
c 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 cm3
c 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
4A
4D

566 A n s w e r s
answers
6 Triangular prism
7 a 105.84 cm2
b 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°
7 a 35°30′ b 27°13′48″ c 68°7′30″
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 elevation
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 elevation
Angle of
depression
Angle of
elevation
4D
5A

A n s w e r s 567
answers
➔
7 B 8 C
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
6 a 12.5 m b 89.3 mm c 10.1 m
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
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′
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
oppadj
γ
24°
13.5 m
60°
1.4 m
15°
60 m
12°
400 m
5A
5F

568 A n s w e r s
answers
2 98 km 3 66 m
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
5 The shortest distance between two points on a
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–
2Tropic of Capricorn (23 ° S)
Equator (0°)
S
N
50° W 0° 20° E
Equator
Tropic of Capricorn
N
S
5B
6C

A n s w e r s 569
answers
➔
4 a 8:00 pm b 1:00 pm Friday
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
WaterX
Y
6A
7E

570 A n s w e r s
answers
4 8.6 m3
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)
3 a QR = 18 m, PQ = 6 m, ∠TQV = 20°
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
2.7m
2.7
m
2.7 m 2.7 m
5 m
5 m
2.7 m
7A
7I

A n s w e r s 571
answers
➔
4 a East b Rectangular
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
d 100 m2
e 4 m f 53°
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 m10 m 6 m10 m
10 m
5 m5 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
7F
8B

572 A n s w e r s
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
4 a 60 b $2664 c 57.6 m3
d $1728
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 12Year 10
Year 11
No.ofstudents
Year level
8 9 10 11 12
0
10
20
30
40
50
60
70
80
90
100
110
120
8A
9A

A n s w e r s 573
answers
➔
3 a Numerical and discrete
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
10
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
H
olden
Ford
N
issan
M
azda
Toyota
M
itsubishi
Frequency
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
Numberofstudents
Spelling test results
10
0
40–4950–5960–6970–7980–8990–99
1
2
3
4
5
6
7
8
9
Numberofstudents
Maths exam mark
40–49
50–59
60–69
70–79
80–89
90–99
Marks on maths examNumber of students
Married
Widowed
Separated
Divorced
Never
married
8C
9C

574 A n s w e r s
answers
Exercise 9D — Graphical methods of
misrepresenting data
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
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
5
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)
Numberofdrivers
(frequency)
8
10
12
14
1
0
1
2
3
2 3 4 5 6
No. of children in family
Frequency
4
5
6
7
8
9
18
0
2
4
6
19 20 21 22 23
Age
No.ofmembers
8
10
12
24 25
14
16
53 5447
0
2
4
6
48 49 50 51 52
No. of matches in a box
Frequency
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
304.5
314.5
324.5
334.5
344.5
354.5
0
5
10
15
Length of fish (mm)
Frequency
20
197
0
2
4
6
9 11 13 15 17
Time taken (s)
Frequency
8
10
12
14
16
18
Key 0 | 6 = 6 errors
Stem
0
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 min
Stem
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
Stem
8*
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
Stem
13*
14*
14*
15*
15*
Leaf
8 9
0 2 3 3
5 6 6 7 7 8 8
1 2 2
5 6 7 9 9B
9F

A n s w e r s 575
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 c Continuous
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 cm
Stem
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 = 82
Stem
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
Scales
40 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
Frequency
Number of people in a household
1
2
3
4
5
6
Number of people
in a household
10
0
0–4
5–910–1415–1920–2425–2930–3435–39
1
2
3
4
5
6
7
8
9
Numberofstudents
Number of CDs purchased
0–4
5–9
10–14
15–19
20–24
25–29
30–34
35–39
Number of CDs
purchased
9D
9G

576 A n s w e r s
answers
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
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
60
0
2
4
6
1 2 3 4 5
Number of sales
Frequency
8
10
12
0
7500
12 500
17 500
22 500
27 500
32 500
2
4
6
No. of people at a football match
Frequency
8
10
Key 2 | 1 = 21
Stem
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 14 180 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
Σ f = 30 Σ fx = 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
Σ f = 30 Σ fx = 210
9G
10B

A n s w e r s 577
answers
➔
3 a
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.
6 D
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
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
Σ f = 52 Σ fx = 1060
Score (x) Frequency (f) fx
0 4 0
1 9 9
2 18 36
3 10 30
4 5 20
5 4 20
Σ f = 50 Σ fx = 115
Score (x) Frequency (f) fx
8 2 16
10 7 70
12 11 132
14 6 84
16 2 32
18 2 36
Σ f = 30 Σ fx = 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
Σ f = 30 Σ fx = 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
Σ f = 30 Σ fx = 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
Σ f = 95 Σ fx = 5044.5
10A
10C

578 A n s w e r s
answers
6 a 6.6 b 30.67
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
15 a 17 b 148, 151 c No mode
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
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
5.515.525.535.545.5
0
5
10
15
Score
Frequency
20
25
30
35
40
5.515.525.535.545.5
0
5
10
15
Score
Frequency
20
25
30
35
40
10C
10E

A n s w e r s 579
answers
➔
6 Check with your teacher; answers depend on
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
8 a x– = 17.45, σ = 3.69 b x– = 14.95, σ = 7.49
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 11 C
12 x– = $1825, sample SD = $797
13 a 500 hours
b x– = 455.3 h, sample SD = 88.9 h
14 Crinkle, because the standard deviation in the weight
of each pack is lower and therefore you are more
likely to get the correct amount.
1 23.3 2 21.5 3 16 4 29 5 19
6 24 7 5 8 7.93
9 Median, because the outlier inﬂates the mean.
10 The outlier makes the range very large.
Exercise 10H — Comparing sets of
data
1
2 a Text b Text
c The ‘text’ group showed more variability.
3
4 a
5 a
6 a Smith: (0, 17.5, 57.5, 62, 85), Jones: (3, 31.5, 39,
46, 61)
b
11 a Before: (20.3, 20.75, 21.1, 21.45, 21.8)
After: (19.3, 19.7, 20.1, 20.95, 22.2)
b
12 a Key: 2 1 = 21 fruit
b
Class
Class
centre Frequency
Cumulative
frequency
1–15 8 1 1
16–30 23 13 14
31–45 38 2 16
46–60 53 0 16
61–75 68 5 21
76–90 83 4 25
a Brand A b Brand A c Brand B
d Brand A e Brand A f Brand B
g Brand A
7 C 8 E 9 B 10 C
Unsprayed Sprayed
Leaf
9 9 8 7 5
9 7 5 4 3 2 1 0
8 6 2 1 0
8 8 5 3 2 2
1
Stem
2
3
4
5
6
7
8
Leaf
1 7 8 9 9
2 3 4 4 5 8
2 2 5 8
4 9
1 2 2 6
1 3 6
5
10 15 2520 30 35 Scale
Group X
Group Y
15 2520 30 35 40 Age
Women
Men
5 1510 20 25 30 Words per sentence
Children's book
Geography text
Newspaper
0 4020 60 80100 Runs
Smith
Jones
19 20 21 22
Before
kg
After
20 40 60 80
Sprayed
Fruit
Unsprayed 10D
10H

580 A n s w e r s
answers
13 a Key: 2 3 = 23 hours
Key: 2* 5 = 25 hours
b
Chapter review
1 a 5.2 b 64.875 c 7.7 d 35.8
2 a 31.1 b 23.2 c 0.445
3 a 7.025 b 9.46
4
Mean = 38.2
5 a 29.9 b 26.4 c 18.6
6 a 27 b 6 c 3.2
d 5.5 e 128
7 a 2 b 56 c 68.5
8 a
b 50–59
9 a 2 b 23, 27 c No mode
10 a 2 b 15, 18
11 46–49
12 a 27.8 b 24.5 c 28
d Median
14 a 7 b 159 c 1.4
15 a Population b 17.3
16 a Sample b 0.89
17 a x– = 0.81, σ = 0.42 b x– = 67.25, σ = 75.3
c x– = 28.1, σ = 1.2 d x– = 27.5, σ = 7.03
18 C 19 D
20 a Key: 3* 9 = 3.9
b (3.9, 4.4, 4.9, 5.85, 6.8)
c
21 a Elena: 2, 6, 11.5, 15, 25;
Victoria: 3, 14, 20, 25, 35
b
22 a Key: 1 3 = 13
b Text A: (13, 35, 59, 82, 98);
Text B: (37, 55, 63.5, 70, 82)
c
CHAPTER 11 Scatterplots and
time series
Skills check
1 An independent variable is one whose variation does
not depend on changes in another variable. A
dependent variable is one whose variation responds to
changes in the independent variable.
2 Independent variable
3 a Height b Distance travelled
c Temperature d Reaction time
e Test results f Overtime pay
g Value of car h Travelling time
4 a Increase b Increase c Decrease
d Decrease e Increase f Increase
g Decrease h Decrease
Starlet Glow-worm
Leaf
8 6
4
9 8
2 1
6 6 5
3
7 6
4
9 5
4
8
2 2
Stem
1*
2
2*
3
3*
4
4*
5
5*
6
6*
7
Leaf
3 3
7 8
1
5 5 8 9
1 1 2
5 7 8 8 9
0 2 4
Class
Class
centre Frequency fx
21–24 22.5 3 67.5
25–28 26.5 9 238.5
29–32 30.5 17 518.5
33–36 34.5 31 1069.5
37–40 38.5 29 1116.5
41–44 42.5 25 1062.5
45–48 46.5 19 883.5
49–52 50.5 10 505.0
Σ f = 143 Σ fx = 5461.5
Class
Class
centre Frequency
Cumulative
frequency
30–39 34.5 18 18
40–49 44.5 34 52
50–59 54.5 39 91
60–69 64.5 45 136
70–79 74.5 29 165
80–89 84.5 10 175
90–99 94.5 5 180
10 30 50 70
Glow-worm
Hours
Starlet
Stem
3*
4
4*
5
5*
6
6*
Leaf
9
0 0 2 3
5 6 7 8 8
0 3
5 8 8 9
1 2 2
8
Text B Text A
Leaf
9 7
8 2
9 9 8 8 5 5 3 2
8 8 8 6 5 4 4 3 2
9 9 5 2 2
2 1
Stem
1
2
3
4
5
6
7
8
9
Leaf
3
1 2 5 8
5 5
4 8
2 5 6 9
4 9
2 2 6
1 3 4 4
4 5 8
3.5 4.5 6.55.5 kg
0 10 3020
Elena
Number of
lessons
Victoria
0 20 40 60 80100
Text A
Result
Text B
10F
10H

A n s w e r s 581
answers
➔
5 a b
c d
e f
g h
Exercise 11A — Scatterplots
1
2
3
4 a
b The greater the English mark, the greater the
history mark, generally. However, as the points on
the scatterplot do not form a straight line, the
relationship is not linear.
5 a
b The greater the temperature, the fewer pies are
sold. The points on the scatterplot approximate a
straight line and so the relationship can be said to
be linear.
6 a
b More workers on the team reduces the amount of
time taken to unload the ship and, as the points on
the scatterplot approximate a straight line, the
relationship is linear.
7 D
8 A
Exercise 11B — Regression lines
Note: Best fit lines are indicated as a guide only.
1 a b
c d
e
2
3 a y = 5x + 12 b y = 70 − 0.4x
c y = 80x + 750
4 a b L = 0.05M + 220
5 a b V = 0.05T + 3.2
6 a b S = 1.25B + 21
7 a $17.40 b $8.40 c 20 km d 8.5 km
8 a 159.7 cm b 178 cm
c 31.15 cm d 25.74 cm
9 a 755 b 295 c 20°C d 38°C
Height
Age
Distance
Time
Temperature
Elevation
Reaction
time
Blood ale
level
Testresults
IQ
Overtime
pay
Hours
worked
Valueofcar
Age
Travelling
time
Speed
0
40
80
0 40 80
Geography
History
0
200
400
0 20 40
Numberat
cinema
Temperature (°C)
0
0
100
200
200
400
600
800
Amountspenton
entertainment($)
Wages ($)
0
40
80
0 40 80
History
English
0
80
0 20 40
Numberof
piessold
Temperature (°C)
0
10
20
30
0 10 20 30
Hourstaken
Number in work team
x
y
x
y
x
y
x
y
x
y
0
40
80
0 40 80
Maths
English
0
240
280
0
400
800
Lengthof
spring(mm)
Mass (g)
20–20–60 60
2
4
6
8
Temperature (°C)
Volume (L)
0
20
40
60
0 10 20 30 40
Lifttest(kg)
Circumference of
biceps (cm)
11A
11B

582 A n s w e r s
answers
10 a, b c C = 0.4d + 2100
d i $8100 ii $2500 iii 14 750 km iv 34 750 km
11 a, b c N = 135 − 20p
d i 73 000 ii 43 000
e $2.75 f $1.75
12 a b A = 0.45d + 280
c i $582 ii $1236 iii $740 iv $1762
1 $115
2 $235
3 $85
4 3 h 30 min
5 6 h
6 2 h 45 min
7 80
8 35
9 2 h
10 4 h 30 min
Exercise 11C — Time series and trend
lines
Note: Your answers to questions 2 to 8 may vary slightly
because you are using the ‘eye’ method.
1 a Seasonal
b Random
c Secular, upwards
d Random or cyclical
e Cyclical
2 Definite secular trend
downward
3 Although there are some
random variations, the trend
could also be secular.
4 Prediction is about $5.40
(see dotted line at right).
This price is an extrapolated
value (outside the plotted
values) and can only be
treated as an approximate
value at best.
5 Impossible to fit a trend line, given cyclical nature of
the data.
6 a b Prediction for t = 25
is about $92.
7 Difficult to fit an
accurate trend line, due
to likely cyclical nature
of software sales
business.
8 At current rate
(about 300/month),
bank will have no
employees in
another year!
Although not likely,
there is a clear
downward trend.
Chapter review
1
2 a
b There appears to be a positive relationship which
is linear.
3 a
b There is no apparent relationship.
4 D 5 D 6 C
7 a, b c y = 99 − 5x
8 a $242 400 b $73 000
9 a b F = 107 − 8I
c 73 d 13.4 mg
0
0
8000
16000
100002000030000
Annualcost($)
Distance (km)
0
80
160
0.00
2.00
4.00
Weeklysales
(×1000)
Price ($)
0
800
1400
0
1000
2000
3000
Price($)
Distance (km)
Days
Temp.(°C)
10
15
20
25
30
35
40
0 1 2 3 4 5 6 7 8 9 10 t
0
10
20
0 2 4 6 8 10 12 t
y
2
3
4
5
6
0 2 4 6 8 10
Price($)
12 t
y
Price(cents)
20
40
60
80
100
0 5 10 15 20 25 t
Sales(×1000)
240
220
200
180
160
140
120
100
1999 2000 2001
Numberofemployees
7000
6000
5000
4000
3000
2000
1000
0
1086
Months
420 t
0
10
20
0 20 40
Maximum
temperature (°C)
Minimum
temperature(°C)
0
4
8
12
0 2 4 6
Number of children
Numberofsickdays
0
2
4
0 2
Number of cars
Numberof
televisions
0
40
80
0 8 16
y
x
0
40
80
120
0 4 8 12
Amount of insecticide (µg)
Numberofblowflies
11A
11C

A n s w e r s 583
answers
➔
10 C
11
Impossible to fit a trend line as trend is seasonal.
Summer uniform bought at the end of the year and
then the beginning of the year. Winter uniform bought
near winter.
CHAPTER 12 Introduction to
probability
Skills check
1 a 50-50 b Almost impossible
c Almost certain d Not very likely
e 50-50 f Impossible
2 a 6 b 1, 2, 3, 4, 5, 6
c 1 in 6 d 3
e 3 in 6 f 3 (2, 3 and 5)
g 3 in 6
3 a
b 8 c 2 d 3
4 a 0.833 b 0.667 c 0.167
d 0.077 e 0.417
5 a 83.3% b 66.7% c 16.7%
d 7.7% e 41.7%
6 a , 0.125 b , 0.444 c , 0.875
d , 0.938 e , 0.875 f , 0.009
Exercise 12A — Informal description of
chance
1 a Probable b Unlikely c Impossible
d Fifty-fifty
2 a Impossible b Certain c Even chance
d Even chance e Probable f Unlikely
g Impossible h Even chance
4 More likely during school term
5 a More likely b Equally likely c Less likely
d More likely e Less likely
6 Rolling a 6
Rolling a number less than 3
Rolling an even number
Rolling a number greater than 2
7 Winning a raffle with 5 tickets out of 30
Selecting a court card from a standard deck
Drawing a green marble from a bag containing 4 red,
5 green and 7 blue marbles
Rolling a die and getting a number less than 3
Tossing a coin and having it land Heads
8 Australia
9 Carl Bailey because he has better past performances.
10 A 11 B 12 C
13 Probable 14 Unlikely 15 Fifty-fifty
Exercise 12B — Sample space
1 S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
2 a S = {Heads, Tails}
b S = {1, 2, 3, 4, 5, 6}
c S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
d S = {a, b, c, d, …, y, z}
e S = {Sun, Mon, Tue, Wed, Thu, Fri, Sat}
f S = {Jan, Feb, Mar, …, Dec}
3 a 52 b 15 c 45
d 1500 e 901 f 11
4 a S = {M, I, S, S, I, S, S, I, P, P, I}
b 11 c 4
5 a 52 b i 4 ii 2 iii 13
6 a S = {1, 2, 3, 4, 5, 6} b E = {5, 6}
7 a 100 b 40
8 D 9 B 10 D
11 a S = {NSW win, Qld win, draw}
b 3
c No, because the teams may not be of equal
ability.
12 a S = {20, 20, 20, 20, 20, 10, 10, 10, 10, 5}, 10
b S = {20, 20, 20, 20, 10, 10, 10, 10, 5}
c S = {20, 20, 20, 20, 20, 10, 10, 10, 5}
d S = {20, 20, 20, 20, 20, 10, 10, 10, 10}
1 Unlikely 2 Fifty-fifty 3 Probable
4 100 5 18 6 3
7 10 8 1 9 0
10 4
Exercise 12C — Tree diagrams
1 S = {HH, HT, TH, TT}
2 S = {11, 12, 13, 21, 22, 23, 31, 32, 33}
Child 1 Child 2 Child 3
Boy Girl Girl
Boy Boy Girl
Boy Girl Boy
Boy Boy Boy
Girl Boy Boy
Girl Boy Girl
Girl Girl Boy
Girl Girl Girl
6
Month
42 12108
50
30
110
90
70
10
Numberofuniformssold
Impossible
b d a c
e
f
Certain
1
8
---
4
9
---
7
8
---
15
16
------
7
8
---
9
1024
------------
11C
12C

584 A n s w e r s
answers
3 S = {BBB, BBG, BGB, BGG, GBB, GBG, GGB,
GGG}
4 a 12 b No
5 S = {13, 14, 18, 31, 34, 38, 41, 43, 48, 81, 83, 84}
6 S = {DZ, DM, DK, DS, ZD, ZM, ZK, ZS, MD, MZ,
MK, MS, KD, KZ, KM, KS, SD, SZ, SM, SK}
7 S = {AM, AS, AL, PM, PS, PL, YM, YS, YL}
8 S = {CA, CR, CL, CK, AR, AL, AK, RL, RK, LK}
9 a Check with your teacher.
b S = {HHHH, HHHT, HHTH, HHTT, HTHH,
HTHT, HTTH, HTTT, THHH, THHT,
THTH, THTT, TTHH, TTHT, TTTH, TTTT}
c 6
10 C 11 D 12 B
13 The statement is not correct because there are 4
elements to the sample space. The one Head and
one Tail can occur in either order.
14 a S = {22, 25, 27, 28, 52, 55, 57, 58, 72, 75, 77, 78,
82, 85, 87, 88}
b S = {25, 27, 28, 52, 57, 58, 72, 75, 78, 82, 85,
87}
15 a 12 b 24 c 24
16 a S = {TJ, TS, TR, TM, JT, JS, JR, JM, ST, SJ, SR,
SM, RT, RJ, RS, RM, MT, MJ, MS, MR}
b 20 c 2 d 6 e 12
17 a 36
b
c 6
Exercise 12D — Equally likely
outcomes
1 No. The players are not of equal ability.
2 No. The runners are not of equal ability.
3 Yes. The number is chosen randomly.
4 a Yes b No c No d Yes
5 a True. The letter is chosen randomly.
b False. On a page of writing, each letter of the
alphabet does not occur equally often.
6 B
7 No, there are two chances of a boy and a girl, as they
could be born in either order.
8 a S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
b No
9 a 24
b No. The chance of each combination depends on
people’s taste.
10 a 10
b No. Each horse has a different rider and ability.
c Yes. Yes. The selection of horse is made
randomly.
1 Unlikely 2 8 3 3
4 1 5 Yes
6 S = {BB, BG, GB, GG}
7 S = {AL, AM, AJ, SL, SM, SJ}
8 9 9 6 10 No
Exercise 12E — Using the fundamental
counting principle
1 50 625
2 a 4 b 36 c 12
3 1000 4 7776 5 6 760 000
6 D 7 B 8 1833
9 72
10 a 64 b 144 c 168
d 112 e 384
11 a 3 200 000 b 240
12 a 5408 b 676
13 36
14 a 100 000 000 b 80 000 000
c 1 000 000 d 2 000 000
15 96
16 C
17 a 1200 b 550
18 20 000
19 307 328 000
Investigation — Q-lotto: frequencies
1 Unlikely
2 Almost impossible
3 Less likely
4 No
5 {1, 2, 3, 4, . . . 44, 45}, 45
6 {4, 5, 8, 15, 22, 30, 23, 35}
7 8, no
8 No, at least 3, plus either bonus
9 {4, 5, 8, 15, 22, 30}
10 Yes, they occur only once each
11 No
12 60
13 3
14 28, 76
15 6, 43
16 {10, 20, 21, 25, 38, 40, 41, 43}
2 supplementary or bonus numbers
17 {9, 11, 27, 28, 29, 38, 43}
6 of these
18 {2, 5, 8, 12, 15, 37}
Exercise 12F — Relative frequency
1 0.74 2 0.79 3 0.375
4 a 0.45 b 0.55
5 4%
6 a 0.03 b 0.97
7 a 0.96 b 0.04
8 A 9 A
10 a 0.525 b 0.4375 c 0.0375
11 a 6.67% b 80
12 a 0.02 b $400
13 Yes, the relative requency is 27%.
14 a 2.5% b 51.5% c 17.5%
15 40 000 km
16 a
b Win = 0.375, Loss = 0.35, Draw = 0.275
Total 2 3 4 5 6 7 8 9 10 11 12
No. of elements 1 2 3 4 5 6 5 4 3 2 1
Result Number
Win
Loss
Draw
15
14
11
12A
12F

A n s w e r s 585
answers
➔
Exercise 12G — Single event
probability
1 S = {Heads, Tails}, 1
2 a S = {1, 2, 3, 4, 5, 6}, 1
b S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, 3
c S = {a, b, c, d, e, … y, z}, 5
d S = {Sun, Mon, Tue, Wed, Thu, Fri, Sat}, 2
e S = {Jan, Feb, Mar, … Nov, Dec}, 3
3 a 26, 52 b 1, 15 c 1, 45
d 5, 1500 e 3, 11
4
5 a b c
d e f
6 a b c
d e f
g g i
7 a b c
d e f
8 a b c
9 a b c
d e f
10
11 a b c
d e
12 C 13 C 14 C 15 D
16 a b
17 a b c
18 a b c
d e f
20 a Because there are two numbers which could go in
the last place.
b A number greater than 400
1 2 3 4 5
6 True 7 False 8 0.2 9 0.75 10 0.5%
Exercise 12H — Writing probabilities
as decimals and percentages
1 0.5
2 37.5%
3 a 0.5 b 50%
4 a 0.17 b 0.5 c 0.33
5 a 16.7% b 50% c 83.3%
6 a 0.02 b 0.25 c 0.08
d 0.5 e 0.23
7 a 1.9% b 25% c 7.7%
d 50% e 23.1%
8 A 9 D 10 B
11 a 0.2 b 0.4 c 0.6
d 0.8
12 a 20% b 40% c 40%
Exercise 12I — Range of probabilities
1 a Even chance b Probable c Unlikely
d Certain e Probable f Unlikely
g Probable h Impossible i Unlikely
2 a 0, impossible b 1, certain
c , even chance d , even chance
e , unlikely f 0, impossible
g , even chance
4 , , , ,
5 A, D, C, B, E
6 D 7 B 8 D
9 a b Unlikely
10 , very probable
11 a Very unlikely b Even chance
c Probable d Unlikely
12 a True, as there are 4 Aces from 52 cards in the
deck.
b False, as each letter does not occur equally often.
c False, as each student is not of equal ability.
d True, as the name is chosen randomly.
1 2 3 , , 4 62.5%
5 0.375 6 0.154 7 23.1% 8 1
9 0 10 Probable
Exercise 12J — Complementary events
1 a S = {1, 2, 3, 4, 5, 6}
b c 1
2 a i ii iii
b 1
3 a Losing a race
b Failing a test
c Your birthday not falling on a Monday
4 A coin landing Heads A coin landing Tails
An odd number on a die An even number on a die
A picture card from a A non-picture card from a
standard deck standard deck
A red card from a A black card from a
standard deck standard deck
Winning 1st prize in a Not winning 1st prize in
rafﬂe with 100 tickets the rafﬂe
Making the last 4 teams A team not making the
in a 20-team last four
tournament
1
2
---
1
6
---
1
6
---
1
2
---
1
2
---
2
3
---
1
3
---
1
45
------
1
45
------
22
45
------
23
45
------
1
5
---
1
3
---
19
45
------
2
9
---
2
15
------
1
52
------
1
13
------
1
4
---
1
2
---
3
13
------
3
13
------
1
12
------
1
3
---
7
12
------
1
4
---
1
4
---
1
4
---
3
4
---
1
2
---
3
4
---
5
6
---
1
4
---
3
4
---
1
4
---
1
4
---
1
2
---
1
200
---------
4
999
---------
3384
160 000
-------------------
6768
160 000
-------------------
10 152
160 000
-------------------
1
5
---
1
5
---
4
5
---
1
5
---
4
5
---
1
5
---
1
6
---
1
13
------
7
11
------
33
100
---------
5
9
---
3
6
---
26
52
------
4
52
------
6
12
------
13
20
------
7
13
------
9
18
------
8
19
------
6
25
------
50
2000
------------
98
100
---------
1
2
---
1
4
---
4
9
---
1
2
---
10
19
------
1
6
---
7
20
------
8
20
------
5
20
------
12D
12J

586 A n s w e r s
answers
5 a , , , , ,
b , , , , ,
c 1
6 a Rolling an odd number
b Rolling a number less than 4
c Rolling a number greater than 2
d Not rolling a 6
e Rolling a 1
7 a Choosing an even-numbered ball
b Choosing a ball numbered greater than 19
c Choosing a ball that has a number less than 24
d Choosing a ball that is not a multiple of 5
8 a Selecting a coloured ball
b Selecting a black ball
c Not selecting a pink ball; that is, selecting a
black or orange ball
9 A 10 C
11 a b
12 a b
13 a b c
d e f
14 a b c
d e
15 a b
16 a b c
17 0.3
18 a 91% b 9%
1 S = {heart, club, diamond, spade}
2 3 4
5 6 7
8 9 10
Investigation — Q-lotto: conclusion
1 45 × 44 × 43 × 42 × 41 × 40 = 5 864 443 200
2 6 × 5 × 4 × 3 × 2 × 1 = 720
3 5 864 443 200 ÷ 720 = 8 145 060
4
Chapter review
1 Marcia will probably get a higher card.
2 a Probable b Impossible c Even chance
d Unlikely e Unlikely
4 Hot weather
5 Rolling a die and getting a number greater than 1
Selecting a blue marble from a bag containing 14
blue, 15 red and 21 green marbles
Selecting a picture card from a standard deck
Winning the lottery with 1 ticket out of 100 000
tickets sold
6 Mark is most likely to win based on past
performances.
7 S = {S, A, M, P, L, E}
8 a S = {Heads, Tails}
b S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16, 17, 18}
c S =
{ace club, ace spade, ace diamond, ace heart}
d S = {black, black, black, black, white, white,
white, green, green, green, green, green}
9 a S = {1, 2, 3, 4, 5, 6}
b E = {5, 6}
10 a i 2 ii 1
b i 52 ii 32
c i 15 ii 11
11 S = {HH, HT, TH, TT}
12 36
13 a S = {56, 57, 59, 65, 67, 69, 75, 76, 79, 95, 96, 97}
b 9
14 a S = {MN, MP, MR, MS, NM, NP, NR, NS, PM,
PN, PR, PS, RM, RN, RP, RS, SM, SN, SP,
SR}
b 8
15 a S = {TCB, TCM, TCZ, TDB, TDM, TDZ, THB,
THM, THZ, TIB, TIM, TIZ, KCB, KCM,
KCZ, KDB, KDM, KDZ, KHB, KHM, KHZ,
KIB, KIM, KIZ}
b 15
16 a 8
b No. Each greyhound is not of equal ability.
17 a Each is equally likely, as the winning ticket is
selected randomly.
b Each outcome is not equally likely, as the teams
have different abilities.
c Each letter is not equally likely, as each letter is
not used equally often.
18 759 375
19 20
20 272
21 160
22 a 10 000 b 500
23 a 100 000 000 b 94 109 400
24 0.02
25 a 0.15 b $750
26 S = {1, 2, 3, 4, 5}, E = {3, 4, 5}
27 a b c
d e f
28 a b c
d e f
29 a b c
1
2
---
1
2
---
3
13
------
1
2
---
1
100
---------
1
5
---
1
2
---
1
2
---
10
13
------
1
2
---
99
100
---------
4
5
---
1
8
---
7
8
---
1
5
---
4
5
---
9
20
------
11
20
------
3
20
------
17
20
------
3
5
---
2
5
---
2
5
---
3
10
------
3
5
---
7
10
------
3
10
------
7
20
------
13
20
------
3
25
------
21
50
------
29
50
------
1
10
------
1
8
---
1
10 000
----------------
8
15
------
7
15
------
3
10
------
1
5
---
4
5
---
4
5
---
1
8 145 060
-----------------------
1
25
------
1
25
------
13
25
------
1
5
---
9
25
------
16
25
------
1
52
------
1
13
------
1
4
---
1
2
---
4
13
------
10
13
------
7
20
------
1
10
------
3
4
--- 12G
12J

A n s w e r s 587
answers
➔
30 a b c
d e
31 a b
32 a 0.025 b 0.5 c 0.75
33 a 50% b 33 % c 66 %
34 Probable
35 . It is probable that the car will have a defect.
36 a Tossing a coin that lands Heads
b Rolling a die and getting a number greater than 4
c Not choosing a blue ball
37 a b
38 39
1
24
------
3
4
---
1
4
---
3
4
---
1
2
---
1
400
---------
4
1999
------------
1
3
---
2
3
---
7
8
---
3
10
------
7
10
------
5
12
------
18
25
------

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