1. Answers
515
Answers
CHAPTER 1 Simple and
compound interest
Exercise 1C — Graphing simple interest
functions
Skills check
1 a
4 a 450
d 1.157 625
$8.75
$4
0.0725
0.125
1
-- years
6
5
4 ----- years
12
b 525
e 1.083
c
f
c
f
c
f
$1.50
$0.25
0.2
0.001
2
-- years
3
-2 1 years
2
b
1000
500
0
2 a
16 000
14 000
12 000
10 000
8000
6000
4000
2000
0
3
4
Years
5
1
2
3
4
5
$1600 $3200 $4300 $6400 $8000
0 1 2 3 4 5 6 7 8 9 10
Years
c 1600
d $16 000
3 a
6000
4000
2000
0
0
1
2
3 4
Years
5
2
3
4
Years
5
1000
Interest ($)
b
800
600
400
200
0
c
0
1
4000
3000
2000
1000
0
0
1
2
3
4
Years
5
1A
➔
d Yes ($1281.60)
2
No. of years
Interest
c $5425
6 $352
9 C
13 A
1
0
Interest ($)
b
Exercise 1B — Finding P, R and T
c 80%
e 3.36%
c 3 months
3
4
5
$1200 $1600 $2000
1500
Exercise 1A — Simple interest
1 a $3070
b $4400
d $236.36
e $2500
2 a 10%
b 6.25%
-d 2.125% or 2 1 %
8
b 18 months
3 a 1 year
d 7 years
e 1 month
4 $1515.79
5 $2133.33
7 24 months
8 3 years
10 B
11 B
12 D
14 a Yes ($1112.50)
b No
c Yes ($1600 in 23 months)
2
$800
2000
c 21 000
f 1.877
1 a $136.00
b $56.70
c $145.25
d $110.40
e $255
f $336.89
g $178.57
h $43.88
i $11.76
j $229.68
k $544.05
2 a $103.50
b $2700
c $325
d $131.25
3 a $360
b $1020
c $27 700
d $17.70
e $13.67
4 C
5 A
6 B
7 B
8 B
9 A
10 D
11 B
12 A
13 $465.50 14 $25.50 15 $2418.75
16 $584.50
17 a The Big-4 Bank offers the best rates.
-b The Big-4 Bank charges 11 1 % p.a. for a loan
3
while The Friendly Building Society charges 12%
(=12 × 1% per month).
18 a $627.13
b $12 542.50
19 a i $1540.63
ii $6162.50
b Yes
-20 a $2247
b $15 729
c 7 1 years
2
1
$400
Interest ($)
b
e
b
e
b
e
Interest ($)
$1
$0.25
7.25
0.002
1
-- years
4
1
2 ----- years
12
Interest ($)
1 a
d
2 a
d
3 a
d
No. of years
Interest
answers
Maths A Yr 12 - Answers Page 515 Wednesday, September 11, 2002 3:41 PM
1C

2. 516
Answers
10 Quick Questions 1
Interest ($)
20 000
1 $800
5 $7000
9 54c
15 000
10 000
5000
1
0
2
3 4
Years
5
Interest ($)
400
300
200
100
0
b
Investment ($)
0
3 4
Years
5
3500
0
1
2 3
Years
4
5
1 a
No. of years
1
2
3
4
5
Interest (5%) $1250 $2500 $3750 $5000 $6 250
Interest (6%) $1500 $3000 $4500 $6000 $7 500
Interest (8%) $2000 $4000 $6000 $8000 $10 000
b
5000
2 a
2
3 4
Years
1
2
3
4
5
$8400
$8820
$9261
$9724
$10 210
3
4
5
5
1
2
3
4
5
Interest (3%)
$165.00 $330.00 $495.00 $660.00
$825.00
Interest (3.5%)
$192.50 $385.00 $577.50 $770.00
$962.50
Interest (3.75%) $206.25 $412.50 $618.75 $825.00 $1031.25
0
1
2
3 4
Years
5
8 a $4500, $5000, $5200
c $25 900
25 000
20 000
15 000
10 000
25 000
20 000
15 000
b $875
0
9
5000
4000
Future value ($)
b
6.2%
5.8%
5.2%
4500
2
0 1 2 3 4 5 6 7 8 9 10
Years
3 a
500
0
1
5
0
Future value ($)
1000
2 3 4
Years
30 000
3.75%
3.5%
3%
1500
Interest ($)
b
1
No. of years
Future value ($)
No. of years
0
Future value $12 960 $13 997 $15 117 $16 326 $17 632
b
7 a
10 000
9500
9000
8500
8000
0
0
1
No. of years
Future value
8%
6%
5%
10 000
0
0
1
2
3 4
Years
5
4000
3000
2000
0
0
1
2
3
Years
4
5
4 $1.90
8 $1998.75
Exercise 1E — Graphing compound
interest functions
3000
Interest ($)
b
2
4000
0
6 a
1
3 $2700
7 $215.44
1 $6655
2 $17 173.50
3 $2938.66
4 a $4630.50 b $9274.19
c $24 488.80
d $13 503.78 e $12 588.72
5 $70 555.26
6 $502
7 $14 059.91
8 $31 850.33
9 a $1003.69 b $8985.76
c $181 402.12
d $20 039.67 e $1 264 568.95
10 B
11 B
12 B
13 C
14 a $15 746.40
b $15 793.09
c $15 817.40
d $15 833.99
15 a 0.0219%
b $108 320.71
c $8320.71
d $320.71
16 a $4720
b $4726.24
c Compounding interest
4 288
5 a
2 $1260
6 $138
10 $173.58
Exercise 1D — Calculation of
compound interest
0
Future value ($)
d
Interest ($)
answers
Maths A Yr 12 - Answers Page 516 Wednesday, September 11, 2002 3:41 PM
0
0
1
2
3 4
Years
5

3. 517
Answers
Chapter review
4 a
Years 0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
FV $2060 $2122 $2186 $2252 $2318 $2388 $2460 $2534 $2610 $2688
2700
2600
2500
2400
2300
2200
2100
2000
0
Interest
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
b
Years
Future value ($)
1800
1600
1400
1200
600
500
400
300
200
100
0
0 1 2 3 4 5 6 7 8 9 10
Years
6 a No. of years
Interest ($)
b
Compound interest
earned ($)
5 a
0
0 1 2 3 4 5 6 7 8 9 10
Years
1
2
3
4
5
Interest (4%)
$320
$653
$999
$1359
$1733
Interest (6%)
$480
$989
$1528
$2100
$2706
Interest (8%)
$640
$1331
$2078
$2884
$3755
b
Interest ($)
12 000
Interest (8%)
Interest (6%)
Interest (4%)
10 000
1
2
3 4
Years
7 a No. of years
Future value ($)
1
Annually
$4240
Six-monthly $4244
3
$4764
$4776
4
$5048
$5068
5
$5352
$5376
Annually
Six-monthly
5500
5000
4500
4000
0
0
1
2 3
Years
4
5
10 Quick Questions 2
1
4
7
10
$2051.28
$429.69
$6792.58
$14 700.68
2 $17 253
5 $2315.25
8 $6805.66
3
4
5
$1350 $1800 $2250
1
2
3
4
5
Future value $20 800 $21 632 $22 497 $23 397 $24 333
5
2
$4496
$4504
2
$900
$455
C
B
0 1 2 3 4 5 6 7 8 9 10
Years
No. of years
b
0
4500
4000
3500
3000
2500
2000
1500
1000
500
0
1
$450
$42
c 450
d $4500
13 $2778.30
14 $5700.47
15 a $3932.39 b $12 596.90
c $14 457.96
d $23 031.76 e $5334.67
16 $756.94
17 a $12 024.02
b $12 052
c Compounding interest
18 a
8000
0
b
b $2820
c
e $7617.58
b $39 780
c
5 B
6
8 15 months 9
11 C
12 a No. of years
3 $3437.50
6 $315.25
9 $6812.41
Exercise 1F — Nominal and effective
interest rates
28 000
27 000
26 000
25 000
24 000
23 000
22 000
21 000
20 000
0
0
1
2
3
4
5 6 7
Years
8
9 10
c $29 600
19 3.94% p.a.
20 4.18% p.a., 4.08% p.a.
Choose 4.1% p.a. compounding monthly.
21 a 3.95% p.a. effective
b 3.97% p.a. effective
c 3.96% p.a. effective
Choose 3.895% p.a. compounding monthly.
CHAPTER 2 Appreciation and
depreciation
Skills check
1 a
d
2 a
d
3 a
d
4 a
d
5 a
d
1.1
0.9625
$4
41c
$44
$18
40%
4.5%
1.06
0.97
b
e
b
e
b
e
b
e
b
e
1.01
0.9775
$5
$1.10
$3
$135.94
87.5%
51.4%
0.94
1.03
c
f
c
f
c
f
c
f
c
f
1.0175
0.9975
$3.95
$4.37
$7.64
$3940
64.5%
1.56%
1.04
0.97
1D
➔
1 4.06% p.a.
2 4.08% p.a.
3 3.79% p.a.
4 a 4.27% p.a. effective rate
b 4.26% p.a. effective rate
So 4.2% p.a. compounding quarterly is better.
5 5.095% effective rate, 5.12% effective rate.
Choose 5% p.a. compounding monthly.
Future value ($)
Future value ($)
b
1 $1000
2 a $1296
d $4.05
3 a $7280
4 D
7 6.5%
10 B
answers
Maths A Yr 12 - Answers Page 517 Wednesday, September 11, 2002 3:41 PM
1F

4. 518
Answers
1 $20 800
2 a $618
d $579.60
3 a $878.05
4 $117.90
7 $1.20
10 $500
b
e
b
5
8
11
$48.15
$932.40
$901.76
$619
$122.80
$2350
6 $2.52
9 D
12 $2460
8 B
9 a
Value ($)
3 a
Value ($)
22 000
18 000
4
14 000
5
V = 50 000 − 8000A
26 000
3
0 2 4 6 8 10
Age (years)
30 000
2
10 000
b See part d.
c
Age (years)
Value ($)
New (0)
50 000
40 000
30 000
20 000
10 000
0
7000
6000
5000
4000
3000
2000
1000
0
12 228
5
c 4
15 360
4
d
19 200
3
c 9 years
24 000
2
0 2 4 6 8 10
Age (years)
30 000
1
0 2 4 6 8 10
Age (years)
b $20 000
4 a V = 6400 − 2000A
b
Value ($)
0 2 4 6 8 10
Age (years)
1
Value ($)
Value ($)
50 000
40 000
30 000
20 000
10 000
0
iii $102 400
New (0)
b V = 100 000 − 10 000A
2
200 000
160 000
120 000
80 000
40 000
0
Age (years)
Value ($)
100 000
80 000
60 000
40 000
20 000
0
ii $128 000
b
c $1.91
Exercise 2B — Modelling depreciation
1 a
7 a i $160 000
iv $81 920
Value ($)
Exercise 2A — Inflation and
appreciation
9 830
30 000
24 000
18 000
12 000
6 000
0
Straight line value
Declining balance
value
0 2 4 6 8 10
Age (years)
e 6 years
0 1 2 3 4
Age (years)
b $2000
1 $20 000
2 a $1000
d $145
3 a $7 125 000
4 $10 600
5 8 years
6 a 6 years
c 8 years
7 $2500/year
8 a $4000/year
9 $900/year
10 $25 000
11 a $110 000
12 $78 000
Value ($)
20 000
16 000
12 000
8 000
4 000
0
Exercise 2C — Straight line
depreciation
b $17 000 c 7
5 a
6 a
Value ($)
answers
Maths A Yr 12 - Answers Page 518 Wednesday, September 11, 2002 3:41 PM
0 2 4 6 8 10
Age (years)
620 000
480 000
360 000
240 000
120 000
0
0 2 4 6 8 10
Age (years)
b $10 300
e $32 000
b $3 750 000
c $270 000
b 5 years
d 7 years
b $12 500/year c $14 500/year
b $26 500
c $1450

5. Answers
Exercise 2D — Declining balance or
diminishing value method of
depreciation
1
2
3
4
5
6
7
8
9
10
11
12
$20 480
a $2220
7 years
$383 000
a $5900
d $62 100
$6174
$676 000
a $14 600
A
C
a $5360
c $3591
5 years
3 a
100 000
90 000
85 000
80 000
72 250
3
70 000
61 400
4
60 000
52 200
5
50 000
44 350
6
40 000
37 700
7
30 000
32 050
8
20 000
27 250
9
10 000
23 150
10
c $1200
b $20 400
b $2640
d $1769
b
0
19 700
Straight line
100 000
value
80 000
Diminishing
value
60 000
40 000
20 000
0
0 2 4 6 8 10
Age (years)
Value ($)
2 $2350/year
4 $21 000
R
5 S = Vo  1 – --------

100
100 000
2
1 $650
3 7 years
Diminishing
value ($)
New (0)
ii $390
b $68 100
e $3900
Straight line
value ($)
1
b i $750
10 Quick Questions 1
7 $11 000
9 $37 500
Age of
equpment
(years)
519
T
6 $7250
8 $389 000
10 16 years
4
Age of
computer
(years)
Salvage value
at 35% ($)
3520.00
2860.00
2
2816.00
2288.00
3
2252.80
1830.40
4
1802.24
1464.32
5
1 a $1638.50
b $9537.50
c $34 870
2 a
Age of car
Straight line
Diminishing
(years)
value ($)
value ($)
Salvage value
at 20% ($)
1
Exercise 2E — Depreciation tables
1441.79
1171.46
New (0)
40 000
40 000
1
35 000
32 000
2
30 000
25 600
6
1153.43
937.16
3
25 000
20 500
7
922.75
749.73
4
20 000
16 400
8
738.20
599.79
5
15 000
13 100
9
590.56
479.83
6
10 000
10 500
10
472.45
383.86
7
5 000
8 400
5
Salvage value
($)
Tax deduction
($)
1
4355.00
2145.00
2
2917.85
1437.15
3
1954.96
962.89
4
1309.82
654.14
5
877.58
432.24
6
0
877.58
Years
8
Value ($)
b
answers
Maths A Yr 12 - Answers Page 519 Wednesday, September 11, 2002 3:41 PM
40 000
32 000
24 000
16 000
8 000
0
0
Straight line
value
Diminishing
value
c After 6 years
2A
➔
0 2 4 6 8 10
Age (years)
6 700
2E

6. 520
Answers
6
Salvage
value —
declining
balance ($)
Tax
deduction
($)
1
200 000
50 000
2
160 000
40 000
4 746
3
128 000
32 000
3 560
4
102 400
25 600
2 670
5
81 920
20 480
65 536
16 384
Salvage value
($)
Tax deduction
($)
1
33 750
11 250
2
25 313
8 438
3
18 984
6 328
4
14 238
5
10 679
6
8 009
Years
Age of
truck
(years)
7
6 007
2 002
6
8
4 505
1 502
7
52 429
13 107
8
41 943
10 486
9
33 554
8 389
10
26 844
6 710
7 a
Age of
truck
(years)
New (0)
Straight line
value
($)
Diminishing
value
($)
250 000
225 000
200 000
2
200 000
160 000
3
175 000
128 000
4
150 000
102 400
5
125 000
81 920
6
100 000
65 536
7
75 000
52 429
8
50 000
41 943
9
25 000
33 554
10
b
250 000
1
Value ($)
answers
Maths A Yr 12 - Answers Page 520 Wednesday, September 11, 2002 3:41 PM
0
26 844
250 000
Straight line
200 000
value
150 000
100 000
50 000 Diminishing
0 value
0 2 4 6 8 10
Age (years)
c
8 a $10 000
b
9 a $3000
b $75
1
-4
Exercise 2F — Future and present
value of an annuity
1 $7049.37
2 a $6691.13
b $16 859.14
c $6158.56
d $3974.56
e $17 713.21
f $3530.21
3 $4472.93
4 $90 237.49
5 a $20 326.23
b $24 297.37
c $45 881.32
d $69 770.03
6 C
7 $4067.23
8 a $4524.37
b $7068.59
c $1930.08
9 $4787.76
10 a $1324.00
b $23 932.35
c $7503.81
d $62 953.50
11 a 4%
b 10
c $6003.05
12 a $4103.92 b $5535.38
c $7546.74
13 5% for 6 years. $1 will grow to $6.8019 but at 6%
for 5 years it will grow to $5.6371.
14 D
15 $6918.50
16 a $1845.09
b $12 289.20
c $4455.79
d $16 604.40
Salvage
value —
straight line
($)
Tax
deduction
($)
1
225 000
25 000
2
200 000
25 000
3
175 000
25 000
4
150 000
25 000
5
125 000
25 000
6
1 A = 20 000  1 + --------

100
6
100 000
25 000
2
7
75 000
25 000
8
50 000
25 000
9
25 000
25 000
10
0
25 000
Age of
truck
(years)
c $2500
c $1600
d $750
10 Quick Questions 2
1
3
5
7
9
$15 937.42
$13 537.79
$5084.04
$22 094.93
$10.63
2
4
6
8
10
$15 937.42
$1435.91
$19 277.16
$8513.56
$13 295.75
Investigation — A growing investment
T

7. 521
Answers
The investment will
grow to $30 000 in 7
years.
8
10 000
8000
6000
4000
2000
0
Value ($)
3
4
The investment grows to $30 000 in 6 years; that is, a
year earlier.
The graph shows that $30 000 is actually reached in
5.3 years.
5
0 2 4 6 8 10
Age (years)
9
10
11
14
15
16
$6500
a $1300
b $15 000
c $235 000
12 years
12 $250/year
13 After 6 years
$20 880
$474 000
a $23 620
b $1000
c $24 290
d $27 210
e $49 380
17 a $167 100
b $432 900
18 a
Salvage value
Salvage
Age
— straight line
value —
(years)
($)
15% p.a. ($)
New (0)
Value ($)
200 000
160 000
120 000
80 000
40 000
0
61 400
60 000
52 200
50 000
44 400
40 000
37 700
7
30 000
32 100
8
20 000
27 200
9
10 000
23 100
10
5 a
70 000
6
0 2 4 6 8 10
Age (years)
72 300
5
3 $7900
b V = 200 000 − 20 000A
80 000
4
2 $149.90
85 000
3
Chapter review
100 000
90 000
2
Investing $15 000 at 9.1% p.a. will reach $30 000 in 8
years.
100 000
1
1 $83.44
4 a
0
19 700
0 2 4 6 8 10
Age (years)
b V = 3500 − 250A
6 a
c $1250
Salvage
value
— 15% p.a.
0 2 4 6 8 10
Age (years)
19
60 000
50 000
40 000
30 000
20 000
10 000
0
0 2 4 6 8 10
Age (years)
1485
2
2020
995
3
1353
667
907
446
0
907
20 $41 039.20
21 a $4399.95
c $1842.84
22 $2242.95
23 a $1516.32
c $4055.45
b $34 641.25
d $51 014.25
b $14 047.20
d $11 177.64
2F
➔
c 9 years
3015
5
c 17 years
Tax deduction
($)
4
0 2 4 6 8 10
Age (years)
Salvage value
($)
1
b $10 500
7 a
Value ($)
Salvage
value — straight line
Year
Value ($)
16 000
12 000
8 000
4 000
0
b $6500
100 000
80 000
60 000
40 000
20 000
0
Value ($)
Value ($)
b
3 000
2 000
1 000
0
answers
Maths A Yr 12 - Answers Page 521 Wednesday, September 11, 2002 3:41 PM
2F

8. answers
Maths A Yr 12 - Answers Page 522 Wednesday, September 11, 2002 3:41 PM
522
Answers
CHAPTER 3 Consumer credit and
investments
4 a
Month
1
2
3
4
5
6
7
8
9
10
11
12
1 a
d
2 a
d
3 a
d
4 a
b
c
5 a
-b 11
2
0.1
0.0375
18
2
i 30
i 45
i 25 Feb.
$440
c
e
1
----12
1
2 -2
1
----52
f
b
e
b
e
ii
ii
ii
b
0.01
0.005
33
69
30
33
24 Aug.
$20
c
f
c
f
iii
iii
iii
c
1
-------365
1
----26
0.025
0.0125
8
15
31
56
13 Apr.
37.5%
Exercise 3A — Flat rate interest
1 a $700
b $1200
c $7500
d $2850
e $390
2 $1584
3 $5000
4 a $4060
b $21 330
c $1803.75
d $308.25
e $275 000
5 a $1650
b $3850
c $693
d $6193
6 a $1600
b $6600
c $137.50
7 a $800
b $2800
c $53.85
8 a $2000
b $6000
c $2160
d $8160
e $226.67
9 $43.33
10 B
11 C
12 8% p.a.
13 a $2400
b $9600
c $16 319.88
d 15% p.a.
14 15% p.a.
Exercise 3B — Home loans
1 a $800
b $79 950
2 a $312.50, $49 848.99 b $151.01
c $311.56, $49 697.04 d $151.95
3
Principal
($)
Month
Interest ($)
Balance
owing ($)
1
150 000.00
1200.00
149 791.99
2
149 791.99
1198.34
149 582.37
3
149 582.32
1196.66
149 370.93
4
149 370.97
1194.97
149 157.98
5
149 157.93
1193.26
148 943.12
6
148 943.18
1191.55
148 726.72
7
148 726.72
1189.81
148 508.52
8
148 508.52
1188.07
148 288.58
9
148 288.58
1186.31
148 066.88
10
148 066.88
1184.54
147 843.41
Interest
($)
637.50
636.55
635.58
634.61
633.64
632.66
631.66
630.67
629.66
628.65
627.63
626.60
Balance
owing ($)
84 872.73
84 744.51
84 615.32
84 485.16
84 354.03
84 221.92
84 088.81
83 954.71
83 819.60
83 683.48
83 546.34
83 408.17
Month
1
2
3
4
5
6
7
8
9
10
11
12
Skills check
Principal
($)
85 000.00
84 872.73
84 744.51
84 615.32
84 485.16
84 354.03
84 221.92
84 088.81
83 954.71
83 819.60
83 683.48
83 546.34
Principal
($)
85 000.00
84 837.50
84 673.78
84 508.83
84 342.65
84 175.22
84 006.53
83 836.58
83 665.35
83 492.84
83 319.04
83 143.93
Interest
($)
637.50
636.28
635.05
633.82
632.57
631.31
630.05
628.77
627.49
626.20
624.89
623.58
Balance
owing ($)
84 837.50
84 673.78
84 508.83
84 342.65
84 175.22
84 006.53
83 836.58
83 665.35
83 492.84
83 319.04
83 143.93
82 967.51
b
c $440.66
$243 123
a $302 308.80 b $241 500
c $60 808.80
A
B
a $112 034
b $86 072
c $61 789.40
d $39 329.60
10 a Smith – $6000, Jones – $9000
5
6
7
8
9
b i
Smith family
Principal Interest Balance owing
($)
($)
($)
Month
1
50 000.00 395.83
49 895.83
2
49 895.83 395.01
49 790.84
3
49 790.84 394.18
49 685.02
4
49 685.02 393.34
49 578.36
5
49 578.36 392.50
49 470.86
6
49 470.86 391.64
49 362.49
7
49 362.49 390.79
49 253.28
8
49 253.29 389.92
49 143.21
9
49 143.21 389.05
49 032.26
10
49 032.26 388.17
48 920.43
11
48 920.43 387.29
48 807.72
12
48 807.72 386.39
48 694.11

9. Answers
Jones family
b ii
Principal Interest Balance owing
($)
($)
($)
523
Exercise 3E — Bonds, debentures and
term deposits
1
50 000.00
395.83
49 645.83
2
49 645.83
393.03
49 288.86
3
49 288.86
390.20
48 929.06
$3200
2 $315
3 $472.50
4 $1500
$1800
6 $612.50 7 B
8 A
C
10 D
11 C
12 B
a $22.15
b $84.99
c $297
a i $1406.25 ii $1350
iii $1321.88
b No difference
4
48 929.06
387.36
48 566.42
Exercise 3F — Bank savings accounts
5
48 566.42
384.48
48 200.90
6
48 200.90
381.59
47 832.49
7
47 832.49
378.67
47 461.16
b $9.47
1 a $2066.10
b 12 cents
2 a 8 cents
3 9%
4 1998
Transaction
Debit
8
47 461.16
375.73
47 086.89
372.77
46 709.66
10
46 709.66
369.78
46 329.44
11
46 329.44
366.77
45 946.21
12
45 946.21
363.74
1 May
3 May
7 May
17 May
26 May
31 May
2 June
8 June
19 June
21 June
23 June
30 June
1 July
4 July
18 July
26 July
31 July
47 086.89
9
1
5
9
13
14
45 559.95
c $3134.16
10 Quick Questions 1
1
3
5
7
9
answers
Maths A Yr 12 - Answers Page 523 Wednesday, September 11, 2002 3:41 PM
$420
$7025
$5525
$8342.75
$1640
2
4
6
8
10
$1135.20
$975
$2817.75
$231.74
$265 577
Exercise 3C — The cost of a loan
1 11.6%
2 a 11.6%
b 8.32%
c 15.2%
d 10.6%
e 12.2%
3 a 8.32%
b 8.66%
c 9.01%
d 9.39%
e 11.6%
f 18.3%
4 a $213 996
b $128 996
c 6.0704%
5 9.01%
6 Loan 1
7 a $231 546
b $200 745.60
c $145 593.60
8 Loan 2 – they will save $6041
9 C
10 a $341 376
b $337 578
11 D
12 a $562 279.20 b 6.25%
c 5.8%
5 a $34.03
6
1998
4 Aug
5 Aug
10 Aug
15 Aug
18 Aug
20 Aug
30 Aug
31 Aug
1 Sept
2 Sept
5 Sept
5 Sept
15 Sept
20 Sept
29 Sept
30 Sept
Exercise 3D — Loan repayments
Credit
1740.60
11.02
Balance
2132.20
1671.93
1902.09
1010.89
2751.49
2757.18
3172.28
955.28
526.78
509.98
2250.58
2253.45
2276.25
2239.53
1958.57
3699.17
3710.19
Credit
Balance
1410.20
1410.20
1082.60
1150.80
1000.54
2410.74
1789.74
1609.74
1615.99
3026.19
2845.55
3306.82
2979.22
4389.42
3768.62
5178.82
5196.60
460.27
230.16
891.20
1740.60
5.69
415.10
2217.00
428.50
16.80
1740.60
2.87
22.80
36.72
280.96
b $14.45
Transaction
Salary
Health fund
Health fund
Electricity a/c
Salary
Rent
Visa
Interest
Salary
Telephone a/c
Tax refund
Health fund
Salary
Rent
Salary
Interest
7 a i $6.25
b i $4.79
c i $10.94
Debit
327.60
68.20
150.26
1410.20
620.80
180.00
6.25
1410.20
180.64
461.27
327.60
1410.20
620.80
1410.20
17.78
ii $13.35
ii $4.76
ii $16.86
iii $7.10
iii –$0.03
iii $5.92
10 Quick Questions 2
1
3
5
7
9
$2835
$299 191.20
6.0%
$264.40
$5825
2
4
6
8
10
160% p.a.
10.3%
$45.23
$375
$2.23
3A
➔
1 $674.25
2 a $90.46
b $341.25
c $819.84
d $1101.00
e $1515.54
3 a $400
b $3600
c $123.05
4 They will not need to increase their repayments.
5 a $1510.20
b $1620.14
6 Yes. The repayment is $744 and the most he can
afford is $750.
7 a $7000
b $1750
c $178 000
8 a $733.40
b $174.80
Balance B/F
Cheq 4217
Deposit
Cheq 4218
Wages
Interest
Deposit
Cheq 4220
Cheq 4219
Cheq 4222
Wages
Interest
Deposit
Cheq 4221
Cheq 4223
Wages
Interest
3F

10. 524
Answers
b $3656.25
b $365.63
b $124 228.12
c $12 000
c $1200
c $448 800
b $3175.50
b $272 415.50
b $278 375
c $12 832.50
c $554 952.50
c $8682.50
$19 131.25
$5071
25 c/share
6 c/share
a $1.224 million
c 43.52 c/share
10 a $5.22 million
c $1.66/share
11 $3.276 million
12 4.57%
13 Dividend
2
4
6
8
b
$2511.25
$1540
$1.50/share
29.27 c/share
$2.176 million
b $9.28 million
Share price
$8.40
$7.40
$23.40
$15.76
$0.76
$0.56
$0.78
$1.20
$1.09
$0.04
2.91%
15
a 6.6%
a $1.14
8.5%
a 0.59%
c 6.44 c/share
a $77.50
b
a $60
b
a 5000
b
23.3
D
Dividend yield
6.7%
10.5%
5.1%
6.9%
5.3%
16 $364
b $1.06/share
b $5.928 million
b $10.64
d 0.61%
1.2%
c 82.6
1.2%
c 83.3
0.75%
c 133.3
Month
b $1.20
4 a
16.00
14.00
12.00
10.00
n b r r y n l g p t v c n b r r y n
Ja Fe a p a Ju Ju u Se Oc o e Ja Fe a p a Ju
1– 1– 1–M 1–A 1–M 1– 1– 1–A 1– 1– 1–N 1–D 1– 1– 1–M 1–A 1–M 1–
Month
b $16.00
5 a
14.50
Share price ($)
1
3
5
7
9
21
22
23
24
2.04
2.02
2.00
1.18
1.16
1.14
1.12
1.10
1.08
1.06
1.04
1.02
1.00
14.00
13.50
13.00
12.50
12.00
1–
Ja
1– n
Fe
1– b
M
1– ar
A
1– pr
M
1– ay
Ju
1– n
J
1– ul
A
1– ug
Se
1– pt
O
1– ct
N
1– ov
De
c
Exercise 3H — Investing in the stock
market
14
17
18
19
20
3 a
1–
J
1– an
F
1– eb
M
1– ar
A
1– pr
M
1– ay
J
1– un
1– Jul
A
1– ug
Se
1– pt
O
1– ct
N
1– ov
D
1– ec
J
1– an
F
1– eb
M
1– ar
A
1– pr
M
1– ay
J
1– un
1– Jul
A
1– ug
Se
1– pt
Oc
t
a $2448.75
a $244.88
a $77 256.37
$80 750
a $1873
a $189 123
a $169 692.50
$8745
$127 500
$146 450
$289 500
Share price ($)
1
2
3
4
5
6
7
8
9
10
11
Share price ($)
Exercise 3G — Investing in real estate
Month
b $14.50
History of mathematics — The Wall
Street Crash
1 Soaring share prices were suddenly reversed.
2 Share prices declined rapidly.
3 People stopped investing, banks and businesses
collapsed, unemployment rose and Hitler came to
power.
History of mathematics — The Dow
Jones Industrial Average
1 a
1 Wall Street Journal journalists Charles Dow and
Eddie Jones.
2 30.
3 Sum of 30 stock prices divided by 0.2252.
4 Technology, telecommunications.
7.30
7.10
6.90
6.70
6.50
6.30
6.10
5.90
5.70
1–
M
ay
1–
Ju
n
1–
Ju
l
1–
Au
g
1–
Se
pt
1–
Oc
t
Share price ($)
Exercise 3I — Graphing share
performance
Month
Share price ($)
b $7.00
2 a
4.50
4.00
3.50
3.00
2.50
1–
Ju
1– n
J
1– ul
A
1– ug
Se
1– pt
O
1– ct
N
1– ov
D
e
1– c
Ja
1– n
Fe
1– b
M
1– ar
A
1– pr
M
ay
answers
Maths A Yr 12 - Answers Page 524 Wednesday, September 11, 2002 3:41 PM
b $1.75
Chapter review
1 a $1120
d $39.60
2 $6760
3 $191.02
4 6.15%
5 a $1250
b $7187.50 c $1281.60
e $12 285.00
b $124 873.64

11. Answers
6 a
Balance
owing ($)
1
130 000.00
866.67
129 779.30
2
129 779.30
865.20
129 557.12
3
129 557.12
863.71
129 333.47
4
129 333.47
862.22
129 108.32
5
129 108.32
860.72
128 881.67
6
128 881.67
859.21
128 653.51
857.69
128 423.83
8
128 423.83
856.16
128 192.62
9
128 192.62
854.62
127 959.87
10
127 959.87
853.07
127 725.56
11
127 725.56
851.50
127 489.70
12
127 489.70
849.93
127 252.26
Month
Principal
($)
Interest
($)
Balance
owing ($)
1
130 000.00
866.67
129 366.67
2
129 366.67
862.44
128 729.11
3
128 729.11
858.19
128 087.31
4
128 087.31
853.92
127 441.22
5
127 441.22
849.61
126 790.83
6
126 790.83
845.27
126 136.10
7
126 136.10
840.91
125 477.01
8
125 477.01
836.51
124 813.52
9
124 813.52
832.09
124 145.61
10
124 145.61
827.64
123 473.25
11
123 473.25
823.15
122 796.40
12
122 796.40
818.64
122 115.05
Month
b
7
8
9
10
11
12
c $5137.21
a $596 844
a 7.25%
c 25.65%
a $18 223.20
Loan 2
$21.15
a $316.75
c $2369.11
a $2453.49
B
$2700
$5000
a $1.08
a $3.33
$3075
$270 662.50
$1.93/share
b $18 884
b 13.70%
d 14.11%
b $4723.20
c 7%
15
18
21
25
28
31
b $599.40
d $5100
b $2618.06
A
16 D
$694.17
19 $2520
D
b $1.15
b $3.64
$401.63
26 $236 425.45
$15 832.50
29 $46 687.50
$14.74/share 32 5.22%
16.50
16.00
15.50
Month
b $18.00
CHAPTER 4 Populations,
samples, statistics and
probability
Skills check
1
2
3
4
5
a 0.375
b 0.083
c 0.813
d 0.590
a 75%
b 12.5% c 42.5% d 4%
Answers will vary.
a 4
b 4
c 3
d 7
e 1
a a=8
b b=9
c c = 22.5
d d = 17.5
e e = 10.5
6 Scale on axes, omitting certain values, giving a 3D
visual impression, using a non-linear scale on the
axes.
7 a 73
b 7.3
c 7
d 6
e 6
f 8
g 6
h 2
Investigation — Australia’s population
and housing census
1 This is a statistical collection of data to determine the
number of people in Australia on Census Night, the
characteristics of these people and the dwellings in
which they live.
2 All people in Australia on Census Night take part.
3 It is compulsory.
4 Questions asked include: age, marital status,
birthplace, income, type of dwelling, type of job…
The questions have changed over the years to take
into account changing social conditions of the
population; such as language spoken at home,
computer usage…
5 A census can provide information necessary for future
planning.
6 The ABS has access to the information and details of
individuals are protected by the Privacy Act.
7 All dwellings are issued with census booklets, which
are delivered and collected by ABS workers. The
booklets are completed by all individuals on the same
night.
Exercise 4A — Populations and
samples
1 Census, sample
2 Census — every member of the population
participates.
3 Survey
4 a Survey
b Survey
c Census
d Census
e Survey
5 a Survey
b Census
c Census
d Survey
6 Survey
3G
➔
13
14
17
20
22
23
24
27
30
34 81.8 c/share
b 2.5%
c 40.4
128 653.51
7
33 1.6%
35 a $260
36 a
17.00
Share price ($)
Interest
($)
1–
Ja
1– n
Fe
1– b
M
1– ar
A
1– pr
M
1– ay
Ju
1– n
J
1– ul
Au
1– g
Se
1– pt
O
1– ct
No
1– v
De
c
Principal
($)
525
answers
Maths A Yr 12 - Answers Page 525 Wednesday, September 11, 2002 3:41 PM
4A

12. answers
Maths A Yr 12 - Answers Page 526 Wednesday, September 11, 2002 3:41 PM
526
Answers
Exercise 4B — Samples and sampling
1
2
3
4
5
6
7
8
9
10
11
12
14
15
16
17
80, 84, 70, 85, 79, 54, 56, 51, 81, 67
Range of answers
Range of answers
Should be three different sets of numbers.
a Random sampling
b Judgemental sampling
c Accessibility sampling
d Systematic sampling
e Stratified sampling
a Systematic b Stratified
c Systematic
d Random
e Stratified
A
C
Year 7— nine, Year 8 — eleven, Year 9 — nine, Year
10 — eight, Year 11 — seven, Year 12 — six
36 men and 24 women
Age
20–29
30–39
40–49
50–59
Male
10
7
12
1
Female
7
8
3
2
4000
13 400
a 10 000
b 25 000
c 3663
No — estimated population 20 000
a 625
b 500
c 625
a 833
b 1000
c 882
d 905
c Residents not at the neighbourhood watch meeting
have been ignored.
d Other music students who play instruments and
don’t belong to the choir have been excluded.
e The composition of cars in a shopping centre car
park is not representative of the cars on the road.
f Females have been excluded.
g Users of the local library would not reflect the
views of teenagers.
Investigation — Contingency tables
from census data
1 a 37.8%
b 41.9%
c Part (a) compares the number of males in the retail
trade with the total number of male workers, while
in part (b) the comparison is with the total number
in the retail trade.
d It would be easier to survey those in the retail
trade rather than surveying the male population, as
the former number is smaller than the second.
2 Choose another category to survey.
3 Percentage of persons in agriculture, forestry and
fishing
324 330
= ---------------------- × 100%
7 636 319
= 4.2%
4 Analyse data from the 2001 census.
Exercise 4D — Contingency tables
1
Test results
Accurate
1
3
5
7
9
Census
Census
Systematic sample
Cluster sample
Quota sample
2
4
6
8
10
Survey
Random sample
Stratified sample
Judgemental sample
Random sample
Not accurate
Total
98
2
100
Without virus
388
12
400
Total
10 Quick Questions 1
486
14
500
With virus
Test results
2
Exercise 4C — Bias
1 Check with your teacher.
2 Check with your teacher.
3 a Sample does not represent characteristics of
population.
b No control over responses
c Unrepresentative sample
d Abnormal conditions
e Only extreme groups in sample
4 The decrease in the value of the Australian dollar
compared with the American dollar is accentuated by
the large scale on the y-axis. The decrease is actually
only 2 cents. The scale on the x-axis is not uniform (9
May, 11 May, 12 May).
5 What type of university tests? What do the terms
‘consistently’, ‘majority’, ‘more effective’, ‘most
other’ mean? No hard evidence has been provided to
support the claim.
6 a There would be many more student drivers in
Year 12 than in Year 11 — perhaps also some in
Year 10.
b Students with part-time jobs are in lower year
levels as well.
Accurate
Not accurate
Total
Telling truth
777
23
800
Telling lies
156
44
200
Total
933
67
1000
3
4
a 1000
a 200
e 94%
5 B
8 a
b 75
c 96.7% d 60%
b 44
c 90.9% d 5.1%
f Check with your teacher.
6 D
7 A
Test results
Accurate
Not
accurate
Total
48
2
50
Bags with no
prohibited
items
145
5
150
Total
193
7
200
Bags with
prohibited
items
b i 96%
ii 3.3%
iii 4%
iv 96.5%

13. 527
Answers
9 a ii
10 a
b ii
c ii
12 a
Education
b
Education
Female
Total
In
2641
1752
4393
Not in
1728
3144
4872
4369
4896
9625
Female
3 685
4 071
239 389
240 029
Male
Other
Male
Total
Male
Female
Total
3 685
4 071
7 756
Other
239 389
240 029
479 418
Total
243 074
244 100
answers
Maths A Yr 12 - Answers Page 527 Wednesday, September 11, 2002 3:41 PM
b i 35.8%
ii 39.9%
c No — more than 39% of the labour force are
female.
13 a
Male Female Total
487 174
Aust.
Male
Other
Total
d
1.5%
98.5%
98.3%
100%
Female
Total
Education
47.5%
52.5%
100%
Other
49.9%
50.1%
100%
e 1.7%
f 52.5%
g Survey a sample of those in education rather than
conducting a survey on a sample of females as
the total education group is fewer in number than
the total female group.
11 a
Male
Female
Other
b
184 287
355 776
4 087 764 3 008 492
Male
Education
2156
4217
6127
6624
12 751
b No — 33% of the males in the community were
born overseas, while 49% of the people born
overseas were male.
100%
Male
Education
2061
Total
1.7%
8534
Female
355 776
1 a Yes b 3 c Yes, both equal 3 d 3
2 a No
b 5–9 and 20–24
c No
d 5–9 and 20–24
e 25–29
3 a
b Yes
540 063
Other
4 272 051 3 364 268 7 636 319
0 1 2 3 4 5
Number of goals
d Yes, both equal 2.5
b 2
25
20
15
10
5
0
c 5
b 0.73
0 0 0 0 0
–2 –3 –4 –5 –6
11 21 31 41 51
4 087 764 3 008 492 7 096 256
Total
6
5
4
3
2
1
0
c 0 and 5
e 0
4 a 2
5 a
Total
184 287
Exercise 4E — Applications of statistics
and probability
Frequency
Education
4468
Overseas
Female
4066
Frequency
c
Number of goals
Male
Education
Other
Total
d
Female
4.3%
10.6%
95.7%
Frequency
c
6 A
7 a
89.4%
100%
b No
10
8
6
4
2
0
50 00 50 00 50
1– 1–1 1–1 1–2 1–2
5 10 15 20
100%
Number of people
Male
Female
Total
Education
34.1%
65.9%
100%
Other
57.6%
42.4%
100%
151–200 and 201–250
0.67
0.17
Chemistry is symmetrical.
Maths is not symmetrical.
b Chemistry: mode = 41–50 and 81–90,
Maths: mode = 71–80
c Maths, because there are more scores further
away from the centre of the distribution.
4B
➔
e 10.6%
f 65.9%
g Same as g in question 10. Comments should note
increases in percentage and the reasons for this.
c
d
e
8 a
4E

14. answers
528
Answers
d Yes, both 0.275
e Mathematics
f P(>90% Chem) = 0.05
P(>90% Maths) = 0.1
9 157
10 31.8, or 32 visitors
11 a 7
b 18.3
12 a Lines vary.
b Factory 1 is cheaper at $43.21 (compared to
Factory 2 at $56.61).
c Factory 2 is cheaper at $168.16 (compared to
Factory 1 at $216).
d Factory 2 is marginally more linear.
Investigation — Modelling Olympic
Games times
1 Scatterplot
4
5
6
7
8
9
2 Line of best fit
10
12
Systematic sample — where a system is used to
select the participants.
Accessibility sample — where those within easy
access form the sample.
Quota sample — where a quota is placed on the
number in the sample.
Judgemental sampling — where a judgement is
made regarding those who should form the sample.
Cluster sampling — where the sample is selected
from clusters within the population.
Capture–recapture sampling — used mainly to
estimate populations in wildlife where an initial
sample is tagged then another sample selected from
the whole population.
a Systematic b Random
c Stratified
Check with your teacher.
Year 7 — 12, Year 8 — 12, Year 9 — 11,
Year 10 — 10, Year 11 — 8, Year 12 — 7
2000
750
a Barry — 2667 Viet — 1667 Mustafa — 1571
b 1968
B
11 1984
Check with your teacher.
13
Test results
Accurate Not accurate Total
With virus
48
2
50
Without virus
149
1
150
Total
197
3
200
Accurate
Not accurate
Total
Telling truth
77
3
80
Telling lies
3 Prediction
17
3
20
14
The line of best fit predicts a time of 9.5 seconds in
the year 2035. The Olympic Games closest to this
year is 2036.
Investigation — The door game
Part 11
-1 P(winning if stay) = 1
3
P(winning if change mind) =
2
-3
If you change your mind you will double your change
of winning from 1 in 3 to 2 in 3.
10 Quick Questions 2
1
3
5
7
9
10
23.3
2 21.5
16
4 29
5
6 7.93
No
8 Yes, 45 is an outlier.
Median, because the outlier inflates the mean.
The outlier makes the range very large.
Chapter review
1 a Survey
b Census
c Census
d Survey
2 D
3 Random sample — where the participants are chosen
by luck.
Stratified sample — where the participants are
chosen in proportion to the entire population.
Test results
Total
15
16
17
18
19
a
a
A
a
a
c
20 B
21 a
140
130
94
b 30
b 33.8%
6
c 90%
c 97.5%
200 b 96% c 34
9.7%
b 8.0%
No significant difference
Attitude
Primary
100
d 10%
-d 93 1 % e 93%
3
Secondary
Fewer
7.5%
4.3%
Same
43.3%
19.1%
More
49.2%
76.6%
Total
100%
100%
b Secondary students were much keener on having
more holidays than were primary students.
22 a Yes
b Both are 17.5.
c 17 and 18
d 17 and 18

15. 529
Answers
Frequency
23 a
12
10
8
6
4
2
0
b No
1 2 3 4 5 6
Class centre
c 0.15
24 a A variety of answers
b 131
CHAPTER 5 Navigation
Skills check
1 Lines of latitude run parallel to the equator. Lines of
longitude run from one pole to the other and are east
or west of Greenwich.
2 0°
3 0°
4 Latitude
5 C = 2π r
opposite
6 40 030 km
7 Tangent = ------------------adjacent
distance
8 Speed = -----------------time
9 The time at the prime meridian (0° longitude)
10 A triangle which has 2 sides congruent, and base
angles congruent
Exercise 5A — Review of Earth
geometry
1 a (30°N, 60°W)
b (40°S, 20°W)
c (30°S, 50°E)
d (40°N, 60°W)
e (20°N, 20°W)
f (30°S, 20°E)
2 Any 2 meridians; for example, NDS, NGS; or any
line of longitude; for example, 20°W
3 a 40°
b 30°
c 10°
d 60°
4 a Johannesburg
b Shanghai
c Montreal
d Perth
5 a (35°N, 118°W)
b (35°S, 20°E)
c (0°, 100°E)
d (38°N, 115°E)
6 a 4448 km
b 7784 km
c 6672 km
d 7339 km
7 a 7784 km
b 6450 km
8 4226 km
Exercise 5B — Accurate position
description
1 a 27°9.6′S, 153°36′E
c 27°S, 153°36′E
e 27°1.1′S, 153°33.6′E
2 Sketch
3 a Mt Sydney
c Pinnacle Point
4 a 20°2.2′S, 148°52.7′E
c 20°4.8′S, 148°52.2′E
e 20°10.5′S, 148°55′E
b 27°S, 153°45.9′E
d 27°0.9′S, 153°37.6′E
f 27°8′S, 153°44.5′E
b Black Island
b 20°4.3′S, 148°58.3′E
d 20°10′S, 148°53.6′E
Exercise 5C — The nautical mile and
the knot
b 150′
c 1422′
b 39°8.7′
b 57.3′
d 2871.7′
10 Quick Questions 1
1 Latitude
2 Latitude
4 1852 metres
5 150 n mile
distance
6 Speed = -----------------time
8 6 knots
9 5400 n mile
3 60′
7 The knot
10 5 pm
Investigation — Distance to the horizon
1 Angle PHC = 90° (PH is a tangent to the circle, so CH
is perpendicular to PH.)
2 PC2 = CH2 + HP2 (by Pythagoras’ theorem)
3 CH = AC (Both are radii of the Earth;
both = 6371 km.)
4 a 25.2 km b 79.8 km c 112.9 km d 357.1 km
5 As height increases, distance also increases. (On a flat
Earth, distance to horizon would be greater.)
Exercise 5D — Using the compass
1 a 128°C
2 291°T
4 a 120°C
b 292°C
b 226°C
c 193°C
3 6°E
c 4°W
d 40°C
d 257°29′T
Exercise 5E — Compass bearings and
reverse bearings
1 a 50°T
b 300°T c 230°T d 145°T
2 a 230°T b 120°T c 50°T
d 325°T
5 a 6 n mile
b 5 n mile
c 11.2 n mile
d 11.4 n mile e 15.7 n mile f 10.9 n mile
6 b 12 knots
7 a 187°T b 176°C c 50 min d 356°C
8 a Great Keppel Is.
b North Keppel Is.
9 a (23°5.6′S, 150°54′E) b (23°13′S, 150°58.2′E)
10 a 56°T
b 46°C
c 7.2 n miles
d 54 minutes
11 a 304°(C) , 1.8 n mile b 271°(C), 8.2 n mile
c 328°(C), 7 n mile
d 296°(C), 11.5 n mile
5A
➔
1 a 120′
2 a 9°43′
3 a 17°17′
4 a J, D
b A, H
c H, I
d i 50°N, 80°E
ii 0°, 0°
iii 60°S, 0°
iv 0°, 30°W
v 50°N, 0°
e i 2400 n mile ii 2400 n mile iii 5400 n mile
iv 9000 n mile v 9000 n mile
f i 6600 n mile ii 6600 n mile
g i 3600 n mile ii 3600 n mile iii 3000 n mile
5 a 1650 n mile
b 3750 n mile
c 7050 n mile
d 1110 n mile
6 8 knots
7 a 3.5 knots
b 6.5 km/h
8 a 3.85 knots
b 12.6 knots
c 289 n mile
d 52.1 n mile
e 30 hours
f 10 minutes
9 a 7872 hours
b 6.4 km/h, 3.4 knots
10 a 3600 n mile
b ii 3600 n mile
ii The Earth is a sphere and any arc joining 2
points on its surface subtending an angle of
60° must be separated by the same distance.
c 200 hours
11 a 570 n mile
b 4.63 knots
12 3.08 am
13 A separation of 1′ near the equator on a line of
latitude is greater than that further from the equator.
answers
Maths A Yr 12 - Answers Page 529 Wednesday, September 11, 2002 3:41 PM
5E

16. answers
Maths A Yr 12 - Answers Page 530 Wednesday, September 11, 2002 3:41 PM
530
Answers
10 Quick Questions 2
1
3
5
9
Exercise 5K — Dead reckoning
Compass
2 True north
Magnetic variation
4 Compass
True
6 60°T 7 158°C
8 180°
Latitude
10 7 knots
Exercise 5F — Fixing position
1 a
b
d
2 a
b
3 a
c
4 a
5 b
e
6 b
Check with your teacher.
155°T
c 7.5 n mile
15 knots
e 3.5 n mile
Check with your teacher.
9.3 n mile
c 18.6 knots
131°T, 18°T, 299°T b 198°T, 340°T, 265°T
11 knots
d A 219°, B 293°, C 254°
Tower 53°, Antenna 88°
14 n mile
c 14 n mile
d 19.8 n mile
i 243°
ii 252°
56 n mile
c 250°
Exercise 5G — Come to the rescue!
1
2
5
6
Man and Wife Rocks 108°T; Miall Island 220°T
plot
3 9.4 n mile
4 28 minutes
3.48 pm
Vessel has moved 1.75 n mile out to sea to 23°6.3′S,
150°59′E
7 2.5 n miles to the east
8 The wind had greater impact on pushing the boat than
it did on the swimmer.
i 6 n mile ii 5.6 n mile iii 5.3 n mile
Plot
d 20 knots
B 250°, D 291°, E 316°
7.5 n mile
Exercise 5I — Running fix
1 b 6 n mile
2 b 197°
Exercise 5J — Doubling the angle on
the bow
1 a
b
c
d
e
f
2 a
3 b
c
4 b
d
i 50°
ii 130° iii 80°
iv 3 n mile
i 100° ii 40°
iii 7 n mile
i 42°
ii 96°
iii 84°
iv 11 n mile
i 130° ii 25°
iii 6.5 n mile iv 45°T
i 45°
ii 90°
iii 45°
iv 10 n mile
i 20°
ii 140° iii 20°
iv 8 n mile
v 8 n mile
25°
b 5 n mile
At 1300, 30°; at 1330, 60°
9 n mile
d 9 n mile
8 n mile
c 6.2 n mile (from sketch)
7.03 am
e 100°
10 Quick Questions 3
1
4
6
7
9
Two
2
Isosceles
5
Angle on the bow
9 knots
8
84 n miles
10
Cocked hat
Front
4 hours
One
2 a
b
c
d
3 a
c
Check with your teacher.
20°08.3′S, 148°59.7′E
Check with your teacher.
iii 20°07.3′S, 149°01.5′E
iii 20°06.3′S, 149°03.3′E
iii 20°05.3′S, 149°04.9′E
20°07.3′S, 149°14′E
20°00.2′S, 149°07′E
20°05.2′S, 149°09.2′E
20°01.4′S, 149°07.3′E
3.8 n mile
b 11.4 knots
ii 20°05.4′S, 149°04.2′E
ii 20°03.3′S, 149°01′E
Exercise 5L — The lighthouse and
navigation
1 a AB = 10.5 m
b 1908 m
c 1°48′
d 1.345 n mile
2 a 4 short flashes of light followed by a long period
of darkness every 20 seconds
c 3105 m
3 a 2 flashes, then darkness every 12 seconds
c 5156 m
f 7.6 n mile
g i 0.48°
ii 0.36°
4 b 6875 m
d 0.68°
Exercise 5M — Let’s go cruising
Exercise 5H — Transit fix
1 b
c
2 c
3 b
1 a
b
c
d
3 Transit line
1 a 11°18′ east
b 11° east
2 a 27°30.9′S, 153°20.7′E b 27°30.1′S, 153°22.4′E
c 27°32.7′S, 153°25.2′E d 27°30.6′S, 153°17.3′E
e 27°34.8′S, 153°21.6′E
3 a Coochiemudlo Island b The Bluff
c Submerged rocks
d Myora Light
4 a i 308°
ii 338°
iii 0°
iv 266°
b i 297°
ii 327°
iii 349°
iv 255°
c iii 5.1 n mile
iii 5.1 n mile
iii 4.8 n mile
iv 2.6 n mile
5 a iii Yellow light flashes every 2.5 seconds
iii Red every 4 seconds
iii Green every 6 seconds
b So that they can be readily identified as different
from neighbouring lights.
6 a 5 n miles
b 150°T, 139°C
c 33 minutes
d 10.58 am
e A southwest wind could push the vessel towards
the rocks near Goat Island.
7 Approx. 15 n mile, so approx. 160 litres.
8 a 351°T, 227°T
b 27°32.8′S, 153°21.6′E
Exercise 5N — Air navigation
1 a
c
2 a
3 a
4 a
5 a
b
26°15′S, 151°56′E
b 26°40′S, 152°00′E
26°·17′S, 152°41′E
d 26°33′S, 151°51′E
Tansey
b The Bluff
c Abbeywood
1998
b 2457
c 2043
350°T, 339.5°C
b 05°T, 355°C
149°30′C
Barambah Ck, Clonya, Murgon, Nanango.

17. 531
Answers
Chapter review
1 a A, 30°N, 60°W; B, 40°S, 20°W; C, 30°S, 50°E;
D, 40°N, 60°W
b NDS, NGS, NHS or any line of longitude (for
example, 40°W)
c F
d PG, PN, PH, PC etc.
2 a 20°2.2′S, 148°52.7′E
b 20°10′S, 148°53.7′E
3 a 5400 n mile
b 10 800 n mile
c 4200 n mile
d 7920 n mile
4 a 1080 n mile
b 5340 n mile
5 a 360′
b 1110′
c 1695′
d 3457.4′
6 540 n mile, 1000 km
7 a 6 knots
b 13.3 knots c 522 n mile
d 198.3 n mile
e 50 hours
f 15 minutes
8 6 hours 24 minutes
9 a 400 n mile
b 180°T
c 5 hours
d 6.45 pm
10 a 114°C
b 253°C
c 6°W
d 206°T
11 286°T
12 b 9.8 n mile c 29.4 knots
d 48°T
13 a = 55°, b = 125°, c = 70°, PR = 7.4 n mile
14 a 18°
b 36°
c 13 n mile
d 13 n mile
15 b 50°, 100° c 12 n mile
d 12 n mile
16 a 5.57 m
b 65.8 m
c 1.68°
d 5810 m
17 a 3 short flashes then long period of darkness every
16 seconds
b 130 m
c 16 n mile
d 2480 m
18 a 8.1 n mile
b 8°T
c Approx. 1 h 20 min trip, ETA 8.20 am
19 a 240°T
b 16.5 n mile
c Plot
d 11.45 am
CHAPTER 6 Land measurement
Skills check
b
H
A
O
O
A
H
c
H
A
O
opposite
adjacent
11 Sine = -------------------------Cosine = -------------------------hypotenuse
hypotenuse
opposite
Tangent = ------------------adjacent
12 a 6.8 cm
b 7.7 m
c 65.0 m
Exercise 6A — Perimeters and areas of
triangles
1 a 1.73 cm
b 23.1 m
c 11.4 m
2 a 1.73 cm2
b 277 m2
c 55.3 m2
3 a 12.5 m2
b 4.5 m2
c 7443 m2
d 118.2 m2
4 a 26 m, 13 m
b 90.9 m, 45.45 m
c 42.4 km, 21.2 km
5 a 27.9 m2
b 250 m2
c 52.4 km2
Exercise 6B — Perimeters and areas of
polygons
1 a 5797 m2
2 a 97.4 m2
3 Approx. 36 ha
b 1062 m2
b 3195 m2
c 27 952 m2
Exercise 6C — Surveying on level
ground without obstacles
1 a 32 m
b 28 m
c 59 m
d 73 m
e 47 m
2 a 86.3 m
b 107.5 m
c 47.4 m
d 49.0 m
3 Sketch
4 a 120 m
b 5
c i 48 m ii 39 m iii 37 m iv 32 m v 35 m
d i 65.8 m ii 44.7 m iii 34.4 m iv 90.2 m
e i 43.15° ii 1014 m2 iii 81.2°
f Sketch
g AB survey line established and measured. Staffs at
features Z and C, measurements taken. Staffs at V
and D, measurements taken.
h 2340 m2
10 Quick Questions 1
1 5.47 m
3
5
7
8
9
10
2
1
-2
× a × b × sin C
4 S(S – a)(S – b)(S – c)
48.5 m , 196.6 m
24.2 m2
6 AB
KF, JE, ID, HC
36 m, 59 m, 73 m, 32 m, 84 m
240 m2
a 51.2°
b 59 m
2
2
5F
➔
1 Millimetre, centimetre, metre, kilometre
2 Perimeter
3 a 24 cm
b 30 m
c 15.6 cm
d 16.8 m
e 12.6 m
f 36.0 m
g 38 m
4 a l2
b l×w
c πr 2
-d b×h× 1
e l×h
2
5 a 1.5 cm
b 0.18 m
c 12 300 cm
d 680 m
e 12 500 m
6 a 40.7 m2
b 435.8 m2
c 51.7 m2
d 177 m2
e 25 m2
7 a 0.9397
b 0.9659
c 0.3249
8 c2 = b2 + a2
9 a 5 cm
b 8 cm
c 9.6 m
10 a
answers
Maths A Yr 12 - Answers Page 531 Wednesday, September 11, 2002 3:41 PM
6C

18. answers
Maths A Yr 12 - Answers Page 532 Wednesday, September 11, 2002 3:41 PM
532
Answers
Exercise 6D — Surveying around
obstacles
1 a 42 m
b 31 m
c 52 m
2 Sketch
3 a Sketch
b The distance between the second and third staffs
placed by Peter.
Exercise 6E — Plane table surveying:
intersection or triangulation
1 a
b
c
d
2 a
b
c
d
3 a
4 a
b
c
d
61 m
i 43 m ii 28 m iii 106 m iv 124 m
i 065° ii 310° iii 180° iv 150°
301 m
e 0.38 ha
59 m
ii 28.5 m ii 31.5 m iii 32 m iv 73 m
v 49 m
0.25 ha
i 15° ii 81° iii 151°
83 m
b $1328
c 450 m2
Sketch
i 100 m ii 66 m iii 50 m iv 90 m v 86 m
i 270° ii 310° iii 240°
4300 m2
Exercise 6F — Plane table surveying:
radiation and traversing
1 a
b
c
2 a
b
3 a
c
d
4 a
c
d
i 25 m ii 35 m iii 30.5 m iv 51.5 m
i 0° ii 070° iii 180°
1900 m2
ii 23 m ii 72 m iii 51 m iv 12.5 m
v 104 m vi 109 m vii 75 m
0.31 ha
Radiation
b sketch
A, 123°; B, 136°; C, 152°; D, 180°.
3160 m2
Sketch
b traversing
i 212° ii 270°
i 107 m ii 77 m e 3800 m2
Offset and triangulation
41 m, 10 m
Intersection (or triangulation), radiation, traversing
Intersection
Radiation
Traversing
287.5 mm
4 triangles
Area = S ( S – a ) ( S – b ) ( S – c ) = 310 m2
10 m2
Exercise 6G — Levelling: vertical
measurements in relation to a datum
1 a i 50.00 m ii 51.69 m
b 1.94 m
c 53.63 m
d
Sta.
BS
A
3.63
B
IS
FS
HI
RL Dist.
Notes
53.63 50.00 0.00
TBM
1.94 53.63 51.69 20.00
i 3.60 m ii 2.80 m iii 53.60 m iv 50.00 m
50.80 m
61.25 m
b 61.25 m
c 61.25 m
61.25 m
e 60.00 m
f 59.50 m
58.75 m
h 58.25 m
i 5.00 m
10.00 m
k 15.00 m
Exercise 6H — Topographic maps
1 Easting 84, northing 46
2 a Maculata Park
b oval
c building at quarry
3 a GR 871464
b GR 854487
c GR 813488
4 a 3350 m
b 1250 m
5 a 352°
b 090°
6 a Abattoirs, bridge over river on Warrego Highway,
then along river and over slag heaps
b 155°. Yes. A scale diagram could be sketched and
trigonometry used to calculate angles.
Exercise 6I — Contour maps
1 a 10 m
b 80 m
c 50 m
d Up a hill then down a steep descent, then up and
down another smaller hill.
e Sketch
f 5
2 a 93 m
b 68 m
3 a 20 m
b 10.3 km
c Sketch
d 20
e 293°
f No, not if X and Y are at the surface.
1
4 a --------b 16.4°, steep
3.41
5 a 45°
b 18.4°
c 0.57°
d 1.15°
e 2.97°
6 a 1.27°
Exercise 6J — Cadastral maps and site
plans
10 Quick Questions 2
1
2
3
4
5
6
7
8
9
10
2 a
b
3 a
d
g
j
1 a
c
e
f
g
2 a
b
d
e
630 m2
b 23.0 × 27.499 m
632.477 m2
d 1 : 1500
Rectangle of length 60 mm and width 42 mm
ii $57.88/m2 ii 850 m2
ii Lot 109
ii location, elevation, road frontage size, views
2100 m2, 83 perches
103.68 m2 c 56.3 m
1
0.049 or approx. ----20
i rising ii 1800 mm iii 1.375°
Exercise 6K — Orienteering
1 a 8°
b 137°
c 222°
2 a 67 m
b 136 m c 77 m
3 Any suitable set of 8 instructions.
Chapter review
d 45°
d 130 m
1 a 126 m2
b 165 m2
c 516 m2
2
2
d 2325 m
e 8850 m
2 0.2 ha
3 a ii 150 m ii 52 m iii 63.2 m iv 13 m
v 75 m vi 141.9 m
b ii 936 m2 ii 1533 m2 iii 4500 m2
iv 5912.5 m2
4 Sketch

19. 533
Answers
5 a 84 m
b i 050° ii 115° iii 295° iv 238° v 090°
c 2000 m2 d 190 m
6 a i 43 m ii 48 m iii 46 m iv 56 m v 86 m
b i 051° ii 090° iii 253°
c 3200 m2
7 a i 3.90 m ii 2.70 m iii 53.60 m iv 50.00 m
b 50.90
c Sketch
8 a i Industrial Estate ii Finlay Island
b 2.5 km
c 153°
9 a 250
b 1 in 5
c 11.3°, steep to moderate
10 a 45°
b 26.6°
c 1.1°
d 2.9°
e 7.2°
11 10
12 a 90 m
b 20 m
c Sketch
13 a 630 m2
b Sketch
c
Re
Re
Pi
Mo
Ce
VG
Ma
Ga
62
58
104
108
147
179
0
Pi
62
0
41
65
46
85
123
Mo
58
41
0
46
76
126
121
Ce
104
65
46
0
30
90
75
VG
108
46
76
30
0
60
98
Ma
147
85
126
90
60
0
38
Ga
179
123
121
75
98
38
0
Re
Pi
Mo
Ce
VG
Ma
Ga
47
44
84
81
119
143
d
1 a ABDE
2 a
120
Ya
U1
b 487 km c 254 km
160
118
Pi
47
0
25
45
34
75
100
44
25
0
40
59
97
99
84
45
40
0
20
58
59
VG
b ABCE
0
Ce
Exercise 7A — Networks, nodes and
arcs
Re
Mo
CHAPTER 7 Networks
81
34
60
20
0
38
66
Ma
119
72
97
58
38
0
28
Ga
143
104
99
59
28
28
0
L
2.40
4 a
2.40
Ya
85
U1
5 C
History of mathematics
Ba
75
34
An
82
iv
Ulawatu
Ulawatu
1.80
T
ii 357 min iii 191 min
120
80
BR
Yallingup Black Rock Angourie
Bargara
0
120
100
209
254
Yallingup
120
0
220
118
160
Black Rock
100
220
0
109
154
Angourie
209
118
109
0
Bargara
254
160
154
45
1 Men of Mathematics by E. T. Bell.
2 The Nobel Prize and the Leroy P. Steele Prize.
3 An algorithm is a procedure for solving a problem by
a number of steps.
45
0
Exercise 7B — Minimal spanning trees
1 a
b
B
4
A
A
Ulawatu
Yallingup
Black Rock
Angourie
Bargara
0
85
75
157
191
85
0
160
80
114
157
80
82
0
34
191
114
116
34
0
c
12
A
17
B
3 a 185 km
b ii
75
Pi
ii 321 min iii 143 min
Ma
34
47
38
45
Re
75
160
0
82
116
Bargara
VG
28
25
Ga
20
C
15
2 a Sturt
d
4
C
D
Ce
30
C
B
E
b Rockdale
15
D
15
E
c To Sturt
Pallas 55
Sturt
Urchin
6D
➔
40
20
A
18
52
Mo
d
Xavier
Yule 50
52
42
50
Zenith Walga
67
View Rockdale
50
64
59
D
5
D
5
C
Yallingup Black Rock Angourie
B
4
8
v
Ulawatu
c $3.80
B
1.50
109
d i
b $3.30
1.80 K 2.00
45
An
1.50
P
Ba
100
BR
answers
Maths A Yr 12 - Answers Page 533 Wednesday, September 11, 2002 3:41 PM
7B

20. answers
Maths A Yr 12 - Answers Page 534 Wednesday, September 11, 2002 3:41 PM
534
Answers
10 Quick Questions 1
3 a 585 m
b 245 m
c Check with your teacher.
4 a
b A
E
B
E
45
B
45
D
48
48
F
2 9
4
5 AC, AD, DF, CF
7 D–C–E–F
6 $16 600
8
C E F
D
A B C E F
A B
A
18
9 $16 200
23
24
C
c
45
18
D
20
C
1 6
3 1
A
Exercise 7D — Network flow
F
d
B
C
E
D
17
6
4
G
40
5 a
6
A
1 a
B
6
C
F
b
G
E
20
E
A
B
8
F
8
G
I
5
5
J
8
5
5 a
J
6
8
E
8
F
2 a 23
3 a 6
4 a i 250
c i 24
H
E
5
G
E
R
5
8
5
5 A
5
50
12
3
D
5
8
C
8
17
C
15
U
12
O
10
Q
d
10
B 10
100
T
5
M
15
D
15
N
20
B
12
200
S
E
300
E
c
12
c
250
R
D
250
100
C
A
50
200
D
F
10
b
B
15
A
13
100
A
7
23
23
20
20
C
D
E
50
F
10 B–A–C
2
H
b 16
b 3
ii No
ii Yes
c 16
c 3
b i 150
ii Yes
d i 15
ii No
6
7
8
9
10
1 a
d
2 a
3 a
d
4 a
20
45
165 km
37
72
b
e
b
b
e
30
B
50
38
28
202 km
90
30
D
25
30
70
A
25
74
139
202 km
32
44
3
B
2
E
4
D
C
2
D
b
3
E
E
6
From
To
Flow capacity
A
B
4
A
C
5
D
3
B
E
3
B
C
2
C
20
60
C
b 80 min
E
c
f
c
c
f
5
D
B
Exercise 7C — Shortest paths
4
C
A
b $1.7 million
b $1740
11 D
B
A
A
53 km
54 km
a 68 km
a $215
B
Flow capacity
C
K
To
A
G
From
C
D
E
4
D
C
2
D
E
6

21. 535
Answers
c
From
To
Flow capacity
A
B
4
A
C
7
A
D
3
A
E
5
B
E
3
C
E
B
E
To
B
C
7
A
D
12
A
E
5
C
F
7
D
B
2
D
E
6
D
6 a 10
7 a i
F
E
100
250
d 22
S
D
250
200
N
T
15
300
100
5
20 Q
G
1
J
F
15
E
14
45
40
D
35
30
A
C
2 a 117 km
8
E
8
2
D
3
20 15 B
b 160 km
Exercise 8A — Critical path analysis
1 a
b
B
D
E
H
C
c
64 km
45 km
30
80
72
C
A
D
B
E
F
J
G
H
I
7C
➔
2
4
6
8
10
G
F
A
B
A–D–F
B–C–E–F
30
10
45
B
10
Skills check
ii 25
10 Quick Questions 2
1
3
5
7
9
ii 29
30
6
F
13
10
50
5
8
4
CHAPTER 8 Critical path analysis
and queuing
R
3
H
3
ii 150
50
E
15
E
14
10
C
U
F
3
2
13
c 35
c 70
10
D
E
12
10
10
D
8
12
O
4
G
16
5
M
8
B
6 10
6
E
d i
13
12
A
100
20
A
b 15
b 70
C
100
100
c i
117 km
ADFG, 40
ACFIK, 70
a 20
a 70
ii 300
B
C
R
c 18
50
200
b i
6
7
8
9
10
11
8
b 10
A
E
A B C E H I K
D
4
F
8
4 7
C
4
A
D
3 Step 1 Choose any node at random and connect it to
its closest neighbour.
Step 2 Choose any unconnected node which is
closest to any connected node. Connect this
node to the nearest connected node.
Step 3 Repeat Step 2 until all nodes are connected.
4 A–B–E–C–D–F–G
5
F G
Flow capacity
A
11
12
6
From
b 10
B
A
2
D
1 a 7
2
5
8
D
d
Chapter review
answers
Maths A Yr 12 - Answers Page 535 Wednesday, September 11, 2002 3:41 PM
8A

22. answers
Maths A Yr 12 - Answers Page 536 Wednesday, September 11, 2002 3:41 PM
536
d
Answers
N
O
S
R
X
B, 20
Q
W
U V
Y
2 a
12 a A–D–G
b Float (H) = 1, Float (J) = 3, Float (E) = 1,
Float (B) = 10, Float (C) = 1, Float (F) = 1
c Activity B can be delayed 10 minutes, activity C
can be delayed 1 minute, activity E can be
delayed 1 minute, activity F can be delayed 1
minute, activity H can be delayed 1 minute,
activity J can be delayed 3 minutes.
13 a A–F–G–J–K
b M, L, H, C, E, B, D
P
T
Z
F, 5
G, 10
A, 2
H, 12
C, 4
D, 5
3
4
5
6
7
8
E, 3
b 49 minutes
a B
a 23 minutes
A–C–F
a B
b D
A–D–G
a
B, 15
0
A, 10
10
25
b D
b B, C, E, F, G
c A
D, 8
22
C, 12
Exercise 8B — Critical path analysis
with backward scanning
E, 10
41
G, 6
35
H, 10
J, 11
52
L, 8
49
M, 7
K, 9
61
F, 25
1 Critical path = B–D; Float (E) = 1 min,
Float (C) = 1 min, Float (A) = 1 min
2 Critical path = B–F–G; Float (C) = 3 h,
Float (E) = 5 h, Float (A) = 3 h, Float (D) = 5 h
3 D
4 a 31 days
b Critical path = A–C–E–G
5 D
6 C
7 a Activity
Immediate
b 61 minutes
9
10
11
letter
Activity letter
A
B
C
D
E
F
Activity letter
A
B
C
D
E
F
G
H
J
Immediate
predecessor
—
—
—
A
B, F
C
D
E
E
Time
3
4
5
6
5
8
18
8
6
Activity letter
A
B
C
D
E
F
G
H
J
K
L
M
Immediate
predecessor
—
A
A
B
C
A
D, E, F
D, E, F
G
J
G
H, L
Time
10
15
12
8
10
25
6
10
11
9
8
7
Time
Collect parts
—
12
B
Paint frame
A
35
C
Assemble brakes
A
16
D
Assemble gears
B
20
E
Install brakes
C
12
F
Install seat
C
5
G
Time
7
9
12
8
4
9
predecessor
A
Immediate
predecessor
—
—
A
B
B
C, D
Activity
Final assembly
D, E
18
b
c 85 minutes
D, 20
B, 35
A, 12
G, 18
E, 12
C, 16
F, 5
d
B, 35
12 12
67 67
C, 16
G, 18
E, 12
28 55
8
9
10
11
A–B–D–G
D, 20
A, 12
0 0
47 47
85 85
F, 5
C
28%
a 29
b B–E–J–N
a 35
b C–F–J–M–Q
4 11
E, 5
13 16
G, 9
B, 4
0 0
C, 10
X, 3
10 10
24 25
F, 9
A, 15 15 16
D, 3
H, 5
19 19
P, 10
J, 7
26 26
26
M, 4
26
K, 5
c 3
24 27
N, 6
L, 3
30 30
35 35
Q, 5

23. Answers
12 a
3 C
5 a
B, 7
A, 4
C, 3
E, 5
F, 3
10 Quick Questions 1
1 C
2 The earliest starting time of an activity is the earliest
time by which all prior activities can be completed.
3 The latest start time of an activity is the latest time
the activity can start if the project is not to be
delayed.
4 Float time = latest finish time − earliest start time −
activity time.
5
6 6
A, 5
D, 8
F,2
B, 4 4 4
0 0
14 14
E, 5
6
Customer
served
Arrivals
Length of
queue
People in
queue
0
1
2
3
4
5
6
7
8
9
10
11
12
H, 5
b Float (D), Float (E) = 2, Float (G), Float (H) = 2
C, 6
A
A
A
B
B
B
C
C
C
D
D
D
E
—
—
B
—
C
—
D
—
E
—
F
—
G
0
0
1
0
1
1
1
1
2
2
2
2
2
—
—
B
—
C
C
D
D
DE
E
EF
EF
FG
b 2
a 3 min
c
c 4 min
b Yes
Time
Customer
served
Arrivals
Length of
queue
People in
queue
0
3
6
9
12
15
18
A
A
B
B
C
C
D
—
B
C
D
E
F
G
0
1
1
2
2
3
3
—
B
C
CD
DE
DEF
EFG
6 9
6
7
8
9
10
4 B
Time
J, 2
D, 7
G, 3
537
6
14
9
3
B, F, D
Exercise 8C — Queues: one service
point
1 a
Time
Customer
served
Arrivals
Length of
queue
People in
queue
8
9
10
11
12
13
14
15
16
D
D
E
E
F
G
G
G
H
—
I
—
J
K
—
—
L
—
4
5
4
5
5
4
4
5
4
EFGH
EFGHI
FGHI
FGHIJ
GHIJK
HIJK
HIJK
HIJKL
IJKL
b 5 min
e 2.28 min
2 a
c 9 min
f 1.5 min
d 2 min
Time
Customer
served
Arrivals
Length of
queue
People in
queue
10
11
12
13
14
15
16
D
E
F
G
G
G
H
—
—
—
—
—
—
—
4
3
2
1
1
1
0
EFGH
FGH
GH
H
H
H
c 7 min
d 1 min
7 a 2 min
d 4 min
g F
i
Time
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
b 3, 10
c 2 min
e 3
f 1
h 3 min and 6 min
Customer
(ix)
served
Arrivals
A
A
B
B
B
C
C
C
D
D
E
E
E
E
F
F
F
G
—
B
—
CD
—
—
EF
—
—
—
—
—
G
—
—
—
—
—
Length of
queue
People in
queue
0
1
0
2
2
1
3
3
2
2
1
1
2
2
1
1
1
0
—
B
—
CD
CD
D
DEF
DEF
EF
EF
F
F
FG
FG
G
G
G
—
8B
➔
b 3 min
answers
Maths A Yr 12 - Answers Page 537 Wednesday, September 11, 2002 3:41 PM
8C

24. 538
Answers
9
A
B•
C•
D
E
F
G
H
I
J
K
L
•
0
2
•
•
4
1
3
•
•
6
5
•
8
7
Customer
8
Customer
answers
Maths A Yr 12 - Answers Page 538 Wednesday, September 11, 2002 3:41 PM
A•
B •
C
•
D
•
•
E
•
F
•
G
•
H
0 2 4 6 8 10 12 14 16
1 3 5 7 9 11 13 15
7 A
9
•
0.00
300
2 min
3 min
5
F, G, H, I
2
4
6
8
10
B
C
C
1
A
B
D
C, D
2
C
D
C
D
E
E
1
C
D
F
E, F
2
3.45
C
D
G
E, F, G
3
4.00
E
F
G
1
4.30
Exercise 8D — Queues: multiple service
points
A
3.00
Greater than 1.5 minutes
1 min
5 min
D, E, F
3
B
2.15
10 Quick Questions 2
A
2.00
Minutes
Nurse 2
0.45
•
10 12 14 16
9 11 13 15
Nurse 1
1.30
•
10 17 min
1 a
b
2 4
4 a
b
5 a
Arrivals
E
F
H
G, H
2
0
5.15
4 had been completely served.
2
c 9
d 7
Time
Teller 1
Teller 2
Arrivals
9
G
H
J, K
G, H, I
3
J
I, J
2
G
H
K
I, J, K
3
G
H
L
I, J, K, L
4
8.00
Length of
queue
I
H
7.30
e 3
F
G
6.45
3 Yes
E
6.00
234 s (3 mins 54 s)
3
I
J
K, L
2
Chapter review
3
10
G
H
11
G
H
12
G
H
13
I
J
14
I
L
J
1
5
C
2 D
15
K
16
K
6
A, 5
17
K
5
L
O
J, 4
13
E, 1
5
H, 3
9
C, 4
14
F, 1
20
K, 3
23
J, 4
16
The refit can be completed in 23 hours.
4
7
2
0 0
A, 5
5 5
D, 8
13 13
E, 1
G, 2
3
B, 5
5 7
3
c 5 min
D, 8
G, 2
B, 5
3
L
K, 3
C, 4
5
L
4 D
F, 1
H, 3
G, 2
4
N
E, 1
B, 5
4
M
3 C
D, 8
A, 3
0
b 2 min
6 a 2 min
b 5 min
c
People in Length of
queue
queue
Time
Minutes
1
3
5
7
9
8 B
d 4 min
8
Activity
letter Time
C, 4
9 11
14 19
F, 1
20 20
K, 3
23 23
H, 3 J, 4
16 16
Earliest Earliest
start
finish Float Immediate
time
time
time predecessor
Service 1 Service 2 Arrivals
0
A
B
1
C
B
2
C
D
3
C
D
4
E
D
5
E
F
d 2 min
E
People in Length of
queue
queue
5
0
5
0
—
B
5
0
5
0
—
C
Time
A
4
5
11
2
B
D
8
5
13
0
A
2
E
1
13
19
5
D, G
E, F
2
F
1
14
20
5
E
E, F
G
3
D, E
F
C, D, E
2
G
2
9
13
2
C
2
H
3
13
16
0
D
J
4
16
20
0
H
K
3
20
23
0
F, J
F, G
G

25. 539
Answers
9
14
a
Time
Customer
Arrivals
0
A
B
a
People in Length of
queue
queue
Point Point
1
2
Time
People in Length of
queue
queue
Arrivals
1
A
2
B
3
C
4
C
0
B
C, D, E
C, D, E
3
A
C
F, G
D, E, F, G
4
2
A
D
H
E, F, G, H
4
3
1
A
1
B
E
D
I, J
F, G, H, I,
J
5
K
G, H, I, J
4
B
1
C, D
C, D
2
E, F
D, E, F
3
4
E
F
D, E, F
3
5
G
H
L
I, J, L
3
G
H
M, N
I, J, L,
M, N
5
G
I
O
J, L, M,
N, O
5
5
D, E, F, G
4
D
H, I
E, F, G,
H, I
5
7
E
F. G. H. I
4
8
F
J
F, G, H,
I, J
4
9
Task
G
7
10
C
6
6
b
c
d
e
F
K
G, H, I,
J, K
5
b 1 min
c (0 + 0 + 0 + 1 + 0 + 1 + 1 + 0 + 1 + 1 + 1 + 0 +
1) ÷ 13 = 0.54 min
d (0 + 1 + 2 + 3 + 3 + 4 + 3 + 4) ÷ 8 = 2.5 min
a
15
Moths
Entry
5 min
3 min
(2 + 1 + 3 + 1 + 1 + 2) ÷ 6 = 1.67 min
(0 + 2 + 0 + 1 + 0 + 2 + 1 + 0 + 2 + 1) ÷ 10
= 0.9 min
K
J
I
H
G
F
E
D
C
B
A
•
•
•
•
•
•
•
•
•
•
Tour
information
Butterflies
(Rainforest)
Arachnids
(Scorpions)
•
Butterflies
(Temperate)
Glowworms
(Caves)
Arachnids
(Spiders)
Exit
b
D, 2
A, 12
B, 13 C, 12
G, 6
E, 4
H, 6
I, 5
J, 12
F, 2
0 1 2 3 4 5 6 7 8 9
Time hours
11
Time
Customer
served
0
A
—
—
—
1
A
B
B
1
2
B
C
C
1
c The room would quickly become crowded.
d Five people per minute
People in Length of
Arrivals
queue
queue
CHAPTER 9 Probability and the
binomial distribution
Skills check
1 a 6
b 2
c 52
d 36
3
B
D
C, D
2
2 a
1
----12
4
C
E
D, E
2
d
1
----36
e
1
----54
5
C
F
D, E, F
3
6
D
G
E, F, G
3
7
D
H
E, F, G, H
4
I
F, G, H, I
4
0.04
0.72
0.125
0.154
Less than
Greater than
0.03
c 0.54
0.67
f 0.125
0.188
c 0.75
0.684
f 0.058
b Greater than or equal to
E
3 a
d
4 a
d
5 a
c
b
e
b
e
8
b
2
-3
c
5
-6
f
5
----16
Exercise 9A — Compound events —
independent events
1
1
-4
2 a
1
-2
b
1
-2
8D
➔
----------a Inter-arrival time = 3600 s = 3.6 s (less than
1000
service time)
b 3
13 a Inter-arrival time = 0.75 s
b Number of service points = 40
12
answers
Maths A Yr 12 - Answers Page 539 Wednesday, September 11, 2002 3:41 PM
9A

26. answers
Maths A Yr 12 - Answers Page 540 Wednesday, September 11, 2002 3:41 PM
540
Answers
3 S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
4
-P(9) = ----- = 1
36
9
6
-4 7 is mostly likely, P(7) = ----- = 1
6
36
5 a 0.2646
b 0.0204
c 0.1764
6 {(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H),
(T, H, T), (T, T, H), (T, T, T)}
a
1
-8
3
-8
b
c
7
-8
d
17
P
S
T
P(P − F) = 0.4 × 0.25 = 0.1
18 a P(no drug) =
9
= 0.35
14
----40
P(small dose) =
16
----40
= 0.40
P(large dose) =
3
-8
10
----40
= 0.25
b, c, d
7 C
8 B
1
-6
B PB 0.4 x 0.3 = 0.12
F PF 0.4 x 0.25 = 0.10
L
PL 0.4 x 0.45 = 0.18
B SB 0.25 x 0.3 = 0.075
F
L SF 0.25 x 0.25 = 0.063
SL 0.25 x 0.45 = 0.112
B
F TB 0.35 x 0.3 = 0.105
L TF 0.35 x 0.25 = 0.088
TL 0.35 x 0.45 = 0.157
R'
N
×
×
1
-6
1
-6
=
lia
ustra
k
Yor
New
New
Yor
k
A
Australia down
p
yo u
Tok
Tokyo dow
n
up
dow
lia up
Austra
Australia down
0.7 × 0.45 × 0.5 = 0.16
R'
LR' 0.25 x 0.20 = 0.05
e Although few patients were tested, it appears
that a greater percentage (80%) of those given
a large dose of the drug recovered, whereas
a much smaller percentage (29%) of those not
given the drug recovered. 20% of people tested
were given a large dose of the drug and
recovered, 15% of people tested were given a
small dose and recovered, whereas only 10%
of people were not given the drug and recovered.
So it could be said that a patient is more likely
to recover if the drug is taken.
0.7 × 0.55 × 0.5 = 0.19
0.3 × 0.45 × 0.5 = 0.07
0.3 × 0.55 × 0.5 = 0.08
0.3 × 0.45 × 0.5 = 0.07
0.3 × 0.55 × 0.5 = 0.08
0.7 × 0.45 × 0.5 = 0.1575
11 0.3 × 0.55 × 0.5 = 0.0825
12
0.55 HH 0.55 × 0.55 = 0.3025
H
H
T
0.55
T 0.45 HT 0.55 × 0.45 = 0.2475
H 0.55 TH 0.45 × 0.55 = 0.2475
0.45
T
0.45 TT 0.45 × 0.45 = 0.2025
P(2 Tails) = 0.2025
1
H P(H, H, H) = —
8
1
—
T P(H, H, T) = 8
1
H P(H, T, H) = —
8
H
H
T
1
—
T P(H, T, T) = 8
1
H P(T, H, H) = —
8
1
8
T P(T, H, T) = —
1
H P(T, T, H) = —
8
H
T
T
T
a There are 8 paths.
14 D
15
0.2
B
W
M
0.6
B' 0.8
B 0.2
1 a, d, e, g
1
4
2 a ----- = ----13
52
16
----45
16 + 76
----------------178
8
WB 0.6 x 0.2 = 0.12
WB' 0.6 x 0.8 = 0.48
MB 0.4 x 0.2 = 0.08
4
5 D
6 a
7 a
8
9
10
11
a
a
a
a
b
=
7
-9
c
0.8
=
1
-3
0.258
0.037
0.32
0.4999
=
72
-------148
=
18
----37
24
----36
b
d
19
----45
e 1
b
=
19
----37
2
-3
c
15
----36
=
5
----12
b 0.449
c 0.865
b 0.296
c 0.667
d 0.333
b 0.46
c 0.31
b 0.9997
c 649 773
Exercise 9C — Compound events —
Venn diagrams
1 a 4
2 a S
b 5
MB' 0.4 x 0.8 = 0.32
b 0.32 = 32%
29
----45
15
----52
= 0.517
59 + 13
----------------148
12
----36
35
----45
c
6
----13
b
7 o'clock 11 o'clock 31
B'
16 b, d, e
1
P(T, T, T) = —
0.4
a 0.12 = 12%
Exercise 9B — Compound events —
mutually exclusive events
3 a
13
SR' 0.40 x 0.625 = 0.25
LR 0.25 x 0.80 = 0.20
R
L
0.7 × 0.55 × 0.5 = 0.19
Australia up
Aus
trali
a do
wn
n
R'
0.7 × 0.45 × 0.5 = 0.16
up
Australia
Australia
down
Tokyo up
Tok
yo d
ow
n
up
NR' 0.35 x 0.714 = 0.25
SR 0.40 x 0.375 = 0.15
R
S
1
-------216
10
NR 0.35 x 0.286 = 0.10
R
80 55 34
55
-------200
c 8
= 0.275
b 0.4

27. 3
IPT
TS
31
0
b (0.75)6
b 0.0413
11 a 0.25
12 a 0.2090
13 0.1342
S
16
541
c 0.0330
29
Career profile — Gail Twemlow
The events are mutually exclusive and the Venn
diagram could have been drawn as two circles which
did not overlap.
4 S
0.18
S
A
0.51
1 Selling betting tickets, calculating dividends,
Cashbook and basic accounting
2 A boxed trifecta is more expensive because you have
more chances of winning.
3 Reading cashbooks and using computer screens to
follow what money has gone through the system.
answers
Answers
0.08 0.18 0.23
Investigation — Pascal’s triangle
5
1
0.9009
S
A
1
1
4 7
14 6 3
2
0
C
9
C
10
3 9
8 5
4
8
N
10 Quick Questions 1
1
1
-6
2
4 0.16 or 16%
7
10
1
-6
3 0.36 or 36%
1
----26
5 0.48 or 48%
6
8 4
7
----13
1
----20
9 14
Exercise 9D — The binomial
distribution using Pascal’s triangle
1 7 21
1 9 36
1 5 10
1 7 21
1
b
0.0256
0.0132
0.0179
0.2344
0.2322
0.4019
0.5
0.5
35
84
10
35
4
4
6
1
4
35 21 7 1
126 84 36 9 1
5 1
35 21 7 1
c 70
d 1
e 110
b 0.1176
c 0.125
e 0.0720
f 0.0156
b 0.0284
c 0.3456
b 0.3125
b 0.8936
b 0.8038
b 0.2734
b (0.5)10
2 The triangle is symmetrical about a vertical line
through the centre.
3 Number of entries in row = row number + 1
4 Odd-numbered rows have an even number of entries.
Even-numbered rows have an odd number of entries.
5 An odd number of trials has two middle numbers of
the same value.
An even number of trials has one middle number.
6 Sum of numbers in row = 2row number (2 to the power
of the row number)
7 Yes. 113 = 1331
Yes. 114 = 14 641
8 They are square numbers.
9 Fibonacci’s sequence
1
12
35
1 1
8 13
1 2 1
21
34
1 3 3 1
55
1 4 6 4 1
89
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1
10 Use the diagonal
1
1 + 3 = 4 = 22
3
3 + 6 = 9 = 32
6
6 + 10 = 16 = 42
10
15
11 The triangular numbers are ocated in the diagonal
shown in question 10.
12 Sum of 10 lies in the position below the 4 to the
right. This pattern continues. The same pattern
continues for the numbers in the second diagonal.
9B
➔
1 a
b
2 a
b
3 a
4 a
d
5 a
6 a
7 a
8 a
9 a
10 a
1
3
1
B
S
2
3
Row 0
Row 1
Row 2
Row 3
1
5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1
6 C
b 63%
7 a 37%
8 0.27, much higher probabilities of winning with
roulette.
9
36
10
1
1
0.0291
0.0009
0.0691
A
1
B 0.9009
9D

28. answers
Maths A Yr 12 - Answers Page 542 Wednesday, September 11, 2002 3:41 PM
542
13
Answers
Row (r)
0
1
2
3
4
5
6
Sum (s)
1
3
7
15
31
63
127
s = 2r + 1 − 1
14 a Multiples of 2
9 0.1275
1 10
b  --
 3
1
10 a -3
c Approximately 0.2
10 Quick Questions 2
1
1
-4
2 1 4 6 4 1
4 4p3q
5
-6
1
-6
3 p= ,q= ,n=4
5 0.0154
8 0.0592
6 0.3602 or 36% 7 0.9408
9 0.0139
10 0.0026
Chapter review
1 D
4 a
Sum
2
3
4
5
6
7
8
9 10 11 12
Prob.
1
----36
2
----36
3
----36
4
----36
5
----36
6
----36
5
----36
4
----36
b
b Multiples of 3
5 a
6
9
10
12
13
14
2 C
1
-2
c
0.3975
a 0.5
D
a 0.5625
D
----a i 25
49
b i
2
-9
b
1
-8
ii
16 years old
A calculating machine
The Puy de Dôme mountain
For probability, permutations and combinations
A brain tumour and stomach ulcer
3
----36
2
----36
1
----36
8
1
-9
0.9999
c
32
----36
c 0.843 75
20
----49
ii
20
----42
P(both A and B) = 0.25
A
1
2
3
4
5
d
7 0.4928
----b 15
36
11 C
b 0.375
20
----42
C
3
-8
15 B
16 6
17 S
History of mathematics — Blaise
Pascal
3
0.05
B
0.25
0.25
18 D
19 a S
Yes
18
No
12
13
Exercise 9E — Binomial probabilities
through tables
1
2
3
4
5
6
a 0.0008 b 0.9527 c 0.5793 d 0.9907
a 0.8281 b 0.9389 c 0.9887 d 0.9532
a 0.5000 b 0.6964 c 0.4142 d 0.0000
0.8684
a 0.6550 b Between 0.6167 and 0.9666
a 0.6230 b 0.5881 c 0.5000 d 0.0781
e 0.0139 f 0.0034
7 a 0.0404 b 0.9536 c 0.9940
8 a 0.2
b i 0.2013 ii 0.3222 iii 0.1074
c The probability of this is very slight; there may
be some error in the sampling technique.
b
30
----43
20 D
21 a Two outcomes, success or failure, same event
repeated
b Tossing a coin 6 times
c Rolling a die and noting the upper-most face
22 a 0.402
b 0.032
23 0.016
24 a 0.39
b 0.39
c 0.78
25 a 0.8725
b 0.8042
26 a 0.2
b 0.3704
27 a 0.12
b 0.2517

29. Answers
CHAPTER 10 The normal
distribution and games of
chance
Skills check
1
2
3
4
5
Answers will vary. Check with your teacher.
a 6.7
b 2.4
c 0.4 below the mean
Distribution b
45 to 55
a the value of x is larger than 40
b the value of x is less than or equal to 40
c The value of x is larger than 20 and less than 30.
Exercise 10A — z-scores
1
2
3
4
5
6
7
8
3
−2
a 0
b 1
c −2
a 10.5 b 13.7 c 16.9
−0.27
1.5
a −0.48 b 1.44 c 0.08
a 10.3 s
b 10.58 s
d 9.88 s
e 10.251 s
9 a x = 19.55, sn = 1.76
e −1
e 0.9
d −2.24 e 2.8
c 10.37 s
f 10.524 s
b 1.68
$10
$30
19
60–<80
$70
15
80–<100
$90
6
10 Quick Questions 1
1
2
3
4
5
6
7
8
9
10
b x = 56, σn = 20.1
c i 0.30
ii 2.2
iii −2.0
B
B
C
a x = 64.7, σn = 11.4
b Highest score z = 2.66, Lowest score z = −1.73
English 1, Mathematics 1.31, Biology 1.5,
Computing studies −2, Visual arts 0.67, Music −0.8
Exercise 10B — Comparison of scores
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
a 68%
b 95%
c 99.7%
a 68%
b 95%
c 99.7%
95%
16%
a 68%
b 16%
c 0.15%
21.1 and 33.9
a 68% of the values have a z-score between −1
and 1.
b 95% of the values have a z-score between −2
and 2.
c 99.7% of the values have a z-score between −3
and 3.
B
A
0.15%
a 16%
b 16%
a 95%
b 16%
c 34%
d 15.85%
e 83.85%
a 95 g to 105 g
b 92.5 g to 107.5 g
163 cm − 181 cm
Faulty, as the one chosen has a z-score greater than 3
2.6 kg − 5 kg
Exercise 10D — Standard normal
tables
1
2
3
4
5
6
7
8
9
10
a
d
g
j
a
a
a
d
a
e
a
a
a
a
b
a
d
0.8413
0.1587
0.6826
0.1359
0
b
0.5
b
0.8413
0.0013
0.6406 b
0.2812 f
0.0500 b
0.7486 b
75%
i 0.9332
22.6%
0.7881
0.7881
b 0.9192
e 0.0446
h 0.9544
k 0.0215
−0.75
c
−0.5
c
b 0.9452
e 0.3413
0.8577 c
0.6188 g
0.1335 c
0.9082 c
b 37
ii 0.8413
b 0.3446
e 0.5403
c
f
i
l
0.9641
0.2417
0.9974
0.8664
−1
d 1.5
−1.3
d 1.2
c 0.5
f 0.8185
0.5
d 0.3594
0.0509 h 0.0554
0.0294 d 0.8665
0.2514 d 0.6568
c 46
iii 0.1210
c 0.1151
9E
➔
1 a English 1.25, Maths 1.33
b Maths mark is better as it has a higher z-score.
2 2nd test, Barbara’s z-score was −0.33 compared to
−0.5 in the first test.
3 C
4 D
5 Course A, z-score of −0.8 compared to −0.75 on
course B
6 a Atlanta 0.44, Sydney 1
b In Atlanta because of the lower z-score
7 C
8 B
2
−2
−1.03
2.95
One standard deviation above the mean
Two standard deviations below the mean
50
8
English 1.25, Maths 1.4
Maths
Exercise 10C — Distribution of scores
8
$50
9 a Mathematics x = 59.5, sn = 17.9
Chemistry x = 59.6, sn = 16.8
b Mathematics 0.25, Chemistry 0.20. So
Mathematics is the better result.
10 Kory is the better candidate with a z-score of 1.5
compared with 0.875 for Ricardo.
2
40–<60
15
Frequency
20–<40
11
12
13
14
Class centre
0–<20
10 a
Amount ($)
d 3
d 7.3
543
answers
Maths A Yr 12 - Answers Page 543 Wednesday, September 11, 2002 3:41 PM
10D

30. answers
Maths A Yr 12 - Answers Page 544 Wednesday, September 11, 2002 3:41 PM
544
11
12
Answers
4.75%
0.38%, assuming weights to be normally
distributed.
Exercise 10E — Odds
1 a
e
2 a
e
3 a
$105
$15
$140
$60
b
f
b
f
4
-5
2
-7
d
4 a
e
5 a
d
6 a
d
7 a
8 a
$105
$33.33
$175
$83.33
-b 1
4
c
g
c
g
$429
d $300
$66.66
$507
d $420
$216.66
-c 3
5
3
----10
e
2
-3
f
2:1
b 4:1
c 3:2 on
7:5
f 2:1 on g 6:4
Evens
b 5:1
c
12:1
e 3:1
2:1
b 3:1
c
7:5
e 2:1 on
f
$36 000
b i $13 500
ii
$160
b $71.11
c
d 5:2
h 11:9
3:1
Evens
5:2 on
$22 500
$80
Exercise 10F — Two-up
1
-4
2
1
-4
3
1
-2
4
1
-2
5
1
-8
6
1
----16
7 a TH, TH, TH, TH
1
8 ----32
1
-8
b
1
----16
c
b
1
----32
d
1
----64
1
----16
e 0.48
Exercise 10G — Roulette
18
----37
b
6
----37
2 a 19:18
b 31:6
c No, slightly lower
3 a $60
b 0
c $200
d $75
4 Nothing happens except when the ball lands on 0,
then he loses both bets.
Exercise 10H — Common fallacies in
probability
1 a 1/16
b 1/32
c 1/2
2 a i 0.32
ii 0.24
b Her chances of winning any match remain 0.75.
4 a Events are not independent.
b How many people in this group own surfboards?
3.6
15.6
−$2.50
−13.5 cents
7
2
4
6
8
3.1
−40 cents
$0.62
$1.60
10 Quick Questions 2
1
3
5
7
9
Very probable
970 mL
0.0495
0.9010
$500
Chapter review
1
2
3
4
5
7
8
10 Not quite, probability of winning = 0.48
1 a
1
3
5
7
9
6
1
9 a
Exercise 10I — Mathematical
expectation
9
10
11
12
13
14
15
16
17
18
19
20
21
22
2
4
6
8
10
2.5%
0.9505
0.0495
2
-5
$1 loss
−2
a 0
b 1
c −2
d 3
e −1
1.87
a 0.17 b 1.83 c −3
d −1.75 e −2
a x = 1130, σn = 334.2
b i −0.39 ii 2.05 iii −2.62 iv −1.13 v 3.07
a x = 20.1, σn = 2.1
b Highest = 1.86, Lowest = −1.95
a 1.5
b 1
c Physics, higher z-score
a Geography: −0.8, Business studies: −0.53
b Business studies: higher z-score
Numeracy: lower z-score
a 68%
b 95%
c 99.7%
a 68%
b 95%
c 99.7%
a 34%
b 47.5%
c 2.5%
d 0.15%
e 97.35%
Faulty, as it is more than three standard deviations
from the mean.
a 0.9032
b 0.9918
c 0.1587
d 0.0668
e 0.2075
a 0
b 1
c −0.83
d 5.33
a 0.5
b 0.8413
c 0.1587
d 0.0485
e 0.1293
f 0.3779
a 0.5
b 0.8413 c 0.7357 d 0.2342
a Horses 5 and 6
b Horses 1, 3 and 5
Test this by simulation on a computer.
a Same
b Same
a i 0.49
ii 0.25
iii 0.25
b No
a $1.67
b About $2.65 (if the operator’s percentage is based
on this figure)