1

New Century Maths 11 Mathematics General

Preliminary course (Pathway 2)

Worked Solutions

Chapter 1

SkillCheck

1 a sector graph b stem-and-leaf plot c line graph d divided bar graph

3 a 20 b 5 c 500

4 a 38

b 3 1100 37 %8 2× =

5 a !"#°

!"#°= !

!"

b !!"×100 = 35%

6 !"!!"!

= 24.5

Exercise 1-01

1 a 13.4% b 13% 8% 5%− = = 5% (to the nearest whole number)

c 10.8% of 35 650 10.8 35650100

= ×

3850≈ d 100% – 13.4% = 86.6%

86.6% of 42 320 86.6 42320100

= ×

36650≈ e The percentage of people drinking at a risky

level will be higher.

2 a 14

b labour

c 15% of 13.50

15 13.501002.025$2.03

= ×

=

≈

d 5% $285=

2851%5

=

100% 57 100= ×

$5700=

e 15% of 360 o

15 36010054

= ×

=

o

o

f 20% of $5300

20 5300100$1060

= ×

=

3 a The bar measures 120 mm.

20 1120 6

=

b

42 100 35%120

× =

c

2

45 100 37.5% ( )120

suspicious× =

d

7 275 16 fires

120× ≈

4 a male

b 25–34

c 32%

d 8% of 14 205 = 1136.4 1136≈ e 65–74

f decreases

5 13.7 – 8.9 = 4.8 h. So, B.

6 a Yes

b underweight

c Minimum BMI = 17.5

d 2

78BMI 26.061.73

= =

It would be suggested that Jake needs to lose weight. e 16 to 25

f Answers will vary.

7 a 1 mm

b number of rain days

c 23 mm; 4

d October; 24.5 mm

e July; 6

f April (lowest rainfall)

g 9

8 9% 2475=

24751%9

=

00% 275 100= × 27 500= So, A. 9 a share prices over 6 days

b 25c

c $4.55

d Tuesday

e It fell, then rose.

f Thursday; lowest price.

g NCM Bank

10 a 17

b East; 25 on Thursday

c Monday; first working day

d Wednesday; 23 – 17 = 6

e Saturday; no industry

Exercise 1-02

1 a The vertical axis starts at $1.50 so increases in share price appear steeper than they actually are.

2 a Because the 2010 picture is double the length and double the width, it is actually four times the size of the 2008 picture instead of two times the size.

3

3 a a company’s sales

b The new director has made sales go down.

c sales figures and months

4 a The $800 note is double the length and double the width of the $400 note and this makes it four times the size of the $400 note instead of two times the size.

5 a By starting the scale on the vertical axis at 53.

c The Labor votes are not overwhelmingly higher. They are just 8 more. 6 a The picture for ‘$100 of oil today’ is actually

about 13

the size of the picture for ‘10 years ago’.

b

$100 of oil today $100 of oil 10 years ago

7 a 7 hours b The hours scale does not begin at 0. c Most of the day is spent at school or sleeping. d

Exercise 1-03

1 a C b Q c C d Q e Q f C

g C h C i Q j Q k Q l C

2 Categorical (words, symbols);

Quantitative (quantities, numbers)

3 a N b O c O d N e N f O

g O h N

4 a C b C c C d C e D f C

g D h C

5 a HSC subjects

b size of hot chips at a fast food store

c number of children in a family

d heights of boys in Year 11

6 a quantitative b categorical

c continuous d nominal

7 B

Exercise 1-04

1 a C b F c D d H e E

f I g A h G i B

2 a Commonwealth Scientific and Industrial Research Organisation

4

b Road Traffic Authority

c United Nations Children’s Fund

d Government Insurance Office

e Bureau of Meteorology

f Australian Securities Exchange

g Australian Security Intelligence Organisation

h World Health Organisation

i National Rugby League

3–4 Teacher to check.

5 a stage 5

b stage 1

c stage 4

d stage 2

6 Teacher to check.

7 a bank account details, amount of transaction, time and date

b personal details, email address, interests and preferences

c your location, time and date of message

d amount of spending, your location

e your location and speed, time and date of driving

f type of book/video borrowed, time and date, your location

8 theft of identity; money stolen from accounts

Exercise 1-05

1 a C b S c S d C e S f S g C h S

2 2016, 2021

3 Teacher to check reasons.

a systematic b random c stratified

d random e random f random

g random h random

4 Total = 4851

female3347 2004851

= ×

137.99...138

=

≈ 5 Total = 830 960

260450West 600830960

= ×

188.05...188

=

≈

6 Total = 38

5Teachers 838

= ×

1.05...1

=

≈ So, B.

7a Not all teens read magazines.

b Only those diners interested/volunteering to complete the survey are sampled.

c Need to select more students and not only those who arrive early.

d Need to sample workers as well, not only management who may have a biased view.

e People at a premiere are not the usual moviegoers.

f It is restricted to one radio station.

8a systematic sample

b shoppers in 1 store only; only females or males

Exercise 1-06

1 a

5

b data is discrete (not continuous)

c 3

d 6; 1 student

e Total = 2 + 1 = 3

3 100% 7.5%4× =

2 a shows parts of the whole amount

b 235000home loan 360 106800000

= × ≈o o

96000new car 360 43800 000

= × ≈o o

144000home reno 360 65800000

= × ≈o o

125 000travel 360 56800 000

= × ≈o o

200000savings 360 90800 000

= × =o o

c saved it

d 144000 9800 000 50

=

e 96 000 100% 12%800 000

× =

3 a 3460 855 4140 4215 2300 14 970+ + + + =

b sector; divided bar; column

c Draw a bar 6 cm long (could choose any length)

3460ABC 6 1.414 970

= × ≈ cm

855SBS 6 0.314 970

= × ≈ cm

4140Seven 6 1.714 970

= × ≈ cm

4215Nine 6 1.714 970

= × ≈ cm

2300Ten 6 0.914 970

= × ≈ cm

d 3460 100% 23%14970

× ≈

e Seven and Nine 4140 4215= + = 8355 Yes, this is more than half of 14 970.

6

f No, since the survey only included Sydney

households.

4 a 7 5 11 21 15 9 4 72+ + + + + + =

b column graph; discrete data

c 7 100% 9.7%12× ≈

d Total ‘no more than 3’ = 7 5 11 21 44+ + + = 44 1172 18

∴ =

5 D

6 a Total 20 35 7 10 3 12 6 93= + + + + + + =

Draw a bar 7.2 cm long (could choose any length)

UK 20 7.2 1.5 cm93

= × ≈

NZ 35 7.2 2.7 cm93

= × ≈

Mid East 7 7.2 0.5 cm93

= × ≈

India 10 7.2 0.8 cm93

= × ≈

Africa = 3 7.2 0.2 cm93× ≈

6Other 7.2 0.593

= × ≈ cm

b UK and NZ = 20 + 35 = 55 which is more than half of the 93 ∴ True

c 12 493 31

=

d 7 100% 8%93× ≈

e 10.75% of 93

10.75 931009.97510

= ×

=

≈ ∴ India

b 2003

c 2006

d home theft

e home thefts rose from 2001 to 2003, then declined steadily.

f Decreased; table and graph show a steady decline.

Exercise 1-07

7

3 a 6 14 28 11 8 3 70 people+ + + + + =

6 a none

b 7 3 4 1 2 5 6 3 2 4 6 43+ + + + + + + + + + =

c 7 100% 16.3%43× ≈

8

d No, since the last column only tells those who made more than 30 calls.

Exercise 1-08

2 a 10

b mode = most frequent = 7

c 12; a student with big feet

d 4 210 5

=

5 a 30

b

15 100% 50%30× =

c around 6–10

d Mostly good results but 3 quite low scores

9

b

5 100% 25%20× =

b

26 100% 87%30× ≈

c 28; raining day and few customers 8 a 36

b 91 seconds

c

10 100% 28%36× ≈

b 10

c 110, heart is beating quickly

d 4 people had a heart rate less than 60 beats per minute

10 a $975 000

b 50

c $385 000

b 24

c i 11.6 s ii 18.7 s

d 12 100% 50%24× =

e 524

Exercise 1-09

1 a 41 Co

b 5.00 a.m.; 37.5 Co

c 8

d 7.00 a.m. and 9.00 a.m.

e 7.00 a.m., 42 37.5 4.5 C− = o

f temperature dropped 2 Co then increased 2 Co

2 a B

b April and December

c July

d Miami

e 27 12 15 C− = o

10

b 60 at 3.00 a.m.

c She was sleeping.

d from 6.00 p.m. to 9.00 p.m.

e No, only possible to know the actual readings.

4 a about 70 mm; September

b about 70 mm; October

c Sydney

d Melbourne

e March and June are about the same.

b 5

c June

d 1400; May

e Bill; he sells more plants.

6 a i sector graph; divided bar graph

ii dot plots; stem-and leaf plots

iii frequency histogram and polygon

iv line graphs; radar chart

b stem-and-leaf plot

c radar chart

d columns graph, line graph, frequency histogram, frequency polygon

Sample HSC problem

a A

b Select some fans from each teams home

ground.

c 23% of 360

23 36010082.883

= ×

=

≈ o d

4500 100% 15%3000

× =

∴ players’ salaries e Doesn’t show exact values; it is difficult to

compare similar values.

Revision

1 a 1477

b rectum

c 6

d prostate = 5950

Next 3 cancers 2024 1853 1477 5354= + + =

∴ True

11

e These cancers do not represent parts of a whole.

b sector graph, divided bar graph

3 a Q b C c C d Q e Q f C

4 b N c O f N

5 a QD c QC d QC e QD

6 Teacher to check.

7 Stage 4: Summarising and displaying data.

8 Systematic, for example, take every 10th bottle and test

9 a The sample may not necessarily take students from each Year into account.

b Total = 114 120 114 128 105 96+ + + + + = 677 Number of yr 10 students

128 506779.453...9

= ×

=

≈

11 a 3 8 32 28 17 5 93+ + + + + =

b 30 : 360 1293× ≈o o

81 3: 360 3193

− × ≈o o

324 10 : 360 12493

− × ≈o o

281 1 20 : 360 10893

− × ≈o o

17 21 30 : 360 6693

− × ≈o o

5 31 : 360 1993

+ × ≈o o

c 12o

d 32 100% 34.4%93× =

e 11 or more countries = 28 17 5 50+ + = , which is more than half of 93

∴ True f The data is not continuous; the class intervals

are not equal in size.

d 60–<70

e 8 140 5

=

12

b 24 c

6 124 4

=

d The 8-year-old is an outlier; scores are clustered around 3-6 years.

14 a 3 years

b 29

c 12

d

12 100% 41%29× ≈

15 a November

b about $3300

c May

d June to July

e 4