S1.1 Homework Answers - Cambridge...

Cambridge Essentials Mathematics Core 8 S1.1 Homework Answers

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S1.1 Homework Answers

1 a D b B c C d A e E

2 a R b 61 c A spinner which is half shaded. For example,

3 a A1, A2, A3, A4 b 121 c

41

B1, B2, B3, B4

C1, C2, C3, C4

4 It is not 31 because there are not equal numbers of office workers, managers and canteen

staff, so they are not equally likely outcomes.

5 a 4 b 203 c red d yellow




1 a 1911 b

198

2 98%

3 0.2

4 a Because 18 + 1

2 + 14 + 1

8 = 1, so it is certain that all the balls are either red, blue,

green or yellow.

b Kerry cannot be right because 18 of 20 is not a whole number and there must be

whole numbers of red and yellow counters.

Spinner B 5 a 2 4 6 8

3 5 7 9 11 Spinner A 5 7 9 11 13 7 9 11 13 15 9 11 13 15 17

b i 0 ii 316 iii 3

16 iv 1016 or 5

8 v 1116




1 a 4015 or

83 b

10040 or

52

c b should be more reliable because the more trials you do, the more reliable the result.

2 Pupil’s own results in the table, graph and comments.

3 Pupil’s own experimental results and calculation.

Cambridge Essentials Mathematics Core 8 S2.1 Homework 1 Answers


S2.1 Homework 1 Answers

1 a Quantitative b Qualitative c Quantitative

d Quantitative e Qualitative

2 a i £5 ii comedy (film)

b i four (wheels) ii red (bus)

c i 50 cm ii blonde (hair)

3 a Discrete b Discrete c Continuous

d Discrete e Continuous

4 a i The number of goals scored by Premier League teams and lower league teams.

ii Collect results yourself one weekend (primary).

Or use results published for the whole season (secondary).

b i Temperatures at various stages of cooling of water in metal containers and plastic

containers.

ii Carry out an experiment – check the temperature of water in both containers after

1 minute, 2 minutes etc (primary).

Or use data regarding thermal conduction of the metal and plastic from the internet

(secondary).

c i The gender of maths teachers in secondary schools.

ii Count the numbers of male and female teachers in your own school (primary).

Get in touch with the Local Education Authority for information on all schools in

your area, or use the internet to obtain nationwide statistics (secondary).




1 a The groups overlap; 10 minutes and 15 minutes are each included in two groups.

A better question would be: How long does it take you to get to school?

less than 5 minutes

less than 10 minutes but not less than 5 minutes



20 minutes or more

b ‘A lot’ of pocket money is a qualitative measure and is not well defined.

The question could be improved by offering a choice of amounts as shown below,

but this may be too personal and people may not answer honestly. How much pocket money do you receive each week?

£1–£5 £5.01–£10 £10.01–£15 more than £15

c The data will be easier to analyse if options are given, as shown below.

‘Exercise’ needs to be defined more precisely. In week, how many times do you do any form of exercise?

0 1–3 4–6 7–9 10 or more

2 As it is a small village, all people living there and affected by the new road could receive

a questionnaire, with free return postage so that no expense is incurred by the person

filling in the questionnaire. Alternatively a sample could be collected by using the

electoral roll and contacting every 10th person to give a sample of 100 people.

3 The population is all the pupils in Katya’s school. The sample could be selected by

picking at random a given number from each year group.

4 The first 20 spins suggest that the spinner is biased in favour of 2.

However, after 80 spins the results even out, suggesting that the spinner is not biased.

5 a There are too many values for each value to be listed.

There is no way of recording a time that is not a whole number.

b The values 15 s, 20 s etc each belongs to two groups in the table, so it is not clear

where such results should be recorded.

c It allows all times to be recorded and is not ambiguous in any way.




1 a Range = 38 – 10 = 28 passengers

b Mode = 28 passengers

c Mean = 268 ÷ 10 = 26.8 passengers

d Median = 28 passengers

2 a Total distance = 140 km b Mean distance = 28 km

c Total distance cycled must be 6 × 30 = 180 km. On the last day he must cycle 40 km.

3 a Median b Mode c Mean

4 a 34 years b 45 years c 36 years

5 a Adults’ viewing times

0 5 6 8 8 9 1 0 1 1 2 4 4 4 4 5 6 7 8 9 9 2 0 3 3 7 9 3 3 4

Key 2 | 3 represents 23 hours

Teenagers’ viewing times

0 0 6 1 1 2 3 4 4 5 7 8 9 9 2 0 7 8 9 9 9 9 9 3 0 1 1 5 4 0

Key 1 | 9 represents 19 hours

b Modal time is 14 hours for the adults, 29 hours for the teenagers.

c Range is 28 hours for the adults, 40 hours for the teenagers.

d Median is 14 hours for the adults, 20 hours for the teenagers.

e Mean is 15.8 hours for the adults, 21.8 hours for the teenagers.

f 50% of the adults watched TV for 14 hours or more each week; 50% of the teenagers

watched TV for 20 hours or more each week. The teenagers’ watching hours have a



greater range, with one teenager who did not watch TV and one who watched for 40

hours.

6 a 4 shots

b 1 + 4 + 7 + 10 = 22 golfers

c 3.8 shots

d 4 shots

e It is not difficult to reach par score or better. 73% of golfers took 4 shots or fewer.




1 a 1 Pupil = 360 ÷ 30 = 12°

b 132°

c 151

302=

d Pupils’ pie chart. Check that the angle of each sector is as follows:

Playing sport 11 × 12° = 132°

Reading 9 × 12° = 108°

Computer games 5 × 12° = 60°

Listening to music 3 × 12° = 36°

Watching TV 2 × 12° = 24°

2 a 1 person = 360 ÷ 240 = 1.5°

b 28 × 1.5° = 42°

c 12240

= 120

d Pupils’ pie chart. Check that the angle of each sector is as follows:

Comedy 86 × 1.5 = 129°

Sci-Fi 40 × 1.5° = 60°

Cartoon 64 × 1.5° = 96°

Documentary 12 × 1.5° = 18°

Drama 28 × 1.5° = 42°

Other 10 × 1.5° = 15°



3 a There were 90 customers.

b

Vanilla Strawberry Coffee Chocolate Other

c There are of 90 customers in total, so each customer would be represented by 4°. This makes it easy to draw the pie chart.

d A bar chart shows more clearly which flavours are most popular, as they are represented by the tallest bars. A pie chart shows the proportion of each type of ice cream sold in relation to the total.

4 a

b The modal height group is 300 ≤ h < 400.

c 570

= 114




1 a £3.50

b £2.00

c Yes. Share prices can go up or down hourly/daily but the graph shows the values

only on certain dates.

2 a

b The biggest increase was between 1980 and 1985. The line joining these years is the

steepest on the graph.



3 Graph of distance run against time taken

0

5

10

15

20

25

30

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Distance in metres

Tim

e in

min

utes




1 a 1700 thousand = 1 700 000

b 78%

c 59%

d 1994 and 1998

e 500 000

f 3 500 000

2 a The age group 45–54 years shows the biggest difference between male and female.

This is shown by the biggest difference in the heights of the columns.

b 75+

c The graph shows a gradual increase for both males and females between the ages 19

and 55. The gap between males and females gradually widens up to age 45–54, but in

the age group 55–64 the percentages of males and females eating five or more

portions of fruit and vegetables is nearly the same. After the age of 64, the

percentage decreases for both men and women overall. Over the age of 75, less than

one-quarter of men and women eat five or more portions of fruit and vegetables each

day.

d Age (in years) is considered to be a discrete quantity.

e No. In 2004 the highest percentage is less than 35%.




1 Time T Tally Frequency

30 ≤ T < 35 \\ 2

35 ≤ T < 40 \\\\ \ 6

40 ≤ T < 45 \\\\ \\\\ 9

45 ≤ T < 50 \\\\ \\ 7

50 ≤ T < 55 \\\\ 5

55 ≤ T < 60 \ 1

2 Magnitude M Tally Frequency

6.0 ≤ M < 6.2 \\\\ \\\ 8

6.2 ≤ M <6.4 \\\\ 4

6.4 ≤ M < 6.6 \\\\ \\ 7

6.6 ≤ M < 6.8 \\\\ 4

6.8 ≤ M < 7.0 \\\\ 4

7.0 ≤ M < 7.2 \ 1

7.2 ≤ M <7.4 \\ 2



3 a This is one possible frequency table.

Height H Tally Frequency

0 ≤ H < 5 \\ 2

5 ≤ H < 10 \\\\ \ 6

10 ≤ H < 15 \\\\ \\ 7

15 ≤ H < 20 \\\\ \\\ 8

20 ≤ H < 25 \\ 2

b A possible reason is that 5 class intervals are enough to show the spread of the data

but not too many so there is very low frequency in each class interval.




1 a i 13.7 seconds ii 13.4 seconds

iii 11.5 seconds iv 6.1 seconds

b Time, T seconds Tally Frequency

10 ≤ T < 12 \\\ 3

12 ≤ T < 14 \\\\ 4

14 ≤ T < 16 \\\ 3

16 ≤ T < 18 \\ 2

c i 13.7 seconds ii 12 ≤ t < 14

2 a 20 ≤ t < 24 b 23.35 minutes (or 23 minutes and 21 seconds)

3 a Arm length, A cm Mid-interval value Frequency

40 < A ≤ 45 42.5 4

45 < A ≤ 50 47.5 24

50 < A ≤ 55 52.5 48

55 < A ≤ 60 57.5 14

60 < A ≤ 65 62.5 6

65 < A ≤ 70 67.5 4

b 50 < A ≤ 55 c 52.8 cm




1 a

b 156.1 litres

2 a

b 14 ºC. It might not be accurate because the temperature was not measured then, it

was only estimated from the graph.



3 a

b

c 214.5 g d 188.3 g

e On average the tomatoes grown without fertiliser were a lower mass than those

grown with fertiliser.

4 Generally the trend is for life expectation to increase for both males and females from

1900 to 2030.

There was a dip in life expectation for males around 1930 – 1945. This was due to the

second world war.

In general, the life expectation for females is higher than that for males.

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