Revision Library

revisionlibrary.co.uk

HIGHER

H17 Comparative and Proportional Pie Charts

EDEXCEL 1ST0 · Calculator allowed · about 90 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A gym surveyed 180 members to find out which exercise class was their favourite. The results are shown in the table below.

Class	Yoga	Spin	Pilates	Zumba
Frequency	45	63	27	45

A pie chart is going to be drawn to show this information.

(a)Work out the sector angle for the Spin category.(2)

(b)Work out the sector angle for the Pilates category.(2)

(c)Show that the four sector angles for the pie chart add up to 360 degrees.(1)

(Total for Question 1 is 5 marks)

The pie chart shows how 120 visitors travelled to a museum one day. The sector angles for Foot, Car and Train are marked on the chart. The angle for Bus is not given.

(a)Work out the sector angle representing Bus.(2)

(b)Work out how many of the 120 visitors travelled to the museum by car.(2)

(c)Work out the percentage of visitors who travelled to the museum by train.(2)

(Total for Question 2 is 6 marks)

Club P has 40 members, split by favourite activity as follows: Football 16 members, Netball 14 members, Athletics 10 members. A pie chart is to be drawn to show this information.

(a)Work out the sector angle for Football.(1)

(b)Work out the sector angle for Netball.(1)

(c)Work out the sector angle for Athletics.(1)

(Total for Question 3 is 3 marks)

For each statement about drawing comparative pie charts, write down whether it is True or False.

(i)To fairly compare two data sets of different totals using pie charts, the radii of the two circles should be drawn in direct proportion to the totals (for example, if one total is double the other, its radius should be double).(1)

(ii)The correct method is to choose the radii so that the ratio of the two circles' areas is equal to the ratio of the two totals.(1)

(iii)If total2 : total1 = 9 : 1, the two pie charts should be drawn with radii in the ratio r2 : r1 = 3 : 1.(1)

(iv)Two categories that make up the same percentage of their own pie chart will always be drawn with sectors of the same angle, and the same area, even if the two pie charts have different radii.(1)

(Total for Question 4 is 4 marks)

A student wants to draw two pie charts to compare the number of items sold last month in Shop A (total 40 items) and Shop B (total 160 items). She says: 'Shop B sold 4 times as many items as Shop A, so I will make the radius of Shop B's circle 4 times the radius of Shop A's circle.'

(a)Explain why the student's method will not give a fair visual comparison between the two shops.(2)

(b)Shop A's pie chart is drawn with radius 3 cm. Work out the radius that should be used for Shop B's pie chart.(2)

(Total for Question 5 is 4 marks)

In a survey, Village A had 60 respondents and its results are shown on a pie chart of radius 3.5 cm. Village B, in the same survey, had 140 respondents. Work out the radius that should be used for Village B's pie chart, giving your answer correct to 1 decimal place.

(Total for Question 6 is 3 marks)

A cinema compares ticket sales for two screens on the same evening. Screen 1 sold tickets to 80 people and its pie chart is drawn with radius 4 cm. Screen 2 sold tickets to 245 people. Work out the radius that should be used for Screen 2's pie chart.

(Total for Question 7 is 3 marks)

Two pie charts, drawn to compare two data sets, have radii in the ratio r2 : r1 = 5 : 3. Work out the ratio of the two totals, total2 : total1, giving your answer in its simplest form.

(Total for Question 8 is 2 marks)

Year 10 has 288 pupils and its results in a travel survey are shown on a pie chart of radius 8 cm. Year 11's results, from the same survey, are shown on a pie chart of radius 6 cm. Work out the number of pupils in Year 11.

(Total for Question 9 is 3 marks)

A charity records total donations collected in 2024 and 2025.

Category	Direct Debit	Events	Shop	Legacies
2024 donations (GBP)	3200	2000	1600	1200

The total donations in 2024 were GBP 8000, and the 2024 pie chart is drawn with radius 5 cm. Total donations in 2025 were GBP 12500.

(a)Work out the sector angle representing Direct Debit donations in the 2024 pie chart.(2)

(b)Work out the radius that should be used for the 2025 pie chart, giving your answer correct to 2 decimal places.(3)

(c)In 2025, Legacies donations totalled GBP 3750. Work out the sector angle for Legacies in the 2025 pie chart, and use it to determine whether the proportion of donations from Legacies increased or decreased between 2024 and 2025.(4)

(Total for Question 10 is 9 marks)

Two branches of a bakery record the type of loaf sold one morning.

Branch	White	Wholemeal	Sourdough
Branch 1 (total 72 loaves)	30	24	18
Branch 2 (total 128 loaves)	40	56	32

(a)Work out the sector angles for Branch 1's pie chart (White, Wholemeal, Sourdough).(3)

(b)Branch 1's pie chart is drawn with radius 4.5 cm. Work out the radius that should be used for Branch 2's pie chart.(3)

(c)Work out the sector angles for Branch 2's pie chart (White, Wholemeal, Sourdough).(3)

(d)On the grid provided, draw comparative pie charts for Branch 1 and Branch 2, using your answers to parts (a) to (c). Label each sector.(3)

(Total for Question 11 is 12 marks)

A student wants to investigate whether the way pupils travel to school differs between Year 7 and Year 9 at her school. She plans to survey a sample of pupils from each year group and display the results using comparative pie charts.

(a)Write down two features the student's survey should include so that the comparison between Year 7 and Year 9 is fair and the results are reliable.(2)

(b)50 pupils in Year 7 were surveyed: Walk 20, Bus 15, Car 10, Cycle 5. Work out the sector angles for Year 7's pie chart.(4)

(c)Year 9 has 98 pupils. Year 7's pie chart is drawn with radius 4 cm. Work out the radius that should be used for Year 9's pie chart.(3)

(d)In Year 9, 28 pupils walk to school. Determine whether the proportion of pupils who walk to school is higher, lower, or the same in Year 9 compared with Year 7. Show your working.(3)

(Total for Question 12 is 12 marks)

Town A (90 households, pie chart radius 3 cm) and Town B (250 households, pie chart radius 5 cm) were surveyed about how often they recycle paper. The comparative pie charts below show the results, with each sector angle marked.

(a)Use the pie chart to work out the percentage of households in Town A that recycle regularly.(2)

(b)Use the pie chart to work out the number of households in Town B that recycle regularly.(2)

(c)A student says: 'Town A's sector for Recycle regularly takes up a bigger share of its pie chart than Town B's, so more households in Town A recycle regularly than in Town B.' Using your answers to parts (a) and (b), comment on whether the student is correct.(3)

(d)Given that Town A's pie chart has radius 3 cm, work out the radius that should be used for Town B's pie chart.(3)

(Total for Question 13 is 10 marks)

In a traffic survey, Junction A recorded 30% more vehicles than Junction B. Junction B's pie chart has radius 5 cm.

(a)Work out the radius that should be used for Junction A's pie chart, giving your answer correct to 2 decimal places.(3)

(b)A different student works out the radius by increasing 5 cm by 30%, giving 6.5 cm. Explain why this method is incorrect.(2)

(Total for Question 14 is 5 marks)

Two departments in a company recorded the reason for sick-leave requests over a year.

Reason	Illness	Injury	Stress	Other
Department X (total 45 requests)	18	9	13	5
Department Y (total 80 requests)	20	24	28	8

(a)Work out the sector angles for Department X's pie chart.(4)

(b)Department X's pie chart is drawn with radius 3.6 cm. Work out the radius that should be used for Department Y's pie chart, giving your answer correct to 1 decimal place.(3)

(c)Work out the sector angles for Department Y's pie chart.(4)

(Total for Question 15 is 11 marks)

Department X (total 45 sick-leave requests, pie chart radius 3.6 cm) and Department Y (total 80 requests, pie chart radius 4.8 cm) are described in Question 15.

(a)By comparing percentages, determine which department has the greater proportion of its sick-leave requests due to Stress, and state by how many percentage points the proportions differ.(3)

(b)On the grid provided, draw comparative pie charts for Department X and Department Y, using your answers to Question 15 parts (a) to (c). Label each sector.(3)

(Total for Question 16 is 6 marks)

Mark scheme · H17 Comparative and Proportional Pie Charts

Question 1

(a) M1 63/180 x 360, oe
(a) A1 126 (degrees) cao
(a) Answer: 126 degrees
(b) M1 27/180 x 360, oe
(b) A1 54 (degrees) cao
(b) Answer: 54 degrees
(c) B1 90 + 126 + 54 + 90 = 360, with the Yoga and Zumba angles (each 45/180 x 360 = 90) also shown
(c) Answer: 90 + 126 + 54 + 90 = 360

Question 2

(a) M1 360 - (108 + 126 + 54), oe
(a) A1 72 (degrees) cao
(a) Answer: 72 degrees
(b) M1 126/360 x 120, oe
(b) A1 42 cao
(b) Answer: 42
(c) M1 54/360 x 100, oe
(c) A1 15% cao
(c) Answer: 15%

Question 3

(a) B1 144 (degrees) cao
(a) Answer: 144 degrees
(b) B1 126 (degrees) cao
(b) Answer: 126 degrees
(c) B1 90 (degrees) cao
(c) Answer: 90 degrees

Question 4

(i) B1 False cao
(i) Answer: False
(ii) B1 True cao
(ii) Answer: True
(iii) B1 True cao
(iii) Answer: True
(iv) B1 False cao
(iv) Answer: False

Question 5

(a) E1 recognises that the area of a circle is proportional to the square of its radius, not the radius itself
(a) E1 so multiplying the radius by 4 multiplies the area (the apparent size of Shop B's data) by 4 squared = 16, not by 4, making Shop B look far bigger than is fair
(a) Answer: A radius 4 times as large gives an area 16 times as large, not 4 times, so Shop B's chart would look unfairly large.
(b) M1 √160/40, oe
(b) A1 6 cm cao
(b) Answer: 6 cm

Question 6

M1 140/60, oe (finds the ratio of totals)
M1 √their ratio, dependent on the first mark
A1 5.3 (cm), awrt cao
Answer: 5.3 cm

Question 7

M1 245/80, oe (= 3.0625)
M1 √3.0625, dependent on the first mark
A1 7 (cm) cao
Answer: 7 cm

Question 8

M1 total2:total1 = (r2:r1)², oe, e.g. 5² : 3²
A1 25 : 9 cao
Answer: 25 : 9

Question 9

M1 (6/8)², oe (= 0.5625)
M1 288 x their 0.5625, dependent on the first mark
A1 162 cao
Answer: 162

Question 10

(a) M1 3200/8000 x 360, oe
(a) A1 144 (degrees) cao
(a) Answer: 144 degrees
(b) M1 12500/8000, oe (= 1.5625)
(b) M1 √1.5625, dependent on the first mark
(b) A1 6.25 (cm) cao
(b) Answer: 6.25 cm
(c) M1 3750/12500 x 360, oe
(c) A1 108 (degrees) cao
(c) M1 1200/8000 x 360, oe (= 54 degrees, the 2024 Legacies angle)
(c) A1 'increased', with correct comparison (54 degrees / 15% in 2024 rising to 108 degrees / 30% in 2025) cao
(c) Answer: Increased, from 54 degrees (15%) in 2024 to 108 degrees (30%) in 2025

Question 11

(a) B1 White: 150 degrees
(a) B1 Wholemeal: 120 degrees
(a) B1 Sourdough: 90 degrees
(a) Answer: White 150 degrees, Wholemeal 120 degrees, Sourdough 90 degrees
(b) M1 128/72, oe (= 16/9)
(b) M1 √16/9, dependent on the first mark (= 4/3)
(b) A1 6 (cm) cao
(b) Answer: 6 cm
(c) B1 White: 112.5 degrees
(c) B1 Wholemeal: 157.5 degrees
(c) B1 Sourdough: 90 degrees
(c) Answer: White 112.5 degrees, Wholemeal 157.5 degrees, Sourdough 90 degrees
(d) B1 Branch 1 pie chart drawn with radius 4.5 cm and sectors at 150, 120 and 90 degrees (± 2 degrees)
(d) B1 Branch 2 pie chart drawn with radius 6 cm and sectors at 112.5, 157.5 and 90 degrees (± 2 degrees)
(d) B1 both pie charts fully labelled with categories and a title/key so the branches can be compared
(d) Answer: Two pie charts: Branch 1 (radius 4.5 cm, sectors 150 deg / 120 deg / 90 deg) and Branch 2 (radius 6 cm, sectors 112.5 deg / 157.5 deg / 90 deg).

Question 12

(a) B1 asks pupils in both year groups the same closed question, with the same fixed list of travel-method categories, oe
(a) B1 surveys a large enough, randomly chosen sample from each year group (not just one class), so the results are representative, oe
(a) Answer: Use the same closed question/categories for both year groups, and survey a large, representative sample from each.
(b) B1 Walk: 144 degrees
(b) B1 Bus: 108 degrees
(b) B1 Car: 72 degrees
(b) B1 Cycle: 36 degrees
(b) Answer: Walk 144 degrees, Bus 108 degrees, Car 72 degrees, Cycle 36 degrees
(c) M1 98/50, oe (= 1.96)
(c) M1 √1.96, dependent on the first mark
(c) A1 5.6 (cm) cao
(c) Answer: 5.6 cm
(d) M1 20/50 x 100, oe (= 40%, Year 7)
(d) M1 28/98 x 100, oe (awrt 28.6%, Year 9)
(d) A1 'lower', with correct comparison (28.6% compared with 40%) cao
(d) Answer: Lower (about 28.6% in Year 9 compared with 40% in Year 7)

Question 13

(a) M1 216/360 x 100, oe
(a) A1 60% cao
(a) Answer: 60%
(b) M1 144/360 x 250, oe
(b) A1 100 cao
(b) Answer: 100
(c) B1 states the student is correct about the PROPORTION: Town A has a higher percentage of households recycling regularly (60%) than Town B (40%)
(c) B1 but Town B actually has more households recycling regularly in absolute number: 100 households (part b), compared with 54 in Town A (60% of 90), allow ft from (a)/(b)
(c) B1 concludes the student's overall claim about the NUMBER of households is incorrect, because Town B's total number of households surveyed is much larger, so a smaller percentage there still represents more people
(c) Answer: The student is right about the proportion (60% vs 40%) but wrong about the actual numbers: Town B has more households (100) recycling regularly than Town A (54).
(d) M1 250/90, oe (= 25/9)
(d) M1 √25/9, dependent on the first mark (= 5/3)
(d) A1 5 (cm) cao
(d) Answer: 5 cm

Question 14

(a) M1 1.3, oe (identifies the ratio of totals as 130/100)
(a) M1 √1.3, dependent on the first mark
(a) A1 5.70 (cm), awrt cao
(a) Answer: 5.70 cm
(b) E1 recognises the method wrongly applies the percentage increase in the TOTAL directly to the RADIUS, as if radius and total were directly proportional
(b) E1 explains that only the AREA (not the radius) should increase in proportion to the total, so the radius should increase by √1.3, about 14%, not by 30%, meaning 6.5 cm is too large
(b) Answer: The method incorrectly increases the radius by the same 30% as the total; the radius should only increase by √1.3, about 14%, giving 5.70 cm, not 6.5 cm.

Question 15

(a) B1 Illness: 144 degrees
(a) B1 Injury: 72 degrees
(a) B1 Stress: 104 degrees
(a) B1 Other: 40 degrees
(a) Answer: Illness 144 degrees, Injury 72 degrees, Stress 104 degrees, Other 40 degrees
(b) M1 80/45, oe (= 16/9)
(b) M1 √16/9, dependent on the first mark (= 4/3)
(b) A1 4.8 (cm) cao
(b) Answer: 4.8 cm
(c) B1 Illness: 90 degrees
(c) B1 Injury: 108 degrees
(c) B1 Stress: 126 degrees
(c) B1 Other: 36 degrees
(c) Answer: Illness 90 degrees, Injury 108 degrees, Stress 126 degrees, Other 36 degrees

Question 16

(a) M1 13/45 x 100, oe (awrt 28.9%, Department X)
(a) M1 28/80 x 100, oe (= 35%, Department Y)
(a) A1 'Department Y', with a correct difference of awrt 6.1 percentage points cao
(a) Answer: Department Y, by about 6.1 percentage points (35% compared with 28.9%)
(b) B1 Department X pie chart drawn with radius 3.6 cm and sectors at 144, 72, 104 and 40 degrees (± 2 degrees)
(b) B1 Department Y pie chart drawn with radius 4.8 cm and sectors at 90, 108, 126 and 36 degrees (± 2 degrees)
(b) B1 both pie charts fully labelled with categories and a title/key so the departments can be compared
(b) Answer: Two pie charts: Department X (radius 3.6 cm, sectors 144/72/104/40 degrees) and Department Y (radius 4.8 cm, sectors 90/108/126/36 degrees).

Comparative and Proportional Pie Charts - Worksheets, Questions and Revision