What is R11: Compound measures?

Write the formula before substituting: speed=distance/time, density=mass/volume, pressure=force/area. Rates of pay and unit prices are a total divided by the hours or the number of items.

How many marks are R11 questions worth?

In verified past-paper appearances, R11 questions on Edexcel GCSE Maths 1MA1 have been worth 2–7 marks.

Which past exam papers has R11 appeared in?

R11 has appeared in 85 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

R11

Use compound units such as speed, rates of pay, unit pricing, density and pressure

Compound measures

Worked answers, methods and verified real exam appearances for R11 on Edexcel GCSE Maths 1MA1.

Definition

Specification R11: use compound units such as speed, rates of pay, unit pricing, density and pressure. A compound unit is a rate formed from two quantities, so its name states the division: metres per second, grams per cubic centimetre, newtons per square metre.

Explanation

Write the formula before substituting: $\text{speed}=\dfrac{\text{distance}}{\text{time}}$ , $\text{density}=\dfrac{\text{mass}}{\text{volume}}$ , $\text{pressure}=\dfrac{\text{force}}{\text{area}}$ . Rates of pay and unit prices are a total divided by the hours or the number of items.
Make the units match the unit you must answer in before you calculate: $180$ km per hour becomes metres per second by multiplying by $1000$ and dividing by $3600$ . Rearrange when the unknown is not the subject; mass is density multiplied by volume, and time is distance divided by speed.
Multi-step problems chain these: mass and density give a volume, subtracting a known volume gives the volume of the remaining material, and dividing its mass by that volume gives its density.
The unit in the question tells you which quantity is divided by which.
State the unit with the value; some schemes award it a separate mark.

Worked example

A solid metal block has mass

18.9

kg and volume

0.0075

^3

. Work out the density of the metal. Give the units with your answer.

(3)

(Total for Question 1 is 3 marks)

Working

1.Density is mass divided by volume: $\text{density}=\dfrac{18.9}{0.0075}$ .
2.Multiply numerator and denominator by $10\,000$ to clear the decimal: $\dfrac{189\,000}{75}$ .
3.Divide: $189\,000\div75=2520$ .
4.The mass is in kilograms and the volume in cubic metres, so the unit is kg/m $^3$ .

Answer: $2520$ kg/m $^3$

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Additional guidance
1	for a process to find the density, eg $18.9\div0.0075$	P1	oe
	for $2520$	A1	Ignore incorrect or absent units for this mark
	(indep) for kg/m $^3$	B1	Ignore incorrect or absent numerical answer for this mark

Common mistakes

Don't divide volume by mass when calculating density.
Don't substitute minutes into a formula when the requested speed is per hour.
Don't give a numerical answer without the required compound unit.

Mark-scheme wording to use

“for conversion from km per hour to metres per second, … for a complete process eg 180 × 1000 ÷ 3600 … cao” — Pearson 1MA1, November 2022 Paper 3H, Q7(b)
“for process to find volume of tin eg 600 ÷ 0.6 (= 1000) … for process to find volume of salt eg “1000” – 700 (= 300) … for a process to find density of the salt eg 600 ÷ “300”” — Pearson 1MA1, June 2024 Paper 3H, Q5
“P1 start to process eg. 3 × 80 (=240) P1 ‘240’ ÷ 5” — Pearson 1MA1, Sample Paper 1H, Q4(a)

What the examiner wants

Each stage of the process written down, with the right quantity on top. The June 2024 Paper 3H report says most students divided mass by density to find a volume, but many did not see that the remaining volume was that answer minus $700$ , and a surprising number wrote $600/300$ and gave $0.5$ or $0.2$ instead of $2$ .

Exam tip

Write the compound-unit formula first, because a correct formula can earn a method mark despite arithmetic error.

Worked practice

Tier 1 · Easy

A shift lasting

7

hours pays £52.50. Work out the hourly rate of pay.

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	£7.50 per hour	2	Divide total pay by time: £ $52.50/7=£7.50$ per hour.

Tier 2 · Standard

A coach travels

156\,\text{km}

2

hours

24

minutes. Calculate its average speed in

\text{km}/\text{h}

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$65\,\text{km}/\text{h}$	3	$24$ minutes is $24/60=0.4$ hours, so the time is $2.4$ hours. Average speed is $156/2.4=65\,\text{km}/\text{h}$ .

Tier 3 · Hard

A force of

3.6\,\text{kN}

acts uniformly on a rectangular pad measuring

24\,\text{cm}

15\,\text{cm}

. Calculate the pressure in pascals, where

1\,\text{Pa}=1\,\text{N}/\text{m}^2

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$100\,000\,\text{Pa}$	4	Convert the force to $3600\,\text{N}$ and the dimensions to $0.24\,\text{m}$ and $0.15\,\text{m}$ . The area is $0.24\times0.15=0.036\,\text{m}^2$ , so the pressure is $3600/0.036=100\,000\,\text{Pa}$ .

Tier 1 · Easy

A machine packs

54

cartons in

6

minutes. Work out the rate in cartons per minute.

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$9$ cartons per minute	2	Divide the number of cartons by the time: $54\div6=9$ cartons per minute.

Tier 2 · Standard

A material has mass

5.46\,\text{kg}

and density

780\,\text{kg}/\text{m}^3

. Work out its volume.

(3)

(Total for Question 5 is 3 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$0.007\,\text{m}^3$	3	From $\text{density}=\dfrac{\text{mass}}{\text{volume}}$ , volume $=\dfrac{\text{mass}}{\text{density}}$ . Therefore the volume is $5.46\div780=0.007\,\text{m}^3$ .

Tier 3 · Hard

A printer uses

0.45

litres of ink to print

18\,000

pages, and the ink costs £28 per litre. Work out the ink cost per

1000

pages.

(4)

(Total for Question 6 is 4 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	£0.70 per $1000$ pages	4	The ink used per $1000$ pages is $0.45\div18=0.025$ litres. The cost is $0.025\times£28=£0.70$ per $1000$ pages.

Tier 2 · Standard

750\,\text{g}

pack of cereal costs £3.30. A

1.2\,\text{kg}

pack costs £5.16. Work out which pack is better value and by how much per kilogram.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	The $1.2\,\text{kg}$ pack, by £0.10 per kilogram	3	The smaller pack costs £ $3.30\div0.75=£4.40$ per kilogram. The larger pack costs £ $5.16\div1.2=£4.30$ per kilogram. The $1.2\,\text{kg}$ pack is cheaper by £ $4.40-£4.30=£0.10$ per kilogram.

Tier 3 · Hard

A technician works

40

hours in one week. The first

36

hours are paid at £12.40 per hour and the remaining hours are paid at one and a half times this rate. Work out the technician's average rate of pay for the week.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	£13.02 per hour	4	The overtime rate is $1.5\times£12.40=£18.60$ per hour. The total pay is $36\times£12.40+4\times£18.60=£446.40+£74.40=£520.80$ . The average rate is £ $520.80\div40=£13.02$ per hour.

Tier 3 · Hard

A driver travels

72\,\text{km}

48\,\text{km}/\text{h}

, stops for

18

minutes, then travels

96\,\text{km}

64\,\text{km}/\text{h}

. Work out the average speed for the whole journey, including the stop. Round your answer to the nearest

0.1\,\text{km}/\text{h}

(5)

(Total for Question 9 is 5 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$50.9\,\text{km}/\text{h}$	5	The travel times are $72\div48=1.5$ hours and $96\div64=1.5$ hours. The stop is $18\div60=0.3$ hours, so the total time is $3.3$ hours and the distance is $168\,\text{km}$ . The average speed is $168\div3.3=50.909\ldots$ , which rounds to $50.9\,\text{km}/\text{h}$ . This is $0.0409\ldots$ from the upper rounding boundary $50.95$ , a margin of more than $0.03\,\text{km}/\text{h}$ .

Q10

Tier 3 · Hard

A cuboid has dimensions

0.5\,\text{m}

0.25\,\text{m}

0.08\,\text{m}

and density

2400\,\text{kg}/\text{m}^3

. It rests on its

0.5\,\text{m}

0.25\,\text{m}

face. Work out the pressure it exerts on the floor. Use

10\,\text{N}/\text{kg}

for gravitational field strength.

(5)

(Total for Question 10 is 5 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$1920\,\text{Pa}$	5	The volume is $0.5\times0.25\times0.08=0.01\,\text{m}^3$ , so the mass is $2400\times0.01=24\,\text{kg}$ . Its weight is $24\times10=240\,\text{N}$ . The contact area is $0.5\times0.25=0.125\,\text{m}^2$ , so the pressure is $240\div0.125=1920\,\text{Pa}$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2023-06	3H	Q6	3	Allowed	Higher	QP MS
2019-06	3H	Q13	4	Allowed	Higher	QP MS
2024-11	2F	Q22	3	Allowed	Foundation	QP MS
2024-11	1H	Q8	3	Non-calculator	Higher	QP MS
2023-11	2F	Q14	4	Allowed	Foundation	QP MS
2023-11	3F	Q27	3	Allowed	Foundation	QP MS
2019-11	3H	Q13	4	Allowed	Higher	QP MS
2019-11	2F	Q10	3	Allowed	Foundation	QP MS
2019-11	1H	Q9	4	Non-calculator	Higher	QP MS
2024-11	2H	Q12	5	Allowed	Higher	QP MS
2021-11	3H	Q4	4	Allowed	Higher	QP MS
2022-06	2F	Q27	4	Allowed	Foundation	QP MS
2022-06	3H	Q6	4	Allowed	Higher	QP MS
2019-06	3F	Q22	4	Allowed	Foundation	QP MS
2024-06	1H	Q5	4	Non-calculator	Higher	QP MS
2022-11	3H	Q25	5	Allowed	Higher	QP MS
2023-11	2F	Q28	4	Allowed	Foundation	QP MS
2024-11	1F	Q9	7	Non-calculator	Foundation	QP MS
2022-06	2H	Q9	3	Allowed	Higher	QP MS
2022-06	3H	Q4	4	Allowed	Higher	QP MS
2024-06	3H	Q5	4	Allowed	Higher	QP MS
2023-11	1F	Q13	4	Non-calculator	Foundation	QP MS
2024-06	2F	Q14	5	Allowed	Foundation	QP MS
2024-06	1F	Q16	3	Non-calculator	Foundation	QP MS
2024-11	1F	Q22	4	Non-calculator	Foundation	QP MS
2022-11	2H	Q23	5	Allowed	Higher	QP MS
2021-11	1F	Q14	4	Non-calculator	Foundation	QP MS
2024-11	2H	Q3	3	Allowed	Higher	QP MS
2023-06	3H	Q8	2	Allowed	Higher	QP MS
2023-06	3F	Q25	3	Allowed	Foundation	QP MS
2023-06	1H	Q8	3	Non-calculator	Higher	QP MS
2022-11	3F	Q15	5	Allowed	Foundation	QP MS
2019-06	1F	Q9	4	Non-calculator	Foundation	QP MS
2022-06	1F	Q29	3	Non-calculator	Foundation	QP MS
2023-06	2F	Q18	6	Allowed	Foundation	QP MS
2022-06	1H	Q7	3	Non-calculator	Higher	QP MS
2019-11	2F	Q14	3	Allowed	Foundation	QP MS
2024-11	2F	Q28	3	Allowed	Foundation	QP MS
2019-11	1F	Q16	3	Non-calculator	Foundation	QP MS
2023-06	2F	Q16	3	Allowed	Foundation	QP MS
2022-11	1H	Q7	2	Non-calculator	Higher	QP MS
2023-11	2F	Q6	2	Allowed	Foundation	QP MS
2019-11	1F	Q27	5	Non-calculator	Foundation	QP MS
2023-06	3F	Q14	4	Allowed	Foundation	QP MS
2023-11	3H	Q8	3	Allowed	Higher	QP MS
2021-11	2F	Q14	3	Allowed	Foundation	QP MS
2022-11	3F	Q27	4	Allowed	Foundation	QP MS
2023-06	3F	Q13	5	Allowed	Foundation	QP MS
2019-11	1H	Q8	5	Non-calculator	Higher	QP MS
2022-11	1F	Q14	5	Non-calculator	Foundation	QP MS
2022-06	3F	Q27	4	Allowed	Foundation	QP MS
2023-11	1F	Q25	2	Non-calculator	Foundation	QP MS
2019-11	3H	Q6	4	Allowed	Higher	QP MS
2021-11	3F	Q22	4	Allowed	Foundation	QP MS
2022-06	2F	Q24	5	Allowed	Foundation	QP MS
2022-11	1F	Q25	2	Non-calculator	Foundation	QP MS
2023-11	3F	Q17	3	Allowed	Foundation	QP MS
2021-11	3H	Q2	4	Allowed	Higher	QP MS
2023-11	3H	Q7	3	Allowed	Higher	QP MS
2023-06	3F	Q27	2	Allowed	Foundation	QP MS
2019-06	3H	Q11	3	Allowed	Higher	QP MS
2022-11	3F	Q19	4	Allowed	Foundation	QP MS
2024-06	2F	Q9	4	Allowed	Foundation	QP MS
2024-06	3F	Q28	4	Allowed	Foundation	QP MS
2023-06	1F	Q27	3	Non-calculator	Foundation	QP MS
2024-11	3F	Q14	4	Allowed	Foundation	QP MS
2021-11	2F	Q23	5	Allowed	Foundation	QP MS
2021-11	3F	Q11	3	Allowed	Foundation	QP MS
2021-11	3F	Q24	4	Allowed	Foundation	QP MS
2019-11	3F	Q27	4	Allowed	Foundation	QP MS
2022-06	2H	Q4	5	Allowed	Higher	QP MS
2024-06	1H	Q3	5	Non-calculator	Higher	QP MS
2022-11	3H	Q7	4	Allowed	Higher	QP MS
2019-06	2F	Q18	4	Allowed	Foundation	QP MS
2024-06	3F	Q26	4	Allowed	Foundation	QP MS
2021-11	2H	Q7	3	Allowed	Higher	QP MS
2022-11	2F	Q13	4	Allowed	Foundation	QP MS
2024-06	3H	Q7	4	Allowed	Higher	QP MS
2022-06	2H	Q7	4	Allowed	Higher	QP MS
2022-06	1F	Q16	4	Non-calculator	Foundation	QP MS
2024-11	1H	Q5	4	Non-calculator	Higher	QP MS
2023-11	3F	Q26	3	Allowed	Foundation	QP MS
2021-11	2H	Q3	5	Allowed	Higher	QP MS
2023-11	2F	Q12	2	Allowed	Foundation	QP MS
2022-06	3F	Q25	4	Allowed	Foundation	QP MS

Other points in R Ratio, proportion and rates of change

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