What is R9: Percentages?

A percentage is a number of parts per hundred, so p%=p/100. Percentage change is multiplicative: an increase of r% uses multiplier 1+r/100 and a decrease uses 1-r/100.

How many marks are R9 questions worth?

In verified past-paper appearances, R9 questions on Edexcel GCSE Maths 1MA1 have been worth 1–6 marks.

Which past exam papers has R9 appeared in?

R9 has appeared in 80 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as fractions/decimals, multiplicatively; percentages > 100%; percentage change and simple interest

Percentages

Worked answers, methods and verified real exam appearances for R9 on Edexcel GCSE Maths 1MA1.

Explanation

A percentage is a number of parts per hundred, so $p\%=\dfrac{p}{100}$ . Percentage change is multiplicative: an increase of $r\%$ uses multiplier $1+\dfrac{r}{100}$ and a decrease uses $1-\dfrac{r}{100}$ .
Percentages above $100\%$ correspond to multipliers greater than $1$ .
To reverse a change, divide by the multiplier; do not apply the opposite percentage to the changed value.
Simple interest is calculated each year from the original principal, so the yearly interest is constant.
Examiners expect the original amount to be the denominator when calculating percentage change.

Worked example

After a $12\%$ decrease, a machine is worth £704. Find its value before the decrease.

1.A $12\%$ decrease leaves $100\%-12\%=88\%$ .
2.Write $0.88\times\text{original}=704$ .
3.Original $=704\div0.88=800$ .

Answer: £800.

Common mistakes

Don't add $12\%$ to the reduced value when reversing a $12\%$ decrease.
Don't use the new value rather than the original value as the denominator for percentage change.
Don't calculate simple interest from a growing balance as though it were compound interest.

Exam tip

For reverse percentage, write the multiplier equation and divide by the multiplier.

Worked practice

Tier 1 · Easy

Work out

35\%

240

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$84$	2	$35\%=0.35$ , so $0.35\times240=84$ .

Tier 2 · Standard

After a

12\%

decrease, a machine is valued at £704. Work out its value before the decrease.

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	£800	3	A $12\%$ decrease leaves $88\%=0.88$ of the original value. Divide by the multiplier: £ $704/0.88=£800$ .

Tier 3 · Hard

A saver deposits £2500 in an account paying

3.6\%

simple interest each year. After

5

years, a fee equal to

2\%

of the final balance is charged. Calculate the amount left after the fee.

(5)

(Total for Question 3 is 5 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	£2891	5	The yearly simple interest is $0.036\times£2500=£90$ . Over $5$ years this is £450, giving £2950. The fee is $0.02\times£2950=£59$ , so £ $2950-£59=£2891$ remains.

Tier 1 · Easy

Work out

135\%

80

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$108$	2	$135\%=1.35$ , so $1.35\times80=108$ .

Tier 2 · Standard

The price of an item increases from £72 to £81. Work out the percentage increase.

(3)

(Total for Question 5 is 3 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$12.5\%$	3	The increase is £ $81-£72=£9$ . As a fraction of the original price this is $\dfrac{9}{72}=0.125$ , so the percentage increase is $12.5\%$ .

Tier 3 · Hard

An investment earns £378 in simple interest over

3

years at a rate of

4.5\%

per year. Work out the original amount invested.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	£2800	3	Over $3$ years the simple interest is $3\times4.5\%=13.5\%$ of the original amount. Therefore the original amount is £ $378\div0.135=£2800$ .

Tier 2 · Standard

A workshop makes

840

parts in one month. This is

140\%

of the number made in the previous month. Work out the number of parts made in the previous month.

(2)

(Total for Question 7 is 2 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$600$ parts	2	$140\%=1.4$ , so $1.4\times\text{previous number}=840$ . The previous number was $840\div1.4=600$ .

Tier 3 · Hard

Nadia invests £1800 at

4\%

simple interest per year. She invests another amount at

2.5\%

simple interest per year. After

3

years, the total interest from the two investments is £396. Work out the second amount invested.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	£2400	4	The first investment earns $1800\times0.04\times3=£216$ . The second investment therefore earns £ $396-£216=£180$ . Over $3$ years its simple-interest rate is $3\times2.5\%=7.5\%$ , so the second amount is £ $180\div0.075=£2400$ .

Tier 3 · Hard

A quantity is increased by

20\%

and then decreased by

p\%

. Its final value is

108\%

of its original value. Work out

p

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$p=10$	4	The multipliers satisfy $1.20\left(1-\dfrac{p}{100}\right)=1.08$ . Hence $1-\dfrac{p}{100}=1.08\div1.20=0.9$ , so $p=10$ .

Q10

Tier 3 · Hard

A tank is initially

80\%

full. Then

15\%

of the water in it is used. After

102

litres are added, the tank is

92\%

full. Work out the capacity of the tank.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$425$ litres	4	Let the capacity be $C$ litres. After $15\%$ is used, $0.8C\times0.85=0.68C$ litres remain. Therefore $0.68C+102=0.92C$ , so $0.24C=102$ and $C=425$ litres.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-06	3F	Q15	3	Allowed	Foundation	QP MS
2019-11	3F	Q21	3	Allowed	Foundation	QP MS
2024-11	2F	Q17	6	Allowed	Foundation	QP MS
2023-11	3F	Q1	1	Allowed	Foundation	QP MS
2022-06	3F	Q1	1	Allowed	Foundation	QP MS
2021-11	3F	Q1	1	Allowed	Foundation	QP MS
2023-11	1H	Q8	2	Non-calculator	Higher	QP MS
2019-11	2F	Q20	4	Allowed	Foundation	QP MS
2023-11	2H	Q2	4	Allowed	Higher	QP MS
2024-11	2F	Q12	4	Allowed	Foundation	QP MS
2024-11	2F	Q25	4	Allowed	Foundation	QP MS
2019-11	2F	Q3	1	Allowed	Foundation	QP MS
2022-11	3H	Q25	5	Allowed	Higher	QP MS
2024-11	1F	Q1	1	Non-calculator	Foundation	QP MS
2023-06	3F	Q21	5	Allowed	Foundation	QP MS
2022-06	3F	Q30	2	Allowed	Foundation	QP MS
2022-06	3H	Q4	4	Allowed	Higher	QP MS
2019-06	2H	Q9	4	Allowed	Higher	QP MS
2019-06	1F	Q20	3	Non-calculator	Foundation	QP MS
2024-11	3F	Q21	5	Allowed	Foundation	QP MS
2024-11	3F	Q9	5	Allowed	Foundation	QP MS
2024-06	3F	Q1	1	Allowed	Foundation	QP MS
2021-11	1F	Q19	3	Non-calculator	Foundation	QP MS
2021-11	1F	Q1	1	Non-calculator	Foundation	QP MS
2024-06	1F	Q26	5	Non-calculator	Foundation	QP MS
2021-11	1H	Q4	4	Non-calculator	Higher	QP MS
2023-11	1F	Q15	4	Non-calculator	Foundation	QP MS
2019-11	3F	Q15	4	Allowed	Foundation	QP MS
2023-06	1F	Q14	5	Non-calculator	Foundation	QP MS
2023-06	1H	Q7	2	Non-calculator	Higher	QP MS
2024-11	2H	Q6	4	Allowed	Higher	QP MS
2024-06	1H	Q9	1	Non-calculator	Higher	QP MS
2023-06	1F	Q26	2	Non-calculator	Foundation	QP MS
2019-11	1F	Q5	1	Non-calculator	Foundation	QP MS
2024-11	1H	Q9	6	Non-calculator	Higher	QP MS
2022-11	1F	Q18	5	Non-calculator	Foundation	QP MS
2019-06	3H	Q2	3	Allowed	Higher	QP MS
2023-06	2F	Q19	5	Allowed	Foundation	QP MS
2024-06	2F	Q18	3	Allowed	Foundation	QP MS
2022-06	2F	Q5	1	Allowed	Foundation	QP MS
2024-11	3H	Q12	6	Allowed	Higher	QP MS
2019-06	3H	Q10	3	Allowed	Higher	QP MS
2019-06	1H	Q12	3	Non-calculator	Higher	QP MS
2022-11	2F	Q2	1	Allowed	Foundation	QP MS
2024-06	1F	Q27	2	Non-calculator	Foundation	QP MS
2024-06	1H	Q7	5	Non-calculator	Higher	QP MS
2022-06	2F	Q19	5	Allowed	Foundation	QP MS
2023-06	2F	Q25	3	Allowed	Foundation	QP MS
2022-06	3H	Q10	3	Allowed	Higher	QP MS
2023-06	2H	Q6	3	Allowed	Higher	QP MS
2024-11	3H	Q5	5	Allowed	Higher	QP MS
2021-11	2F	Q28	2	Allowed	Foundation	QP MS
2023-06	3F	Q2	1	Allowed	Foundation	QP MS
2024-11	3H	Q10	2	Allowed	Higher	QP MS
2023-06	2F	Q27	4	Allowed	Foundation	QP MS
2023-06	3H	Q2	5	Allowed	Higher	QP MS
2024-11	2F	Q1	1	Allowed	Foundation	QP MS
2019-06	3F	Q23	5	Allowed	Foundation	QP MS
2021-11	2F	Q1	1	Allowed	Foundation	QP MS
2021-11	2F	Q17	5	Allowed	Foundation	QP MS
2023-06	3F	Q19	3	Allowed	Foundation	QP MS
2022-06	1F	Q19	3	Non-calculator	Foundation	QP MS
2022-11	2F	Q26	2	Allowed	Foundation	QP MS
2021-11	1F	Q23	4	Non-calculator	Foundation	QP MS
2022-11	2H	Q8	3	Allowed	Higher	QP MS
2019-06	1F	Q2	1	Non-calculator	Foundation	QP MS
2024-06	1F	Q2	1	Non-calculator	Foundation	QP MS
2023-06	3H	Q9	2	Allowed	Higher	QP MS
2019-11	2F	Q16	2	Allowed	Foundation	QP MS
2023-06	1F	Q17	4	Non-calculator	Foundation	QP MS
2019-06	3F	Q5	1	Allowed	Foundation	QP MS
2023-11	3F	Q14	2	Allowed	Foundation	QP MS
2022-06	3F	Q19	4	Allowed	Foundation	QP MS
2021-11	3F	Q13	4	Allowed	Foundation	QP MS
2023-11	2F	Q23	4	Allowed	Foundation	QP MS
2023-11	1F	Q16	2	Non-calculator	Foundation	QP MS
2022-11	2F	Q11	4	Allowed	Foundation	QP MS
2023-06	1F	Q1	1	Non-calculator	Foundation	QP MS
2022-06	3F	Q25	4	Allowed	Foundation	QP MS
2024-06	2F	Q15	2	Allowed	Foundation	QP MS

Other points in R Ratio, proportion and rates of change

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