Percentages and percentage change - Edexcel GCSE Maths (Calculator) Exam Questions

Practise 36 exam-style questions on Percentages and percentage change for Edexcel GCSE Maths (Calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.

36 questions
1–5 marks each
Instant marking
No sign-up needed

20 questions, marked as you go

Sample questions with model answers

Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.

Question 1

2 marks

Work out 17.5% of £86.40

Model answer

17.5% = 0.175
0.175 × 86.40 = £15.12

Explanation

Write the percentage as a decimal (divide by 100) and multiply. On a calculator, 0.175 × 86.40 is quickest; without one you could build it up from 10%, 5% and 2.5%. Give money answers to 2 decimal places.

Mark scheme

1 mark
M1 for \(0.175 \times 86.40\) or \(\frac{17.5}{100} \times 86.40\)
oe, e.g. 10% + 5% + 2.5% = 8.64 + 4.32 + 2.16
1 mark
A1 for £15.12
cao; correct answer with no working scores full marks

Question 2

2 marks

A bank increases its interest rate from 4% to 5%.

Jo says, "The interest rate has increased by 1%."

Jo is wrong. Work out the actual percentage increase in the interest rate.

Model answer

Increase = 5 − 4 = 1 percentage point
Percentage increase = \(\frac{1}{4} \times 100 = 25\%\)
The rate has increased by 1 percentage point, which is a 25% increase.

Explanation

When the quantity itself is a percentage, the difference (1) is in "percentage points". The percentage increase compares the change with the original rate: 1 ÷ 4 = 0.25 = 25%. So on £1000 the yearly interest rises from £40 to £50, which is 25% more.

Mark scheme

1 mark
M1 for \(\frac{5 - 4}{4} \times 100\) or \(\frac{1}{4} \times 100\)
oe; correct answer with no working scores full marks
1 mark
A1 for 25%
cao; accept a correct explanation that the rate has gone up by 1 percentage point, which is a 25% increase

Question 3

3 marks

Three shops sell the same jacket.
The table shows the normal price and the offer in each shop.

In which shop is the jacket cheapest?
You must show your working.

Table with columns "Shop", "Normal price", "Offer". Shop: A; Normal price: £68.00; Offer: 25% off | Shop: B; Normal price: £72.00; Offer: 1/3 off | Shop: C; Normal price: £61.50; Offer: £14 off.

Model answer

Shop A: 75% of £68 = 0.75 × 68 = £51
Shop B: \(\frac{2}{3}\) of £72 = £48
Shop C: 61.50 − 14 = £47.50
The jacket is cheapest in Shop C.

Explanation

Work out the actual price in each shop before comparing: a percentage, a fraction and an amount of money off cannot be compared directly. "25% off" leaves 75% and "\(\frac{1}{3}\) off" leaves \(\frac{2}{3}\) of the price.

Mark scheme

1 mark
M1 for a correct offer price in one shop, e.g. Shop A: 0.75 × 68 = £51
1 mark
M1 for correct offer prices in all three shops: £51, £48 and £47.50
1 mark
C1 for Shop C, with correct supporting figures

Question 4

4 marks

The price of a bike is increased by \(x\%\).
The new price is then decreased by \(x\%\).
The final price is 6.25% less than the original price.

Work out the value of \(x\).

Model answer

\(\left(1 + \frac{x}{100}\right)\left(1 - \frac{x}{100}\right) = 1 - 0.0625 = 0.9375\)
\(1 - \frac{x^2}{10000} = 0.9375\)
\(\frac{x^2}{10000} = 0.0625\)
\(x^2 = 625\)
\(x = 25\) (\(x\) is positive)
Check: 1.25 × 0.75 = 0.9375 ✓

Explanation

Write each change as a multiplier and multiply them. The product is a difference of two squares, \(1 - \frac{x^2}{10000}\), which must equal the overall multiplier 0.9375. Only the positive square root makes sense for a percentage increase.

Mark scheme

1 mark
P1 for the multipliers \(1 + \frac{x}{100}\) and \(1 - \frac{x}{100}\)
oe; correct answer with no working scores full marks
1 mark
P1 for \(\left(1 + \frac{x}{100}\right)\left(1 - \frac{x}{100}\right) = 0.9375\)
oe
1 mark
P1 for \(1 - \frac{x^2}{10000} = 0.9375\) or \(x^2 = 625\)
oe
1 mark
A1 for 25
cao; do not accept −25 as the final answer

Ready to try the rest? Every answer you write is marked against the mark scheme, so you can see exactly where the marks are.

AI Tutor Hints first, answers after you try

Hi! Stuck? Ask me for a hint and I’ll help you work it out. Once you’ve checked your answer I can explain exactly where the marks are.