Practise 38 exam-style questions on Percentages and percentage change for Edexcel GCSE Maths (Non-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.
38 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.
Both quantities must be in the same units before you compare them, so change 6 minutes into 360 seconds. Then write the first quantity as a fraction of the second and multiply by 100. Forgetting to change the units gives the impossible answer 750%.
Mark scheme
1 mark
M1 for \(\dfrac{45}{360}\) oe
e.g. \(\dfrac{0.75}{6}\) or \(\dfrac{1}{8}\); the units must be the same; correct answer with no working scores full marks
Work out the mass of salt, in grams, in 2.5 kg of the solution.
Model answer
2.5 kg = 2500 g 1% of 2500 g = 25 g 0.4% of 2500 g = 0.4 × 25 = 10 g
Explanation
0.4% means 0.4 parts in every hundred, which is 0.004 as a decimal. Changing 2.5 kg to grams first gives the answer directly in grams; a common error is to use 0.04 instead of 0.004.
Mark scheme
1 mark
M1 for \(0.004 \times 2500\) or \(\dfrac{0.4}{100} \times 2.5\) (= 0.01 kg) oe
correct answer with no working scores full marks
1 mark
A1 for 10 g
accept 0.01 kg only if clearly converted to 10 g
Question 3
3 marks
The length of a rectangle is increased by 20%. The width of the rectangle is decreased by 20%.
Work out the percentage change in the area of the rectangle. State whether it is an increase or a decrease.
Model answer
New area = \(1.2l \times 0.8w = 0.96lw\) The new area is 96% of the original area. The area decreases by 4%.
Explanation
Area is length × width, so the multipliers for the length and width multiply together: 1.2 × 0.8 = 0.96. The area becomes 96% of what it was, a 4% decrease. The changes do not cancel out, because the 20% decrease acts on a length that has already been made bigger.
Mark scheme
1 mark
M1 for 1.2 and 0.8, or a numerical example, e.g. 10 by 10 becomes 12 by 8
correct answer with no working scores full marks
1 mark
M1 for \(1.2 \times 0.8\) (= 0.96) or areas 100 and 96 from an example
1 mark
A1 for 4% decrease
must state decrease; 0% change scores 0
Question 4
4 marks
Hassan buys a car. He pays a deposit of 20% of the cash price of the car, then 24 monthly payments of £575. The total amount he pays is 12% more than the cash price of the car.
Work out the cash price of the car.
Model answer
Monthly payments = 24 × 575 = £13 800 Let the cash price be \(C\). \(0.2C + 13\,800 = 1.12C\) \(13\,800 = 0.92C\) \(C = 13\,800 \div 0.92 = 1\,380\,000 \div 92 = 15\,000\) The cash price is £15 000.
Explanation
The deposit and the total are both percentages of the unknown cash price, so the monthly payments make up 112% − 20% = 92% of the cash price. Check: deposit £3000 + £13 800 = £16 800, and 112% of £15 000 is £16 800.
Mark scheme
1 mark
P1 for 24 × 575 (= 13 800)
correct answer with no working scores full marks
1 mark
P1 for \(0.2C + 13\,800 = 1.12C\) oe
or 92% of the cash price = 13 800
1 mark
P1 for \(13\,800 \div 0.92\) oe
1 mark
A1 for £15 000
cao
Ready to try the rest? Every answer you write is marked against the mark scheme, so you can see exactly where the marks are.
Ctrl + Enter to check
AI TutorHints 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.
