Pearson Edexcel International GCSE Mathematics A 4MA1: Percentages, ratio and proportion – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover sections 1.6 (Percentages) and 1.7 (Ratio and proportion) of topic 1, Numbers and the number system, in the Pearson Edexcel International GCSE Mathematics A (4MA1) specification, Issue 2 (November 2017), for the January and June series examined on it. Questions 1–10 are for both tiers, except part 7(a), which is marked (Higher) because writing a proportion formula (statement 2.5A) is Higher tier only. Questions 11 and 12 are (Higher): they use repeated percentage change and compound interest problem-solving, which the specification lists for the Higher tier only. A calculator may be used on every 4MA1 paper, but show your working: most marks are for method.

Learn the content first in the study guide and the revision notes. These questions are different from the ones in the topic 1 practice questions, so try both. The course hub is Edexcel IGCSE Mathematics and the printable checklist lists every statement.

Questions

1. (Both tiers)

(a) Write 42% as a decimal. [1] (b) Write 42% as a fraction in its simplest form. [1] (c) Increase £240 by 17.5%. [2]

2. (Both tiers) Express 270 g as a percentage of 1.8 kg. [2]

3. (Both tiers)

(a) Write the ratio 1.2 m : 45 cm : 75 cm in its simplest form. [2] (b) Write the ratio 5 : 18 in the form 1 : n. [1]

4. (Both tiers) Ali, Bea and Chen share some money in the ratio 2 : 5 : 6. Chen receives £84 more than Ali.

(a) Calculate how much Bea receives. [3] (b) What fraction of the money does Bea receive? [1]

5. (Both tiers) The price of a laptop falls from £640 to £552. Calculate the percentage decrease. [3]

6. (Both tiers)

(a) In a sale, all prices are reduced by 15%. A jacket costs £57.80 in the sale. Calculate the price of the jacket before the sale. [3] (b) A restaurant bill is £81 after a 12.5% service charge has been added. Calculate the service charge. [3]

7. w varies directly as d. When d = 6, w = 16.8.

(a) (Higher) Find a formula for w in terms of d. [2] (b) Complete the table. [2]

d	6	15	?
w	16.8	?	9.8

8. (Both tiers) A map has a scale of 1 : 40 000.

(a) Two farms are 7.5 cm apart on the map. Calculate the real distance between them in kilometres. [2] (b) A cycle path is 5.2 km long. Calculate its length on the map in centimetres. [2]

9. (Both tiers)

(a) A recipe for 6 people uses 450 g of flour. Calculate how much flour is needed for 10 people. [2] (b) Pack A has 6 cans of juice for £4.32. Pack B has 15 cans of the same juice for £10.50. Which pack is better value? Show your working. [3]

10. (Both tiers) Kofi and Lena share £14 000 in the ratio 3 : 4. Kofi invests his share at 3.5% per year compound interest. Lena invests her share at 2.5% per year compound interest. Both invest for 3 years.

(a) Show that Kofi invests £6000. [2] (b) Calculate the value of Kofi’s investment after 3 years. [2] (c) Who earns more interest, and by how much? [3] (d) Calculate the total interest earned by Kofi and Lena together as a percentage of £14 000. Give your answer to 3 significant figures. [2]

11. (Higher) The price of a bicycle is increased by 20%. The new price is then increased by 15%. This price is then reduced by 25% in a sale. Calculate the overall percentage change in the price. [3]

12. (Higher)

(a) A van costs £12 000 when new. Its value depreciates by 14% per year. Find the number of whole years after which its value is first less than half of its value when new. [3] (b) An investment grows from £5000 to £5618 in 2 years at a fixed rate of compound interest. Find the rate of interest. [3] (c) After 3 years at 5% per year compound interest, an account holds £9261. Calculate the amount first invested. [3]

Answers

1. (a) 42 ÷ 100 = 0.42 [1] (b) 42/100 = 21/50 [1] (c) Multiplier 1.175 [1]; 240 × 1.175 = £282 [1] Examiner insight: In (b) 42/100 is not in its simplest form, so it does not earn the mark; in (c) finding 17.5% of 240 (42) and stopping scores the method mark only.

2. 1.8 kg = 1800 g and 270/1800 [1]; 270/1800 × 100 = 15% [1] Examiner insight: 270/1.8 × 100 = 15 000% shows no unit conversion and earns nothing; the method mark needs both quantities in the same units.

3. (a) 120 : 45 : 75 in cm [1]; divide by 15: 8 : 3 : 5 [1] (b) 18 ÷ 5 = 3.6, so 1 : 3.6 [1] Examiner insight: A correct but not fully simplified ratio such as 24 : 9 : 15 earns the method mark only; the accuracy mark needs the simplest form.

4. (a) Chen − Ali = 6 − 2 = 4 parts = £84 [1]; one part = 84 ÷ 4 = £21 [1]; Bea = 5 × 21 = £105 [1] (b) Total parts = 13, so 5/13 [1] Examiner insight: Dividing £84 by 13 (the total parts) earns nothing, because £84 is the difference between two shares, not the total.

5. Decrease = 640 − 552 = 88 [1]; 88/640 × 100 [1] = 13.75% [1] Examiner insight: Dividing by 552 (the new price) loses both the second method mark and the accuracy mark; the original value must be the denominator.

6. (a) Sale price is 85% of the original, multiplier 0.85 [1]; 57.80 ÷ 0.85 [1] = £68 [1] (b) Bill is 112.5% of the cost before the charge, so 81 ÷ 1.125 [1] = £72 [1]; service charge = 81 − 72 = £9 [1] Examiner insight: Working out 15% of £57.80 and adding it on gives £66.47 and scores 0, because the method mark is for dividing by the correct multiplier.

7. (a) k = 16.8 ÷ 6 = 2.8 [1]; w = 2.8d [1] (b) d = 15: w = 2.8 × 15 = 42 [1]; w = 9.8: d = 9.8 ÷ 2.8 = 3.5 [1] Examiner insight: A wrong value of k in (a) can still earn both marks in (b) on follow-through if it is used correctly, so always write your formula down.

8. (a) 7.5 × 40 000 = 300 000 cm [1]; = 3 km [1] (b) 5.2 km = 520 000 cm [1]; 520 000 ÷ 40 000 = 13 cm [1] Examiner insight: An answer of 300 000 earns the method mark only; the accuracy mark needs the conversion to kilometres the question asks for.

9. (a) For 1 person: 450 ÷ 6 = 75 g [1]; for 10 people: 75 × 10 = 750 g [1] (b) Pack A: 4.32 ÷ 6 = £0.72 per can [1]; Pack B: 10.50 ÷ 15 = £0.70 per can [1]; Pack B is better value [1] Examiner insight: The final mark needs a correct conclusion supported by two comparable figures; “B” with no calculation scores 0.

10. (a) 14 000 ÷ 7 = 2000 per part [1]; Kofi = 3 × 2000 = 6000 [1] (b) 6000 × 1.035³ [1] = £6652.31 [1] (c) Lena’s value: 8000 × 1.025³ = £8615.13, so her interest is £615.13 [1]; Kofi’s interest is 6652.31 − 6000 = £652.31 [1]; Kofi earns more, by £37.18 [1] (d) Total interest = 652.31 + 615.13 = £1267.44 [1]; 1267.44/14 000 × 100 = 9.05% [1] Examiner insight: On a “show that” in (a), the answer 6000 is given, so the marks are for the working: write 14 000 ÷ 7 and × 3 in full.

11. Multipliers 1.2, 1.15 and 0.75 [1]; 1.2 × 1.15 × 0.75 = 1.035 [1]; an increase of 3.5% [1] Examiner insight: Adding the percentages (20 + 15 − 25 = 10%) scores 0; the method mark is for a product of the three correct multipliers.

12. (a) Half of 12 000 is 6000, and the yearly multiplier is 0.86 [1]; after 4 years 12 000 × 0.86⁴ = £6564.10 and after 5 years 12 000 × 0.86⁵ = £5645.12 [1]; 5 years [1] (b) 5618 ÷ 5000 = 1.1236 = m² [1]; m = √1.1236 = 1.06 [1]; 6% per year [1] (c) 1.05³ = 1.157625 [1]; 9261 ÷ 1.157625 [1] = £8000 [1] Examiner insight: In (a), “5 years” with no values for n = 4 and n = 5 can lose the method marks, because trial and improvement must show the values either side of the target.

Where marks are usually lost

• Dividing the change by the new value instead of the original in a percentage change.
• Taking 15% of a sale price and adding it on, instead of dividing by 0.85.
• Treating a given difference between shares as the total when dividing in a ratio.
• Leaving ratios with mixed units (m with cm) or not fully simplified.
• Using simple interest (adding the same amount each year) when the question says compound.
• Giving the final value when the question asks for the interest, or the interest when it asks for the value.
• Rounding the value at the end of each year, so the final answer is a few pence out.
• Leaving a map length in cm when the answer must be in km.
• (Higher) Adding successive percentage changes instead of multiplying the multipliers.
• (Higher) Giving only the final number of years without the values either side of the target.

Next steps

• Refresh the methods: revision notes
• Re-learn anything you missed: study guide
• Wider topic 1 practice: Numbers and the number system practice questions
• Course hub: Edexcel IGCSE Mathematics
• Track coverage: printable checklist
• Check other topics: all free 10-minute diagnostics
• Want help from a teacher? Book a free trial class

Official syllabus

Pearson Edexcel International GCSE in Mathematics (Specification A) (4MA1), Specification, Issue 2, November 2017, Pearson Education Limited (first assessment June 2018). Topic 1, Numbers and the number system, sections 1.6 Percentages and 1.7 Ratio and proportion (Foundation Tier content and Higher Tier content).