Edexcel International GCSE Maths Percentages Past Paper Questions and Solutions (4MA1 Higher)

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Edexcel International GCSE Maths A (4MA1) · Higher · Numbers and the Number System

Percentages: Edexcel 4MA1 Past Paper Questions and Worked Solutions

This page collects every percentages question from the Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier Paper 1H and Paper 1HR, January 2020 to June 2025: 25 questions worth 101 marks. Questions run from easier to harder. Try each one first, then click “Show solution” for a step-by-step method with the reason for every step. All answers are checked against the official Pearson mark schemes.

16 marksHigherJune 2025 · Paper 1H (4MA1/1H) · Q2

Anna makes cups. Each cup costs 6 Swiss francs to make. Anna puts the cups into boxes to sell. Each box contains 4 cups. Anna sells 80 boxes of cups for a total of 2160 Swiss francs.

(a) Work out the percentage profit Anna makes. Show your working clearly. (4)

The height of each cup is 9 cm, correct to the nearest cm.

(b) Write down the lower bound of the height. (1)

The weight of each cup is 120 g, correct to the nearest 10 g.

(c) Write down the upper bound of the weight. (1)

Show solution

Part (a)

  1. Number of cups = 80 × 4 = 320
  2. Cost of making them = 320 × 6 = 1920 Swiss francs
  3. Profit = selling price − cost = 2160 − 1920 = 240 Swiss francs
  4. Percentage profit = profit⁄cost × 100 = 240⁄1920 × 100

Answer: 12.5%

Part (b)

  1. Correct to the nearest cm means the true height is within half of 1 cm (0.5 cm) either side of 9.

Answer: 8.5 cm

Part (c)

  1. Correct to the nearest 10 g means the true weight is within half of 10 g (5 g) either side of 120.

Answer: 125 g

24 marksHigherJune 2023 · Paper 1H (4MA1/1H) · Q3

Nanette buys 60 notebooks for a total cost of 780 dirhams. Nanette sells 70% of the notebooks for 22 dirhams each. She sells the remaining notebooks for 19 dirhams each. Work out Nanette’s percentage profit. Give your answer correct to 3 significant figures.

Show solution
  1. 70% of 60 = 42 notebooks at 22 dirhams: 42 × 22 = 924 dirhams
  2. The remaining 60 − 42 = 18 notebooks at 19 dirhams: 18 × 19 = 342 dirhams
  3. Total income = 924 + 342 = 1266 dirhams, so profit = 1266 − 780 = 486 dirhams
  4. Percentage profit = profit⁄original cost × 100 = 486⁄780 × 100 = 62.307…

Answer: 62.3%

35 marksHigherJanuary 2022 · Paper 1H (4MA1/1H) · Q4

Sarah makes and sells mugs. One day she makes 150 mugs. Her total cost for making these mugs is £1140. Of these mugs, 2⁄5 are small mugs, 32% are medium mugs and the rest are large mugs. Sarah sells small mugs for £8.50, medium mugs for £11.20 and large mugs for £14.20. Sarah sells all 150 mugs. Work out her percentage profit. Give your answer correct to the nearest whole number.

Show solution
  1. Small: 2⁄5 × 150 = 60. Medium: 32% of 150 = 48. Large: 150 − 60 − 48 = 42.
  2. Income: 60 × 8.50 = £510, 48 × 11.20 = £537.60, 42 × 14.20 = £596.40. Total = £1644
  3. Profit = 1644 − 1140 = £504
  4. Percentage profit = 504⁄1140 × 100 = 44.2…

Answer: 44%

44 marksHigherJune 2022 · Paper 1HR (4MA1/1HR) · Q4

The language department of a college has 180 students. Each student studies exactly one of French, German, Italian or Spanish. 15 students study French. 45% of the students study German. Express the percentage of students studying Italian or Spanish as a percentage of those studying French or German.

Show solution
  1. German: 45% of 180 = 0.45 × 180 = 81 students
  2. French or German: 15 + 81 = 96 students
  3. Italian or Spanish: 180 − 96 = 84 students
  4. As a percentage of French or German: 84⁄96 × 100

Answer: 87.5%

54 marksHigherJanuary 2023 · Paper 1HR (4MA1/1HR) · Q4

Divya and Yuan each pay for a holiday at a special offer price. Divya’s holiday: normal price 1600, special offer 16% off the normal price. Yuan’s holiday: normal price 1400, special offer k% off the normal price. The amount that Divya pays is the same as the amount that Yuan pays. Work out the value of k.

Show solution
  1. Divya pays 84% of 1600: 1600 × 0.84 = 1344
  2. Yuan pays 1344 out of 1400: 1344⁄1400 = 0.96 = 96%
  3. So Yuan’s discount is 100% − 96% = 4%

Answer: k = 4

63 marksHigherJune 2024 · Paper 1H (4MA1/1H) · Q4

Ava records the number of kilometres she drives each month. In April, Ava drove 943 kilometres. This is 15% more than the number of kilometres she drove in March. Work out the number of kilometres Ava drove in March.

Show solution
  1. March is the original amount (100%). April is 15% more, so April is 100% + 15% = 115% of March.
  2. 115% as a multiplier is 1.15, so March × 1.15 = 943
  3. To undo the increase, divide by the multiplier: 943 ÷ 1.15

Answer: 820 kilometres

Tip: Do not find 15% of 943 and subtract it. The 15% is of March’s distance, not April’s.
76 marksHigherJune 2020 · Paper 1HR (4MA1/1HR) · Q5

In 2017, the population of a village was 7500. In 2019, the population of the village was 8265.

(a) Work out the percentage increase in the population of the village from 2017 to 2019. (3)

In a sale, normal prices are reduced by 30%. The sale price of a T-shirt was 31.50 euros.

(b) Work out the normal price of the T-shirt. (3)

Show solution

Part (a)

  1. Increase = 8265 − 7500 = 765
  2. Percentage increase = increase⁄original × 100 = 765⁄7500 × 100

Answer: 10.2%

Part (b)

  1. The sale price is 70% of the normal price: normal price × 0.7 = 31.50
  2. Normal price = 31.50 ÷ 0.7

Answer: 45 euros

83 marksHigherJune 2024 · Paper 1HR (4MA1/1HR) · Q5

Slavomir invests 5200 euros in a savings account for 4 years. He gets 2.5% per year compound interest. Work out how much money Slavomir will have in the savings account at the end of 4 years. Give your answer correct to the nearest euro.

Show solution
  1. Each year the amount is multiplied by 100% + 2.5% = 102.5%, which is a multiplier of 1.025.
  2. Compound interest over 4 years means multiplying by 1.025 four times: 5200 × 1.0254
  3. 5200 × 1.0254 = 5739.82…
  4. Round to the nearest euro.

Answer: 5740 euros

93 marksHigherJune 2025 · Paper 1H (4MA1/1H) · Q5

In a sale, normal prices are reduced by 28%. The sale price of a watch is 198 euros. Work out the normal price of the watch.

Show solution
  1. The normal price is 100%. After a 28% reduction the sale price is 100% − 28% = 72% of the normal price.
  2. So normal price × 0.72 = 198
  3. Normal price = 198 ÷ 0.72

Answer: 275 euros

Tip: Do not add 28% of 198. The 28% is of the normal price, which we do not know yet.
106 marksHigherJune 2022 · Paper 1H (4MA1/1H) · Q6

Asha bought an apartment. The table gives information about the value of apartments, in euros, and the annual service charge band.

Value (x euros)Service charge band
x ≥ 700 000A
600 000 ≤ x < 700 000B
500 000 ≤ x < 600 000C
400 000 ≤ x < 500 000D
0 < x < 400 000E

In 2021, the value of Asha’s apartment was 634 400 euros. The value of Asha’s apartment had increased by 4% from its value in 2020.

(a) Has the annual service charge band changed for Asha’s apartment? Show your working clearly. (3)

Pam bought a boat. In each year after Pam bought the boat, the value of the boat depreciated by 15%.

(b) Work out the total percentage by which the value of the boat had depreciated by the end of the second year after Pam bought the boat. (3)

Show solution

Part (a)

  1. The 2021 value is 104% of the 2020 value, so the 2020 value = 634 400 ÷ 1.04 = 610 000 euros
  2. 610 000 is in band B (600 000 ≤ x < 700 000), and 634 400 is also in band B.

Answer: No, it is band B in both years

Part (b)

  1. Each year the value is multiplied by 0.85 (100% − 15%).
  2. After two years: 0.85 × 0.85 = 0.7225, so the boat is worth 72.25% of its original value.
  3. Total depreciation = 100% − 72.25%

Answer: 27.75%

Tip: The answer is not 30%. The second 15% is taken from the already reduced value.
117 marksHigherJanuary 2023 · Paper 1H (4MA1/1H) · Q6

Shane bought a car for 32 000. Theresa also bought a car. To pay for this car, Theresa paid a deposit of 18 000 together with 14 monthly payments of $1160. Theresa paid more for her car than Shane paid for his car.

(a) Work out how much more Theresa paid as a percentage of the amount Shane paid. (4)

Kylie bought a van. After 1 year, the value of the van was $39 865. During this year, the value of the van decreased by 15%.

(b) Work out the value of the van when Kylie bought it. (3)

Show solution

Part (a)

  1. Theresa paid 18 000 + 14 × 1160 = 18 000 + 16 240 = $34 240
  2. Difference = 34 240 − 32 000 = $2240
  3. As a percentage of Shane’s amount: 2240⁄32 000 × 100

Answer: 7%

Part (b)

  1. After a 15% decrease the van is worth 85%: original × 0.85 = 39 865
  2. 39 865 ÷ 0.85

Answer: $46 900

123 marksHigherJanuary 2020 · Paper 1HR (4MA1/1HR) · Q7

In a sale, the normal price of a hat is reduced by 15%. The sale price of the hat is 20.40 euros. Work out the normal price of the hat.

Show solution
  1. The sale price is 85% of the normal price: normal price × 0.85 = 20.40
  2. 20.40 ÷ 0.85

Answer: 24 euros

136 marksHigherJanuary 2021 · Paper 1H (4MA1/1H) · Q7

Chen invests 40 000 yuan in a fixed-term bond for 3 years. The bond pays compound interest at a rate of 3.5% each year.

(a) Work out the value of Chen’s investment at the end of 3 years. Give your answer to the nearest yuan. (3)

Wang invested P yuan. The value of his investment decreased by 6.5% each year. At the end of the first year, the value of Wang’s investment was 30 481 yuan.

(b) Work out the value of P. (3)

Show solution

Part (a)

  1. Multiplier 1.035 for three years: 40 000 × 1.0353 = 44 348.71…

Answer: 44 349 yuan

Part (b)

  1. A 6.5% decrease is a multiplier of 0.935: P × 0.935 = 30 481
  2. P = 30 481 ÷ 0.935

Answer: P = 32 600

143 marksHigherJanuary 2021 · Paper 1HR (4MA1/1HR) · Q7

Kuro invests 50 000 yen for 3 years in a savings account. She gets 2.4% per year compound interest. Work out how much money Kuro will have in her savings account at the end of the 3 years. Give your answer correct to the nearest yen.

Show solution
  1. A 2.4% increase means the money becomes 100% + 2.4% = 102.4% each year, so the multiplier is 1.024.
  2. Compound interest: multiply by 1.024 once for each of the 3 years.
  3. 50 000 × 1.0243 = 53 687.09…

Answer: 53 687 yen

153 marksHigherJune 2020 · Paper 1HR (4MA1/1HR) · Q8

Harold bought an antique clock for £1200. The clock increased in value by 8% per year. Find the value of the clock exactly 3 years after Harold bought the clock. Give your answer correct to the nearest £.

Show solution
  1. An 8% increase each year is a multiplier of 1.08.
  2. 1200 × 1.083 = 1511.65…

Answer: £1512

163 marksHigherNovember 2021 · Paper 1H (4MA1/1H) · Q8

In 2018, the population of Sydney was 5.48 million. This was 22% of the total population of Australia. Work out the total population of Australia in 2018. Give your answer correct to 3 significant figures.

Show solution
  1. 22% of the total = 5.48 million, so 0.22 × total = 5.48
  2. Total = 5.48 ÷ 0.22 = 24.909…

Answer: 24.9 million

173 marksHigherJune 2022 · Paper 1HR (4MA1/1HR) · Q8

Jane bought a new car for 18 000. The car depreciates in value by 15% each year. Work out the value of the car at the end of 4 years. Give your answer correct to the nearest .

Show solution
  1. Each year the value is multiplied by 0.85.
  2. 18 000 × 0.854 = 9396.11…

Answer: $9396

183 marksHigherJune 2020 · Paper 1H (4MA1/1H) · Q9

In a sale, normal prices are reduced by 20%. A bag costs 1080 rupees in the sale. Work out the normal price of the bag.

Show solution
  1. The sale price is 100% − 20% = 80% of the normal price: normal price × 0.8 = 1080
  2. Normal price = 1080 ÷ 0.8

Answer: 1350 rupees

193 marksHigherJune 2023 · Paper 1HR (4MA1/1HR) · Q9

Kazi buys a car for 700 000 taka. The value of the car depreciates by 12% each year. Work out the value of the car at the end of 3 years. Give your answer correct to the nearest taka.

Show solution
  1. Depreciating by 12% leaves 88% of the value each year: multiplier 0.88.
  2. After 3 years: 700 000 × 0.883 = 700 000 × 0.681472 = 477 030.4

Answer: 477 030 taka

206 marksHigherJanuary 2022 · Paper 1HR (4MA1/1HR) · Q10

Jonty has a storage container in the shape of a cuboid 12 m long, 2.5 m wide and 3 m high. Jonty is going to paint the outside of his storage container, apart from the base. He needs enough paint to cover the four sides and the top. Each tin of paint covers an area of 15 m2. The cost of each tin of paint recently increased by 10%. After the increase, the cost of each tin of paint is £26.95. Jonty says “Before the increase, I could have bought enough paint for less than £200″. Show that Jonty is correct. Show your working clearly.

Show solution
  1. Area to paint: top 12 × 2.5 = 30 m2; two long sides 2 × 12 × 3 = 72 m2; two ends 2 × 2.5 × 3 = 15 m2. Total = 117 m2
  2. Tins needed = 117 ÷ 15 = 7.8, so he needs 8 tins.
  3. Price before the 10% increase: 26.95 ÷ 1.1 = £24.50
  4. Cost of 8 tins before the increase = 8 × 24.50 = £196

Answer: £196 < £200, so Jonty is correct

213 marksHigherJanuary 2020 · Paper 1H (4MA1/1H) · Q11

Max invests 6000 in a savings account for 3 years. The account pays compound interest at a rate of 1.5% per year for the first 2 years. The compound interest rate changes for the third year. At the end of 3 years, there is a total of 6311.16 in the account. Work out the compound interest rate for the third year. Give your answer correct to 1 decimal place.

Show solution
  1. After 2 years: 6000 × 1.0152 = $6181.35
  2. Multiplier for year three = 6311.16 ÷ 6181.35 = 1.0210…
  3. A multiplier of 1.021 means an increase of 2.1%.

Answer: 2.1%

223 marksHigherJanuary 2022 · Paper 1H (4MA1/1H) · Q11

Himari invests 200 000 yen for 3 years in a savings account paying compound interest. The rate of interest is 1.8% for the first year and x% for each of the second year and the third year. The value of the investment at the end of the third year is 209 754 yen. Work out the value of x. Give your answer correct to one decimal place.

Show solution
  1. After year 1: 200 000 × 1.018 = 203 600 yen
  2. The same multiplier m is used for years 2 and 3: 203 600 × m2 = 209 754, so m2 = 1.030 22…
  3. m = √1.030 22… = 1.015
  4. A multiplier of 1.015 is 1.5% interest.

Answer: x = 1.5

235 marksHigherJune 2025 · Paper 1HR (4MA1/1HR) · Q11

Zhou invests some money for 2 years. He invests 2500 with Bank A, where amount of money invested : total amount of interest after 2 years = 20 : 3. He invests 3000 with Bank B at 4% per year compound interest for 2 years. Zhou receives more interest from Bank A than from Bank B. How much more?

Show solution
  1. Bank A: the ratio 20 : 3 means the interest is 3⁄20 of the amount invested: 3⁄20 × 2500 = $375
  2. Bank B: value after 2 years = 3000 × 1.042 = 3000 × 1.0816 = $3244.80
  3. Bank B interest = 3244.80 − 3000 = $244.80
  4. Difference = 375 − 244.80

Answer: $130.20

243 marksHigherJune 2020 · Paper 1H (4MA1/1H) · Q13

Jan invests 8000 in a savings account. The account pays compound interest at a rate of x% per year. At the end of 6 years, there is a total of 8877.62 in the account. Work out the value of x. Give your answer correct to 2 decimal places.

Show solution
  1. 8000 × m6 = 8877.62, where m is the yearly multiplier.
  2. m6 = 8877.62 ÷ 8000 = 1.109 702…
  3. m = ⁶√1.109 702… = 1.0175
  4. A multiplier of 1.0175 means 1.75% interest.

Answer: x = 1.75

253 marksHigherJune 2025 · Paper 1H (4MA1/1H) · Q13

Charlotte bought an apartment for 750 000. In the first year, the value of the apartment decreased by 4%. In the second year, the value decreased by 6.5%. In the third year, the value increased by x%. At the end of the third year, the value of Charlotte’s apartment was 698 445. Work out the value of x.

Show solution
  1. A 4% decrease is a multiplier of 0.96 and a 6.5% decrease is a multiplier of 0.935.
  2. Value after two years = 750 000 × 0.96 × 0.935 = $673 200
  3. Multiplier for year three = 698 445 ÷ 673 200 = 1.0375
  4. A multiplier of 1.0375 means an increase of 3.75%.

Answer: x = 3.75

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