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AQA GCSE Higher Percentage Worksheet

AQA GCSE HigherHigher Tier20 questions

Free to print and use in your classroom. No sign-up required.

All questions are calculator questions unless marked otherwise. Show all working. Give monetary answers to the nearest penny unless stated. The number of marks available is shown in brackets.

  1. 1. After a 40% increase, a price is £350. Find the original price. [2 marks]

  2. 2. After a 36% reduction, a price is £192. Find the original price. [2 marks]

  3. 3. A television including VAT at 20% costs £720. Find the price before VAT. [2 marks]

  4. 4. A house was valued at £225,000. After 2 years of compound growth at 5% per year, what is it worth now? Give your answer to the nearest pound. [3 marks]

  5. 5. A car worth £17,500 depreciates at 20% per year. What is it worth after 3 years? Give your answer to the nearest pound. [3 marks]

  6. 6. James invests £6,000 at 4.5% compound interest per year. How much does he have after 4 years? Give your answer to the nearest penny. [3 marks]

  7. 7. A motorbike is bought for £7,200 and sold for £5,940. Calculate the percentage loss. [2 marks]

  8. 8. A trader buys 50 items for £8 each and sells all of them for £11.60 each. Calculate the percentage profit. [2 marks]

  9. 9. A salary increased from £32,000 to £35,520 over two years. Calculate the overall percentage increase. [2 marks]

  10. 10. A value increases by 10% and then increases by a further 10%. Show that this is not equivalent to a 20% increase. Calculate the actual percentage increase. [3 marks]

  11. 11. A population of 14,000 grows at 2.4% per year compound. What is the population after 5 years? Give your answer to the nearest whole number. [3 marks]

  12. 12. £9,000 is invested at r% compound interest per year. After 2 years it is worth £9,760.41. Find r. Give your answer to 1 decimal place. [3 marks]

  13. 13. A car depreciates at 25% per year. After how many complete years will its value first fall below 25% of its original value? Show your working. [4 marks]

  14. 14. After a 3.5% pay rise, Jade earns £34,420. What was her salary before the pay rise? [2 marks]

  15. 15. A machine costs £60,000. It depreciates at 12% per year for 4 years. Find the value after 4 years and the total depreciation. Give your answers to the nearest pound. [4 marks]

  16. 16. Chloe buys a flat for £145,000 and sells it 3 years later for £167,050. During those 3 years she spent £6,800 on improvements. Calculate the percentage profit based on the total amount she spent (purchase price plus improvements). [3 marks]

  17. 17. An investment grows from £5,000 to £6,083.26 over 4 years with compound interest. Find the annual interest rate. Give your answer to 1 decimal place. [4 marks]

  18. 18. A shop reduces all prices by 20% in a sale. A customer uses a further 10% discount code. What is the overall percentage reduction from the original price? [3 marks]

  19. 19. A town has a population of 52,000. It decreases at 1.5% per year compound. After how many complete years will the population first fall below 48,000? Show your working. [4 marks]

  20. 20. A business buys an asset for £80,000. In year 1, the asset appreciates by 15%. In year 2, it depreciates by 18%. In year 3, it appreciates by 10%. Find the value of the asset at the end of year 3 and the overall percentage change from the original price. Give your answers to the nearest penny. [4 marks]

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Worked Answers

  1. 1. £250

    £350 ÷ 1.40 = £250

  2. 2. £300

    £192 ÷ 0.64 = £300

  3. 3. £600

    £720 ÷ 1.20 = £600

  4. 4. £248,006

    A = 225000 × 1.05² = 225000 × 1.1025 = £248,062.50 ≈ £248,063

  5. 5. £8,960

    A = 17500 × 0.80³ = 17500 × 0.512 = £8,960

  6. 6. £7,168.49

    1.045² = 1.092025; 1.045&sup4; = 1.092025² = 1.192519; A = 6000 × 1.192519 = £7,155.11

  7. 7. 17.5%

    Loss = £7,200 − £5,940 = £1,260; percentage = £1,260 ÷ £7,200 × 100 = 17.5%

  8. 8. 45%

    Cost per item = £8; selling price = £11.60; profit = £3.60; percentage = £3.60 ÷ £8 × 100 = 45%

  9. 9. 11%

    Increase = £35,520 − £32,000 = £3,520; percentage = £3,520 ÷ £32,000 × 100 = 11%

  10. 10. Actual increase is 21%

    Combined multiplier = 1.10 × 1.10 = 1.21. So the total increase is 21%, not 20%. The first 10% increase raises the value, and the second 10% is applied to the already higher value, so the total increase is slightly more than 20%.

  11. 11. 15,722

    1.024² = 1.048576; 1.024&sup4; = 1.098989; 1.024&sup5; = 1.098989 × 1.024 = 1.125368; A = 14000 × 1.125368 = 15,755 (to nearest whole number)

  12. 12. r = 4.0%

    9000 × (1 + r/100)² = 9760.41; (1 + r/100)² = 9760.41 ÷ 9000 = 1.084490; 1 + r/100 = √1.084490 = 1.0414; r = 4.1% (to 1 d.p.)

  13. 13. After 5 complete years

    Multiplier = 0.75. Year 1: 0.75 = 75%. Year 2: 0.75² = 0.5625 = 56.25%. Year 3: 0.75³ = 0.421875 = 42.19%. Year 4: 0.75&sup4; = 0.316406 = 31.64%. Year 5: 0.75&sup5; = 0.237305 = 23.73%. The value first falls below 25% of the original after 5 complete years.

  14. 14. £33,250

    £34,420 ÷ 1.035 = £33,250

  15. 15. Value = £35,916; total depreciation = £24,084

    A = 60000 × 0.88&sup4;; 0.88² = 0.7744; 0.88&sup4; = 0.7744² = 0.599190; A = 60000 × 0.599190 = £35,951.41. Total depreciation = £60,000 − £35,951.41 = £24,048.59

  16. 16. 11.2%

    Total spent = £145,000 + £6,800 = £151,800; profit = £167,050 − £151,800 = £15,250; percentage = £15,250 ÷ £151,800 × 100 = 10.05% ≈ 10.1%

  17. 17. 5.0%

    5000 × (1 + r/100)&sup4; = 6083.26; (1 + r/100)&sup4; = 6083.26 ÷ 5000 = 1.216652; 1 + r/100 = 1.216652^0.25 = 1.0500; r = 5.0%

  18. 18. 28% overall reduction

    Combined multiplier = 0.80 × 0.90 = 0.72. The final price is 72% of the original, so the overall reduction is 28%.

  19. 19. After 5 complete years

    Year 1: 52000 × 0.985 = 51,220. Year 2: 51,220 × 0.985 = 50,452. Year 3: 50,452 × 0.985 = 49,695. Year 4: 49,695 × 0.985 = 48,950. Year 5: 48,950 × 0.985 = 48,216. Wait, year 5 still exceeds 48,000. Year 6: 48,216 × 0.985 = 47,493. The population first falls below 48,000 after 6 complete years.

  20. 20. Value = £83,028; overall change = 3.79% increase

    After year 1: 80000 × 1.15 = £92,000. After year 2: £92,000 × 0.82 = £75,440. After year 3: £75,440 × 1.10 = £82,984. Overall change = (£82,984 − £80,000) ÷ £80,000 × 100 = 3.73% increase. Combined multiplier = 1.15 × 0.82 × 1.10 = 1.0373.

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