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OCR GCSE Percentage Worksheet

OCR GCSE MathsFoundation and Higher30 questions

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

These questions are written in the style of OCR GCSE Maths papers. They are not official OCR material.

Section A (questions 1 to 15) is non-calculator. Section B (questions 16 to 30) allows a calculator. Show all working. Some questions ask you to explain your reasoning as well as calculate. The number of marks available is shown in brackets.

Section A: Non-Calculator (Foundation)

  1. 1. Find 20% of 350. [1 mark]

  2. 2. A library has 600 books. 45% are fiction. How many fiction books are there? [2 marks]

  3. 3. Write 24 out of 60 as a percentage. [1 mark]

  4. 4. A shirt costs £40. It is reduced by 15% in a sale. What is the sale price? [2 marks]

  5. 5. A meal costs £32. A tip of 12.5% is added. What is the total amount paid? [2 marks]

  6. 6. A gardener plants 180 bulbs. 30% fail to grow. How many bulbs successfully grow? [2 marks]

  7. 7. In a survey, 90 out of 360 people said they cycled to work. What percentage is this? [1 mark]

  8. 8. A price is increased by 5% from £260. What is the new price? [2 marks]

  9. 9. Find 65% of 80. [2 marks]

  10. 10. A council tax bill of £1,200 is increased by 2.5%. What is the new bill? [2 marks]

  11. 11. A charity raises £4,800. 60% goes directly to the cause. How much is that? [2 marks]

  12. 12. A car park has 500 spaces. On Monday morning 420 spaces were taken. What percentage were empty? [2 marks]

  13. 13. Find 5% of £640. [1 mark]

  14. 14. A factory produced 800 items in January and 920 items in February. What is the percentage increase? [2 marks]

  15. 15. A bag of rice weighs 2 kg. 35% of the bag has been used. How many grams remain? [2 marks]

Section B: Calculator (Higher)

  1. 16. After a 28% increase, a house is worth £192,000. What was its original value? [2 marks]

  2. 17. A price including VAT at 20% is £108. What is the price without VAT? [2 marks]

  3. 18. A car is bought for £14,500 and sold for £11,020. Calculate the percentage loss. [2 marks]

  4. 19. Show that £5,000 invested at 4% compound interest for 3 years gives a total of £5,624.32. Show all steps clearly. [3 marks]

  5. 20. A car depreciates at 22% per year. It is currently worth £9,500. What will it be worth after 2 years? Give your answer to the nearest pound. [3 marks]

  6. 21. A school roll increases by 3% per year compound. The school has 800 pupils now. How many pupils will it have after 4 years? Give your answer to the nearest whole number. [3 marks]

  7. 22. Explain why a 10% increase followed by a 10% decrease does not return a value to its original amount. Use an example to support your answer. [3 marks]

  8. 23. After a 45% reduction in a sale, a sofa costs £330. What was the original price? [2 marks]

  9. 24. A company made a profit of £42,000 last year. This year the profit has fallen to £35,700. Calculate the percentage decrease in profit. [2 marks]

  10. 25. Show that a value which increases by 25% and then decreases by 20% returns to exactly its original value. Explain what is happening mathematically. [3 marks]

  11. 26. A savings account pays 3.2% compound interest per year. How much must be invested now so that the total after 5 years is at least £10,000? Give your answer to the nearest pound. [4 marks]

  12. 27. A city has a population of 320,000. It grows at 1.8% per year compound. After how many complete years will the population first exceed 350,000? Show your working. [4 marks]

  13. 28. A laptop is priced at £680 before VAT. During a sale it is reduced by 15% before VAT is added at 20%. Calculate the final price. [3 marks]

  14. 29. A machine is bought for £50,000. Its value depreciates at r% per year. After 4 years it is worth £26,244.70. Find r. Show your working. [4 marks]

  15. 30. Two competing investments are available. Investment A: £8,000 at 5% compound interest for 3 years. Investment B: £8,000 at 6% simple interest for 3 years. Which investment gives a greater return and by how much? [4 marks]

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Worked Answers

  1. 1. 70

    20% of 350 = 350 ÷ 5 = 70

  2. 2. 270

    45% of 600 = 10% × 4.5 = 60 × 4.5 = 270

  3. 3. 40%

    24 ÷ 60 = 0.4 = 40%

  4. 4. £34

    15% of £40 = £6; sale price = £40 − £6 = £34

  5. 5. £36

    12.5% of £32 = £4; total = £32 + £4 = £36

  6. 6. 126

    30% of 180 = 54 failed; 180 − 54 = 126 grew successfully

  7. 7. 25%

    90 ÷ 360 = 0.25 = 25%

  8. 8. £273

    5% of £260 = £13; new price = £260 + £13 = £273

  9. 9. 52

    50% of 80 = 40; 10% = 8; 5% = 4; 65% = 40 + 8 + 4 = 52

  10. 10. £1,230

    2.5% of £1,200 = £30; new bill = £1,200 + £30 = £1,230

  11. 11. £2,880

    60% of £4,800 = £4,800 × 0.6 = £2,880

  12. 12. 16%

    Empty = 500 − 420 = 80; percentage = 80 ÷ 500 × 100 = 16%

  13. 13. £32

    5% of £640 = £640 ÷ 20 = £32

  14. 14. 15%

    Increase = 920 − 800 = 120; percentage = 120 ÷ 800 × 100 = 15%

  15. 15. 1,300 g

    35% of 2,000 g = 700 g used; 2,000 − 700 = 1,300 g remain

  16. 16. £150,000

    £192,000 ÷ 1.28 = £150,000

  17. 17. £90

    £108 ÷ 1.20 = £90

  18. 18. 24%

    Loss = £14,500 − £11,020 = £3,480; percentage = £3,480 ÷ £14,500 × 100 = 24%

  19. 19. Total = £5,624.32

    Year 1: £5,000 × 1.04 = £5,200. Year 2: £5,200 × 1.04 = £5,408. Year 3: £5,408 × 1.04 = £5,624.32. Using the formula: A = 5000 × 1.04³ = 5000 × 1.124864 = £5,624.32.

  20. 20. £5,776

    A = 9500 × 0.78² = 9500 × 0.6084 = £5,779.80 ≈ £5,780

  21. 21. 901 pupils

    A = 800 × 1.03&sup4;; 1.03² = 1.0609; 1.03&sup4; = 1.0609² = 1.12551; A = 800 × 1.12551 = 900.4 ≈ 900

  22. 22. The final value is 1% less than the original

    Example: start with £100. After 10% increase: £110. After 10% decrease: £110 × 0.90 = £99. The decrease is applied to £110, not £100, so the amount removed (£11) is greater than the amount added (£10). The combined multiplier is 1.10 × 0.90 = 0.99, giving a 1% decrease overall.

  23. 23. £600

    £330 ÷ 0.55 = £600

  24. 24. 15%

    Decrease = £42,000 − £35,700 = £6,300; percentage = £6,300 ÷ £42,000 × 100 = 15%

  25. 25. The value returns exactly to the original

    Combined multiplier = 1.25 × 0.80 = 1.00. Example: start with £100. After 25% increase: £125. After 20% decrease: £125 × 0.80 = £100. Mathematically, multiplying by 1.25 and then by 0.80 is equivalent to multiplying by 1 because 5/4 × 4/5 = 1.

  26. 26. £8,613

    Need P × 1.032&sup5; ≥ 10000. 1.032² = 1.065024; 1.032&sup4; = 1.134276; 1.032&sup5; = 1.170573; P = 10000 ÷ 1.170573 = £8,543. So £8,543 is needed (to nearest pound).

  27. 27. After 5 complete years

    Year 1: 320000 × 1.018 = 325,760. Year 2: 325,760 × 1.018 = 331,624. Year 3: 331,624 × 1.018 = 337,593. Year 4: 337,593 × 1.018 = 343,669. Year 5: 343,669 × 1.018 = 349,855. Year 6: 349,855 × 1.018 = 356,152. The population first exceeds 350,000 after 6 complete years.

  28. 28. £693.60

    Price after 15% reduction = £680 × 0.85 = £578. Price with VAT = £578 × 1.20 = £693.60.

  29. 29. r = 15%

    50000 × (1 − r/100)&sup4; = 26244.70. (1 − r/100)&sup4; = 26244.70 ÷ 50000 = 0.524894. 1 − r/100 = 0.524894^0.25 = 0.85. r/100 = 0.15. r = 15%.

  30. 30. Investment A gives a greater return by £45.40

    Investment A (compound 5%): 8000 × 1.05³ = 8000 × 1.157625 = £9,261. Investment B (simple 6%): 8000 + (8000 × 0.06 × 3) = 8000 + 1440 = £9,440. Investment B gives £9,440 and Investment A gives £9,261, so Investment B gives a greater return by £179.

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