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GCSE Higher Percentage Revision Sheet

GCSE HigherRevision15 questions

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Formula Reminders

Percentage change

(Change ÷ Original) × 100

Multipliers

r% increase: × (1 + r/100)

r% decrease: × (1 − r/100)

Reverse percentage

Original = Final ÷ multiplier

Repeated percentage change

Apply each multiplier in sequence

Compound interest / growth and decay

A = P(1 + r/100)n

A = final amount  |  P = starting amount (principal)  |  r = rate per period (%)  |  n = number of periods

For decay / depreciation, use (1 − r/100) instead.

Answer all 15 questions. Show your working clearly. A calculator may be used.

  1. A price rises from £380 to £437. Calculate the percentage increase.

  2. After a 45% reduction, a sofa costs £440. What was the original price?

  3. A value increases by 12% and then by a further 8%. What is the combined percentage increase? Do not just add 12 and 8.

  4. Amy invests £6,000 at 3.5% compound interest per year. How much does she have after 5 years? Give your answer to the nearest penny.

  5. A car is worth £22,000 when new. It depreciates at 18% per year. What is it worth after 3 years? Give your answer to the nearest pound.

  6. Express 0.064 as a percentage.

  7. A salary of £32,000 is increased by 4% and then, one year later, decreased by 4%. What is the final salary? Explain why it is not £32,000.

  8. After a 22% rise, an item costs £732. What was the original price?

  9. The population of a town grows at 2.4% per year. The current population is 48,000. What will the population be after 6 years? Give your answer to the nearest whole number.

  10. A radioactive substance decays at 15% per year. If there is initially 500 g, how much remains after 4 years? Give your answer to 2 decimal places.

  11. Fatima invests £8,000 at 1.8% compound interest per year. After how many complete years will her investment first exceed £9,000? Show all working.

  12. An item is sold at a 35% profit for £540. What was the cost price?

  13. A company's revenue fell by 12% in 2023 and rose by 18% in 2024. Calculate the overall percentage change from the start of 2023 to the end of 2024.

  14. Zara borrows £2,500 at a compound interest rate of 6% per year. She does not make any payments. How much does she owe after 3 years? Give your answer to the nearest penny.

  15. A house increases in value by 5% per year. How many complete years does it take for the value to increase by at least 30% of its original value? Show your working.

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Worked Answers

  1. Q1: Increase = £437 − £380 = £57. Percentage increase = (57 ÷ 380) × 100 = 15%
  2. Q2: £440 = 55%. Original = £440 ÷ 0.55 = £800
  3. Q3: Combined multiplier = 1.12 × 1.08 = 1.2096. Overall increase = 1.2096 − 1 = 0.2096 = 20.96%
  4. Q4: A = £6,000 × 1.035&sup5; = £6,000 × 1.18768607 = £7,126.12
  5. Q5: A = £22,000 × 0.82³ = £22,000 × 0.551368 = £12,130
  6. Q6: 0.064 × 100 = 6.4%
  7. Q7: After 4% rise: £32,000 × 1.04 = £33,280. After 4% fall: £33,280 × 0.96 = £31,948.80. The final value is less than £32,000 because the 4% decrease is applied to a larger amount, so it removes more money than the 4% increase added.
  8. Q8: £732 = 122%. Original = £732 ÷ 1.22 = £600
  9. Q9: 48,000 × 1.024&sup6; = 48,000 × 1.15380 = 55,382
  10. Q10: 500 × 0.85&sup4; = 500 × 0.52200625 = 261.00 g
  11. Q11: Year 1: £8,144. Year 2: £8,290.59. Year 3: £8,439.62. Year 4: £8,591.13. Year 5: £8,745.57. Year 6: £8,902.99. Year 7: £9,063.25. The investment first exceeds £9,000 after 7 complete years.
  12. Q12: £540 = 135%. Cost price = £540 ÷ 1.35 = £400
  13. Q13: Combined multiplier = 0.88 × 1.18 = 1.0384. Overall change = +3.84%. This is a 3.84% increase overall.
  14. Q14: A = £2,500 × 1.06³ = £2,500 × 1.191016 = £2,977.54
  15. Q15: Year 5: 1.05&sup5; = 1.2763 (+27.6%). Year 6: 1.05&sup6; = 1.3401 (+34.0%). The value first exceeds 30% growth after 6 complete years.

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