Year 11 Percentage Worksheet
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Year 11 Percentage Worksheet
Year 11 | Ages 15–16 | GCSE Higher
Answer all questions. Show full working. Give answers to 2 decimal places unless stated otherwise.
Answer all questions. Show full working. Give answers to 2 decimal places unless stated otherwise.
60 questions · 152 marks
Set 1 (Questions 1–20): Starter — core GCSE percentage skills
What is 12.5% of 360?
Increase £480 by 15%.
Decrease 720 by 30%.
Express 45 as a percentage of 180.
Express £2.40 as a percentage of £16.
A value rises from 60 to 78. Calculate the percentage increase.
Calculate 17.5% of £280.
Decrease £900 by 12.5%.
A value falls from 400 to 340. Calculate the percentage decrease.
Calculate 8% of £1,350.
Increase £760 by 22.5%.
A value rises from 520 to 598. Calculate the percentage increase.
Decrease £2,400 by 17.5%.
Express £6.30 as a percentage of £42.
A value falls from 840 to 672. Calculate the percentage decrease.
Increase 3,600 by 12.5%.
What is 35% of 2,840?
A value falls from 250 to 185. Calculate the percentage decrease.
Decrease £3,200 by 22%.
A value rises from 1,240 to 1,519. Calculate the percentage increase.
Set 2 (Questions 21–40): Main — compound interest, depreciation and reverse percentages
After a 12% increase, a price is £392. Find the original price.
After a 20% reduction, an item costs £144. Find the original price.
£5,000 is invested at 4.5% compound interest per year for 2 years. Find the total value. Give your answer to the nearest penny.
A car bought for £20,000 depreciates at 18% per year for 2 years. Find its value after 2 years.
A shop buys goods for £260 and sells them for £325. Calculate the percentage profit.
After a 14% pay rise, a salary is £28,500. Find the original salary.
£6,000 is invested at 3% compound interest per year for 3 years. Find the total value. Give your answer to the nearest penny.
A price is reduced by 25% and then increased by 20%. Starting from £600, find the final price and the overall percentage change.
A piece of machinery costs £8,000 and depreciates at 12% per year for 3 years. Find its value after 3 years. Give your answer to the nearest penny.
After an 8% reduction, a price is £184. Find the original price.
£10,000 is invested at 2.5% compound interest per year for 4 years. Find the total value. Give your answer to the nearest penny.
A shop sells an item for £138, making a 15% profit on the cost price. Find the cost price.
A camera is bought for £480 and sold for £384. Calculate the percentage loss.
A price is increased by 15% and then decreased by 10%. Starting from £2,000, find the final price and the overall percentage change.
£1,800 is invested at 4% compound interest per year for 3 years. Find the total value. Give your answer to the nearest penny.
After a 22% reduction, a coat costs £117. Find the original price.
A bike worth £2,000 depreciates at 35% per year for 3 years. Find its value after 3 years. Give your answer to the nearest penny.
A value falls from 7,200 to 6,048. Calculate the percentage decrease.
£4,200 is invested at 3.5% compound interest per year for 2 years. Find the total value. Give your answer to the nearest penny.
After 3 years of compound growth at 4% per year, an investment is worth £4,499.46. Find the original amount invested.
Set 3 (Questions 41–60): Challenge — complex multi-step and GCSE Higher reasoning
£7,000 is invested at 4.5% compound interest per year for 4 years. Find the total value. Give your answer to the nearest penny.
A car bought for £22,000 depreciates at 18% per year for 3 years. Find its value after 3 years. Give your answer to the nearest penny.
After 4 years of compound interest at 5% per year, a savings account holds £6,077.53. Find the original amount invested.
A house worth £320,000 rises in value by 7% in year 1, falls by 3% in year 2 and rises by 5% in year 3. Find its value at the end of year 3. Give your answer to the nearest penny.
A price is increased by 12% and then decreased by 8%. Starting from £1,500, find the final price and the overall percentage change.
A car bought for £30,000 depreciates by 25% in year 1, by 20% in year 2 and by 15% in year 3. Find its value after 3 years and the overall percentage decrease in value.
£3,200 is invested at 6.5% compound interest per year for 3 years. Find the total value. Give your answer to the nearest penny.
£4,000 is invested and grows to £4,410 in exactly 2 years with compound interest. Find the annual percentage rate.
A town has a population of 80,000 growing at 3% per year. How many complete years does it take for the population to exceed 95,000?
After 3 years of compound interest at 6% per year, a savings account holds £5,955.08. Find the original amount invested.
£9,000 is invested at 2.8% compound interest per year for 3 years. Find the total value. Give your answer to the nearest penny.
A retailer buys a television for £X, marks the price up by 40% and then offers a 15% discount. The final selling price is £476. Find the cost price.
An asset worth £15,000 depreciates at 8% per year. Find its value after 4 years. Give your answer to the nearest penny.
Sarah invests £8,000 in a fund that grows at 5.5% per year for the first 2 years and then at 3% per year for the next 2 years. Find the total value after 4 years. Give your answer to the nearest penny.
£2,500 is invested at 4% compound interest per year. How many complete years does it take for the investment to exceed £3,000?
Reasoning: A price increases by 20% in January and then falls by 20% in July. Explain why the final price is lower than the original, and calculate the overall percentage change.
Reasoning: Bank A offers 5% compound interest per year for 3 years. Bank B offers 15% simple interest over 3 years. Priya invests £3,000 in each. Show which bank gives a greater return and find the difference to the nearest penny.
Reasoning: A salesman claims: "A 25% increase followed by a 25% decrease returns you to the original price." Explain why this is incorrect and calculate the actual overall percentage change.
Reasoning: A car is bought for £12,000 and depreciates at 20% per year. Its owner claims it will be worth nothing after 5 years because 20% × 5 = 100%. Explain the error and find the actual value after 5 years.
Reasoning: An investment doubles in value over 10 years. Show that the annual compound growth rate is approximately 7.18%, and explain why finding the rate requires a 10th root rather than simply dividing 100% by 10.
Free to print and use in your classroom. percentages.co.uk
Answer Sheet — Year 11 Percentage Worksheet (Set A)
Answers are shown below. When printed, the answer sheet always starts on a new page.
| Q | Answer | Marks |
|---|---|---|
| 1 | 45 | 1 |
| 2 | £552 | 1 |
| 3 | 504 | 1 |
| 4 | 25% | 1 |
| 5 | 15% | 1 |
| 6 | 30% | 1 |
| 7 | £49 | 1 |
| 8 | £787.50 | 1 |
| 9 | 15% | 1 |
| 10 | £108 | 1 |
| 11 | £931 | 2 |
| 12 | 15% | 2 |
| 13 | £1,980 | 2 |
| 14 | 15% | 2 |
| 15 | 20% | 2 |
| 16 | 4,050 | 2 |
| 17 | 994 | 2 |
| 18 | 26% | 2 |
| 19 | £2,496 | 2 |
| 20 | 22.5% | 2 |
| 21 | £350 | 2 |
| 22 | £180 | 2 |
| 23 | £5,460.13 | 3 |
| 24 | £13,448 | 3 |
| 25 | 25% | 2 |
| 26 | £25,000 | 3 |
| 27 | £6,556.36 | 3 |
| 28 | £540; overall decrease of 10% | 3 |
| 29 | £5,451.78 | 3 |
| 30 | £200 | 2 |
| Q | Answer | Marks |
|---|---|---|
| 31 | £11,038.13 | 3 |
| 32 | £120 | 3 |
| 33 | 20% | 2 |
| 34 | £2,070; overall increase of 3.5% | 3 |
| 35 | £2,024.76 | 3 |
| 36 | £150 | 2 |
| 37 | £549.25 | 3 |
| 38 | 16% | 2 |
| 39 | £4,499.15 | 3 |
| 40 | £4,000 | 3 |
| 41 | £8,347.63 | 3 |
| 42 | £12,130.10 | 3 |
| 43 | £5,000 | 4 |
| 44 | £348,734.40 | 4 |
| 45 | £1,545.60; overall increase of 3.04% | 3 |
| 46 | Value: £15,300; overall decrease: 49% | 4 |
| 47 | £3,865.44 | 3 |
| 48 | 5% | 4 |
| 49 | 6 complete years (after 5 years: 92,742; after 6 years: 95,524) | 4 |
| 50 | £5,000 | 4 |
| 51 | £9,777.37 | 3 |
| 52 | £400 | 4 |
| 53 | £10,745.89 | 3 |
| 54 | £9,446.47 | 4 |
| 55 | 5 complete years (after 4 years: £2,924.65; after 5 years: £3,041.63) | 4 |
| 56 | After the 20% rise the price is 120% of the original. A 20% fall of 120% reduces it to 96%. Multiplier: 1.20 × 0.80 = 0.96; overall decrease of 4%. Percentage changes cannot simply be added. | 3 |
| 57 | Bank A: £3,000 × 1.05³ = £3,472.88 (interest: £472.88). Bank B: £3,000 + (£3,000 × 0.15) = £3,450 (interest: £450). Bank A gives more. Difference: £22.88. | 3 |
| 58 | The 25% decrease is applied to the already-increased price, not the original. Multiplier: 1.25 × 0.75 = 0.9375; overall decrease of 6.25%. Example: £100 → £125 → £93.75. | 3 |
| 59 | Each year the 20% loss is calculated on the current value, not the original. After 5 years: £12,000 × 0.80⁵ = £12,000 × 0.32768 = £3,932.16. The value never reaches zero. | 3 |
| 60 | r¹⁰ = 2; r = 2^(1/10) ≈ 1.0718; annual rate ≈ 7.18%. Dividing 100% by 10 assumes simple linear growth and gives 10%. Compound growth is multiplicative, so the 10th root gives the equivalent annual multiplier. | 3 |
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