Percentage Diagnostic Worksheet
Free to print and use in your classroom. No sign-up required.
Percentage Diagnostic Worksheet
Skills checklist - tick after completing:
Complete each pair of questions and tick the skill on the checklist above if you feel confident. Show your working throughout.
Skill 1: Finding a percentage of an amount
1a. Find 40% of 350.
1b. Find 17.5% of 680. Give your answer to 2 decimal places.
Skill 2: Percentage increase and decrease
2a. Increase 450 by 20%.
2b. A price of £320 is decreased by 35%. Find the new price.
Skill 3: Expressing one quantity as a percentage of another
3a. Express 18 as a percentage of 72.
3b. A student scores 63 out of 84 in a test. Express their score as a percentage. Give your answer to 1 decimal place.
Skill 4: Percentage change
4a. A book costs £8.00 one year and £9.20 the next year. Calculate the percentage increase.
4b. A town's population fell from 32,000 to 27,200. Calculate the percentage decrease.
Skill 5: Reverse percentages
5a. After a 25% increase, a value is 125. Find the original value.
5b. A price after a 30% reduction is £175. What was the original price?
Skill 6: Compound interest
6a. £3,000 is invested at 5% compound interest per year. What is it worth after 2 years?
6b. A car bought for £12,000 depreciates at 20% per year. What is it worth after 3 years?
Skill 7: Converting between fractions, decimals, and percentages
7a. Write these in order from smallest to largest: 0.72, 3/4, 68%, 7/10.
7b. Express 5/8 as a percentage. Express 0.065 as a percentage.
Skill 8: VAT and discounts
8a. A laptop costs £650 plus VAT at 20%. What is the total price?
8b. A receipt shows £228 including VAT at 20%. What was the price before VAT?
Skill 9: Profit and loss
9a. A trader buys items for £25 each and sells them for £34. Calculate the percentage profit.
9b. A company bought equipment for £8,000 and later sold it for £5,600. Calculate the percentage loss.
Skill 10: Word problems
10a. A cinema sold 1,200 tickets on a Saturday. 35% of tickets sold were for the evening showing. How many evening tickets were sold?
10b. A factory produces 3,600 items per day. Quality control rejects 4.5% of items. How many items pass quality control each day?
Free to print and use in your classroom. No sign-up required. percentages.co.uk
Worked Answers
1a. 140
40% of 350 = 0.40 × 350 = 140
1b. 119.00
17.5% of 680 = 0.175 × 680 = 119.00
2a. 540
450 × 1.20 = 540
2b. £208
£320 × 0.65 = £208
3a. 25%
18 ÷ 72 × 100 = 25%
3b. 75.0%
63 ÷ 84 × 100 = 75.0%
4a. 15% increase
Change = £9.20 − £8.00 = £1.20. % change = 1.20 ÷ 8.00 × 100 = 15%
4b. 15% decrease
Change = 32,000 − 27,200 = 4,800. % change = 4,800 ÷ 32,000 × 100 = 15%
5a. 100
125 ÷ 1.25 = 100
5b. £250
£175 ÷ 0.70 = £250
6a. £3,307.50
After year 1: 3,000 × 1.05 = £3,150. After year 2: £3,150 × 1.05 = £3,307.50
6b. £6,144
12,000 × 0.803 = 12,000 × 0.512 = £6,144
7a. 68%, 7/10, 0.72, 3/4
Convert all to decimals: 0.72, 0.75, 0.68, 0.70. Order: 0.68, 0.70, 0.72, 0.75 = 68%, 7/10, 0.72, 3/4
7b. 5/8 = 62.5%; 0.065 = 6.5%
5 ÷ 8 = 0.625 = 62.5%. 0.065 × 100 = 6.5%
8a. £780
£650 × 1.20 = £780
8b. £190
£228 ÷ 1.20 = £190
9a. 36% profit
Profit = £34 − £25 = £9. % profit = 9 ÷ 25 × 100 = 36%
9b. 30% loss
Loss = £8,000 − £5,600 = £2,400. % loss = 2,400 ÷ 8,000 × 100 = 30%
10a. 420 tickets
35% of 1,200 = 0.35 × 1,200 = 420
10b. 3,438 items
Rejected = 4.5% of 3,600 = 162. Passing = 3,600 − 162 = 3,438
Related resources
Percentage of a Number Calculator
Work out any percentage of any amount instantly.
KS3 Percentages
KS3 percentage guide covering increase, decrease, reverse percentages and change.
Assessment Worksheet
Full assessment worksheet covering all percentage topics.
Medium Difficulty Worksheet
Medium-difficulty percentage questions for KS3 and Foundation GCSE.