Percentages (GCSE Maths) - Worksheets, Questions and Revision

18 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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GCSE · EDEXCEL

3.7 Percentages

EDEXCEL 1MA1 · Calculator allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Revision notes: Percentages

A percentage is a number expressed as a fraction of 100 (percent means 'per hundred'). GCSE percentages questions ask you to find a percentage of an amount, express one number as a percentage of another, and increase or decrease a quantity by a percentage, both with and without a calculator.

Non-calculator: build up from 10% (divide by 10), 5% (halve the 10% value) and 1% (divide by 100), then add or subtract these building blocks to make the percentage you need.
Calculator: convert the percentage to a decimal multiplier (divide by 100), then multiply by the amount.
To increase by a percentage, use a multiplier greater than 1 (e.g. +12% is x1.12). To decrease, use a multiplier less than 1 (e.g. -15% is x0.85).
To write one quantity as a percentage of another, divide the first quantity by the second, then multiply by 100.

Worked example. A laptop costs 480 pounds. In a sale its price is reduced by 15%. Work out the sale price.

Method 1 (find the decrease): 10% of 480 = 48; 5% of 480 = 24; so 15% = 48 + 24 = 72.
Sale price = 480 - 72 = 408 pounds.
Method 2 (multiplier check): a 15% decrease is a multiplier of 1 - 0.15 = 0.85; 480 x 0.85 = 408 pounds.

Answer: 408 pounds.

(Non-calculator)

(a)Write 45% as a decimal.(1)

(b)Write 3/4 as a percentage.(1)

(c)Write 0.2 as a percentage.(1)

(Total for Question 1 is 3 marks)

(Non-calculator)

(a)Work out 10% of 340.(1)

(b)Work out 25% of 60.(1)

(c)Work out 30% of 150.(2)

(Total for Question 2 is 4 marks)

(Non-calculator) Work out 17.5% of 240.

(Total for Question 3 is 3 marks)

Work out 23% of 560 pounds.

(Total for Question 4 is 2 marks)

In a class of 25 students, 17 are right-handed. Work out the percentage of the class that is right-handed.

(Total for Question 5 is 2 marks)

(Non-calculator) A jacket costs 80 pounds. In a sale, the price is reduced by 15%.

(a)Work out the sale price of the jacket.(3)

(Total for Question 6 is 3 marks)

The population of a village is 1500. Over one year the population increases by 12%.

(a)Work out the population at the end of the year.(2)

(Total for Question 7 is 2 marks)

A car is worth 9000 pounds. Over one year its value decreases by 8%.

(a)Work out the value of the car at the end of the year.(2)

(Total for Question 8 is 2 marks)

A restaurant bill for food comes to 45 pounds. VAT is then added at 20%.

(a)Work out the total cost of the bill including VAT.(2)

(Total for Question 9 is 2 marks)

Yusuf invests 2000 pounds in a savings account. The account pays 3% simple interest each year.

(a)Work out the total interest Yusuf earns after 4 years.(3)

(Total for Question 10 is 3 marks)

A shopkeeper buys a bicycle for 120 pounds. She sells it for 150 pounds.

(a)Work out her percentage profit.(3)

(Total for Question 11 is 3 marks)

Amelia and Noah each sit a test. Amelia scores 42 out of 60. Noah scores 55 out of 80.

(a)By working out each score as a percentage, determine who did better in the test. You must show your working.(3)

(Total for Question 12 is 3 marks)

A shop sells rice in two sizes.
A 2 kg bag costs 3.20 pounds.
A 5 kg bag costs 7.50 pounds, with 10% off the marked price at the till.

(a)Determine which bag is the better value for money. You must show your working.(4)

(Total for Question 13 is 4 marks)

Priya has 240 pounds. She spends 35% of it on a coat. She then spends 1/4 of what is left on a pair of shoes.

(a)Work out how much money Priya has left.(4)

(Total for Question 14 is 4 marks)

A theatre has 800 seats. For one show, 65% of the seats are sold in advance. On the night of the show, a further 120 seats are sold.

(a)Work out what percentage of the theatre's seats are sold in total.(3)

(Total for Question 15 is 3 marks)

A shop increases the price of a coat by 20%. In a later sale, it reduces the new price by 20%. A customer says:
"The price is now back to what it started at, because a 20% increase and a 20% decrease cancel each other out."

(a)Using a starting price of 50 pounds, show that the customer is wrong and explain why.(3)

(Total for Question 16 is 3 marks)

In a sale, all normal prices are reduced by 20%. The sale price of a coat is 68 pounds.

(a)Work out the normal price of the coat before the sale.(3)

(Total for Question 17 is 3 marks)

Kwame invests 3000 pounds in an account paying 5% compound interest per year.

(a)Work out the value of the investment at the end of 2 years.(3)

(Total for Question 18 is 3 marks)

Mark scheme · 3.7 Percentages

Question 1

(a) B1 0.45
(a) Answer: 0.45
(b) B1 75%
(b) Answer: 75%
(c) B1 20%
(c) Answer: 20%

Question 2

(a) B1 34
(a) Answer: 34
(b) B1 15
(b) Answer: 15
(c) M1 10% of 150 = 15 seen, or 0.3 x 150 (oe method)
(c) A1 45
(c) Answer: 45

Question 3

M1 10% of 240 = 24
M1 5% = 12 and 2.5% = 6 (oe building blocks)
A1 42
Answer: 42

Question 4

M1 0.23 x 560 (oe)
A1 128.80 (pounds)
Answer: 128.80 pounds

Question 5

M1 17/25 x 100 (oe)
A1 68%
Answer: 68%

Question 6

(a) M1 15% of 80: 10% = 8 and 5% = 4 (oe), so reduction = 12
(a) M1 80 - 12 (oe)
(a) A1 68 (pounds)
(a) Answer: 68 pounds

Question 7

(a) M1 1.12 x 1500 (oe: 12% of 1500 = 180)
(a) A1 1680
(a) Answer: 1680

Question 8

(a) M1 0.92 x 9000 (oe: 8% of 9000 = 720)
(a) A1 8280 (pounds)
(a) Answer: 8280 pounds

Question 9

(a) M1 1.2 x 45 (oe: 20% of 45 = 9)
(a) A1 54 (pounds)
(a) Answer: 54 pounds

Question 10

(a) M1 interest for one year = 3% of 2000 = 60
(a) M1 60 x 4 (oe)
(a) A1 240 (pounds)
(a) Answer: 240 pounds

Question 11

(a) M1 profit = 150 - 120 = 30
(a) M1 30/120 x 100 (oe)
(a) A1 25%
(a) Answer: 25%

Question 12

(a) M1 42/60 x 100 = 70% (oe)
(a) M1 55/80 x 100 = 68.75% (oe)
(a) C1 Amelia did better, because 70% > 68.75%
(a) Answer: Amelia (70% vs 68.75%)

Question 13

(a) M1 2 kg unit price = 3.20/2 = 1.60 pounds/kg
(a) M1 5 kg price after discount = 7.50 x 0.9 = 6.75 pounds
(a) M1 5 kg unit price = 6.75/5 = 1.35 pounds/kg
(a) C1 the 5 kg bag is better value because 1.35 < 1.60 pounds/kg
(a) Answer: 5 kg bag (1.35 pounds/kg vs 1.60 pounds/kg)

Question 14

(a) M1 35% of 240 = 84 (coat)
(a) M1 amount left after coat = 240 - 84 = 156
(a) M1 1/4 of 156 = 39 (shoes)
(a) A1 117 (pounds)
(a) Answer: 117 pounds

Question 15

(a) M1 65% of 800 = 520
(a) M1 (520 + 120)/800 x 100 (oe)
(a) A1 80%
(a) Answer: 80%

Question 16

(a) M1 after increase: 50 x 1.2 = 60 (pounds)
(a) M1 after decrease: 60 x 0.8 = 48 (pounds)
(a) C1 final price is 48 pounds, not 50; the 20% decrease is taken from the larger 60 pounds, not the original 50 pounds
(a) Answer: Final price 48 pounds (not 50); the decrease is of a larger amount

Question 17

(a) M1 recognises 68 represents 80% (0.8) of the normal price
(a) M1 68 / 0.8 (oe)
(a) A1 85 (pounds)
(a) Answer: 85 pounds

Question 18

(a) M1 3000 x 1.05² (oe, or year 1 value = 3150)
(a) M1 3150 x 1.05 (oe evaluation)
(a) A1 3307.50 (pounds)
(a) Answer: 3307.50 pounds

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Percentages (GCSE Maths) - Worksheets, Questions and Revision

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3.7 Percentages

Revision notes: Percentages

Question 1

Question 2

Question 3

Question 4

Question 5

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Question 7

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Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

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Question 18

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Question 18