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AQA GCSE Maths

Topic questions Pure mathematics Linear equations

Linear equations

65 questions · 204 marks · about 4 hours

Linear equations questions

TopicLinear equations

AQA 8300 Linear equations 65 questions

Paper 2: Calculator June 2025 Foundation tier, Question 1 3 marks

(a)

Solve w + 8 = 19

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Solve 3 x = 24

[1]
Reveal mark scheme Mark scheme for question 1(b)
(c)

Solve 20 – y = 7

y =

[1]
Reveal mark scheme Mark scheme for question 1(c)

Paper 3: Calculator June 2025 Foundation tier, Question 16, also on the Higher paper 4 marks

Here is an equilateral triangle. All measurements are in centimetres.

Figure for question 16

Work out the value of the perimeter of the triangle.

[4]
Reveal mark scheme Mark scheme for question 16

Paper 3: Calculator June 2025 Higher tier, Question 4, also on the Foundation paper 4 marks

Here is an equilateral triangle. All measurements are in centimetres.

Figure for question 4

Work out the value of the perimeter of the triangle.

[4]
Reveal mark scheme Mark scheme for question 4

Paper 2: Calculator November 2024 Foundation tier, Question 3 4 marks

(a)

Solve 5 x = 30

[1]
Reveal mark scheme Mark scheme for question 3(a)
(b)

Solve – 2 + y = 10

[1]
Reveal mark scheme Mark scheme for question 3(b)
(c)
Question 3, shown as an image
[2]
Reveal mark scheme Mark scheme for question 3(c)

Paper 3: Calculator November 2024 Foundation tier, Question 11 6 marks

Here is a diagram.

Figure for question 11
(a)

Complete this diagram.

Figure for question 11
[1]
Reveal mark scheme Mark scheme for question 11(a)
(b)

Complete this diagram.

Figure for question 11
[2]
Reveal mark scheme Mark scheme for question 11(b)
(c)
Figure for question 11

Work out the value of b.

[3]
Reveal mark scheme Mark scheme for question 11(c)

Paper 1: Non-calculator June 2023 Foundation tier, Question 8 5 marks

Figure for question 8
(a)

Work out the value of T when P = 4 and W = 2

[2]
Reveal mark scheme Mark scheme for question 8(a)
(b)

Work out the value of P when T = – 40 and W = 10

P =

[3]
Reveal mark scheme Mark scheme for question 8(b)

Paper 3: Calculator June 2023 Foundation tier, Question 1 3 marks

(a)

Solve 5 x = 15

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Solve y + 7 = 50

[1]
Reveal mark scheme Mark scheme for question 1(b)
(c)

y =

Question 1, shown as an image
[1]
Reveal mark scheme Mark scheme for question 1(c)

Paper 2: Calculator November 2021 Foundation tier, Question 21 5 marks

Lynn works as a bus driver. She is paid £10.80 per hour for the first 38 hours she works each week. She is paid 25% more per hour for each extra hour she works. One week, Lynn was paid £491.40 In total, how many hours did she work that week? You must show your working.

[5]
Reveal mark scheme Mark scheme for question 21

Paper 3: Calculator November 2021 Foundation tier, Question 20 2 marks

The n th term of a sequence is 19 – 4 n What is the smallest value of n that gives a negative term?

[2]
Reveal mark scheme Mark scheme for question 20

Paper 1: Non-calculator November 2020 Foundation tier, Question 21 5 marks

(a)

All the terms of a geometric progression are positive. The second and fourth terms are shown. ………. 4 ………. 16 Work out the first and third terms.

[2]
Reveal mark scheme Mark scheme for question 21(a)
(b)

The first two terms of an arithmetic progression are shown. p 5 p ….. The sum of the first three terms is 90 Work out the value of p.

[3]
Reveal mark scheme Mark scheme for question 21(b)

Paper 2: Calculator November 2018 Foundation tier, Question 15 4 marks

Also involves Substitution into formulae

A company uses this formula to work out the cost, £ A, of a taxi ride. A = 4 + 1.8 m + b £4 is a fixed charge m is the number of miles travelled £ b is a charge for booking online

(a)

Clare books a taxi online and travels 8 miles. She pays £20 altogether. How much is the charge for booking online?

[3]
Reveal mark scheme Mark scheme for question 15(a)
(b)

A different company has a fixed charge of £3 charges £1.90 per mile has no charge for booking online. Write a formula for the cost, £ C, of a taxi ride with this company.

[1]
Reveal mark scheme Mark scheme for question 15(b)

Paper 3: Calculator November 2018 Higher tier, Question 9 5 marks

A motor racing circuit consists of two parallel straight sections, each of length 0.75 km a semicircle of diameter 0.9 km three equal, smaller semicircles.

Figure for question 9

The length of a motor race must be greater than 305 km What is the lowest number of full laps needed at this circuit? You must show your working.

[5]
Reveal mark scheme Mark scheme for question 9

Paper 1: Non-calculator June 2018 Foundation tier, Question 31, also on the Higher paper 4 marks

Also involves Area and perimeter

A large rectangle is made by joining three identical small rectangles as shown.

Figure for question 31

The perimeter of one small rectangle is 15 cm Work out the perimeter of the large rectangle.

[4]
Reveal mark scheme Mark scheme for question 31

Paper 1: Non-calculator June 2018 Higher tier, Question 11, also on the Foundation paper 4 marks

A large rectangle is made by joining three identical small rectangles as shown.

Figure for question 11

The perimeter of one small rectangle is 15 cm Work out the perimeter of the large rectangle.

[4]
Reveal mark scheme Mark scheme for question 11

Paper 2: Calculator June 2018 Foundation tier, Question 13 5 marks

Here is a formula for the amount of water needed to cook rice. w = 1.5 r + 0.5 w is the number of cups of water needed r is the number of cups of rice to be cooked

(a)

How many cups of water are needed to cook 7 cups of rice?

[2]
Reveal mark scheme Mark scheme for question 13(a)
(b)

How many cups of rice can be cooked with 20 cups of water?

[3]
Reveal mark scheme Mark scheme for question 13(b)

Paper 2: Calculator June 2018 Foundation tier, Question 15 4 marks

The graph of y = 4 – x for values of x from –2 to 5 is shown on the grid.

(a)

On the grid, draw the graph of y = 2 x – 5 for values of x from –2 to 5

Figure for question 15
[3]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Use your graph to solve 2 x – 5 = 4 – x

x =

[1]
Reveal mark scheme Mark scheme for question 15(b)

Paper 2: Calculator June 2018 Higher tier, Question 28 6 marks

f(x) = 5 – x and g(x) = 3 x + 7

(a)

Simplify f(2 x) + g(x – 1)

[3]
Reveal mark scheme Mark scheme for question 28(a)
(b)

Solve g–1(x) = 2x

x =

[3]
Reveal mark scheme Mark scheme for question 28(b)

Paper 1: Non-calculator November 2017 Foundation tier, Question 5 3 marks

(a)

Solve x – 3 = 14

[1]
Reveal mark scheme Mark scheme for question 5(a)
(b)

x =

Solve 5 y = 45

[1]
Reveal mark scheme Mark scheme for question 5(b)
(c)

y =

Solve 8 + w = 6

w =

[1]
Reveal mark scheme Mark scheme for question 5(c)

Paper 2: Calculator November 2017 Higher tier, Question 21 4 marks

(a)

Meera is using a graphical method to solve 2x2 – 3x = 0 She draws the graph of y = 2x2 and a straight line graph on the same grid.

Question 21, shown as an image
Figure for question 21

Complete her method to solve 2x2 – 3x = 0

[2]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Levi is solving 2x2 + 5x = 0 He uses this method. 2x2 + 5x = 0 subtract 5x from both sides 2x2 = –5x divide both sides by x 2 x = –5 divide both sides by 2 x = –2.5 Evaluate his method and his answer.

[2]
Reveal mark scheme Mark scheme for question 21(b)

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