Inequalities

Paper 1: Non-calculator June 2025 Higher tier, Question 2 Higher Paper 1: Non-calculator · June 2025 · Question 2 2 marks

Work out the value of x.

x =

[2]

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Paper 2: Calculator June 2025 Higher tier, Question 20 Higher Paper 2: Calculator · June 2025 · Question 20 1 mark

David has solved the inequality x² 16 and represented his solution on the number line below.

Give one reason why David’s solution is wrong.

[1]

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Paper 3: Calculator June 2025 Higher tier, Question 19 Higher Paper 3: Calculator · June 2025 · Question 19 4 marks

On the grid, identify the region represented by

Label the region R.

[4]

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Paper 3: Calculator June 2025 Higher tier, Question 22 Higher Paper 3: Calculator · June 2025 · Question 22 4 marks

Solve 2x² 12 – 5x

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Paper 1: Non-calculator November 2024 Higher tier, Question 15 Higher Paper 1: Non-calculator · November 2024 · Question 15 4 marks

(a)

Solve the inequality 20 – 5x 30

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(b)

Represent x –1 on the number line.

[1]

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Paper 1: Non-calculator June 2024 Foundation tier, Question 26, also on the Higher paper Foundation Paper 1: Non-calculator · June 2024 · Question 26 Also on Higher 3 marks

(a)

Represent –2 x 4 on the number line.

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(b)

Solve 5y + 14 11

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Paper 1: Non-calculator June 2024 Higher tier, Question 10, also on the Foundation paper Higher Paper 1: Non-calculator · June 2024 · Question 10 Also on Foundation 3 marks

(a)

Represent –2 x 4 on the number line.

[1]

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(b)

Solve 5y + 14 11

[2]

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Paper 1: Non-calculator November 2023 Higher tier, Question 17 Higher Paper 1: Non-calculator · November 2023 · Question 17 3 marks

x and y are integers.

Work out the largest possible value of y.

[3]

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Paper 1: Non-calculator November 2023 Higher tier, Question 27 Higher Paper 1: Non-calculator · November 2023 · Question 27 1 mark

Write down the solution of x² 16

[1]

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Paper 3: Calculator November 2023 Higher tier, Question 23 Higher Paper 3: Calculator · November 2023 · Question 23 4 marks

Also involves Volume and surface area

A chocolate box in the shape of a prism is being designed. All lengths are in centimetres. The cross section is a regular hexagon with side x The length is 5 x

The total surface area of the box must be less than 650 cm²

Work out the largest possible integer value of x. You must show your working.

[4]

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Paper 1: Non-calculator November 2022 Foundation tier, Question 23, also on the Higher paper Foundation Paper 1: Non-calculator · November 2022 · Question 23 Also on Higher 2 marks

Work out all the integer values of x for which 12 ≤ 4x 25

[2]

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Paper 1: Non-calculator November 2022 Higher tier, Question 9, also on the Foundation paper Higher Paper 1: Non-calculator · November 2022 · Question 9 Also on Foundation 2 marks

Work out all the integer values of x for which 12 ≤ 4x 25

[2]

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Paper 1: Non-calculator November 2022 Higher tier, Question 25 Higher Paper 1: Non-calculator · November 2022 · Question 25 3 marks

(a)

Solve x² – 5x – 6 0

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(b)

Show the solution to x² – 5x – 6 0 on the number line.

[1]

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Paper 2: Calculator June 2022 Higher tier, Question 4 Higher Paper 2: Calculator · June 2022 · Question 4 1 mark

Circle the inequality represented by the diagram.

[1]

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Paper 1: Non-calculator November 2021 Foundation tier, Question 25, also on the Higher paper Foundation Paper 1: Non-calculator · November 2021 · Question 25 Also on Higher 5 marks

(a)

Solve 5x + 6 3x + 15

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(b)

Write down the inequality represented by the number line.

[2]

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Paper 1: Non-calculator November 2021 Higher tier, Question 8, also on the Foundation paper Higher Paper 1: Non-calculator · November 2021 · Question 8 Also on Foundation 5 marks

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(a)

Solve 5x + 6 3x + 15

[3]

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(b)

Write down the inequality represented by the number line.

[2]

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Paper 2: Calculator November 2021 Higher tier, Question 18 Higher Paper 2: Calculator · November 2021 · Question 18 3 marks

On the grid, identify the region represented by

Label the region R.

[3]

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Paper 3: Calculator November 2020 Higher tier, Question 19 Higher Paper 3: Calculator · November 2020 · Question 19 1 mark

Also involves Coordinates

The sketch shows the lines x = 1 and y = – 3

Which pair of inequalities describes the shaded region? Tick one box.

[1]

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Paper 2: Calculator November 2019 Higher tier, Question 24 Higher Paper 2: Calculator · November 2019 · Question 24 3 marks

Here are two inequalities.

x and y are integers. Work out the greatest possible value of y – x

[3]

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Paper 2: Calculator June 2019 Foundation tier, Question 24, also on the Higher paper Foundation Paper 2: Calculator · June 2019 · Question 24 Also on Higher 3 marks

x is an integer.

and

Work out all the possible values of x.

[3]

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Paper 2: Calculator June 2019 Higher tier, Question 10, also on the Foundation paper Higher Paper 2: Calculator · June 2019 · Question 10 Also on Foundation 3 marks

Also involves Place value and ordering numbers

x is an integer.

and

Work out all the possible values of x.

[3]

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Paper 2: Calculator June 2019 Higher tier, Question 24 Higher Paper 2: Calculator · June 2019 · Question 24 3 marks

Also involves Quadratic graphs

Here is a sketch of the curve y = x² + 4x – 12

Work out the values of x for which x² + 4x – 12 0 Give your answer as an inequality.

[3]

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Paper 3: Calculator November 2018 Foundation tier, Question 28 Foundation Paper 3: Calculator · November 2018 · Question 28 2 marks

Solve 8 > 3 – x

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Paper 3: Calculator November 2018 Higher tier, Question 10 Higher Paper 3: Calculator · November 2018 · Question 10 2 marks

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Paper 1: Non-calculator June 2018 Higher tier, Question 5 Higher Paper 1: Non-calculator · June 2018 · Question 5 2 marks

Solve 5(x + 3) < 60

[2]

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Paper 1: Non-calculator November 2017 Foundation tier, Question 31, also on the Higher paper Foundation Paper 1: Non-calculator · November 2017 · Question 31 Also on Higher 3 marks

(a)

Factorise x² – 100

[1]

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(b)

Solve 7x + 6 1 + 2x

[2]

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Paper 1: Non-calculator November 2017 Higher tier, Question 5, also on the Foundation paper Higher Paper 1: Non-calculator · November 2017 · Question 5 Also on Foundation 3 marks

(a)

Factorise x² – 100

[1]

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(b)

Solve 7x + 6 1 + 2x

[2]

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Paper 3: Calculator November 2017 Higher tier, Question 23 Higher Paper 3: Calculator · November 2017 · Question 23 2 marks

Joe draws this graph to identify the region R represented by

Make two criticisms of his graph.

Criticism 1

[2]

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Paper 1: Non-calculator June 2017 Higher tier, Question 14 Higher Paper 1: Non-calculator · June 2017 · Question 14 1 mark

Solve –3 x > 6

[1]

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Paper 3: Calculator June 2017 Foundation tier, Question 27, also on the Higher paper Foundation Paper 3: Calculator · June 2017 · Question 27 Also on Higher 2 marks

How are the whole number solutions to A and B different?

[2]

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Paper 3: Calculator June 2017 Higher tier, Question 6, also on the Foundation paper Higher Paper 3: Calculator · June 2017 · Question 6 Also on Foundation 2 marks

How are the whole number solutions to A and B different?

[2]

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