Inequalities – Higher – GCSE Questions – AQA These questions are the same format as previous GCSE exams. COPY means they use the exact same numbers as the original GCSE question. Otherwise, they are clone questions using different numbers. The worksheets are provided in 2 sizes.

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AQA Higher: November 2017 Paper 3, Q1 Circle the inequality shown by the diagram. 1 Circle the inequality shown by the diagram. 𝑥 𝑥 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 [1 mark] [1 mark] −3 ⩽ x < 7 −3 < x < 7 −3 ⩽ x ⩽ 7 −3 < x ⩽ 7 −3 ⩽ x < 7 −3 < x < 7 −3 ⩽ x ⩽ 7 −3 < x ⩽ 7 2 Circle the inequality shown by the diagram. 2 Circle the inequality shown by the diagram. 𝑥 𝑥 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 [1 mark] [1 mark] 0 < x ⩽ 5 0 ⩽ x ⩽ 5 0 < x < 5 0 ⩽ x < 5 0 < x ⩽ 5 0 ⩽ x ⩽ 5 0 < x < 5 0 ⩽ x < 5 AQA Higher: November 2017 Paper 3, Q1 AQA Higher: November 2017 Paper 3, Q1 1 Circle the inequality shown by the diagram. 1 Circle the inequality shown by the diagram. 𝑥 𝑥 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 [1 mark] [1 mark] −3 ⩽ x < 7 −3 < x < 7 −3 ⩽ x ⩽ 7 −3 < x ⩽ 7 −3 ⩽ x < 7 −3 < x < 7 −3 ⩽ x ⩽ 7 −3 < x ⩽ 7 2 Circle the inequality shown by the diagram. 2 Circle the inequality shown by the diagram. 𝑥 𝑥 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 [1 mark] [1 mark] 0 < x ⩽ 5 0 ⩽ x ⩽ 5 0 < x < 5 0 ⩽ x < 5 0 < x ⩽ 5 0 ⩽ x ⩽ 5 0 < x < 5 0 ⩽ x < 5

AQA Higher: June 2018 Paper 3, Q2 AQA Higher: June 2018 Paper 3, Q2 Circle the list of all the integers that satisfy –3 ⩽ 𝑥 < 2 1 Circle the list of all the integers that satisfy –3 ⩽ 𝑥 < 2 [1 mark] [1 mark] −3, −2, −1, 0, 1, 2 −2, −1, 0, 1 −3, −2, −1, 0, 1, 2 −2, −1, 0, 1 −2, −1, 0, 1, 2 −3, −2, −1, 0, 1 −2, −1, 0, 1, 2 −3, −2, −1, 0, 1 2 Circle the list of all the integers that satisfy –8 ⩽ 𝑥 ⩽ –4 2 Circle the list of all the integers that satisfy –8 ⩽ 𝑥 ⩽ –4 [1 mark] [1 mark] −7, −6, −5, −3 −8, −7, −6, −5, −4 −7, −6, −5, −3 −8, −7, −6, −5, −4 −7, −6, −5, −4 −8, −6, −5, −4, −3 −7, −6, −5, −4 −8, −6, −5, −4, −3 AQA Higher: June 2018 Paper 3, Q2 AQA Higher: June 2018 Paper 3, Q2 1 Circle the list of all the integers that satisfy –3 ⩽ 𝑥 < 2 1 Circle the list of all the integers that satisfy –3 ⩽ 𝑥 < 2 [1 mark] [1 mark] −3, −2, −1, 0, 1, 2 −2, −1, 0, 1 −3, −2, −1, 0, 1, 2 −2, −1, 0, 1 −2, −1, 0, 1, 2 −3, −2, −1, 0, 1 −2, −1, 0, 1, 2 −3, −2, −1, 0, 1 2 Circle the list of all the integers that satisfy –8 ⩽ 𝑥 ⩽ –4 2 Circle the list of all the integers that satisfy –8 ⩽ 𝑥 ⩽ –4 [1 mark] [1 mark] −7, −6, −5, −3 −8, −7, −6, −5, −4 −7, −6, −5, −3 −8, −7, −6, −5, −4 −7, −6, −5, −4 −8, −6, −5, −4, −3 −7, −6, −5, −4 −8, −6, −5, −4, −3

AQA Higher: May 2017 Paper 1, Q14 AQA Higher: May 2017 Paper 1, Q14 Solve −4𝑥>8 [1 mark] 1 Solve −4𝑥>8 [1 mark] Answer Answer 2 Solve 5 ⩽−3𝑥 [1 mark] 2 Solve 5 ⩽−3𝑥 [1 mark] Answer Answer 3 Solve 2−8𝑥<4 [1 mark] 3 Solve 2−8𝑥<4 [1 mark] Answer Answer AQA Higher: May 2017 Paper 1, Q14 AQA Higher: May 2017 Paper 1, Q14 1 Solve −4𝑥>8 [1 mark] 1 Solve −4𝑥>8 [1 mark] Answer Answer 2 Solve 5 ⩽−3𝑥 [1 mark] 2 Solve 5 ⩽−3𝑥 [1 mark] Answer Answer 3 Solve 2−8𝑥<4 [1 mark] 3 Solve 2−8𝑥<4 [1 mark] Answer Answer

AQA Higher: June 2017 Paper 3, Q6 AQA Higher: June 2017 Paper 3, Q6 How are the whole number solutions to A and B different? A Solve 4 ⩽ 4𝑥 < 16 B Solve 4 < 4𝑥 ⩽ 16 1 How are the whole number solutions to A and B different? A Solve 4 ⩽ 4𝑥 < 16 B Solve 4 < 4𝑥 ⩽ 16 [2 marks] [2 marks] AQA Higher: June 2017 Paper 3, Q6 AQA Higher: June 2017 Paper 3, Q6 1 How are the whole number solutions to A and B different? A Solve 4 ⩽ 4𝑥 < 16 B Solve 4 < 4𝑥 ⩽ 16 1 How are the whole number solutions to A and B different? A Solve 4 ⩽ 4𝑥 < 16 B Solve 4 < 4𝑥 ⩽ 16 [2 marks] [2 marks]

AQA Higher: May 2018 Paper 1, Q5 AQA Higher: May 2018 Paper 1, Q5 [2 marks] Solve 6 𝑥+4 ⩽ 72 Answer 1 [2 marks] Solve 6 𝑥+4 ⩽ 72 Answer 2 [2 marks] Solve 4 2𝑥+3 > 68 Answer 2 [2 marks] Solve 4 2𝑥+3 > 68 Answer AQA Higher: May 2018 Paper 1, Q5 AQA Higher: May 2018 Paper 1, Q5 1 [2 marks] Solve 6 𝑥+4 ⩽ 72 Answer 1 [2 marks] Solve 6 𝑥+4 ⩽ 72 Answer 2 [2 marks] Solve 4 2𝑥+3 > 68 Answer 2 [2 marks] Solve 4 2𝑥+3 > 68 Answer

AQA Higher: November 2017 Paper 1, Q5 Factorise 𝑥2 −49 [1 mark] 1 (a) Factorise 𝑥2 −49 [1 mark] Answer Answer 1 (b) Solve 5𝑥+7>1+3𝑥 [2 marks] 1 (b) Solve 5𝑥+7>1+3𝑥 [2 marks] Answer Answer AQA Higher: November 2017 Paper 1, Q5 AQA Higher: November 2017 Paper 1, Q5 1 (a) Factorise 𝑥2 −49 [1 mark] 1 (a) Factorise 𝑥2 −49 [1 mark] Answer Answer 1 (b) Solve 5𝑥+7>1+3𝑥 [2 marks] 1 (b) Solve 5𝑥+7>1+3𝑥 [2 marks] Answer Answer

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