1. 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.

2. Printing To print handouts from slides -
Select the slide from the left. Then click:
File > Print > ‘Print Current Slide’
To print multiple slides -
Click on a section title to highlight all those slides,
or press ‘Ctrl’ at the same time as selecting slides to
highlight more than one. Then click:
File > Print > ‘Print Selection’
To print double-sided handouts -
Highlight both slides before using ‘Print Selection’.
Choose ‘Print on Both Sides’ and ‘Flip on Short Edge’.

3. 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

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

7. 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 ⩽−3𝑥
[1 mark] 2
Solve ⩽−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 ⩽−3𝑥
[1 mark] 2
Solve ⩽−3𝑥
[1 mark]
Answer
Answer 3
Solve 2−8𝑥<4
[1 mark] 3
Solve 2−8𝑥<4
[1 mark]
Answer
Answer

9. 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]

11. 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

13. 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

27. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to