EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Solving Linear Inequalities
Solving linear inequalities · Equations and inequalities · Lesson 1 of 7 · 16 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 NON-CALCULATOR (2 marks)
Solve 3x + 2 ≤ 14.
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(Total for Question 1 = 2 marks)
Question 2 NON-CALCULATOR (3 marks)
Solve 5 − 2x > 11.
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(Total for Question 2 = 3 marks)
Question 3 NON-CALCULATOR (2 marks)
The number line shows an inequality. Write down the inequality.
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(Total for Question 3 = 2 marks)
Question 4 NON-CALCULATOR (2 marks)
n is an integer. Write down all the possible values of n when −2 < n ≤ 3.
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(Total for Question 4 = 2 marks)
Question 5 NON-CALCULATOR (3 marks)
Solve 5 < 2x − 1 ≤ 9.
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(Total for Question 5 = 3 marks)
Question 6 NON-CALCULATOR (4 marks)
On the grid, the region R satisfies y ≥ 1, y ≤ x and x + y ≤ 6. Mark the region R with an R.
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(Total for Question 6 = 4 marks)
TOTAL FOR PAPER = 16 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
3x ≤ 12, so x ≤ 4.
• 3x ≤ 12 M1
• x ≤ 4 A1
Question 2 (3 marks)
−2x > 6, so x < −3.
• −2x > 6 M1
• Dividing by −2 M1
• x < −3 A1
Question 3 (2 marks)
−2 < x ≤ 3.
• x ≤ 3 or x > −2 B1
• −2 < x ≤ 3 B1
Question 4 (2 marks)
−1, 0, 1, 2, 3.
• At least four correct values M1
• All correct A1
Question 5 (3 marks)
6 < 2x ≤ 10, so 3 < x ≤ 5.
• Adding 1 to all parts M1
• Dividing all parts by 2 M1
• 3 < x ≤ 5 A1
Question 6 (4 marks)
The lines y = 1, y = x and x + y = 6 are drawn; the triangle with vertices (1, 1), (5, 1) and (3, 3) is labelled R.
• One line drawn correctly M1
• All three lines drawn correctly M1
• The correct region M1
• R labelled A1