Inequalities: past paper questions

Where the questions come from

• Question 12May/June 2026, paper 22Structured7 marks

  On the grid, draw these four straight lines.

  Try this question
• Question 16Oct/Nov 2025, paper 21Structured4 marks

  Write down all the inequalities that define the region $R$.

  Try this question
• Question 13Oct/Nov 2024, paper 22Structured4 marks

  The region $R$ satisfies these inequalities. $$-3<y⩽2y⩽x-1$$ By drawing suitable straight lines and shading unwanted regions, find and label the region $R$.

  Try this question
• Question 3May/June 2026, paper 23Structured2 marks

  Write down the inequality shown by the number line.

  Try this question
• Question 7Oct/Nov 2024, paper 41Structured12 marksHas a diagram

  A company makes scientific calculators and graphic calculators. Each day they make $x$ scientific calculators and $y$ graphic calculators. These inequalities describe the number of scientific and graphic calculators they make each day.

  Try this question
• Question 15Oct/Nov 2023, paper 21Structured5 marksHas a diagram

  By shading the unwanted regions of the grid, draw and label the region R which satisfies these inequalities.

  Try this question
• Question 7Oct/Nov 2025, paper 41Structured4 marks

  Write down the inequality represented in the diagram.

  Try this question
• Question 11May/June 2024, paper 21Structured4 marksHas a diagram

  Find the inequalities that define the unshaded region, R. Find the inequalities that define the unshaded region, R.

  Try this question
• Question 13Oct/Nov 2023, paper 23Structured4 marksHas a diagram

  The graph of $y=2x+1$ is drawn on the grid. By shading the unwanted regions of the grid, find and label the region R which satisfies these inequalities.

  Try this question
• Question 7May/June 2025, paper 41Structured2 marks

  Write down the inequality in $y$ shown by the number line.

  Try this question
• Question 8May/June 2024, paper 42Structured11 marks

  A baker decorates $x$ small cakes and $y$ large cakes. In one day, he decorates: • not more than 16 small cakes • less than 10 large cakes • more small cakes than large cakes • a total of not more than 24 cakes.

  Try this question
• Question 8May/June 2023, paper 22Structured4 marks

  Solve. $\frac{30}{x}=6$

  Try this question
• Question 16May/June 2025, paper 43Structured5 marksHas a diagram

  By shading the unwanted regions of the grid, draw and label the region $R$ which satisfies these three inequalities.

  Try this question
• Question 8May/June 2023, paper 41Structured12 marks

  A tailor makes $x$ dresses and $y$ shirts in one week. In one week • he makes at least 4 dresses • he makes no more than 7 shirts • he makes less than 14 dresses and shirts altogether • the number of shirts he makes is more than $\frac{2}{3}$ of the number of dresses.

  Try this question