Proportion: past paper questions

Where the questions come from

• Question 16May/June 2026, paper 23Structured3 marks

  $y$ is inversely proportional to $x$. When $y=5$, $x=20$. Find $y$ when $x=4$.

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• Question 23Oct/Nov 2025, paper 41Structured2 marks

  $$y\propto \frac{1}{\sqrt{x+1}}$$ When $x=8$, $y=3$. Find $y$ in terms of $x$.

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• Question 12Oct/Nov 2024, paper 22Structured3 marks

  $y$ is directly proportional to the square root of $x+1$. $y=10.5$ when $x=8$. Find $y$ when $x=1.56$.

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• Question 22Oct/Nov 2023, paper 22Structured2 marks

  $x$ is inversely proportional to the square root of $w$. When $w=16$, $x=3$. Find $x$ in terms of $w$.

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• Question 13May/June 2026, paper 42Structured3 marks

  $y$ is inversely proportional to $x$. When $x=6$, $y=10.5$. Find $y$ when $x=9$.

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• Question 21Oct/Nov 2025, paper 42Structured4 marks

  $y$ is inversely proportional to $(x+2{)}^2$. $w$ is proportional to $x$. When $y=8$, $x=3.5$.

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• Question 19Oct/Nov 2024, paper 23Structured2 marks

  $y$ is inversely proportional to $\sqrt{x+2}$. When $x=2$, $y=3$. Find $y$ in terms of $x$.

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• Question 18Oct/Nov 2023, paper 23Structured3 marks

  $F$ is proportional to the product of $m$ and $a$. Calculate the percentage change in $F$ when $m$ is increased by 40% and $a$ is decreased by 15%.

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• Question 20May/June 2025, paper 22Structured4 marks

  $y\propto \frac{1}{\sqrt{x}}$ When $x=9$, $y=2$. Find the value of $y$ when $x=36$.

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• Question 19May/June 2024, paper 22Structured4 marks

  $y$ is directly proportional to $(x-1{)}^2$. When $x=4$, $y=3$. Find $y$ when $x=7$.

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• Question 14May/June 2023, paper 21Structured3 marks

  $y$ is directly proportional to the square of $(x+3)$. When $x=2$, $y=5$. Find $y$ when $x=1$.

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• Question 15May/June 2025, paper 43Structured3 marks

  $m$ is inversely proportional to the square root of $(t+2)$. $m=0.5$ when $t=23$. Find $m$ when $t=98$.

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• Question 19May/June 2023, paper 22Structured3 marks

  $m$ is inversely proportional to the square of $(t+2)$. $m=0.64$ when $t=3$. Find $m$ when $t=8$.

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• Question 18May/June 2023, paper 23Structured3 marks

  $y$ is inversely proportional to the cube root of $(x+5)$. When $x=3$, $y=12$. Find $y$ when $x=22$.

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