Equations: past paper questions

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• Question 14May/June 2026, paper 11Structured4 marks

  A bag contains 45 balls. The balls are red or green. The balls are in the ratio $\text{red balls}:\text{green balls}=2:3$.

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• Question 8Oct/Nov 2025, paper 11Structured2 marksHas a diagram

  $p=3q-2r$ Work out the value of $q$ when $p=50$ and $r=5$.

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• Question 3Oct/Nov 2023, paper 11Structured2 marks

  Complete these statements.

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• Question 23May/June 2026, paper 11Structured4 marks

  Solve the simultaneous equations.

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• Question 16Oct/Nov 2024, paper 11Structured2 marks

  The diagram shows a trapezium with parallel sides of length $12\text{ cm}$ and $w\text{ cm}$. The height of the trapezium is $8\text{ cm}$. The area of the trapezium is $78{\text{ cm}}^2$.

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• Question 9Oct/Nov 2023, paper 13Structured2 marksHas a diagram

  The diagram shows an equilateral triangle. Find the value of $x$.

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• Question 12Oct/Nov 2025, paper 12Structured5 marks

  The diagram shows a parallelogram. Use the information in the diagram to write an equation and solve it to find the value of $x$.

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• Question 16Oct/Nov 2023, paper 13Structured2 marks

  Solve the equation.

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• Question 22May/June 2026, paper 13Structured3 marks

  In this question, all lengths are in centimetres. The area, in ${\text{cm}}^2$, of the rectangle is $5x+8$. Write an equation to show this information and solve it to find the value of $x$.

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• Question 23Oct/Nov 2025, paper 12Structured6 marksHas a diagram

  There are two charges for crossing a bridge. $$\begin{array}{rl}{\displaystyle \text{Cars}}& {\displaystyle \mathrm{\$}a}\\ {\displaystyle \text{Other vehicles}}& {\displaystyle \mathrm{\$}b}\end{array}$$ On Monday 4 cars and 20 other vehicles pay a total of $130. On Tuesday 6 cars and 15 other vehicles pay a total of $105.

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• Question 3Oct/Nov 2024, paper 12Structured2 marks

  Solve. $5x=14$

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• Question 6Oct/Nov 2025, paper 13Structured2 marks

  Anna thinks of a number, she multiplies it by 2 and then finds the square root. The answer is 12. What number did Anna think of?

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• Question 14Oct/Nov 2024, paper 12Structured2 marks

  The diagram shows a trapezium. The area of the trapezium is $42{\text{ cm}}^2$. Calculate the value of $x$.

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• Question 8May/June 2026, paper 31Structured3 marks

  Solve. $6+x=2$

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• Question 17Oct/Nov 2024, paper 12Structured4 marksHas a diagram

  The diagram shows a parallelogram. Work out the size of the smallest interior angle of the parallelogram.

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• Question 4Oct/Nov 2023, paper 32Structured8 marks

  Complete the table of values for $y=x^2-4x-2$.

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• Question 14May/June 2026, paper 32Structured7 marks

  There are 60 counters in a jar. Kan adds $C$ counters into the jar. Mo adds $2C+7$ counters into the jar.

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• Question 8Oct/Nov 2025, paper 31Structured5 marks

  Solve. $8x=32$

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• Question 6Oct/Nov 2023, paper 32Structured12 marks

  Simplify. $$a+4a-3a$$

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• Question 13May/June 2026, paper 33Structured4 marks

  Solve. $$6=\frac{32.4}{a}$$

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• Question 5Oct/Nov 2025, paper 32Structured2 marks

  Solve. 8x = 5

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• Question 17Oct/Nov 2024, paper 13Structured4 marks

  Ed has $n$ books. Sam has 3 times as many books as Ed Jane has 2 books fewer than Sam. The total number of books is 54.

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• Question 8Oct/Nov 2023, paper 33Structured9 marks

  Expand and simplify.

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• Question 12May/June 2025, paper 11Structured2 marks

  Solve. $$5x+8=3x-2$$ Solve.

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• Question 10Oct/Nov 2024, paper 31Structured9 marks

  Solve. $$4x-7=3$$

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• Question 4Oct/Nov 2024, paper 33Structured10 marks

  $$n=15r+20c$$ Find the value of $r$ when $n=180$ and $c=3$.

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• Question 21May/June 2023, paper 11Structured3 marksHas a diagram

  The diagram shows a right-angled triangle. Use the information in the diagram to write down and solve an equation to find the value of $x$.

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• Question 15May/June 2025, paper 12Structured2 marks

  Beth thinks of a positive number, $n$. She squares $n$ then subtracts 55. The answer is 9.

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• Question 10May/June 2024, paper 11Structured4 marksHas a diagram

  The total surface area of this cuboid is $369{\text{ cm}}^2$. Work out the value of $h$.

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• Question 25May/June 2023, paper 13Structured4 marksHas a diagram

  In this question, both lengths are in centimetres. The diagram shows two lines, $AB$ and $CD$. The length of $AB$ is $10x-12$.

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