Algebraic manipulation: past paper questions

Where the questions come from

• Question 12May/June 2026, paper 12Structured2 marks

  Rearrange the formula to make $m$ the subject. $$k=4(m-p)$$ Rearrange the formula to make $m$ the subject. $$k=4(m-p)$$

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• Question 24Oct/Nov 2025, paper 11Structured10 marks

  The diagram shows a rectangle and a triangle. The length of the rectangle is $x\text{ cm}$ and the area of the rectangle is $30{\text{ cm}}^2$. The triangle has sides of length $(x-1)\text{ cm}$, $(x+2)\text{ cm}$ and $(2x-3)\text{ cm}$.

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• Question 15May/June 2026, paper 22Structured4 marks

  Simplify. $$a^5\times a^3$$

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• Question 25Oct/Nov 2025, paper 11Structured3 marks

  Factorise. $$6x^3+5x^2-4x$$ Factorise.

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• Question 11Oct/Nov 2024, paper 12Structured2 marks

  Factorise. $$4m^2-14m$$ Factorise.

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• Question 20Oct/Nov 2023, paper 12Structured4 marks

  Factorise. 2cd + ce - 6d - 3e

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• Question 21May/June 2026, paper 22Structured4 marks

  Simplify. $$\frac{8}{32x}$$

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

  Rearrange the formula to make a the subject.

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• Question 20Oct/Nov 2024, paper 12Structured4 marks

  Simplify. $$(16a^{20}{)}^{\frac{3}{4}}$$

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• Question 25May/June 2026, paper 22Structured5 marks

  Write $2x^2-8x+7$ in the form $a(x-b{)}^2+c$.

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• Question 22Oct/Nov 2025, paper 21Structured7 marks

  Sketch the graph of y = 2 - 3x.

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• Question 5Oct/Nov 2024, paper 21Structured13 marks

  Solve. $\frac{y}{4}=8$

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• Question 14May/June 2023, paper 11Structured4 marks

  Expand and simplify.

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• Question 7Oct/Nov 2024, paper 22Structured13 marks

  Solve. $$4x+7=16$$

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• Question 7Oct/Nov 2025, paper 22Structured2 marks

  Factorise. $$20x^2-5xy$$ Factorise.

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• Question 12May/June 2024, paper 11Structured3 marks

  Solve. $$4(2x-3)+5(x+5)=20$$ $x=$ Solve.

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• Question 19May/June 2025, paper 12Structured4 marks

  Simplify. $$\frac{3x^2-12}{2x^2+11x+14}$$ Simplify.

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• Question 9May/June 2024, paper 12Structured4 marks

  There are red pens, blue pens and black pens in a box. There are $x$ red pens. The number of blue pens is 5 more than the number of red pens.

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• Question 22May/June 2025, paper 12Structured7 marksHas a diagram

  Write $x^2+4x-12$ in the form $(x+a{)}^2+b$.

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• Question 7May/June 2024, paper 22Structured8 marks

  Solve $\frac{x}{3}=7$.

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• Question 10May/June 2025, paper 22Structured2 marks

  Simplify. $$\frac{7x^2{y}^5}{x^3{y}^2}$$ Simplify.

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