Algebraic fractions: past paper questions

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• Question 24May/June 2026, paper 23Structured4 marks

  Write as a single fraction in its simplest form.

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• Question 7Oct/Nov 2025, paper 21Structured4 marks

  Simplify. $\frac{p}{t}÷\frac{2}{t}$

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• Question 25Oct/Nov 2024, paper 23Structured4 marks

  Simplify. $$\frac{3x-2-3xy+2y}{1-y^2}$$ Simplify.

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• Question 15May/June 2026, paper 42Structured3 marks

  Write $\frac{8}{x+2}+\frac{3}{x-4}$ as a single fraction in its simplest form.

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• Question 22Oct/Nov 2025, paper 21Structured5 marks

  Solve. $$\frac{2}{x-1}=\frac{x}{x+2}$$ Solve.

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• Question 24Oct/Nov 2023, paper 22Structured4 marks

  Simplify. $$\frac{ax-2a-x+2}{a^2-1}$$ Simplify.

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• Question 22May/June 2026, paper 42Structured3 marks

  Write $\frac{8x^2+24x}{2x^2-18}$ as a single fraction in its simplest form.

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• Question 25Oct/Nov 2025, paper 21Structured4 marks

  Simplify. $$\frac{10ax+6bx-25a-15b}{4x^2-25}$$ Simplify.

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• Question 6Oct/Nov 2024, paper 43Structured9 marks

  Simplify ${\displaystyle \frac{24u}{5y}}\times {\displaystyle \frac{10}{3u}}$.

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• Question 17Oct/Nov 2023, paper 23Structured4 marks

  Simplify. $$(64y^{27}{)}^{\frac{2}{3}}$$

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• Question 28Oct/Nov 2025, paper 23Structured4 marks

  Simplify. $\frac{2x^2-11x-21}{x^2-49}$ Simplify.

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• Question 23May/June 2024, paper 23Structured3 marks

  Simplify. $$\frac{2}{y+1}-\frac{3}{y}$$ Give your answer as a single fraction in its simplest form.

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• Question 24Oct/Nov 2025, paper 41Structured11 marks

  Martha walks a distance of $10\text{ km}$ at a speed of $x\text{ km/h}$. She then runs a distance of $5\text{ km}$ at a speed of $(x+4)\text{ km/h}$. The total time taken for the whole journey is 3.5 hours.

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• Question 25May/June 2024, paper 23Structured4 marks

  Simplify. $$\frac{pt-p-t+1}{1-t^2}$$ Simplify.

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• Question 13Oct/Nov 2025, paper 42Structured2 marks

  Simplify. $$\frac{7}{2m}+\frac{3}{8m}$$ Simplify.

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• Question 3May/June 2024, paper 41Structured13 marks

  $C=\frac{1}{4}x{y}^2$ Find $C$ when $x=5$ and $y=8$.

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• Question 21May/June 2023, paper 23Structured4 marks

  Simplify. $$\frac{2x^2+5x-12}{4x^2-9}$$ Simplify.

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• Question 5May/June 2024, paper 42Structured18 marks

  Simplify $(25x^6{)}^{\frac{3}{2}}$.

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• Question 7May/June 2023, paper 41Structured18 marks

  Factorise fully.

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• Question 18May/June 2025, paper 21Structured10 marks

  One day, Anya runs $12\text{ km}$ at a speed of $x\text{ km/h}$. The next day she walks $10\text{ km}$ at a speed of $(x-4)\text{ km/h}$. Write down an expression, in terms of $x$, for the time she spends running.

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• Question 9May/June 2023, paper 42Structured15 marks

  Simplify. $(3x^2{y}^4{)}^3$

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• Question 23May/June 2025, paper 21Structured3 marks

  Simplify. $$\frac{2x^2+10x}{x^2-25}$$ Simplify.

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• Question 19May/June 2025, paper 23Structured3 marksHas a diagram

  Simplify. $$\frac{7x-x^2}{49-x^2}$$ Simplify.

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• Question 23May/June 2025, paper 42Structured3 marks

  Simplify. $$\frac{h^2+4h}{h^2-16}$$ Simplify.

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