Algebraic manipulation: past paper questions

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• Question 21May/June 2026, paper 11Structured3 marks

  Make $T$ the subject of the formula. $$P=Ty$$

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• Question 25Oct/Nov 2025, paper 11Structured2 marks

  Expand and simplify.

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• Question 14Oct/Nov 2023, paper 11Structured2 marks

  Factorise completely.

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• Question 21Oct/Nov 2025, paper 12Structured2 marks

  Simplify. $$\frac{18x^8}{9x^2}$$ Simplify.

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• Question 28May/June 2026, paper 12Structured2 marks

  Make $T$ the subject of the formula. $$Q=3-4T$$ Make $T$ the subject of the formula. $$Q=3-4T$$

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• Question 18Oct/Nov 2024, paper 12Structured2 marks

  Simplify. $$\frac{18x^6}{3x^2}$$ Simplify.

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• Question 12May/June 2026, paper 13Structured2 marks

  Factorise. $$5c-15c^{2}d$$ Factorise.

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• Question 20May/June 2026, paper 31Structured5 marks

  $P=5x+4y$ Find the value of $x$ when $P=18$ and $y=-3$.

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• Question 17Oct/Nov 2025, paper 13Structured5 marks

  $$k^x\times k^5=k^{20}$$ Find the value of $x$.

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• Question 3Oct/Nov 2023, paper 32Structured12 marks

  Write the number fourteen thousand and ninety-seven in figures.

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• Question 12May/June 2026, paper 32Structured1 mark

  Factorise. $x^2+7x$ Factorise.

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

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

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

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

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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 24Oct/Nov 2025, paper 33Structured2 marks

  Make $p$ the subject of the formula $m=9p+32$. Make $p$ the subject of the formula $m=9p+32$.

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• Question 19May/June 2023, paper 12Structured2 marks

  Simplify. $$18x^{12}÷3x^3$$ Simplify.

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• Question 22May/June 2025, paper 13Structured2 marks

  $g=\frac{h}{3}-8$ Rearrange the formula to make $h$ the subject. $g=\frac{h}{3}-8$ Rearrange the formula to make $h$ the subject.

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• Question 8May/June 2023, paper 32Structured15 marks

  $$T=5P+3Q$$ Find the value of $T$ when $P=6$ and $Q=8$.

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• Question 14May/June 2025, paper 32Structured4 marks

  $P=6a+5b$ Find the value of $b$ when $P=25$ and $a=3$.

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• Question 21May/June 2025, paper 32Structured3 marks

  Simplify. $(w^3{)}^{10}$

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• Question 6May/June 2024, paper 33Structured14 marks

  In a sport, teams are given points using the formula $$\text{number of points}=\text{number of wins}\times 4+\text{number of draws}\times 2+\text{bonus points}\mathrm{.}$$ One team has 15 wins, 7 draws and 6 bonus points. Calculate the total number of points for this team.

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