Algebra and graphs: past paper questions

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• Question 2May/June 2026, paper 11Structured2 marks

  Bella is $b$ years old. Alan is 5 years older than Bella. Write an expression, in terms of $b$, for how old Alan is.

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• Question 7Oct/Nov 2025, paper 11Structured2 marks

  These are the first four terms of a sequence. 9 5 1 -3 Find the next term.

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• Question 10Oct/Nov 2024, paper 11Structured3 marks

  These are the first four terms of a sequence. $$\begin{array}{cccc}10& 16& 22& 28\end{array}$$ Write down the next term in the sequence.

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

  Complete these statements.

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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 14Oct/Nov 2023, paper 11Structured2 marks

  Factorise completely.

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• Question 18May/June 2026, paper 11Structured9 marks

  Complete the table of values for $y=x^2+x-3$.

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• Question 16Oct/Nov 2025, paper 11Structured6 marks

  Complete the table of values for $y=\frac{9}{x}$.

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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 16Oct/Nov 2023, paper 11Structured3 marks

  Simplify. $n^5\times n$

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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 23Oct/Nov 2025, paper 11Structured2 marks

  $a^8\times a^x=a^{15}$ Find the value of $x$.

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• Question 2Oct/Nov 2023, paper 12Structured2 marks

  Asha works in a café. Her wage is calculated using the formula $\text{wage}=\text{hourly rate}\times \text{number of hours}+\text{bonus}$. Her hourly rate is $11.52 . One week Asha works 25 hours and receives a bonus of $5.40 .

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

  Solve the simultaneous equations.

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

  Expand and simplify.

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• Question 3Oct/Nov 2023, paper 12Structured2 marks

  These are the first four terms in a sequence. $$\begin{array}{cccc}-3& 4& 11& 18\end{array}$$ Find the next term.

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

  Solve. $5x=14$

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• Question 9Oct/Nov 2023, paper 12Structured2 marks

  $v=u+at$ Find the value of $v$ when $u=30$, $a=-2$ and $t=7$.

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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 20May/June 2026, paper 12Structured2 marks

  Write down the inequality represented on the number line.

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

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

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

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

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• Question 21May/June 2026, paper 12Structured6 marksHas a diagram

  These are the first four diagrams in a sequence. The diagrams are made using grey squares and white squares. Draw diagram 5 on the grid.

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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 15Oct/Nov 2024, paper 12Structured2 marks

  In a league, teams gain 4 points for each win, 2 points for each draw and bonus points.

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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 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 16Oct/Nov 2023, paper 13Structured2 marks

  Solve the equation.

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