Algebra and graphs: past paper questions

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• Question 7May/June 2026, paper 12Structured3 marksHas a diagram

  The diagram shows a trapezium. All the lengths are in centimetres. The area of the trapezium is $100{\text{ cm}}^2$.

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• Question 7Oct/Nov 2025, paper 11Structured3 marks

  Car hire $40 per day plus $0.30 per kilometre Amy hires a car for 10 days. She pays a total of $670. Work out the number of kilometres Amy travels in the car. Car hire $40 per day plus $0.30 per kilometre Amy hires a car for 10 days. She pays a total of $670.

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• Question 16Oct/Nov 2023, paper 11Structured4 marksHas a diagram

  The region $R$ is defined by these inequalities. $$1⩽x⩽3$$ $$2⩽y⩽3$$ $$y⩾\frac{x}{2}+1$$ Find and label region $R$.

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• 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 14Oct/Nov 2025, paper 11Structured3 marksHas a diagram

  Lia cycles $800\text{ m}$ in 105 seconds. The diagram shows the speed–time graph for this journey. Work out the value of $v$.

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• Question 8Oct/Nov 2024, paper 11Structured3 marks

  These are the first four terms of a sequence. $$281420$$ Find the next number in the sequence.

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• Question 17Oct/Nov 2023, paper 11Structured2 marks

  $y$ is directly proportional to the square root of $x$. When $x=16$, $y=2$. Find $y$ when $x=25$.

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• Question 13May/June 2026, paper 12Structured7 marks

  The $n$th term of a sequence is $n+8$. Find the first three terms of this sequence.

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

  Solve the simultaneous equations.

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• Question 19Oct/Nov 2023, paper 11Structured4 marksHas a diagram

  The diagram shows the speed–time graph for part of a car journey. Calculate the acceleration of the car in the first 10 seconds of the journey.

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• Question 15May/June 2026, paper 12Structured8 marks

  The equation of line $L$ is $2y+x=19$. Find the gradient of line $L$.

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• Question 20Oct/Nov 2025, paper 11Structured2 marks

  Write as a single fraction in its simplest form.

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• Question 17Oct/Nov 2024, paper 11Structured4 marksHas a diagram

  The diagram shows the lines $y=2x+1$ and $x+y=2$. The region $R$ is defined by these three inequalities. $$y⩽2x+1x+y⩽2y⩾-2$$ On the diagram, shade and label the region $R$.

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• Question 17May/June 2026, paper 12Structured9 marks

  In a right-angled triangle • the base is $x\text{ cm}$ • the height is $7\text{ cm}$ shorter than the base • the hypotenuse (longest side) is $2\text{ cm}$ longer than the base. Use this information to form an equation and show that it simplifies to $x^2-18x+45=0$.

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• Question 21Oct/Nov 2025, paper 11Structured4 marks

  Evaluate. $${27}^{-\frac{2}{3}}$$

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• Question 19Oct/Nov 2024, paper 11Structured2 marks

  $x$ is inversely proportional to the square root of $y$. When $x=2$, $y=16$. Find $y$ when $x=32$.

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• Question 19May/June 2026, paper 12Structured6 marksHas a diagram

  The diagram shows a solid hemisphere and a solid cylinder. All the lengths are in centimetres. The radius of the hemisphere is $3x$.

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• Question 22Oct/Nov 2025, paper 11Structured10 marks

  The table shows some values for $y=x^3-3x+2$. Complete the table.

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• Question 20Oct/Nov 2024, paper 11Structured2 marks

  $$(a{x}^n{)}^3=4x^{10}$$ Work out the value of $a$ and the value of $n$.

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• Question 24Oct/Nov 2023, paper 11Structured4 marks

  Solve $\frac{3x}{x+1}-\frac{2}{x-1}=3$.

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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 21Oct/Nov 2024, paper 11Structured2 marksHas a diagram

  The diagram shows the speed–time graph for a journey. Calculate the total distance travelled.

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• Question 22May/June 2026, paper 12Structured4 marksHas a diagram

  The diagram shows a sketch of the graph of $y=a^x+b$.

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

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

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• Question 22Oct/Nov 2024, paper 11Structured4 marks

  $$\mathrm{f}(x)=3x^2+5$$ Work out $\mathrm{f}(-1)$.

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• Question 23May/June 2026, paper 12Structured3 marks

  Find the value of $x$.

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• Question 6Oct/Nov 2025, paper 12Structured2 marks

  Solve. $$6x-3=4x+9$$ Solve.

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• Question 24Oct/Nov 2024, paper 11Structured3 marks

  Simplify. $$\frac{2x^2+5x-3}{2x^2+6x}$$ Simplify.

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• Question 15Oct/Nov 2023, paper 12Structured4 marks

  The second term of a linear sequence is 28. The fifth term of the sequence is 16. Find the first term, the third term and the fourth term of this sequence.

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• Question 12May/June 2026, paper 22Structured5 marks

  Solve. $$5k-2=12$$

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