Equations: past paper questions

Where the questions come from

• 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 10Oct/Nov 2024, paper 11Structured3 marks

  Solve the simultaneous equations.

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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 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 26Oct/Nov 2024, paper 11Structured4 marks

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

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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 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 6Oct/Nov 2025, paper 12Structured2 marks

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

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

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

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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 22Oct/Nov 2025, paper 12Structured10 marks

  Ade and Maha make cards. One day they each work for 4 hours making cards. Ade takes $x$ minutes to make one card.

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• Question 10Oct/Nov 2024, paper 21Structured10 marks

  Bag A contains red balls and green balls. The total number of balls in the bag is $x$. The number of green balls in the bag is 6 more than the number of red balls.

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• Question 16Oct/Nov 2023, paper 12Structured3 marks

  T = √(P - 4) Work out the value of T when P = 40.

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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 7Oct/Nov 2024, paper 22Structured13 marks

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

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

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

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• Question 23Oct/Nov 2025, paper 21Structured4 marks

  Solve. x/(x + 3) - 4/(x - 5) = 1 Solve.

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• Question 10Oct/Nov 2024, paper 22Structured10 marks

  The cost of apples is $x$ cents per kilogram.

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• Question 6Oct/Nov 2023, paper 21Structured10 marksHas a diagram

  $ABCD$ is a rectangle with area $30{\text{ cm}}^2$. $AB=x\text{ cm}$. Rectangle $DEFG$ is removed from the corner of rectangle $ABCD$.

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• Question 24May/June 2026, paper 22Structured8 marksHas a diagram

  The diagram shows a solid cuboid. All the lengths are in centimetres. The volume of the cuboid is $720{\text{ cm}}^3$.

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• Question 21Oct/Nov 2025, paper 22Structured6 marks

  Solve the equation.

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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 5May/June 2025, paper 12Structured2 marks

  Solve. $$5(4-x)=35$$ Solve.

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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 4Oct/Nov 2023, paper 22Structured8 marks

  Solve. $$5x+6=3x$$

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• Question 11May/June 2025, paper 12Structured5 marks

  The mass of a small box is $x\text{ kg}$. The mass of a large box is $y\text{ kg}$. The total mass of 4 small boxes and 6 large boxes is $30\text{ kg}$.

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• Question 8Oct/Nov 2023, paper 22Structured9 marksHas a diagram

  The diagram shows a small rectangle inside a large rectangle. The height of the large rectangle is $x\text{ cm}$. The length of the large rectangle is 4 times its height.

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• Question 4May/June 2025, paper 22Structured2 marksHas a diagram

  Find the value of $x$ and the value of $y$.

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• Question 19May/June 2024, paper 11Structured6 marks

  $\mathrm{f}(x)=2x-5$ Find $\mathrm{f}(11)$.

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