Equations: past paper questions

Where the questions come from

• Question 2May/June 2026, paper 21Structured2 marks

  Solve $7x+4=25$.

  Try this question
• Question 8Oct/Nov 2025, paper 21Structured5 marks

  The cost of one orange is $t$ cents. The cost of one apple is $w$ cents. The total cost of 3 oranges and 1 apple is 51 cents.

  Try this question
• Question 12Oct/Nov 2024, paper 21Structured3 marks

  Solve the simultaneous equations.

  Try this question
• Question 3Oct/Nov 2023, paper 21Structured2 marks

  Complete these statements.

  Try this question
• Question 4May/June 2026, paper 21Structured2 marks

  The diagram shows a rectangle with width $6\text{ cm}$. The width of the rectangle is $\frac{1}{12}$ of the perimeter of the rectangle. Work out the length of the rectangle.

  Try this question
• Question 19Oct/Nov 2025, paper 21Structured3 marks

  Solve. $${\left(\frac{1}{3}\right)}^x=9^{x+4}$$ Solve.

  Try this question
• Question 17Oct/Nov 2024, paper 21Structured4 marks

  Solve. $$3x^2-7x-16=0$$ You must show all your working and give your answers correct to 2 decimal places.

  Try this question
• Question 21Oct/Nov 2023, paper 22Structured4 marks

  The line $y=x+1$ intersects the curve $y=x^2+x-3$ at two points. Find the coordinates of the two points.

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

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

  Try this question
• Question 6Oct/Nov 2024, paper 22Structured2 marksHas a diagram

  The diagram shows a trapezium. The area of the trapezium is $42{\text{ cm}}^2$. Calculate the value of $x$.

  Try this question
• Question 9Oct/Nov 2023, paper 23Structured3 marks

  $P=\frac{2w{y}^2}{3}$ Find the positive value of $y$ when $P=108$ and $w=8$.

  Try this question
• Question 24May/June 2026, paper 22Structured3 marks

  $7^{2x+1}={49}^{2-x}$ Find the value of $x$.

  Try this question
• Question 7Oct/Nov 2024, paper 23Structured2 marks

  Solve the equation.

  Try this question
• Question 22Oct/Nov 2023, paper 23Structured5 marks

  Find the coordinates of the point where the line $4x+y=9$ intersects the curve $y+x^2=5$.

  Try this question
• Question 25May/June 2026, paper 22Structured5 marks

  The straight line $y=7-4x$ intersects the curve $y=4+3x-2x^2$ at two points. Find the coordinates of these two points.

  Try this question
• Question 2Oct/Nov 2023, paper 41Structured12 marks

  $s=\frac{1}{2}a{t}^2$ Find the value of $s$ when $a=9.8$ and $t=20$.

  Try this question
• Question 18May/June 2026, paper 23Structured6 marksHas a diagram

  The diagram shows a rectangle. The shaded area is $30{\text{ cm}}^2$. Show that $x^2+16x-36=0$.

  Try this question
• Question 2Oct/Nov 2025, paper 41Structured2 marks

  Solve. $$11-2x=4$$ Solve.

  Try this question
• Question 1Oct/Nov 2024, paper 41Structured19 marks

  Write 70 as a product of its prime factors.

  Try this question
• 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.

  Try this question
• Question 10Oct/Nov 2024, paper 41Structured14 marksHas a diagram

  This rectangle has area $190{\text{ cm}}^2$. By forming and solving an equation, show that $x=8.5$.

  Try this question
• Question 10Oct/Nov 2023, paper 43Structured14 marks

  Expand and simplify.

  Try this question
• Question 18May/June 2026, paper 42Structured8 marks

  In this question, all lengths are in centimetres. Show that the area of triangle $ABC$ is $\frac{1}{2}{x}^2{\text{ cm}}^2$.

  Try this question
• Question 8May/June 2023, paper 22Structured4 marks

  Solve. $\frac{30}{x}=6$

  Try this question
• Question 2Oct/Nov 2025, paper 42Structured2 marks

  Solve. $$8x-17=27$$ Solve.

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

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

  Try this question
• Question 12May/June 2023, paper 22Structured3 marks

  One solution of the equation $a{x}^2+b=181$ is $x=8$. $a$ and $b$ are both positive integers greater than 1. Find the value of $b$.

  Try this question
• Question 7Oct/Nov 2024, paper 43Structured15 marksHas a diagram

  Calculate the area of the trapezium.

  Try this question
• Question 19May/June 2023, paper 23Structured4 marks

  Solve the equation $x^2+5x-7=0$.

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

  Factorise fully.

  Try this question