GCSE · Linear equations

Forming equations from problemsExam-style questions

How to turn a worded setup into an equation: one letter for one unknown NUMBER, every other quantity built from it, and one fact that ties the expressions together — then answer the question that was asked.

Start practising Read the lesson

15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
I think of a number, multiply it by $3$ and add $5$ . The answer is $23$ . Write an equation and find the number.
Level 1 · 2 marksTry it
2
A rectangle has length $(2x + 3)$ cm and width $(x - 1)$ cm.

The perimeter of the rectangle is $46$ cm.

Work out the value of $x$ . (3 marks)
Level 2 · 3 marksTry it
3
The perimeter of this rectangle is $30$ cm. The length is $x + 4$ cm and the width is $x$ cm. Find the value of $x$ .
Level 2 · 2 marksTry it
4
The diagram shows a trapezium and a rectangle.The area of the trapezium is twice the area of the rectangle.

Find the value of $x$ .

(4 marks)
Level 3 · 4 marksTry it
5
A rectangle has length $(2x + 3)$ cm and width $(x - 1)$ cm.Diagram NOT accurately drawn

The perimeter of the rectangle is 34 cm.

(a) Find the value of $x$ .

(b) Find the length and the width of the rectangle.
Level 3 · 4 marksTry it

10 more questions on forming equations from problems

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free