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
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
2
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
3
I think of a number, multiply it by 4, then subtract 5.

The result is the same as three times the sum of my number and 2.

What number am I thinking of?
Level 3 · 3 marksTry it
4
An isosceles triangle has two sides of length $x$ cm and one side of length $(x + 5)$ cm.

The perimeter of the triangle is $35$ cm.

Work out the length of each side.
Level 3 · 3 marksTry it
5
Mia has £ $m$ .

Noah has £ $7$ more than Mia.

Together they have £ $43$ .

How much money does Noah have?
Level 3 · 3 marksTry it