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.

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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
$ABC$ and $DEF$ are right-angled triangles. $\cos p = \tan q$

Find the value of $x$ .

(3 marks)
Level 4 · 3 marksTry it
2
The angles of a triangle are $x°$ , $(2x + 15)°$ and $(3x - 9)°$ .Diagram NOT accurately drawn

Work out the size of the largest angle.
Level 4 · 4 marksTry it
3
Kate is $x$ years old.

Dan is twice as old as Kate.

Sam is 4 years younger than Kate.

The total of their three ages is 44 years.

Work out Dan's age.
Level 4 · 3 marksTry it
4
The sum of three consecutive odd numbers is 111.

Find the three numbers.
Level 4 · 3 marksTry it
5
Three angles lie on a straight line. Their sizes are $2x°$ , $(3x + 10)°$ and $(x + 20)°$ .

Work out the size of the largest angle.
Level 4 · 3 marksTry it

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