Substitution
Substitution is the process of replacing letters in an algebraic expression or formula with given numerical values, then working out the resulting calculation. It is tested throughout GCSE algebra and within formula-based questions in other topics, such as speed, area and physics-style formulae, so accurate handling of negatives and powers is essential.
Before you start
Make sure you're comfortable with these topics first:
Method
- Write out the expression or formula and identify the value given for each letter.
- Replace each letter with its numerical value, putting negative values in brackets to avoid sign errors.
- Apply BIDMAS: work out brackets and powers first, then multiplication and division, then addition and subtraction.
- Take extra care with powers of negative numbers: squaring a negative number always gives a positive answer.
- Give the final answer with the correct units if the formula represents a real quantity, such as speed or cost.
Worked example
a = -4 and b = 3. Work out the value of 2a^2 - 5b.
- Substitute the values: 2 x (-4)^2 - 5 x 3.
- Work out the power first: (-4)^2 = 16.
- Multiply: 2 x 16 = 32, and 5 x 3 = 15.
- Subtract: 32 - 15 = 17.
- Final answer: 17.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
a = 5 and b = -2. Work out the value of a^2 - 3b.
An electrician uses the formula C = 40 + 25h to work out the cost, C pounds, of a job, where h is the number of hours worked. (a) Work out the cost of a job that takes 3 hours. (2) (b) A different job costs 190 pounds. Work out how many hours the electrician worked. (2)
x = -2 and y = 1/2. Work out the value of 1/x + 1/y.
See real past-paper questions on substitution, organised by topic with official mark schemes →
Free printable worksheet
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