Substitution into Expressions and Formulae
Substitution means replacing each letter in an expression or formula with a given numerical value, then evaluating the result using the order of operations (brackets, indices, division and multiplication, addition and subtraction, often remembered as BIDMAS). Substitution turns an algebraic expression into a specific number and is the skill that connects algebra to real formulae, such as those for area, cost, or speed.
Before you start
Make sure you're comfortable with these topics first:
Method
- Write out the expression or formula clearly, noting every letter that needs to be replaced.
- Replace each letter with its given value, writing negative values inside brackets to avoid sign errors.
- Apply the order of operations (BIDMAS): work out brackets and powers first, then multiplication and division, then addition and subtraction.
- Work through the calculation one stage at a time, writing down each step.
- State the final numerical answer, including units if the formula represents a real-world quantity.
- Take extra care with negative numbers and powers: a negative number squared gives a positive result.
Worked example
Find the value of 2x^2 - 5x + 3 when x = -3.
- Substitute x = -3, keeping it in brackets: 2(-3)^2 - 5(-3) + 3.
- Work out the power first: (-3)^2 = 9, so the expression becomes 2(9) - 5(-3) + 3.
- Carry out the multiplications: 2 x 9 = 18, and -5 x -3 = 15, giving 18 + 15 + 3.
- Add the three values: 18 + 15 + 3 = 36.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Find the value of 3x + 4 when x = 5.Show answer
Answer: 19
Q2Find the value of 2a - b when a = 6 and b = 5.Show answer
Answer: 7
Q3Find the value of x^2 + 1 when x = 4.Show answer
Answer: 17
Q4Find the value of 5p when p = -2.Show answer
Answer: -10
Q5Find the value of x^2 when x = -4.Show answer
Answer: 16 (a negative number squared gives a positive result)
Q6The formula for the perimeter of a rectangle is P = 2l + 2w. Find P when l = 8 and w = 3.Show answer
Answer: P = 22
Q7Find the value of 3(x + 2) when x = -5.Show answer
Answer: -9
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
The cost, in pounds, of hiring a bike is given by the formula C = 4h + 6, where h is the number of hours hired. Work out the cost of hiring a bike for 5 hours.
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Find the value of 3x^2 - 2x when x = -2.
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Nothing ticked yet - 3 available
Free printable worksheet
Want more practice on paper? Download the substitution into expressions and formulae worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 21 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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