Edexcel International GCSE Mathematics A · 4MA1
Rearranging formulae
Changing the subject means isolating a chosen variable using inverse operations. When the variable occurs in more than one term, collecting those terms and factorising is usually the key step. The rearranged formula must preserve the original relationship.
Key method
Undo addition or subtraction before undoing multiplication. If the subject appears twice, collect its terms on one side and take it out as a common factor.
Worked example
Make x the subject of y = (3x + 2)/(x − 1).
- Multiply by x − 1: yx − y = 3x + 2.
- Collect x terms: yx − 3x = y + 2.
- Factorise: x(y − 3) = y + 2, then divide by y − 3.
Answer and interpretation
x = (y + 2)/(y − 3), with y ≠ 3; the original expression also requires x ≠ 1.
Common mistake
Dividing individual terms separately before collecting the subject can produce an incorrect denominator.
Practise independently
Make r the subject of A = πr² for a radius r ≥ 0.
Check your answer
r = √(A/π). Only the non-negative root represents a radius.
Syllabus connection
This lesson develops changing the subject of a formula within the algebra area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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