Sheet № 202 · Higher only · AQA · Edexcel · OCR
Rearranging Complex Formulae –
Rearranging complex formulae is a Higher tier GCSE Maths skill that goes beyond basic rearrangement. When the subject appears more than once, or the formula involves powers and roots, you need additional techniques including factorising.
§Key definitions
Question:
This is a Higher only topic. Here is an accessible entry. Make r the subject of A = πr².
Answer:
r = √(A / π)
Q1 (Higher):
Make h the subject of V = πr²h.
Q2 (Higher):
Make x the subject of a = (x + b) / (x - c).
Q3 (Higher):
Make p the subject of q = √(3p + 1).
§Formulas to memorise
When the subject appears twice: collect terms with that variable, factorise it out, then divide
x² = k gives x = ±√k; √x = k gives x = k²
Worked example
This is a Higher only topic. Here is an accessible entry. Make r the subject of A = πr².
Working:
⚠ Common mistakes
- ✗Forgetting to factorise when the subject appears twice. If you have 2xy - 5x on one side, you must write x(2y - 5) before dividing. Dividing without factorising gives an incorrect result.
- ✗Square-rooting only one side. When taking a square root, it must be applied to both sides of the equation, and the right-hand side often needs to remain under a single root.
- ✗Losing the ± symbol. In pure algebra, x² = k gives x = ±√k. In context, you may only need the positive root, but in general both solutions exist.
✦ Exam tips
- →If you see the target variable in two places, your plan should be: collect, factorise, divide.
- →Write out each step on a separate line — method marks are awarded at each stage.
- →After rearranging, substitute numbers to check: pick simple values, work out both sides, and see if they match.