Sheet № 193 · Foundation + Higher · AQA · Edexcel · OCR
Rearranging Formulae –
Rearranging formulae is one of the most frequently tested algebra skills in GCSE Maths. Whether you are working with science equations or pure algebra, you need to be confident changing the subject of a formula using inverse operations.
§Key definitions
Question:
Make t the subject of the formula v = u + at.
Answer:
t = (v - u) / a
Q1 (Foundation):
Make b the subject of P = 2a + 2b.
Q2 (Foundation):
Make h the subject of V = lwh.
Q3 (Higher):
Make u the subject of v² = u² + 2as.
§Formulas to memorise
To isolate a variable, apply inverse operations to both sides in reverse order of BIDMAS
If the subject is squared, take the square root of both sides: x² = k gives x = ±√k
Worked example
Make t the subject of the formula v = u + at.
Working:
⚠ Common mistakes
- ✗Applying inverse operations in the wrong order. Always undo addition/subtraction before multiplication/division, working in reverse BIDMAS order.
- ✗Forgetting ± when square-rooting. In pure algebra, x² = 9 gives x = ±3. In context (e.g. length), you may only need the positive root.
- ✗Not multiplying every term when clearing a fraction. If y = (3x + 5) / 2, multiplying both sides by 2 gives 2y = 3x + 5, not 2y = 3x + 5/2.
✦ Exam tips
- →Show each step clearly — examiners award method marks for each correct inverse operation.
- →When the required subject appears twice, collect those terms on one side, factorise, then divide.
- →Check your answer by substituting numbers into both the original and rearranged formula.