GCSE Maths Algebra - How to Solve: Changing the Subject of a Formula

How to Solve: Changing the Subject of a Formula

GCSE & A-Level (Physics, Chemistry, Biology) – Complete Guide

Introduction

"Mastering this skill lets you rearrange any physics, chemistry, or biology formula in seconds—saving you 5+ marks per question on your exam. Examiners love testing this, and if you mess it up, you lose easy marks. Today, you’ll learn the exact steps to rearrange any formula, spot hidden traps, and avoid the mistakes that cost students grades."

WHAT YOU NEED TO KNOW FIRST

Before you start, you must understand: 1. Basic algebra – Adding, subtracting, multiplying, and dividing both sides of an equation. 2. Inverse operations – What cancels out what (e.g., + cancels –, × cancels ÷). 3. Brackets and fractions – How to expand and simplify them.

If you’re shaky on any of these, pause and review them first.

KEY TERMS & FORMULAS

Key Terms

• Subject of a formula – The variable (letter) that is alone on one side of the equation (e.g., in v = u + at, v is the subject).
• Rearranging – Changing which variable is the subject.
• Inverse operation – The opposite math operation (e.g., the inverse of × is ÷).

Formulas You’ll See (MEMORISE THESE)

(Note: Some formulas are given on the exam sheet—check your syllabus!)

STEP-BY-STEP METHOD

Goal: Make a new variable the subject of the formula.

Step 1: Identify the current subject and the new subject

• Circle the current subject (the variable alone on one side).
• Underline the new subject (the variable you want to isolate).

Step 2: Move terms away from the new subject

• Use inverse operations to shift terms to the other side.
• Rule: Whatever you do to one side, do to the other.

Step 3: Isolate the new subject

• Keep applying inverse operations until the new subject is alone.
• If the new subject is in a fraction, multiply both sides by the denominator.
• If the new subject is in a bracket, expand first, then isolate.

Step 4: Simplify (if needed)

• Combine like terms.
• Factorise if necessary (e.g., ax + bx = x(a + b)).

Step 5: Check your answer

• Plug in numbers to see if both sides balance.
• If it works, you’re done!

WORKED EXAMPLES

Example 1 – Basic (Physics: Kinematics)

Formula: v = u + at Goal: Make a the subject.

Step 1: Current subject = v. New subject = a. Step 2: Subtract u from both sides: v – u = at Step 3: Divide both sides by t: (v – u)/t = a Step 4: Rewrite (optional): a = (v – u)/t

What we did and why: - We moved u first (subtraction) because it was added to at. - Then we divided by t to isolate a.

Example 2 – Medium (Chemistry: Moles)

Formula: n = cV Goal: Make V the subject.

Step 1: Current subject = n. New subject = V. Step 2: Divide both sides by c: n/c = V Step 3: Rewrite (optional): V = n/c

What we did and why: - Since V was multiplied by c, we divided by c to isolate V.

Example 3 – Exam-Style (Physics: Power)

Formula: P = I²R (given on exam sheet) Goal: Make I the subject.

Step 1: Current subject = P. New subject = I. Step 2: Divide both sides by R: P/R = I² Step 3: Take the square root of both sides: √(P/R) = I Step 4: Rewrite (optional): I = √(P/R)

What we did and why: - First, we isolated I² by dividing by R. - Then, we took the square root to get I alone.

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP (Night Before the Exam)

"Listen up—this is your 60-second crash course on rearranging formulas. First, identify the new subject—the variable you need to isolate. Then, move everything else away using inverse operations: if it’s added, subtract; if multiplied, divide. If the new subject is squared, take the square root last. If it’s in a fraction, multiply both sides by the denominator. Always check your answer by plugging in numbers. And watch out for hidden fractions and squared terms—examiners love those. You’ve got this!"