Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Changing the Subject of the Formula — rearranging equations to isolate a chosen letter — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Changing the Subject of the Formula in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Changing the Subject revision-guide angle, while Tutopiya’s Changing the Subject of the Formula subtopic page owns the learning resource and the free Changing the Subject quiz owns the practice.

Changing the Subject of the Formula is one of the first Algebra skills in Cambridge IGCSE Mathematics (0580/0607) that separates students who understand equations from those who only memorise procedures. Examiners ask you to “make x the subject” or “rearrange” standard formulas from physics and geometry. The rules are the same as solving equations — undo operations in reverse order. This guide explains the subtopic, the question types that appear, and where to practise.

Key takeaways

• Changing the subject means isolating one letter on the left-hand side of a formula.
• Use inverse operations in reverse order: undo addition/subtraction before multiplication/division.
• Treat the new subject like the answer — everything else is manipulated to leave it alone.
• This skill feeds directly into Substitution and Linear Equations and Inequalities.

What is Changing the Subject of the Formula in Cambridge IGCSE Maths?

Changing the subject of a formula means rearranging an equation so that a specified letter stands alone on one side — usually the left. If V = IR and you need R, you rearrange to R = V/I. In Cambridge IGCSE Mathematics, formulas may involve fractions, squares or roots, but the core idea is always inverse operations applied consistently to both sides. It is tested in short algebra questions and as a step inside longer problems.

Read the full explanation on Tutopiya’s Changing the Subject of the Formula subtopic page before you attempt questions.

The core operations and their inverses

Operation in formula	Inverse (undo)	Example step
+ a	− a	y = x + 5 → y − 5 = x
− a	+ a	y = x − 3 → y + 3 = x
× a	÷ a	y = 3x → y/3 = x
÷ a	× a	y = x/4 → 4y = x
square	square root	A = πr² → r² = A/π → r = √(A/π)

How to change the subject — step by step

1. Identify the subject letter — the one you must isolate (often stated as “make x the subject”).
2. Deal with addition/subtraction affecting the subject first — move other terms to the opposite side.
3. Deal with multiplication/division — divide or multiply both sides to leave the subject coefficient as 1.
4. Handle fractions by multiplying both sides by the denominator, or treat the formula as “subject over something.”
5. Apply roots or powers last if the subject is squared or inside a root.

Test yourself with the free Changing the Subject quiz once the sequence feels natural.

Simple vs harder rearrangements

Type	Example formula	Target
Linear	y = mx + c	Make x the subject → x = (y − c)/m
With fraction	P = 2(l + w)	Make w the subject → w = P/2 − l
With square	A = πr²	Make r the subject → r = √(A/π)
Subject in denominator	y = k/x	Make x the subject → x = k/y

Changing the Subject in past-paper wording: command words that matter

Command word / phrase	What the question wants	Typical stem
Make x the subject	x alone on left (or stated side)	“Make x the subject of y = 3x − 7.”
Rearrange	Same as change subject	”Rearrange v = u + at to make t the subject.”
Write a formula for …	Rearrange then possibly substitute	”Write a formula for r in terms of A.”
Show that	Prove rearrangement with working	”Show that t = (v − u)/a.”
Express … in terms of	Subject in terms of other letters only	”Express h in terms of V and r.”

Worked exam-style stems (how to answer the wording)

1. “Make x the subject of y = (x + 4)/3.” Multiply both sides by 3: 3y = x + 4. Subtract 4: x = 3y − 4. Reward: correct order — clear denominator before isolating x.
2. “Rearrange A = ½bh to make h the subject.” Multiply by 2: 2A = bh. Divide by b: h = 2A/b. Reward: dealing with the fraction ½ first.
3. “Make r the subject of V = (4/3)πr³.” Multiply by 3/(4π): r³ = 3V/(4π). Cube root: r = ∛(3V/(4π)). Reward: isolating r³ before taking the root.

Work similar stems on the Algebra topical past paper questions and the Changing the Subject quiz.

How Changing the Subject connects to the rest of Algebra

Once a formula is rearranged, you substitute values — see Substitution. The same inverse-operation logic appears in Linear Equations and Inequalities. Use the Cambridge IGCSE Maths resource hub to move between subtopics.

Common mistakes students make

• Moving a term to the other side but forgetting to change its sign.
• Dividing only one term on a side instead of the entire expression.
• Taking a square root without ± when the question context allows negative values.
• Rearranging in the wrong order — e.g. dividing before clearing a sum.

When you need more support

If fraction or root rearrangements keep failing, work through the Linear Equations and Inequalities quiz and the Algebra topical past paper questions, then get help from a Cambridge IGCSE Maths tutor.

Frequently asked questions

Is changing the subject the same as solving an equation? Very similar — you use inverse operations on both sides. The difference is the letter you isolate is specified (the new subject), not always x.

Do I need to write each step on the exam? Yes for method marks. Show addition/subtraction and multiplication/division clearly, especially on “Show that” questions.

What if the subject appears twice? Collect subject terms on one side and non-subject terms on the other, then factorise — common in harder Extended questions.

How do I revise Changing the Subject effectively? Practise five linear rearrangements, then two with fractions, then take the Changing the Subject quiz.

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