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Core + Extended Algebra and Graphs

Rearranging Formulas for IGCSE Maths

Changing the subject of a formula. This subtopic is part of Algebra in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding rearranging formulas is essential for

What You Need to Know

Changing the subject of a formula. This subtopic is part of Algebra in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding rearranging formulas is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Rearranging Formulas

Rearranging a formula means making a specified variable the subject. The techniques mirror solving equations: use inverse operations in reverse order. Harder rearrangements involve the target variable appearing twice — in that case, collect both occurrences on one side and factorise. This is tested in both Core and Extended IGCSE 0580, with Extended questions featuring the variable in denominators or square roots.

Step-by-Step Method

  1. 1

    Identify the target variable

    Circle the variable you are making the subject. Plan which operations surround it — you will undo them in reverse order.

  2. 2

    Isolate the term containing the variable

    Add, subtract, multiply, or divide to move all other terms away from the side containing the target variable.

  3. 3

    If the variable is under a square root, square both sides

    Do this step last. Similarly, if the variable is squared, take the square root at the end (±).

  4. 4

    If the variable appears twice, collect and factorise

    Move all terms with the subject to one side, factorise out the subject, then divide: xb + xa = c → x(a+b) = c → x = c/(a+b).

  5. 5

    Simplify the result

    Write the answer with the subject on the left. Check by substituting back into the original formula with simple test values.

Worked Example

Question

(a) Make r the subject of A = πr². (b) Make x the subject of y = (ax + b)/(x − c).

Solution

Part (a): A = πr² Divide both sides by π: A/π = r² Take the square root: r = √(A/π) Part (b): y = (ax + b)/(x − c) Multiply both sides by (x − c): y(x − c) = ax + b Expand: xy − yc = ax + b Move x-terms to the left: xy − ax = b + yc Factorise: x(y − a) = b + yc Divide: x = (b + yc)/(y − a) Answers: r = √(A/π) and x = (b + yc)/(y − a)

Exam Tips for Rearranging Formulas

  • Undo operations in reverse order: if the formula has +5, then ×3, undo ×3 first (divide), then −5.
  • For variables appearing twice: collect ALL occurrences on one side, then factorise — this is a common Extended question type.
  • If the subject is under a square root, square both sides as the LAST step to avoid introducing extra cases.
  • Show every step — rearranging formulas is a show-your-working question type where method marks count.

Practice Questions

Q1: Make h the subject of V = (1/3)πr²h.

Show hint

Multiply both sides by 3: 3V = πr²h. Then divide by πr².

Q2: Make t the subject of s = ut + (1/2)at².

Show hint

This is quadratic in t. Rearrange to (1/2)at² + ut − s = 0. Use the quadratic formula with coefficients in a, u, s.

Q3: Make x the subject of p = (2x − 3)/(x + 1).

Show hint

Multiply by (x+1): p(x+1) = 2x−3. Expand, collect x-terms: px−2x = −3−p. Factorise x(p−2) = −(3+p).

Frequently Asked Questions

What is rearranging formulas in IGCSE Maths?

Changing the subject of a formula.

Is rearranging formulas in the Core or Extended syllabus?

Rearranging Formulas is part of the Core and Extended syllabus for IGCSE Mathematics 0580.

How do I revise rearranging formulas effectively?

Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on rearranging formulas rather than trying to cover everything at once.

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