IGCSE Math RevisionQuestion 1
Make \(x\) the subject of the formula \(p = 5x + 8\).
Show the worked answer
- Subtract \(8\): \(p - 8 = 5x\).
- Divide by \(5\).
Answer: \(x = \frac{p - 8}{5}\)
Cambridge IGCSE Maths (0580) · Topic 2: Algebra and graphs · 2.5
Cambridge IGCSE Maths 0580 Rearranging Formulae Questions
Rearranging Formulae questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 8 questions
- 4 Core
- 4 Extended
- 7 non-calculator
- Free, no sign-in
What the syllabus asks
- 2.5 Equations Core Extended
Construct expressions, equations and formulas; Solve linear equations in one unknown; Solve simultaneous linear equations in two unknowns; Change the subject of simple formulas.
Extended also: Fractional equations with numerical and linear algebraic denominators; Simultaneous linear and non-linear equations; Quadratic equations by factorising, completing the square and the quadratic formula; Change the subject where the subject appears twice or as a power or root.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Rearranging Formulae questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
Rearrange \(P = 2a + 2b\) to make \(b\) the subject.
Show the worked answer
- Subtract \(2a\): \(P - 2a = 2b\).
- Divide by \(2\).
Answer: \(b = \frac{P - 2a}{2}\)
Question 3
Make the letter in brackets the subject of each formula.
(a) \(C = 2\pi r \quad [r]\) (b) \(y = 3x + 5 \quad [x]\)
Show the answer and mark scheme
- B1 (a) r = C/(2π)
- B1 (b) x = (y − 5)/3
Answer: (a) \(r = \frac{C}{2\pi}\) (b) \(x = \frac{y - 5}{3}\)
Question 4
The area of a triangle is \(A = \frac{1}{2}bh\). Make \(h\) the subject.
Show the worked answer
- Multiply by \(2\): \(2A = bh\).
- Divide by \(b\).
Answer: \(h = \frac{2A}{b}\)
Rearranging Formulae questions: Extended
Extended content, for Papers 2 and 4. Core students can skip these.
Question 5
Make \(r\) the subject of \(A = \pi r^2\), where \(r \gt 0\).
Show the worked answer
- Divide by \(\pi\): \(r^2 = \frac{A}{\pi}\).
- Square root (the positive root, as \(r \gt 0\)).
Answer: \(r = \sqrt{\frac{A}{\pi}}\)
Question 6
Make \(y\) the subject of \(ay + 3 = by - 7\).
Show the worked answer
- Collect the \(y\) terms on one side: \(3 + 7 = by - ay\).
- Factorise: \(10 = y(b - a)\).
Answer: \(y = \frac{10}{b - a}\)
Question 7
Make \(x\) the subject of \(y = \frac{x + 2}{x - 3}\).
Show the worked answer
- Multiply by \((x - 3)\): \(xy - 3y = x + 2\).
- Collect \(x\) terms: \(xy - x = 3y + 2\), so \(x(y - 1) = 3y + 2\).
Answer: \(x = \frac{3y + 2}{y - 1}\)
Question 8
The period of a pendulum is \(T = 2\pi\sqrt{\frac{l}{g}}\). Rearrange the formula to make \(g\) the subject.
Show the worked answer
- Divide by \(2\pi\): \(\frac{T}{2\pi} = \sqrt{\frac{l}{g}}\).
- Square: \(\frac{T^2}{4\pi^2} = \frac{l}{g}\).
- Flip both sides and multiply by \(l\): \(g = \frac{4\pi^2 l}{T^2}\).
Answer: \(g = \frac{4\pi^2 l}{T^2}\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Algebra and graphs practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Algebra and graphs revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test rearranging formulae?
Rearranging Formulae is on both tiers (syllabus 2.5), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more rearranging formulae questions?
In the 0580 practice for topic 2 (Algebra and graphs), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.