Edexcel IGCSE Maths (4MA1) · Unit 2: Algebra Basics
IGCSE Maths Rearranging Formulae Questions and Answers
Rearranging Formulae questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 6 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.
Find the value of \(a^2-2ab\) when \(a=-3\) and \(b=4\).
Solution
\(a^2=(-3)^2=9\).
\(2ab=2\times(-3)\times4=-24\).
\(9-(-24)=33\).
Answer: 33
Tip: Put negative numbers in brackets.
Worked example 4: Subject with a square
Make \(u\) the subject of \(v^2=u^2+2as\).
Solution
Subtract \(2as\): \(u^2=v^2-2as\).
Square root: \(u=\pm\sqrt{v^2-2as}\).
Answer: \(u=\pm\sqrt{v^2-2as}\)
Tip: Square root the whole side, not term by term.
Worked example 5: Subject inside a term
Make \(h\) the subject of \(A=2\pi r^2+2\pi rh\).
Solution
Subtract \(2\pi r^2\): \(A-2\pi r^2=2\pi rh\).
Divide by \(2\pi r\): \(h=\dfrac{A-2\pi r^2}{2\pi r}\).
Answer: \(h=\dfrac{A-2\pi r^2}{2\pi r}\)
Tip: Isolate the term containing h first.
Worked example 6: Subject appears twice
Make \(x\) the subject of \(ax-b=cx+d\).
Solution
Collect \(x\) terms: \(ax-cx=b+d\).
Factorise: \(x(a-c)=b+d\).
\(x=\dfrac{b+d}{a-c}\).
Answer: \(x=\dfrac{b+d}{a-c}\)
Tip: When the subject appears twice, collect and factorise.
Rearranging Formulae exam-style questions
Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.
Question 1 · easy · 2 marks
Make \(x\) the subject of \(ax + b = cx\).
Show the answer and mark scheme
M1 collects x terms on one side and factorises, e.g. x(c − a) = b
A1 x = b/(c − a) oe
Answer: \(x=\dfrac{b}{c-a}\)
Question 2 · medium · 3 marks
Make \(p\) the subject of \(3p + q = pr - 2\).
Show the answer and mark scheme
M1 collects p terms, e.g. 3p − pr = −2 − q
M1 factorises p(3 − r)
A1 p = (q + 2)/(r − 3) oe
Answer: \(p=\dfrac{q+2}{r-3}\)
Question 3 · hard · 3 marks
Make \(m\) the subject of \(k = \dfrac{2m-3}{m+4}\).
Show the answer and mark scheme
M1 km + 4k = 2m − 3
M1 km − 2m = −3 − 4k and factorises m(k − 2)
A1 m = (4k + 3)/(2 − k) oe
Answer: \(m=\dfrac{4k+3}{2-k}\)
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Which Edexcel IGCSE Maths papers test rearranging formulae?
Either Higher tier paper, 1H or 2H, can test rearranging formulae: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more rearranging formulae questions?
In the IGCSE student hub: Unit 2 (Algebra Basics) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.
IGCSE Math Revision