Edexcel IGCSE Maths (4MA1) · Unit 3: Equations & Sequences
IGCSE Maths Quadratic Equations Questions and Answers
Quadratic Equations questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 4 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.
Quadratic Equations 1: Factorising & Solving by Factorisation: Factorising quadratics (including ax² + bx + c and difference of two squares) and solving by factorising.
Quadratic Equations 4: Formula: Solving with the quadratic formula.
Quadratic Equations 5: Context: Quadratic word problems in context.
Quadratic Equations 6: Optimization: Optimising area/volume with a quadratic model.
Quadratic Equations worked examples
Worked example 1: Solving by factorising
Solve \(x^2+2x-15=0\).
Solution
Two numbers multiplying to \(-15\) and adding to \(2\): \(5\) and \(-3\).
\((x+5)(x-3)=0\).
\(x=-5\) or \(x=3\).
Answer: \(x=-5\) or \(x=3\)
Tip: Set each bracket equal to zero.
Worked example 2: Quadratic formula
Solve \(x^2+4x-7=0\), giving answers to 3 significant figures.
The product of two consecutive positive integers is 132. Find them.
Solution
\(n(n+1)=132\), so \(n^2+n-132=0\).
\((n+12)(n-11)=0\).
\(n=11\) (positive), so 11 and 12.
Answer: 11 and 12
Tip: Reject solutions that do not fit the context.
Worked example 4: Maximum area
A rectangle has perimeter 40 cm. Find the greatest possible area.
Solution
Sides \(x\) and \(20-x\): area \(A=x(20-x)=20x-x^2\).
Complete the square: \(A=100-(x-10)^2\).
Maximum 100 cm² when \(x=10\).
Answer: 100 cm²
Tip: The maximum of \(-(x-p)^2+q\) is q.
Quadratic Equations 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
Factorise \(x^2 + 7x + 12\).
Show the answer and mark scheme
B2 (x + 3)(x + 4) (B1 for (x + a)(x + b) with ab = 12 or a + b = 7)
Answer: \((x+3)(x+4)\)
Question 2 · medium · 2 marks
Factorise \(2x^2 + 7x + 3\).
Show the answer and mark scheme
B2 (2x + 1)(x + 3) (B1 for factors giving two of the three terms correct)
Answer: \((2x+1)(x+3)\)
Question 3 · hard · 3 marks
Solve \(6x^2 + x - 12 = 0\) by factorising.
Show the answer and mark scheme
M1 (3x ± 4)(2x ± 3)
A1 (3x − 4)(2x + 3)
A1 x = 4/3, x = −3/2
Answer: \(x=\tfrac43,\ x=-\tfrac32\)
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 quadratic equations?
Either Higher tier paper, 1H or 2H, can test quadratic equations: 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 quadratic equations questions?
In the IGCSE student hub: Unit 3 (Equations & Sequences) 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