A Level Maths: Quadratic Equations Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Completing the Square (OCR)
- Completing the Square (Edexcel)
- Simultaneous Equations (OCR)
- Simultaneous Equations (Edexcel)
- Stealth Quadratics (OCR)
- Modelling With Quadratic Functions (Edexcel)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Indices — needed for expanding squared terms and simplifying after completing the square
- GCSE Maths Quadratic Equations — factorisation and the quadratic formula from GCSE are assumed
A Level Maths quadratic equations are the workhorse topic of Year 1 Pure. Anything of the form $ax^2 + bx + c = 0$ is a quadratic, and the techniques you learn here come up in nearly every other Pure Maths topic — from finding stationary points in Differentiation to solving trig equations in Trigonometry to handling exponential models. Confidence with quadratics makes the rest of A Level Maths feel substantially easier.
You solve quadratics by factorisation, by the quadratic formula, and by completing the square — and learn when each is the right tool. Completing the square is particularly valuable: it lets you find the turning point of a parabola directly ($a(x+p)^2 + q$ has a turning point at $(-p, q)$), solve equations where factorisation will not work, and handle modelling problems where you need maximum or minimum values. You also tackle simultaneous equations involving one linear and one quadratic equation, interpreting your answers as the intersection of a line and a curve, and stealth quadratics — equations that look complicated but become quadratic after a substitution like $u = x^2$ or $u = e^x$.
Quadratic equations are part of the Pure Maths strand of A Level Maths and underpin material across the rest of the course for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: when taking a square root, remember the $\pm$ ($x^2 = 9$ gives $x = 3$ OR $x = -3$); watch the signs when applying the quadratic formula with negative $b$ or $c$; when completing the square with a leading coefficient that is not $1$, factorise that coefficient out first; with stealth quadratics, remember to translate back from $u$ to $x$ at the end; and in modelling questions, check whether negative solutions make physical sense before including them in your answer.