E2E stub topic — OCR GCSE Study Guide

Overview

Quadratic equations are a cornerstone of GCSE Mathematics, bridging the gap between basic algebra and advanced calculus. A quadratic equation contains an x^2 term as its highest power and typically takes the form ax^2 + bx + c = 0. This topic is heavily assessed across all exam boards, often appearing in high-tariff questions that require multi-step problem solving.

Understanding quadratics isn't just about finding 'x'; it's about modelling real-world scenarios like projectile motion, optimizing areas, and analyzing curves. In your exams, you will be expected to solve these equations algebraically—using factorisation, the quadratic formula, or completing the square—and graphically by sketching parabolas and identifying key features like roots and turning points.

This guide will walk you through each method, showing you exactly where examiners award marks and how to avoid common pitfalls.

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Key Concepts

Concept 1: Solving by Factorising

Factorising is the process of putting a quadratic expression back into brackets. It relies on the zero product property: if A \times B = 0, then either A = 0 or B = 0.

When you have x^2 + bx + c = 0, you need to find two numbers that