Quadratic Equations | 40 Worked Examples | AQA GCSE Higher Maths

40 progressive quadratic equation questions with full mark-scheme style worked solutions, written for AQA GCSE Higher Tier Mathematics (8300). Every solution breaks the method down one line at a time, with B, M and A marks annotated exactly where the exam awards them.

What’s inside:
• 15 Easy questions — factorising simple quadratics, difference of two squares, common factors, perfect squares, rearranging to = 0, and completing the square.
• 15 Standard questions — factorising with a leading coefficient (the AC / split-the-middle-term method), the quadratic formula to 2 d.p., completing the square for exact surd answers, forming quadratics from worded problems (consecutive integers, rectangle areas), clearing an algebraic fraction, and the discriminant for ‘no real roots’ and ‘equal roots’.
• 10 Challenging questions — quadratic-formula worded problems, two linear-quadratic simultaneous pairs (points of intersection), a disguised quartic solved by substitution (x⁴ − 5x² + 4), a reciprocal problem, an ‘always positive’ completing-the-square proof, a discriminant inequality for the range of k, an equal-roots problem giving a quadratic in k, and a projectile-motion model solved by factorising and completing the square.

Every method students need for the Higher paper is here: factorising (a = 1 and a ≠ 1), the quadratic formula, completing the square, the discriminant, disguised quadratics, and quadratics from context.

Ideal for: Year 11 students sitting AQA GCSE Mathematics (8300) Higher Tier, November resit candidates, and tutors or teachers building targeted algebra practice with ready worked solutions.