← Algebraic methods

Quadratics (every paper)

Factor → formula → discriminant, in that order of preference. Exam-style Solve 2x² = 4x + 3 (2 d.p.) Rearrange first. 2x² − 4x − 3 = 0 → a=2, b=−4, c=−3 x = (4 ± √(16 + 24))/4 = (4 ± √40)/4 x = 2.58 or −0.58 ✓ x ≈ 2.58 or x ≈ −0.58 (2 d.p.). Both answers required.

Discriminant question template

• "No real roots" → b² − 4ac < 0.
• "Two equal roots" → b² − 4ac = 0.
• "Two distinct roots" → b² − 4ac > 0.
• Solve the resulting linear inequality in k.

Order of preference for solving a quadratic

• Try FACTORISING first — fastest when it works cleanly.
• If it does not factorise easily, use the QUADRATIC FORMULA — always works, and is the safe default under time pressure.
• Use COMPLETING THE SQUARE only when the question specifically asks for vertex form or an (x+p)²−q answer.

Practice for this standard covers the whole topic — flashcards and quiz.