Solving a quadratic is one of the first things students learn — and one of the most common places they lose marks they "should" have. The reason is that the mark scheme rewards a valid method even when the answer is wrong, and demands exactness even when the method is right. Here's how examiners split the marks, across factorising, the quadratic formula and completing the square.
For a question like Solve 3x² − 5x − 2 = 0, a typical mark scheme reads:
(3x+1)(x−2), or correct substitution into the quadratic formula, or completing the square. Awarded even with a slip.x = 2).x = −1/3).Note both A marks depend on the M1. No valid method, no accuracy marks — even if a correct answer appears.
The M1 needs factors that actually expand back to the original (or correct use of the product/sum). A "nearly right" factorisation that doesn't multiply out won't earn it.
The M1 is for correct substitution of a, b, c — a sign slip on b or c is the classic place the method mark is still given but the answer A marks are lost. Examiners often want the discriminant evaluated correctly for the accuracy marks.
Watch the constant: (x − p)² + q with the wrong q keeps the M1 but loses accuracy. For "give exact answers", a decimal where a surd was required can cost the A mark (or trigger cao — correct answer only).
Award the method mark for any valid route, then check each root for exactness against the required form (surd vs decimal, sign, both roots present). Tell the student which root or step lost the mark, not just that the answer was wrong — that's the feedback that changes their next attempt.
Mark quadratics — and every question — point by point against your board's scheme.
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