Exam-depth practice, built around a diagnostic that names the misconception behind each mistake — the why, not just the how.
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Question bankAA SL · 2.7 · The quadratic formula
Solve 2x² − 4x − 3 = 0, giving your answer in exact form.
Ax = (2 ± √10)/2
Bx = (4 ± √10)/4
Cx = 2 ± √10
Dx = (−2 ± √10)/2
Paper 1 · calculator-free · 4 marks
Every wrong option is a real student error — the diagnostic knows exactly which one you made.
Mock exam1:47:22
Paper 1 · No calculatorQuestion 4 of 12
The function is defined by f(x) = 3x² − 12x + 7.
Express f(x) in the form a(x − h)² + k.[3]
Hence write down the coordinates of the vertex.[1]
Marked to the IB scheme — method, accuracy and follow-through marks, not just the final line.
Diagnosticthe moment you answer
Your answer x = (−2 ± √10)/2✕
Misconception identified
Sign of b
With b = −4, the formula opens with −b = +4 — so the numerator begins +4, not −4. You carried the sign of b straight through the substitution: the slip that quietly costs the mark.
Correctx = (−b ± √(b²−4ac))/2a = (4 ± √40)/4
One of 300+ misconceptions the engine can name by sight — so you fix the cause, not just the symptom.
Worked methodmarked the way IB rewards it
identifya = 2, b = −4, c = −3setup
substitutex = (4 ± √((−4)²−4·2·−3)) / 4M1
evaluatex = (4 ± √40)/4A1
simplifyx = (2 ± √10)/2A1
Exact solution · 3 marksx = (2 ± √10)/2
M1 method · A1 accuracy — the engine marks like an IB examiner, awarding the method even when the final line slips. AA stays exact · AI rounds to 3 s.f.
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