Free worked solutions · O-Level A-Math 2022
All 10 questions from O-Level / IP A-Math 2022 Paper 2, each with a verified step-by-step solution.
Exponential decay model
6 marks: 4 + 2 · algebra (exponential-decay model)
Factor theorem
7 marks: 4 + 3 · algebra (factor & remainder theorem)
Double-angle identities
8 marks: 4 + 4 · trigonometry (prove identity, then solve)
Express SA via conservation of volume
10 marks: 4 + 4 + 2 · calculus (surface-area optimisation)
Compound-angle for 75°
8 marks: 4 + 2 + 2 · trigonometry (exact values; no calculator)
Substitution u = 2^x
9 marks: 5 + (2 + 2) · algebra (exponential equation; curve intercepts)
Resolve perpendiculars
9 marks: 3 + 4 + 2 · trigonometry (r-formula in context)
Product & chain rule
10 marks: 4 + 2 + 4 · calculus (product/chain rule; connected rate; integral via a "show that")
Equation of a circle (complete the square)
11 marks: 4 + 5 + 2 · coordinate geometry (circle)
Tangent line via chain rule
12 marks: 6 + 6 · calculus (tangent, intercepts; area between curve and tangent)
Genius Plus Academy · O-Level & IP Mathematics
Our O-Level A-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
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