Free worked solutions · O-Level A-Math 2023
All 13 questions from O-Level / IP A-Math 2023 Paper 1, each with a verified step-by-step solution.
Line-and-curve tangency
3 marks · algebra (tangent condition)
Partial fractions with a repeated linear factor
5 marks · algebra (partial fractions, repeated linear factor)
Pythagorean identities
5 marks · trigonometry (prove an identity)
Product rule with e^-2x
7 marks: 3 + 4 · calculus (product rule, then integrate by reversing)
Solve a trig equation
6 marks · trigonometry (solve over a range)
Quotient rule
6 marks: 2 + 4 · calculus (quotient rule; decreasing interval)
Always-negative condition
6 marks · algebra (quadratic always negative)
Simultaneous equations (one linear
5 marks · algebra (line meets curve, simultaneous)
Stationary points
8 marks: 4 + 4 · calculus (stationary points; maximum gradient)
Equation of a circle (complete the square)
10 marks: 4 + 2 + 4 · coordinate geometry (circle; dividing a line)
Integrate k/2t+1 to a logarithm
9 marks: 1 + 4 + 4 · calculus (rates of change)
Completing the square (vertex)
10 marks: 1 + 3 + 2 + 1 + 3 · algebra (projectile model, completing the square)
Perpendicular bisector
10 marks: 3 + 7 · coordinate geometry (perpendicular bisector)
Genius Plus Academy · O-Level & IP Mathematics
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