A-Math 2024 Paper 2 Worked Solutions

Exponential-decay model

4 marks · algebra (exponential-decay model)

Line-and-curve intersection

5 marks · algebra (line meets curve, discriminant)

Change of base

5 marks · algebra (logarithms, change of base)

Quotient rule

7 marks: 3 + 1 + 3 · calculus (quotient rule; integrate ^2)

Stationary point (derivative =0)

6 marks: 2 + 4 · algebra / calculus (stationary point; exponential equation)

Factor theorem (two simultaneous conditions)

9 marks: 4 + 5 · algebra (factor theorem; cubic roots in surd form)

Circle from a diameter

9 marks: 3 + 2 + 1 + 3 · coordinate geometry (circle, closest point on a line)

Interpret constants from initial/boundary conditions

9 marks: 3 + 2 + 4 · calculus (kinematics: speed model)

Prove a double-angle identity

12 marks: 4 + 6 + 2 · trigonometry (double-angle identity; solve; no-solution range)

Linear law R vs v

12 marks: 4 + 2 + 2 + 4 · coordinate geometry (linear law)

Product rule with e^-2x and x

12 marks: 2 + 5 + 5 · calculus (product rule, second derivative, verify an equation)