A-Math 2025 Paper 2 Worked Solutions

Rationalising the denominator

6 marks · algebra (surds; no calculator)

Completing the square (max/min)

7 marks: 5 + 2 · algebra (completing the square, maximum)

Integrate e^ax and 2x

7 marks · calculus (integration of exponential and trig, constant from a point)

Factor theorem

9 marks: 6 + 3 · algebra (factor and remainder theorems; no calculator)

Quotient rule

6 marks · calculus (quotient rule, increasing function)

Pythagorean identity cosec^2=1+ ^2

7 marks · trigonometry (identity to quadratic, solve over a range)

Integrate acceleration to velocity

7 marks · calculus (kinematics: integrate acceleration)

Solve an exponential equation with logarithms

9 marks: 4 + 5 · algebra (logarithms; simultaneous exponential equations)

Area between a curve and a line

10 marks: 7 + 3 · calculus (area between a curve and a line; equal areas)

Alternate segment theorem

10 marks: (a) 3 + (b)(i) 3 + (b)(ii) 4 · geometry (alternate segment theorem, cyclic quadrilateral)

R-formula R ( - )

12 marks: (a) 1 + (b) 3 + (c)(i) 2 + (c)(ii) 6 · trigonometry (r-formula, kinematics modelling)