E-Math 2025 Paper 2 Worked Solutions

Linear equation with algebraic fraction

10 marks: 2 + 2 + 3 + 3 · number & algebra (manipulation)

Cumulative frequency (median

8 marks: (a) 1 + 2 + 2, (b) 1, (c) 1 + 1 · statistics & probability

Percentage increase

10 marks: 1 + 3 + 3 + (1 + 1 + 1) · number & algebra (percentage, ratio, matrices)

AA similarity (right-angled triangles)

12 marks: (a) 2 + 4, (b) 2 + 1 + 3 · geometry & measurement (similar triangles, regular polygon)

Laws of indices (incl. sum in denominator → factor out)

9 marks: 2 + 4 + 3 · number & algebra (indices, gradient of a curve, exponential)

Area of a triangle ½ab sin C (radians)

13 marks: (a) 2 + 5, (b) 6 · geometry & measurement (radian trig, mensuration, volumes)

Universal set restriction

8 marks: (a) 2, (b) 2, (c) 1 + 3 · number & algebra / statistics (sets, probability)

Intercepts

11 marks: (a) 2 + 3 + 2, (b) 1 + 3 · number & algebra (coordinate geometry, quadratic)

Speed = distance/time

9 marks: (a) 1, (b) 1, (c) 6, (d) 1 · number & algebra (rates, problem-solving with justification)