E-Math 2025 Worked Solutions

Substitution into a formula

1 mark · number & algebra (formula evaluation)

Direct proportion / unitary method

4 marks: (a) 1, (b)(i) 2 + (ii) 1 · number & algebra (ratio / proportion)

Simple interest

2 marks · number & algebra (simple interest)

Estimation & approximation

1 mark · number & algebra (estimation)

Linear equations

6 marks: 2 + 2 + 2 · number & algebra (algebraic manipulation)

Linear inequalities

4 marks: (a) 3 + (b) 1 · number & algebra (inequalities)

Perpendicular bisector

3 marks: 1 + 1 + 1 · geometry & measurement (constructions / loci)

Position from a translation vector

3 marks: (a) 1 + (b) 2 · number & algebra (vectors)

Surface area and volume of a cube

2 marks · geometry & measurement (mensuration, cube)

Prime factorisation

2 marks: (a) 1 + (b) 1 · number & algebra (prime factorisation)

Interpreting statistical graphs

4 marks: 1 + 1 + 1 + 1 · statistics & probability (interpreting graphs)

Parity / properties of integers

1 mark · number & algebra (number reasoning, parity)

Isosceles triangle properties

3 marks · geometry & measurement (angles in triangles)

Successive percentage change

3 marks · number & algebra (percentage change)

Quadratic graphs

3 marks: (a) 2 + (b) 1 · number & algebra (quadratic graphs)

Tangent-radius property

6 marks: (a) 1 + (b) 2 + (c) 3 · geometry & measurement (circle properties / sector area)

Solving exponential equations by common base

2 marks · number & algebra (indices)

Changing the subject

3 marks · number & algebra (changing the subject)

Completing the square

3 marks · number & algebra (completing the square)

Proving congruent triangles (AAS)

6 marks: (a) 3 + (b) 3 · geometry & measurement (congruence / pythagoras)

Volume of a cylinder (proportional to height)

5 marks: (a) 2 + (b) 3 · geometry & measurement (mensuration, similar solids)

Area under speed-time graph = distance

4 marks · number & algebra (kinematics, speed-time graph)

Algebraic fractions

5 marks · number & algebra (algebraic fractions → quadratic)

Laws of indices

2 marks · number & algebra (indices)

Mean of grouped data

4 marks: (a)(i) 1 + (ii) 1, (b) 2 · statistics & probability (mean, standard deviation, comparison)

Solving inequalities graphically

4 marks · number & algebra (solving an inequality from a graph)

Independent events

4 marks: (a) 1 + (b) 3 · statistics & probability (probability of combined events)

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)