E-Math 2018 Paper 2 Worked Solutions

Division of algebraic fractions

9 marks: (a) 1 + 2, (b) 3, (c) 3 · number & algebra (algebraic fractions, factorisation, fractional equation)

Percentage increase

10 marks: (a) 2, (b) 3, (c) 1 + 4 · number & algebra (percentage, compound interest, currency exchange)

Scalar multiple of a matrix

9 marks: (a) 1, (b) 1, (c) 2, (d) 1, (e) 4 · number & algebra (matrices and their interpretation)

Linear (nth-term) rule

10 marks: (a) 2 + 1, (b) 1 + 3 + 3 · number & algebra (sequences, nth-term formula)

Position vector from a known vertex

9 marks: (a) 1, (b) 2, (c) 3, (d) 3 · geometry & measurement (vectors, parallelogram)

Time = quantity ÷ rate

11 marks: (a) 1, (b) 1, (c) 3, (d) 4, (e) 2 · number & algebra (rates, forming and solving a quadratic)

SAS congruence via radii and vertically opposite angles

9 marks: (a) 3, (b) 3 + 3 · geometry & measurement (congruence, tangents, area of an annulus)

Slant edge via 3D Pythagoras

11 marks: (a) 3, (b) 3, (c) 3, (d) 2 · geometry & measurement (3d mensuration, similar solids)

Frequencies from a CF curve

11 marks: (a) 1 + 1 + 1 + 1 + 2, (b) 1 + 2 + 2 · statistics & probability (cumulative frequency, mean & sd, probability without replacement)

Mass from area and density

11 marks: (a) 2, (b) 1 + 1, (c) 7 · number & algebra (cubic volume model, graphical optimisation)