E-Math 2019 Paper 2 Worked Solutions

Division of algebraic fractions

11 marks: 1 + 1 + 2 + 2 + 1 + 4 · number & algebra (algebraic manipulation, completing the square, fractional equation)

Cosine rule for a third side

8 marks: 3 + 2 + 3 · geometry & measurement (sine rule, cosine rule, area of a triangle)

Currency conversion & comparison

10 marks: 2 + 2 + 1 + 2 + 3 · number & algebra (currency, reverse percentage, standard form)

Evaluate a cubic for a table value

11 marks: 1 + 3 + 1 + 2 + 2 + 2 · number & algebra (cubic graph, solving by a drawn line)

Algebraic expression for grid positions

9 marks: 1 + 2 + 3 + 2 + 1 · number & algebra (number patterns, arithmetic sequence)

Isosceles triangle from radii

11 marks: 3 + 3 + 2 + 3 · geometry & measurement (circle angle properties, radian sector area)

Column vector from two points

9 marks: 1 + 2 + 2 + 2 + 2 · geometry & measurement (vectors)

Volume of a prism with a composite cross-section

11 marks: 3 + 4 + 4 · geometry & measurement (mensuration of a prism, 3d trigonometry)

Median & range from a stem-and-leaf diagram

10 marks: 1 + 1 + 1 + 2 + 1 + 2 + 2 · statistics & probability (stem-and-leaf, probability without replacement)

Reading a rate table

10 marks: 1 + 2 + 7 · number & algebra (rate, speed, distance, percentage, problem solving)