E-Math 2019 Worked Solutions

Lower bound (nearest 100)

1 mark · number & algebra (estimation, bounds)

Misleading diagrams (area vs length)

1 mark · statistics & probability (misleading graphs)

Power of a power

2 marks: 1 + 1 · number & algebra (indices)

Prime factorisation

2 marks: 1 + 1 · number & algebra (prime factorisation, cubes)

Repeated-percentage / compound-interest-style growth

2 marks · number & algebra (compound growth)

Algebraic fractions (subtraction, common denominator)

2 marks · number & algebra (algebraic fractions)

Complement of an event

2 marks: 1 + 1 · statistics & probability (single-event probability)

Solving a quadratic by factorisation

3 marks · number & algebra (quadratic by factorisation)

Compare percentage with fraction

3 marks: 1 + 2 · number & algebra (comparing values, linear inequalities)

Direct proportion to a power (cube)

3 marks: 2 + 1 · number & algebra (direct proportion)

Difference of two squares

3 marks: 1 + 2 · number & algebra (factorisation)

Angle bisector

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

Translation by a column vector

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

Back-bearing

3 marks: 1 + 2 · geometry & measurement (bearings)

Graph of a quadratic in completed-square form (vertex, intercepts)

3 marks · number & algebra (quadratic graph)

Tangent ⊥ radius

4 marks: 3 + 1 · geometry & measurement (circle, tangents, congruence)

Gradient = speed on a distance-time graph

4 marks: 1 + 1 + 1 + 1 · number & algebra (travel graphs, rates)

Listing elements within a universal set

4 marks: 1 + 1 + 2 · number & algebra (set notation)

Ratio before/after equal change, solved by equation

4 marks · number & algebra (ratio with change)

Linear scale factor for lengths

4 marks: 2 + 2 · geometry & measurement (similar solids)

Writing a data matrix

4 marks: 1 + 2 + 1 · number & algebra (matrices)

Gradient from two points

4 marks · number & algebra (coordinate geometry)

Scale 1 cm : n m and area

5 marks: 2 + 3 · geometry & measurement (scale) / number & algebra (best-buy)

Median class

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

Form an equation from a partial sum

6 marks: (a) 1 + 3, (b) 2 · number & algebra (sequences and their sums)

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)