E-Math 2017 Worked Solutions

Negative index (reciprocal of a power)

1 mark · number & algebra (indices)

Reading inequalities from a number line (open/closed endpoints)

1 mark · number & algebra (inequalities on a number line)

Range from a stem-and-leaf

2 marks: 1 + 1 · statistics & probability (stem-and-leaf, range & median)

Quadratic graph from factorised form (intercepts, shape)

2 marks · number & algebra (quadratic graph)

Area under a speed-time graph = distance

2 marks: 1 + 1 · number & algebra (speed-time graph, rates)

Reading sets from a Venn diagram

3 marks: 1 + 1 + 1 · number & algebra (set notation, venn diagram)

Forming and solving a percentage inequality (smallest integer)

3 marks · number & algebra (percentage inequality)

Interior angle of a regular polygon

3 marks · geometry & measurement (polygon angles)

Volume of cylinder and hemisphere

3 marks · geometry & measurement (mensuration, surface area)

Perpendicular bisector

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

Solving a linear equation with fractions (clear denominators)

3 marks · number & algebra (fractional linear equation)

Difference of two vectors

3 marks · geometry & measurement (vectors)

Find the principal from the total interest

3 marks · number & algebra (compound interest)

Factorising a quadratic trinomial

4 marks: 2 + 2 · number & algebra (factorisation, substitution)

Angle in a semicircle = 90°

4 marks · geometry & measurement (circle properties, trigonometry)

Base angles of isosceles triangles from radii

4 marks · geometry & measurement (circle, isosceles triangles, parallel lines)

Perfect square via even prime indices

5 marks: 3 + 2 · number & algebra (prime factorisation, squares & cubes)

Writing a data matrix

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

Common difference

5 marks: 2 + 2 + 1 · number & algebra (linear sequences)

Why no solution for some k

6 marks: 1 + 1 + 1 + 3 · number & algebra (graphs, solving quadratics graphically)

Substitution into a formula

6 marks: 2 + 4 · number & algebra (substitution, change of subject)

Test for direct proportion via constant unit rate

5 marks: 2 + 3 · number & algebra (proportion) / geometry & measurement (similar solids)

Linear inequality

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

Mean from a total

8 marks: 2 + 2 + 2 + 2 · number & algebra (standard form, percentage)

Evaluate an exponential model

9 marks: 1 + 1 + 3 + 1 + 2 + 1 · number & algebra (exponential graph, gradient by tangent)

Distance between two points

9 marks: 2 + 2 + 2 + 3 · number & algebra (coordinate geometry)

Angle between two bearings

10 marks: 3 + 3 + 2 + 2 · geometry & measurement (bearings, sine/cosine rule, trigonometry)

Vector path in a parallelogram

9 marks: 2 + 3 + 2 + 2 · geometry & measurement (vectors, similar & congruent triangles)

Express dimensions algebraically

11 marks: 2 + 3 + 3 + 1 + 2 · number & algebra (forming & solving a quadratic) / geometry & measurement (surface area, volume)

Angle at centre via right-angled trig

11 marks: 2 + 4 + 2 + 3 · geometry & measurement (circle segment, mensuration)

Median & quartiles from a CF curve

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