E-Math 2016 Worked Solutions

Expansion of brackets

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

Factorising four terms by grouping

2 marks · number & algebra (factorisation by grouping)

Shading union with a complement

2 marks: 1 + 1 · number & algebra (set notation, venn diagrams)

Difference of two squares used in a proof

2 marks · number & algebra (algebraic proof, difference of two squares)

Factor pairs of a volume under a perimeter and size constraint

2 marks · geometry & measurement (mensuration, volume of a cuboid)

Area = ½ab sin C, two-solution (acute/obtuse) angle

2 marks · geometry & measurement (area of a triangle, ½ab sin c)

Volume ratio of similar cones (cube of length ratio)

2 marks · geometry & measurement (similar cones, volume)

Two-dimensional pictogram distorts a one-dimensional quantity

2 marks · statistics & probability (misleading diagrams)

Algebraic fractions (use 4-x=-(x-4) to share a denominator)

2 marks · number & algebra (algebraic fractions)

Opposite angles of a cyclic quadrilateral

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

Completing the square

3 marks: 2 + 1 · number & algebra (completing the square, quadratic graph)

Currency + unit conversion to compare two rates

3 marks · number & algebra (rate, currency & unit conversion)

Substitute and solve for a variable

3 marks: 1 + 2 · number & algebra (formula, change of subject)

Midpoint from congruent figures

2 marks · geometry & measurement (coordinates)

Angles on a straight line

5 marks: 4 + 1 · geometry & measurement (angles, parallel lines, circle property)

Pythagoras for the rectangle diagonal

4 marks: 2 + 2 · geometry & measurement (pythagoras, circle, rectangle)

Find constants of an exponential from two points

4 marks: 2 + 2 · number & algebra (exponential and linear graphs)

Prime factorisation

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

Rate (fuel consumption → cost)

4 marks: 2 + 2 · number & algebra (rate, percentage)

Linear scale conversion to km

4 marks: 2 + 2 · geometry & measurement (map scale, area scale)

Read a count off a CF curve

4 marks: 2 + 2 · statistics & probability (cumulative frequency, probability)

Magnitude of a vector

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

Semicircle area

5 marks · geometry & measurement (areas of circle parts in a square)

Position vector via a ratio division of a line

6 marks: 2 + 2 + 1 + 1 · number & algebra (vectors)

Evaluate & rearrange a formula

11 marks: (a) 1 + 2, (b) 2, (c) 3, (d) 3 · number & algebra (formula, equations, algebraic fractions)

Scalar multiple of a matrix

7 marks: 1 + 1 + 1 + 1 + 3 · number & algebra (matrices)

SAS congruence reasoning

7 marks: (a) 2, (b) 2 + 1 + 2 · geometry & measurement (congruence, polygon angles)

Continue a pattern

9 marks: 1 + 1 + 3 + 3 + 1 · number & algebra (sequences)

Evaluate to complete a table

13 marks: (a) 1, (b) 3, (c) 2, (d) 2, (e) 2 + 1 + 2 · number & algebra (graph of a cubic)

Angle in a semicircle

8 marks: 2 + 2 + 4 · geometry & measurement (circles, similarity, area)

Share by ratio using the part difference

12 marks: (a) 2, (b) 1 + 1 + 3 + 3 + 2 · number & algebra (ratio, rates, quadratic)

Cosine rule for an angle

12 marks: 3 + 3 + 2 + 4 · geometry & measurement (3d, trigonometry)

Reading rate tables

10 marks: 1 + 2 + 7 · number & algebra (costing, real-world problem solving)