E-Math 2015 Worked Solutions

Solving a linear equation

1 mark · number & algebra (linear equation)

Percentage increase (profit on cost)

2 marks · number & algebra (percentage)

Mean

2 marks · statistics & probability (averages, reasoning)

Multi-step rate calculation

2 marks · number & algebra (estimation, standard form)

Algebraic fractions (common denominator, expansion)

2 marks · number & algebra (algebraic fractions)

Listing elements within a universal set

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

Factorising by grouping (four terms)

2 marks · number & algebra (factorisation by grouping)

Find a point from a position/displacement vector

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

Effect of adding a constant on mean and standard deviation

2 marks · statistics & probability (effect of a shift on mean and sd)

Evaluate a compound-interest formula

3 marks: 1 + 2 · number & algebra (compound growth, percentage)

Form and solve a linear equation from a worded geometric condition

3 marks · number & algebra (forming and solving an equation)

Share a quantity in a given ratio

3 marks: 1 + 1 + 1 · number & algebra (ratio)

Combined rates of work

3 marks · number & algebra (rate / combined work)

Prime factorisation

3 marks: 1 + 2 · number & algebra (prime factorisation, hcf & lcm)

Solve a double linear inequality

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

Interior angle sum of a polygon

3 marks · geometry & measurement (polygon angles)

Length from cube-root of volume ratio

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

Cosine rule for an angle

4 marks · geometry & measurement (bearings, cosine rule)

Perpendicular from centre to a chord

5 marks · geometry & measurement (segment of a circle)

Gradient product for perpendicular lines

5 marks: 2 + 1 + 2 · number & algebra (coordinate geometry, vectors)

Rearrange a formula for a chosen variable

5 marks: 2 + 3 · number & algebra (change of subject) / geometry & measurement (surface area)

Build a data matrix

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

Form an area expression from a composite design

6 marks: 2 + 4 · geometry & measurement (area of circles and semicircles)

Probability without replacement

7 marks: 1 + 1 + 2 + 3 · statistics & probability (probability without replacement) / number & algebra (quadratic)

Difference of two squares

11 marks: (a) 1, (b) 1 + 2, (c) 3, (d) 1 + 3 · number & algebra (algebraic manipulation, quadratic)

Locate points from given vectors

8 marks: (a) 1 + 1, (b) 1, (c) 3, (d) 2 · geometry & measurement (vectors, similar triangles)

Wage + percentage bonus

12 marks: (a) 2, (b) 2 + 2, (c) 3 + 3 · number & algebra (everyday percentage & money)

Angles in the same segment

9 marks: (a) 1 + 1 + 2 + 2, (b) 3 · geometry & measurement (circle properties, sector)

Distance = speed × time to form an equation

7 marks: (a) 1, (b) 1, (c) 3, (d) 2 · number & algebra (simultaneous equations, rate)

Height of a pyramid via 3D Pythagoras

9 marks: (a) 4, (b) 2, (c) 3 · geometry & measurement (3d mensuration, similar/equal volumes)

Nth term of an arithmetic sequence

9 marks: (a) 2 + 1, (b) 1 + 2 + 3 · number & algebra (sequences, number-grid proof)

Pythagoras and tan in a right triangle

13 marks: (a) 2, (b) 4, (c) 4, (d) 3 · geometry & measurement (trigonometry, bearings/3d)

Median & quartiles from a CF curve

10 marks: (a)(i) 1 + 2 + 2, (a)(ii) 1, (b)(i) 1 + 1, (b)(ii) 2 · statistics & probability