E-Math 2015 Paper 1 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)