E-Math 2018 Paper 1 Worked Solutions

Compare fractions, decimals and powers

1 mark · number & algebra (ordering numbers)

Power of a power

2 marks · number & algebra (indices)

Substitute a known root to find a coefficient

2 marks: 1 + 1 · number & algebra (quadratic equations)

Angles on a straight line

2 marks · geometry & measurement (circle geometry)

Show an expression is a multiple of a number

2 marks · number & algebra (algebraic proof)

Reading a peak/modal class from a curve

2 marks: 1 + 1 · statistics & probability (interpreting graphs)

Describe a shaded region

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

Deposit from hire-purchase breakdown

3 marks · number & algebra (percentage)

Isosceles triangles from radii

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

Time = distance ÷ speed

3 marks · number & algebra (time, speed, time zones)

Volume scale factor = (length factor)³

3 marks · geometry & measurement (similar solids, standard form)

Inverse proportion (product constant)

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

Common-factor extraction

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

Angles at a point sum to 360°

4 marks · geometry & measurement (polygons, angles)

Total = mean × frequency

4 marks · statistics & probability (combined means)

Perimeter of a sector = 2r + arc

4 marks · geometry & measurement (arc length, sectors, radians)

Clear the fraction

4 marks · number & algebra (changing the subject)

Magnitude of a column vector

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

Median from an ordered list

4 marks: 1 + 1 + 2 · statistics & probability (stem-and-leaf)

Prime factorisation

4 marks: 1 + 1 + 2 · number & algebra (factors, multiples)

Substitute points into a quadratic

4 marks · number & algebra (simultaneous equations)

Angle bisector and alternate angles

5 marks · geometry & measurement (trigonometry, area)

Line of symmetry from the roots

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

Sine rule for an angle

4 marks: 2 + 2 · geometry & measurement (sine rule, bearings)