E-Math 2018 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)

Division of algebraic fractions

9 marks: (a) 1 + 2, (b) 3, (c) 3 · number & algebra (algebraic fractions, factorisation, fractional equation)

Percentage increase

10 marks: (a) 2, (b) 3, (c) 1 + 4 · number & algebra (percentage, compound interest, currency exchange)

Scalar multiple of a matrix

9 marks: (a) 1, (b) 1, (c) 2, (d) 1, (e) 4 · number & algebra (matrices and their interpretation)

Linear (nth-term) rule

10 marks: (a) 2 + 1, (b) 1 + 3 + 3 · number & algebra (sequences, nth-term formula)

Position vector from a known vertex

9 marks: (a) 1, (b) 2, (c) 3, (d) 3 · geometry & measurement (vectors, parallelogram)

Time = quantity ÷ rate

11 marks: (a) 1, (b) 1, (c) 3, (d) 4, (e) 2 · number & algebra (rates, forming and solving a quadratic)

SAS congruence via radii and vertically opposite angles

9 marks: (a) 3, (b) 3 + 3 · geometry & measurement (congruence, tangents, area of an annulus)

Slant edge via 3D Pythagoras

11 marks: (a) 3, (b) 3, (c) 3, (d) 2 · geometry & measurement (3d mensuration, similar solids)

Frequencies from a CF curve

11 marks: (a) 1 + 1 + 1 + 1 + 2, (b) 1 + 2 + 2 · statistics & probability (cumulative frequency, mean & sd, probability without replacement)

Mass from area and density

11 marks: (a) 2, (b) 1 + 1, (c) 7 · number & algebra (cubic volume model, graphical optimisation)