E-Math 2020 Worked Solutions

Surds

1 mark · number & algebra (calculator evaluation)

Inverse proportion

1 mark · number & algebra (variation / graphs)

Tangent-radius right angle

2 marks · measurement & geometry (circle properties)

Misleading graphs

2 marks: (a) 1, (b) 1 · statistics (interpreting graphs)

Laws of indices

3 marks: (a) 1, (b) 2 · number & algebra (indices, algebraic fractions)

Perimeter and side relationships

2 marks · measurement & geometry (similar figures, area ratio)

Stem-and-leaf

2 marks: (a) 1, (b) 1 · statistics (stem-and-leaf)

Probabilities sum to 1

3 marks: (a) 1, (b) 2 · statistics (probability)

Linear equation with algebraic fractions

3 marks · number & algebra (linear equations)

Completing the square

3 marks: (a) 2, (b) 1 · number & algebra (completing the square)

Linear (arithmetic) sequence

3 marks: (a) 1, (b) 2 · number & algebra (sequences)

Sharing in a ratio

3 marks · number & algebra (ratio)

Substitution

3 marks: (a) 1, (b) 2 · number & algebra (formulae)

Percentage of a percentage

3 marks · number & algebra (percentage)

Compound interest

3 marks · number & algebra (compound interest)

Intersection

3 marks: (a)(i) 1, (a)(ii) 1, (b) 1 · number & algebra (set notation)

Length scale

4 marks: (a) 2, (b) 2 · measurement & geometry (scale)

Angle of elevation

4 marks · measurement & geometry (trigonometry)

Expanding brackets

4 marks: (a) 2, (b) 2 · number & algebra (expansion & factorisation)

Prime factorisation in index form

5 marks: (a) 2, (b)(i) 2, (b)(ii) 1 · number & algebra (primes, lcm & hcf)

Co-interior angles in parallel lines

6 marks: (a)(i) 2, (a)(ii) 2, (b) 2 · measurement & geometry (angles in polygons)

Similar right triangles

5 marks: (a) 1, (b) 4 · measurement & geometry (survey: similar triangles & composite area)

Estimated mean of grouped data

5 marks: (a) 1, (b)(i) 2, (b)(ii) 2 · statistics (grouped data & cumulative frequency)

Position vectors

7 marks: (a) 1, (b)(i) 2, (b)(ii) 3, (b)(iii) 1 · measurement & geometry (vectors)

Linear inequality

12 marks: (a) 2, (b) 3, (c) 2, (d) 2, (e) 3 · number & algebra (manipulation)

Matrix multiplication

9 marks: (a) 1, (b) 1, (c) 2, (d) 1, (e) 1, (f) 3 · number & algebra (matrices, percentage)

Tabulating and plotting a reciprocal-plus-linear curve

13 marks: (a) 1, (b) 3, (c) 2, (d)(i) 2, (d)(ii) 2, (d)(iii) 3 · number & algebra (graphs of functions)

Cosine rule

9 marks: (a) 3, (b) 3, (c) 3 · measurement & geometry (trigonometry, bearings)

Curved surface area of a cone

10 marks: (a) 3, (b)(i) 1, (b)(ii) 2, (b)(iii) 4 · measurement & geometry (mensuration, similar solids)

Congruent triangles (SAS)

11 marks: (a)(i) 3, (a)(ii)(a) 1, (a)(ii)(b) 1, (b)(i) 2, (b)(ii) 4 · measurement & geometry (circle geometry, radian measure)

Mean of a frequency table

6 marks: (a) 3, (b) 1, (c) 2 · statistics (mean, standard deviation)

Length of a segment

9 marks: (a) 2, (b) 4, (c)(i) 2, (c)(ii) 1 · measurement & geometry (coordinate geometry, vectors)

Tree diagram without replacement

11 marks: (a) 2, (b) 3, (c) 3, (d) 1, (e) 2 · statistics (probability)

Reading a time-series graph

10 marks: (a)(i) 1, (a)(ii) 3, (b) 6 · number & algebra (everyday maths: money, graph reading)