E-Math 2021 Worked Solutions

Simple interest

2 marks · number & algebra (simple interest)

Pythagoras' theorem (find a shorter side)

2 marks · geometry & measurement (pythagoras)

Estimation by 1 s.f.

2 marks: 1 + 1 · number & algebra (estimation)

Complement

2 marks: 1 + 1 · statistics & probability

Combining algebraic fractions

2 marks · number & algebra (algebraic fractions)

Reconstructing data from mean/median/mode

2 marks · statistics (averages, reverse)

Volume of a cuboid

2 marks · geometry & measurement (factors / volume)

Percentage increase (>100%)

2 marks · number & algebra (percentage increase)

Linear equation

3 marks: 1 + 2 · number & algebra (equation, simplify)

Pie-chart sector angles

3 marks · statistics (pie chart angles)

Interior/exterior angles of a regular polygon

3 marks · geometry & measurement (polygon angles)

Describing a set

3 marks: 1 + 1 + 1 · number & algebra (set language)

Reading a comparative bar chart

4 marks: 1 + 1 + 2 · statistics (comparing distributions)

AA similarity (common + given angle)

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

Square of a binomial

3 marks: 2 + 1 · number & algebra (expanding, comparing)

Solving a squared formula

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

Laws of indices (fractional power of a quotient)

2 marks · number & algebra (indices)

Reciprocal of a rate

4 marks: (a) 1, (b) 1 + 2 · number & algebra (units, scale)

Angle sum

4 marks · geometry & measurement (sine rule, area)

Prime factorisation

5 marks: (a) 1 + 2, (b) 2 · number & algebra (prime factors, hcf/lcm, cube)

Factorising by grouping

5 marks: 2 + 3 · number & algebra (factorising)

Building a matrix from a context

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

Gradient of a curve by tangent

6 marks: (a) 2, (b) 2 + 2 · number & algebra (cubic graph)

Acceleration from a speed-time graph

6 marks: (a) 1, (b) 1 + 4 · number & algebra (kinematics / speed-time graph)

Linear inequality

10 marks: (a) 2, (b) 1 + 2, (c) 5 · number & algebra (inequality, formula, fractional equation)

Standard form to 3 s.f.

10 marks: 1 + 2 + 2 + 2 + 3 · number & algebra (standard form, percentage, currency)

Forming an area expression

11 marks: (a) 2, (b) 3, (c) 1, (d) 3, (e) 1, (f) 1 · number & algebra (area, graph of a function)

Volume of cone & hemisphere

9 marks: 3 + 6 · geometry & measurement (composite solid)

Equation of a line from point & gradient

11 marks: (a) 2, (b) 3, (c) 2 + 4 · number & algebra (coordinate geometry)

Angle in a semicircle

9 marks: 3 + 3 + 3 · geometry & measurement (circle properties, sector)

Nth term of a fractional sequence

8 marks: 1 + 3 + 3 + 1 · number & algebra (sequences, algebraic fractions)

Translation vector

12 marks: (a)(i)(a) 1 + (b) 2, (ii) 3, (b)(i) 2 + (ii) 4 · number & algebra (vectors)

Cumulative-frequency curve (median

10 marks: (a)(i)(a) 1 + (b) 2, (ii) 2, (iii) 1, (b) 4 · statistics & probability

Gradient to angle (tan)

10 marks: 1 + 3 + 6 · geometry & measurement (trigonometry, modelling)