E-Math 2022 Worked Solutions

Order of operations / roots on a calculator

1 mark · number & algebra (calculator use)

Law of indices (product)

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

Median of an ungrouped set

2 marks: 1 + 1 · statistics (median, range)

Nth term of a linear sequence

4 marks: 1 + 2 + 1 · number & algebra (linear sequence)

Complement (probabilities sum to 1)

3 marks: 1 + 2 · statistics & probability

Simultaneous linear equations (elimination)

3 marks · number & algebra (simultaneous equations)

Interior angle of a regular polygon

5 marks: 2 + 2 + 1 · geometry & measurement (polygon angles, rhombus)

HCF

2 marks · geometry & measurement (hcf, packing)

Scale drawing

4 marks: 2 + 2 · geometry & measurement (bearings, scale drawing)

Area of a circle / annulus

3 marks · geometry & measurement (area of annulus)

Common-factor factorisation

3 marks: 1 + 2 · number & algebra (factorise, expand)

Ratio to dimensions

3 marks · number & algebra (ratio, area)

Speed-distance-time

4 marks: 1 + 3 · number & algebra (speed-distance-time)

Forming an inequality from a word description

4 marks: 2 + 2 · number & algebra (forming & solving an inequality)

Alternate angles on parallel lines

4 marks · geometry & measurement (congruence proof)

Factorising a quadratic (a 1)

2 marks · number & algebra (factorising a quadratic)

Angle at centre = 2× angle at circumference

4 marks · geometry & measurement (circle angle properties)

Matrix product (4-term rows)

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

Obtuse-angle trig (two solutions of sin)

2 marks · geometry & measurement (trig equation, obtuse angle)

Change of subject (variable on both sides)

3 marks · number & algebra (change of subject)

Subtracting algebraic fractions

3 marks · number & algebra (algebraic fractions)

Right-angled trig (sine to find a side

3 marks · geometry & measurement (right-angled trig)

Laws of indices (common base, equate powers)

2 marks · number & algebra (indices)

Grouped-data mean & standard deviation

3 marks: 1 + 1 + 1 · statistics (grouped mean & s.d.; effect of a shift)

Exponential model

5 marks: 1 + 1 + 2 + 1 · number & algebra (exponential growth)

Fractional linear equation

10 marks: 2 + 1 + 4 + 3 · number & algebra (equations, fractions, completing the square)

Simple vs compound interest

11 marks: 1 + 3 + 3 + 4 · number & algebra (interest, currency)

Cumulative-percentage curve

8 marks: (a) 1 + 1 + 1, (b) 2, (c) 3 · statistics (cumulative percentage curve)

Cubic table of values

10 marks: 1 + 3 + 2 + 4 · number & algebra (cubic graph)

Volume & surface area of a (half) cylinder

8 marks: (a) 2 + 3, (b) 1 + 2 · geometry & measurement (mensuration, similar solids)

Angle in a semicircle

12 marks: (a) 2, (b) 3, (c) 4 + 3 · geometry & measurement (circle properties, similar triangles, arc)

Area of a trapezium on a face

10 marks: 3 + 2 + 5 · geometry & measurement (3-d solid)

Distance formula

11 marks: (a) 2 + 1 + 3, (b) 5 · number & algebra (coordinate geometry & vectors)

Set notation (complement

9 marks: (a) 1 + 1 + 2, (b) 1 + 2 + 2 · statistics & probability (sets & probability)

Rate (items per time)

11 marks: 1 + 2 + 8 · number & algebra (rates, modelling, extended reasoning)