E-Math 2024 Worked Solutions

Collecting like terms

2 marks · number & algebra (manipulation)

Representing inequalities on a number line

1 mark · number & algebra (inequalities)

Hire purchase

4 marks: (a) 2, (b) 2 · number & algebra (percentage, hire purchase)

Box-and-whisker plot

2 marks: (a) 1, (b) 1 · statistics & probability (box-and-whisker)

Algebraic fractions (common denominator)

3 marks · number & algebra (algebraic fractions)

Map scale

4 marks: (a) 1, (b) 1, (c) 2 · number & algebra (scale, map)

Common-factor extraction

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

Arithmetic sequence (common difference)

2 marks · number & algebra (sequences, arithmetic)

Area of a sector (angle in degrees)

2 marks · geometry & measurement (mensuration, sectors)

Right-angled trig (sine

5 marks: (a) 2, (b) 2, (c) 1 · geometry & measurement (trigonometry, bearings)

Cumulative frequency curve

4 marks: (a) 2, (b) 2 · statistics & probability (cumulative frequency)

Substitution into a formula

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

Angle in a semicircle

3 marks: (a) 2, (b) 1 · geometry & measurement (circle properties)

Simultaneous linear equations (elimination)

3 marks · number & algebra (simultaneous equations)

Co-interior angles (parallel lines)

3 marks · geometry & measurement (angles, polygons)

Compound interest (find the principal)

3 marks · number & algebra (compound interest)

Venn-diagram regions

2 marks: (a) 1, (b) 1 · number & algebra (set notation, venn diagrams)

Writing in standard form

3 marks: (a) 1, (b)(i) 1, (b)(ii) 1 · number & algebra (standard form)

Prime factorisation

2 marks · number & algebra (hcf, lcm, prime factorisation)

Trigonometric equation (sine, two solutions)

2 marks · geometry & measurement (trigonometric equations)

Mean of a data set with an unknown

5 marks: (a) 3, (b) 2 · statistics & probability (mean, standard deviation)

Expansion (binomial × trinomial)

2 marks · number & algebra (expansion)

Pythagoras' theorem

6 marks: (a) 4, (b) 2 · number & algebra / geometry (pythagoras with algebra)

Factorising (common factor

3 marks · number & algebra (algebraic fractions, factorisation)

Solving a quadratic by completing the square

3 marks · number & algebra (completing the square)

Volume of a cylinder & cone

6 marks: (a) 2, (b) 4 · geometry & measurement (mensuration, cone & cylinder)

Position vectors

7 marks: (a) 2, (b) 4, (c) 1 · geometry & measurement (vectors)

Laws of indices

10 marks: 3 + 3 + 2 + 2 ... · number & algebra (manipulation)

Matrices (order

9 marks: (a) 1 + 2 + 2, (b) 2, (c) 2 · number & algebra (matrices, percentage, ratio)

Coordinate geometry (gradient

9 marks: 3 + 3 + 3 · number & algebra (coordinate geometry)

Cubic/power-function graph

11 marks: (a) 1 + 3 + 1 + 3, (b) 3 · number & algebra (graphs of functions)

Bearings

9 marks: 3 + 3 + 3 · geometry & measurement (bearings, trigonometry)

Forming & solving quadratic equations

11 marks: 5 + 3 + 1 + 2 · number & algebra (quadratic from speed-distance-time)

Grouped-data median & mean

9 marks: (a) 1 + 1 + 1 + 1, (b) 1 + 1 + 3 · statistics & probability

Congruence (RHS) with circle reasons

10 marks: (a) 3 + 2, (b) 5 · geometry & measurement (circle, arc, segments)

Volume of a cylinder

11 marks: 2 + 2 + 7 · number & algebra / mensuration (modelling, similar solids)