GCSE Further Maths Tutor

Overview of the Qualification

This qualification is designed for high-attaining students (those targeting grades 7, 8, and 9 in GCSE Maths) who want to stretch themselves and prepare for A-Level Maths.

Grading: Grades 5–9 (grade 4 allowed). Both papers must be taken in the same series.

Six Key Subject Areas

This specification covers advanced topics including calculus and matrix transformations.

1. Number

Surds (including rationalising the denominator), product rule for counting.

2. Algebra

Functions (domain, range, composite, inverse), factor theorem, completing the square, algebraic fractions, simultaneous equations in three unknowns, algebraic proof, quadratic sequences.

3. Coordinate Geometry (2D)

Equation of a circle (x² + y² = r² and (x – a)² + (y – b)² = r²), tangents to circles, perpendicular gradients.

4. Calculus

Differentiation: dy/dx as gradient and rate of change, tangents and normals, stationary points (maxima/minima), increasing/decreasing functions. Second derivative: d²y/dx² to determine nature of stationary points.

5. Matrix Transformations

2×2 matrices, multiplication, identity matrix, transformations of the unit square (rotations, reflections, enlargements).

6. Geometry

Circle theorems (angle at the centre, angles in same segment, cyclic quadrilaterals, alternate segment theorem), sine and cosine rules, 3D Pythagoras and trigonometry, trigonometric graphs and identities (sin²θ + cos²θ = 1).

Assessment Objectives

The exam papers assess two main skills:

• AO1 (56–64%): Recall and use knowledge of the prescribed content for routine and multi-step procedures.
• AO2 (36–44%): Apply mathematical reasoning, skills and knowledge to solve mathematical problems including rigorous justification and formal proof.