OCR A GCSE Further Maths revision

Topic 1: Algebra

There are 6 parts: we start with surds and indices, and finish with functions.

1. 1.1Surds and indices: fractional and negative indices, simplifying and rationalisingFree 28 questions
2. 1.2Algebraic manipulation: expanding, factorising and algebraic fractions26 questions
3. 1.3Polynomials: the factor theorem, the remainder theorem and solving cubics32 questions
4. 1.4Quadratics: completing the square, the discriminant and quadratic inequalities11 questions
5. 1.5Simultaneous equations: linear with quadratic, and three linear equations27 questions
6. 1.6Functions: domain and range, composite and inverse functions, and piecewise functions36 questions

Topic 2: Enumeration and probability

There are 2 parts: we start with permutations and combinations, and finish with the binomial expansion.

1. 2.1Permutations and combinations: arrangements and selections52 questions
2. 2.2The binomial expansion: Pascal's triangle and nCr48 questions

Topic 3: Coordinate geometry

Coordinate geometry turns shapes into equations.

We will find gradients, midpoints and distances, write equations of straight lines, and spot parallel and perpendicular lines.

Then we meet the equation of a circle and its tangents.

1. 3.1Straight lines: gradient, midpoint, distance, and parallel and perpendicular linesFree 33 questions
2. 3.2Circles: the equation of a circle, completing the square and tangents51 questions

Topic 4: Trigonometry

There are 2 parts: we start with the sine and cosine rules, area of a triangle and 3D trigonometry, and finish with trigonometric graphs, identities and equations.

1. 4.1The sine and cosine rules, area of a triangle and 3D trigonometryFree 52 questions
2. 4.2Trigonometric graphs, identities and equations35 questions

Topic 5: Calculus

Calculus is the mathematics of change.

We will differentiate powers of x to find gradients, tangents, normals and stationary points.

Then we integrate to find areas, and use both in kinematics.

1. 5.1Differentiation: the gradient function of powers of xFree 22 questions
2. 5.2Tangents and normals to curves52 questions
3. 5.3Stationary points: maxima, minima and curve sketching55 questions
4. 5.4Integration: indefinite and definite integrals and the area under a curve47 questions
5. 5.5Kinematics with calculus: displacement, velocity and acceleration47 questions

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