Cambridge GCSE Further Maths revision

Topic 1: Functions

We will go through it step by step.

1. 1.1Functions: domain and range, composite and inverse functions, and piecewise functions36 questions

Topic 2: Quadratic functions

We will go through it step by step.

1. 2.1Quadratics: completing the square, the discriminant and quadratic inequalities11 questions

Topic 3: Factors of polynomials

We will go through it step by step.

1. 3.1Polynomials: the factor theorem, the remainder theorem and solving cubics32 questions

Topic 4: Equations, inequalities and graphs

There are 2 parts: we start with algebraic manipulation, and finish with surds and indices.

1. 4.1Algebraic manipulation: expanding, factorising and algebraic fractions26 questions
2. 4.2Surds and indices: fractional and negative indices, simplifying and rationalisingFree 28 questions

Topic 5: Simultaneous equations

We will go through it step by step.

1. 5.1Simultaneous equations: linear with quadratic, and three linear equations27 questions

Topic 6: Logarithmic and exponential functions

We will go through it step by step.

1. 6.1Logarithms and exponentials: laws of logs, solving equations and eFree 35 questions

Topic 7: Straight line graphs

We will go through it step by step.

1. 7.1Straight lines: gradient, midpoint, distance, and parallel and perpendicular linesFree 33 questions

Topic 8: Coordinate geometry of the circle

We will go through it step by step.

1. 8.1Circles: the equation of a circle, completing the square and tangents51 questions

Topic 9: Circular measure

We will go through it step by step.

1. 9.1Circular measure: radians, arc length and sector area51 questions

Topic 10: Trigonometry

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

1. 10.1Trigonometric graphs, identities and equations35 questions
2. 10.2The sine and cosine rules, area of a triangle and 3D trigonometryFree 52 questions

Topic 11: Permutations and combinations

We will go through it step by step.

1. 11.1Permutations and combinations: arrangements and selections52 questions

Topic 12: Series

There are 2 parts: we start with the binomial expansion, and finish with arithmetic and geometric progressions and their sums.

1. 12.1The binomial expansion: Pascal's triangle and nCr48 questions
2. 12.2Arithmetic and geometric progressions and their sums53 questions

Topic 13: Vectors in two dimensions

We will go through it step by step.

1. 13.1Vectors in two dimensions: position vectors, magnitude and velocity21 questions

Topic 14: Differentiation and integration

There are 5 parts: we start with differentiation, and finish with kinematics with calculus.

1. 14.1Differentiation: the gradient function of powers of xFree 22 questions
2. 14.2Tangents and normals to curves52 questions
3. 14.3Stationary points: maxima, minima and curve sketching55 questions
4. 14.4Integration: indefinite and definite integrals and the area under a curve47 questions
5. 14.5Kinematics with calculus: displacement, velocity and acceleration47 questions

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