Cambridge A-level Further Maths Year 12 revision

Topic 1: Roots of polynomial equations

It builds on what you learned at IGCSE in Factors of polynomials, and takes it further.

There are 2 parts: we start with roots of polynomials, and finish with transforming equations.

1. 1.1Roots of polynomials: relationships between roots and coefficientsFree 10 questions
2. 1.2Transforming equations: new roots by substitution21 questions

Topic 2: Rational functions and graphs

It builds on what you learned at IGCSE in Equations, inequalities and graphs, and takes it further.

There are 2 parts: we start with rational functions, and finish with inequalities involving rational functions and the modulus.

1. 2.1Rational functions: asymptotes and curve sketchingFree 42 questions
2. 2.2Inequalities involving rational functions and the modulus38 questions

Topic 3: Summation of series

It builds on what you learned at IGCSE in Series, and takes it further.

There are 2 parts: we start with series, and finish with the method of differences and partial fractions.

1. 3.1Series: sigma notation and the standard results for Σr, Σr² and Σr³50 questions
2. 3.2The method of differences and partial fractions27 questions

Topic 4: Matrices

Matrices describe transformations and solve systems of equations.

We will multiply matrices, find determinants and inverses, and see what they do to shapes in two and three dimensions.

Then we find invariant points and lines and interpret three planes.

1. 4.1Matrix arithmetic: addition, multiplication and special matricesFree 14 questions
2. 4.2Determinants and inverse matrices (2 × 2 and 3 × 3)15 questions
3. 4.3Matrix transformations in two and three dimensions13 questions
4. 4.4Invariant points and invariant lines13 questions
5. 4.5Systems of linear equations and the geometry of three planes13 questions

Topic 5: Polar coordinates

We will go through it step by step.

1. 5.1Polar coordinates: converting and sketching polar curves11 questions

Topic 6: Vectors

It builds on what you learned at IGCSE in Vectors in two dimensions, and takes it further.

There are 3 parts: we start with vector equations of lines in three dimensions, and finish with equations of planes and the intersection of a line and a plane.

1. 6.1Vector equations of lines in three dimensionsFree 10 questions
2. 6.2The scalar product: angles between vectors and lines, and perpendicularity12 questions
3. 6.3Equations of planes and the intersection of a line and a plane13 questions

Topic 7: Proof by induction

We will go through it step by step.

1. 7.1Proof by induction: series, divisibility and matrices27 questions

Topic 8: Further Mechanics: momentum, collisions and elasticity

There are 4 parts: we start with momentum and impulse, including in vector form, and finish with collisions.

1. 8.1Momentum and impulse, including in vector formFree 51 questions
2. 8.2Work, energy and power with variable resistance53 questions
3. 8.3Elastic strings and springs: Hooke's law and elastic potential energy53 questions
4. 8.4Collisions: the coefficient of restitution and Newton's experimental law52 questions

Topic 9: Further Probability and Statistics: distributions and chi-squared tests

There are 2 parts: we start with discrete random variables, and finish with chi-squared tests.

1. 9.1Discrete random variables: expectation, variance and functions of XFree 49 questions
2. 9.2Chi-squared tests: goodness of fit and contingency tables53 questions

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