OCR A A-level Further Maths Year 12 revision

Topic 1: Proof

We will go through it step by step.

1. 1.1Proof by induction: series, divisibility and matrices27 questions

Topic 2: Complex numbers

Complex numbers let us solve every quadratic, even those with no real roots.

We will add, multiply and divide complex numbers and draw them on an Argand diagram.

Then we use modulus and argument, describe loci, and find the roots of polynomials.

1. 2.1Complex numbers: arithmetic and solving quadratics with complex rootsFree 19 questions
2. 2.2The Argand diagram: modulus, argument and modulus–argument form18 questions
3. 2.3Loci and regions in the Argand diagram17 questions
4. 2.4Roots of polynomials with real coefficients: conjugate pairs11 questions

Topic 3: 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. 3.1Matrix arithmetic: addition, multiplication and special matricesFree 14 questions
2. 3.2Determinants and inverse matrices (2 × 2 and 3 × 3)15 questions
3. 3.3Matrix transformations in two and three dimensions13 questions
4. 3.4Invariant points and invariant lines13 questions
5. 3.5Systems of linear equations and the geometry of three planes13 questions

Topic 4: Further vectors

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. 4.1Vector equations of lines in three dimensionsFree 10 questions
2. 4.2The scalar product: angles between vectors and lines, and perpendicularity12 questions
3. 4.3Equations of planes and the intersection of a line and a plane13 questions

Topic 5: Roots of polynomials and series

It builds on what you learned at GCSE level in Algebra, and takes it further.

There are 4 parts: we start with roots of polynomials, and finish with the method of differences and partial fractions.

1. 5.1Roots of polynomials: relationships between roots and coefficientsFree 10 questions
2. 5.2Transforming equations: new roots by substitution21 questions
3. 5.3Series: sigma notation and the standard results for Σr, Σr² and Σr³50 questions
4. 5.4The method of differences and partial fractions27 questions

Topic 6: Option: Mechanics

There are 5 parts: we start with momentum and impulse, including in vector form, and finish with dimensional analysis.

1. 6.1Momentum and impulse, including in vector formFree 51 questions
2. 6.2Work, energy and power with variable resistance53 questions
3. 6.3Elastic strings and springs: Hooke's law and elastic potential energy53 questions
4. 6.4Collisions: the coefficient of restitution and Newton's experimental law52 questions
5. 6.5Dimensional analysis51 questions

Topic 7: Option: Statistics

It builds on what you learned at GCSE level in Enumeration and probability, and takes it further.

There are 5 parts: we start with discrete random variables, and finish with Type I and Type II errors in hypothesis testing.

1. 7.1Discrete random variables: expectation, variance and functions of XFree 49 questions
2. 7.2The Poisson distribution in Further Statistics: sums and approximations51 questions
3. 7.3Chi-squared tests: goodness of fit and contingency tables53 questions
4. 7.4The geometric and negative binomial distributions52 questions
5. 7.5Type I and Type II errors in hypothesis testing53 questions

Topic 8: Option: Discrete

There are 5 parts: we start with algorithms, and finish with critical path analysis.

1. 8.1Algorithms: sorting, bin packing and order of an algorithmFree 15 questions
2. 8.2Graphs and networks: minimum spanning trees with Kruskal's and Prim's algorithms15 questions
3. 8.3Shortest paths with Dijkstra's algorithm and route inspection11 questions
4. 8.4Linear programming: formulating problems and the graphical method15 questions
5. 8.5Critical path analysis: activity networks, floats and Gantt charts18 questions

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