OCR B A-level Further Maths Year 12 revision

Topic 1: Matrices and transformations

There are 5 parts: we start with matrix arithmetic, and finish with systems of linear equations and the geometry of three planes.

1. 1.1Matrix arithmetic: addition, multiplication and special matricesFree 14 questions
2. 1.2Determinants and inverse matrices (2 × 2 and 3 × 3)15 questions
3. 1.3Matrix transformations in two and three dimensions13 questions
4. 1.4Invariant points and invariant lines13 questions
5. 1.5Systems of linear equations and the geometry of three planes13 questions

Topic 2: Complex numbers

There are 3 parts: we start with complex numbers, and finish with loci and regions in the Argand diagram.

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

Topic 3: Vectors and planes

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. 3.1Vector equations of lines in three dimensionsFree 10 questions
2. 3.2The scalar product: angles between vectors and lines, and perpendicularity12 questions
3. 3.3Equations of planes and the intersection of a line and a plane13 questions

Topic 4: Roots of polynomials

There are 3 parts: we start with roots of polynomials, and finish with roots of polynomials with real coefficients.

1. 4.1Roots of polynomials: relationships between roots and coefficientsFree 10 questions
2. 4.2Transforming equations: new roots by substitution21 questions
3. 4.3Roots of polynomials with real coefficients: conjugate pairs11 questions

Topic 5: Sequences, series and induction

There are 3 parts: we start with series, and finish with proof by induction.

1. 5.1Series: sigma notation and the standard results for Σr, Σr² and Σr³50 questions
2. 5.2The method of differences and partial fractions27 questions
3. 5.3Proof by induction: series, divisibility and matrices27 questions

Topic 6: Option: Mechanics a

There are 5 parts: we start with dimensional analysis, and finish with collisions.

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

Topic 7: Option: Statistics a

There are 4 parts: we start with discrete random variables, and finish with chi-squared tests.

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. 7.3The geometric and negative binomial distributions52 questions
4. 7.4Chi-squared tests: goodness of fit and contingency tables53 questions

Topic 8: Option: Modelling with algorithms

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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