OCR B A-level Further Maths Year 13 revision

Topic 1: Complex numbers

It builds on what you learned at AS in Complex numbers, and takes it further.

There are 4 parts: we start with exponential form of complex numbers, and finish with summing series with complex numbers.

1. 1.1Exponential form of complex numbers: e to the i thetaFree 17 questions
2. 1.2De Moivre's theorem and multiple-angle identities18 questions
3. 1.3Roots of unity and nth roots of complex numbers18 questions
4. 1.4Summing series with complex numbers: the C + iS method34 questions

Topic 2: Further calculus and series

It builds on what you learned at AS in Sequences, series and induction, and takes it further.

There are 5 parts: we start with improper integrals, and finish with limits and reduction formulae.

1. 2.1Improper integralsFree 53 questions
2. 2.2The mean value of a function51 questions
3. 2.3Integrals giving inverse trigonometric and hyperbolic functions, and partial fractions15 questions
4. 2.4Maclaurin series and series expansions51 questions
5. 2.5Limits and reduction formulae53 questions

Topic 3: Polar coordinates and hyperbolic functions

There are 3 parts: we start with areas enclosed by polar curves, and finish with calculus of hyperbolic functions.

1. 3.1Areas enclosed by polar curves10 questions
2. 3.2Hyperbolic functions: identities, equations and inversesFree 15 questions
3. 3.3Calculus of hyperbolic functions14 questions

Topic 4: Differential equations

Differential equations model anything that changes over time.

We will solve first-order equations with an integrating factor and second-order equations with constant coefficients.

Then we model simple harmonic motion, damping and coupled systems such as predators and prey.

1. 4.1First-order differential equations: the integrating factorFree 14 questions
2. 4.2Second-order differential equations with constant coefficients12 questions
3. 4.3Simple harmonic motion and damped oscillations13 questions
4. 4.4Coupled first-order systems: predator–prey and other models13 questions
5. 4.5Modelling with differential equations12 questions

Topic 5: Vectors, matrices and proof

This topic brings together the most powerful tools in pure Further Maths.

We will find intersections, angles and distances between lines and planes, and use the vector product.

Then we find eigenvalues and eigenvectors, diagonalise matrices and extend proof by induction.

1. 5.1Lines and planes: intersections, angles and distancesFree 14 questions
2. 5.2The vector product13 questions
3. 5.3Eigenvalues, eigenvectors and diagonalisation13 questions
4. 5.4Further proof by induction: matrices, divisibility and inequalities13 questions

Topic 6: Option: Mechanics major

It builds on what you learned at AS in Option: Mechanics a, and takes it further.

There are 5 parts: we start with circular motion, and finish with simple harmonic motion in mechanics.

1. 6.1Circular motion: horizontal and vertical circlesFree 51 questions
2. 6.2Centres of mass: particles, laminas and solids by integration41 questions
3. 6.3Variable forces and further kinematics51 questions
4. 6.4Oblique collisions and impulse vectors53 questions
5. 6.5Simple harmonic motion in mechanics: springs and pendulums54 questions

Topic 7: Option: Statistics major

It builds on what you learned at AS in Option: Statistics a, and takes it further.

There are 5 parts: we start with continuous random variables, and finish with correlation and regression.

1. 7.1Continuous random variables: pdf, cdf, expectation and varianceFree 50 questions
2. 7.2The t-distribution: hypothesis tests and confidence intervals for a mean52 questions
3. 7.3Probability generating functions50 questions
4. 7.4Non-parametric tests: sign test and Wilcoxon tests56 questions
5. 7.5Correlation and regression: testing the PMCC and Spearman's rank53 questions

Topic 8: Option: Modelling with algorithms

It builds on what you learned at AS in Option: Modelling with algorithms, and takes it further.

There are 5 parts: we start with network flows, and finish with game theory.

1. 8.1Network flows: maximum flow and minimum cutFree 15 questions
2. 8.2Linear programming: the simplex algorithm14 questions
3. 8.3The travelling salesperson problem: upper and lower bounds14 questions
4. 8.4Allocation and transportation problems15 questions
5. 8.5Game theory: zero-sum games, stable solutions and mixed strategies14 questions

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