Cambridge A-level Further Maths Year 13 revision

Topic 1: Hyperbolic functions

There are 2 parts: we start with hyperbolic functions, and finish with calculus of hyperbolic functions.

1. 1.1Hyperbolic functions: identities, equations and inversesFree 15 questions
2. 1.2Calculus of hyperbolic functions14 questions

Topic 2: Matrices

It builds on what you learned at Year 12 in Matrices, and takes it further.

We will go through it step by step.

1. 2.1Eigenvalues, eigenvectors and diagonalisation13 questions

Topic 3: Differentiation and integration

It builds on what you learned at Year 12 in Polar coordinates, and takes it further.

There are 6 parts: we start with maclaurin series and series expansions, and finish with areas enclosed by polar curves.

1. 3.1Maclaurin series and series expansions51 questions
2. 3.2Integrals giving inverse trigonometric and hyperbolic functions, and partial fractions15 questions
3. 3.3Improper integralsFree 53 questions
4. 3.4The mean value of a function51 questions
5. 3.5Limits and reduction formulae53 questions
6. 3.6Areas enclosed by polar curves10 questions

Topic 4: Complex numbers

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

1. 4.1Exponential form of complex numbers: e to the i thetaFree 17 questions
2. 4.2De Moivre's theorem and multiple-angle identities18 questions
3. 4.3Roots of unity and nth roots of complex numbers18 questions
4. 4.4Summing series with complex numbers: the C + iS method34 questions

Topic 5: Differential equations

There are 3 parts: we start with first-order differential equations, and finish with simple harmonic motion and damped oscillations.

1. 5.1First-order differential equations: the integrating factorFree 14 questions
2. 5.2Second-order differential equations with constant coefficients12 questions
3. 5.3Simple harmonic motion and damped oscillations13 questions

Topic 6: Further Mechanics

It builds on what you learned at Year 12 in Further Mechanics: momentum, collisions and elasticity, and takes it further.

There are 4 parts: we start with circular motion, and finish with oblique collisions and impulse vectors.

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

Topic 7: Further Probability and Statistics

It builds on what you learned at Year 12 in Further Probability and Statistics: distributions and chi-squared tests, and takes it further.

There are 4 parts: we start with continuous random variables, and finish with probability generating functions.

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. 7.3Non-parametric tests: sign test and Wilcoxon tests56 questions
4. 7.4Probability generating functions50 questions

Other exam boards