AQA A-level Further Maths Year 13 revision

Topic 1: Proof by induction

We will go through it step by step.

1. 1.1Further proof by induction: matrices, divisibility and inequalities13 questions

Topic 2: 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. 2.1Exponential form of complex numbers: e to the i thetaFree 17 questions
2. 2.2De Moivre's theorem and multiple-angle identities18 questions
3. 2.3Roots of unity and nth roots of complex numbers18 questions
4. 2.4Summing series with complex numbers: the C + iS method34 questions

Topic 3: Matrices

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

We will go through it step by step.

1. 3.1Eigenvalues, eigenvectors and diagonalisation13 questions

Topic 4: Further algebra and calculus

It builds on what you learned at AS in Further calculus, and takes it further.

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

1. 4.1Improper integralsFree 53 questions
2. 4.2The mean value of a function51 questions
3. 4.3Integrals giving inverse trigonometric and hyperbolic functions, and partial fractions15 questions
4. 4.4Maclaurin series and series expansions51 questions
5. 4.5Limits and reduction formulae53 questions

Topic 5: Further vectors

It builds on what you learned at AS in Further vectors, and takes it further.

There are 2 parts: we start with lines and planes, and finish with the vector product.

1. 5.1Lines and planes: intersections, angles and distancesFree 14 questions
2. 5.2The vector product13 questions

Topic 6: Polar coordinates and hyperbolic functions

It builds on what you learned at AS in Polar coordinates and Hyperbolic functions, and takes it further.

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

1. 6.1Areas enclosed by polar curves10 questions
2. 6.2Hyperbolic functions: identities, equations and inversesFree 15 questions
3. 6.3Calculus of hyperbolic functions14 questions

Topic 7: 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. 7.1First-order differential equations: the integrating factorFree 14 questions
2. 7.2Second-order differential equations with constant coefficients12 questions
3. 7.3Simple harmonic motion and damped oscillations13 questions
4. 7.4Coupled first-order systems: predator–prey and other models13 questions
5. 7.5Modelling with differential equations12 questions

Topic 8: Option: Mechanics

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

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

1. 8.1Circular motion: horizontal and vertical circlesFree 51 questions
2. 8.2Centres of mass: particles, laminas and solids by integration41 questions
3. 8.3Variable forces and further kinematics51 questions
4. 8.4Oblique collisions and impulse vectors53 questions
5. 8.5Simple harmonic motion in mechanics: springs and pendulums54 questions

Topic 9: Option: Statistics

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

There are 3 parts: we start with continuous random variables, and finish with correlation and regression.

1. 9.1Continuous random variables: pdf, cdf, expectation and varianceFree 50 questions
2. 9.2The t-distribution: hypothesis tests and confidence intervals for a mean52 questions
3. 9.3Correlation and regression: testing the PMCC and Spearman's rank53 questions

Topic 10: Option: Discrete

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

There are 5 parts: we start with network flows, and finish with allocation and transportation problems.

1. 10.1Network flows: maximum flow and minimum cutFree 15 questions
2. 10.2Linear programming: the simplex algorithm14 questions
3. 10.3Game theory: zero-sum games, stable solutions and mixed strategies14 questions
4. 10.4The travelling salesperson problem: upper and lower bounds14 questions
5. 10.5Allocation and transportation problems15 questions

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