difficulty mix of each set, easier to harder
1Calculus
- Continuity, first principles and limits (l'Hôpital's rule)10
- Differential equations and Euler's method10
- Further integration (substitution, by parts) and volumes of revolution10
- Implicit differentiation, related rates and further derivatives10
- Integration, definite integrals and areas10
- Kinematics: displacement, velocity, acceleration, distance10
- Limits, derivatives, differentiation rules, tangents and normals10
- Maclaurin series10
- Second derivative, stationary points, inflexion and optimisation10
2Functions
- Further rational functions, odd/even and self-inverse functions, inequalities and modulus10
- Graphs, key features, solving graphically and transformations10
- Polynomial functions, factor and remainder theorems, sum and product of roots10
- Quadratic functions, equations and inequalities; discriminant10
- Reciprocal, rational, exponential and logarithmic functions10
- Straight lines, functions, composite and inverse functions10
3Geometry and trigonometry
- 3D geometry: distance, solids, angles with lines and planes10
- Circular function graphs and trigonometric equations10
- Radians, arcs and sectors, unit circle and trig identities10
- Reciprocal and inverse trig functions, compound angle identities10
- Right and non-right angled trigonometry, sine and cosine rules, bearings10
- Vector product, planes and their intersections10
- Vectors, scalar product and vector equations of lines10
4Number and algebra
- Binomial theorem and counting principles10
- Complex numbers in Cartesian form10
- Exponents and logarithms10
- Partial fractions and systems of linear equations10
- Polar and Euler form, De Moivre's theorem and complex roots10
- Proof (deductive, induction, contradiction)10
- Sequences, series and financial applications10
5Statistics and probability
- Bayes' theorem and continuous random variables10
- Correlation and regression lines10
- Discrete random variables and the binomial distribution10
- Probability, Venn and tree diagrams, conditional probability and independence10
- Sampling, data presentation and summary statistics10
- The normal distribution and standardisation10
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