Revision notes.

Try this with Specialist Mathematics

1. Close your notes and write the main idea in two sentences from memory.
2. Reopen the source and correct the first mistake or omission you find.
3. Add one example and one question to test whether you can apply the idea.

View Specialist Mathematics resources on ATARMAXXING ↗

Topics in the resource inventory

• Implications, equivalence and proof structures (direct, cases, contradiction, contrapositive)
• Proof by mathematical induction (sums, divisibility, inequalities)
• Rational functions: partial fractions and asymptotic behaviour
• Stationary points, inflection and the second-derivative test for curve sketching
• Complex numbers: Cartesian and polar form, the Argand plane and complex regions
• De Moivre's theorem and the nth roots of complex numbers
• Factorisation over C: the conjugate root theorem and solving polynomial equations
• Vector algebra, the dot product, resolutes and the angle between vectors
• The cross product, normals to planes and vector proofs of geometric results
• Vector, parametric and Cartesian equations of lines and planes
• Inverse circular derivatives, second derivatives and implicit/related rates
• Anti-differentiation: recognising inverse-circular and log forms, and the four core techniques
• Areas, arc length of parametric curves, and solids of revolution
• Solving dy/dx = f(x), dy/dx = g(y), separation of variables and second-order by antidifferentiation
• Logistic growth, direction (slope) fields and Euler's method
• Rectilinear motion: velocity-time graphs, calculus links and the acceleration forms
• Vector functions of time: paths, meeting/colliding particles and velocity/acceleration vectors
• Expectation and variance of sums and linear combinations of random variables
• The sample mean as a random variable and the central limit behaviour
• Confidence intervals for a mean and one- and two-tailed hypothesis tests