MathsLinks

Australian Curriculum / Mathematical Methods

Unit 1 Topic 1 Functions and graphs, Functions, Graphs of relations, Inverse proportion, Lines and linear relationships, Powers and polynomials, Review of quadratic relationships, Unit 1 Topic 2 Trigonometric functions, Cosine and sine rules, Trigonometric functions, Unit 1 Topic 3 Counting and probability, Unit 2 Topic 1 Exponential functions, Exponential functions, Unit 2 Topic 2 Arithmetic and geometric sequences and series, Arithmetic sequences, Geometric sequences, Unit 2 Topic 3 Introduction to differential calculus, Applications of derivatives, Unit 3 Topic 1 Further differentiation and applications, Differentiation rules, Exponential functions, The second derivative and applications of differentiation, Trigonometric functions, Unit 3 Topic 2 Integrals, Anti-differentiation, Applications of integration, Definite integrals, Unit 3 Topic 3 Discrete random variables, General discrete random variables, Unit 4 Topic 2 Continuous random variables and the normal distribution, General continuous random variables, Normal distributions, Unit 4 Topic 3 Interval estimates for proportions, Sample proportions

Australian Curriculum / Specialist Mathematics

Unit 1 Topic 1 Combinatorics, Permutations (ordered arrangements):, The inclusion-exclusion principle for the union of two sets and three sets:, The pigeon-hole principle:, Combinations (unordered selections):, Unit 1 Topic 2 Vectors in the plane, Representing vectors in the plane by directed line segments:, Algebra of vectors in the plane:, Unit 1 Topic 3 Geometry, The nature of proof:, Circle properties and their proofs including the following theorems:, Geometric proofs using vectors in the plane including:, Unit 2 Topic 1 Trigonometry, The basic trigonometric functions:, Compound angles:, The reciprocal trigonometric functions, secant, cosecant and cotangent:, Trigonometric identities:, Applications of trigonometric functions to model periodic phenomena:, Unit 2 Topic 2 Matrices, Matrix arithmetic:, Transformations in the plane:, Unit 2 Topic 3 Real and complex numbers, Proofs involving numbers:, Rational and irrational numbers:, An introduction to proof by mathematical induction:, Complex numbers:, The complex plane:, Roots of equations: