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Mathematics
Prelimis/HSC
Yearly Topic Summary based on the NSW Syllabus:
Biology:
Preliminary Mathematics (Advanced)
Algebra and Functions:
Quadratic functions, simultaneous equations, polynomials, and logarithmic and exponential functions.
Coordinate Geometry:
Properties of geometric figures, transformations, and the Cartesian plane.
Trigonometry:
Trigonometric ratios, circular functions, and applications of trigonometry.
Calculus:
Differentiation, integration, and rates of change.
Probability and Data Analysis: Probability theory, data representation, and statistical analysis.
Preliminary Mathematics (Extension 1)
Algebra and Calculus:
Advanced algebraic techniques, polynomial functions, logarithmic and exponential functions, and calculus concepts.
Coordinate Geometry:
Properties of geometric figures, transformations, and the Cartesian plane.
Trigonometry:
Advanced trigonometric ratios, circular functions, and applications of trigonometry.
Calculus:
Further differentiation and integration techniques, applications of calculus, and rates of change.
HSC Mathematics (Advanced)
Algebra and Calculus:
Advanced algebraic techniques, polynomial functions, logarithmic and exponential functions, and calculus concepts.
Measurement and Geometry:
Geometric reasoning, coordinate geometry, and measurement applications.
Statistics and Probability:
Data analysis, probability distributions, hypothesis testing, and sampling techniques.
Financial Mathematics:
Compound interest, annuities, loan repayments, and investment evaluation.
HSC Mathematics (Extension 1):
Calculus:
Integration and its applications, complex numbers, and differential equations.
Algebra:
Advanced algebraic techniques, linear and abstract algebra, and number theory.
Geometry:
Properties of geometric figures, conic sections, and coordinate geometry.
Probability:
Advanced probability theory and stochastic processes.
HSC Mathematics (Extension 2)
Functions and Relations:
Advanced concepts of functions and relations, including polynomial,
exponential, logarithmic, and trigonometric functions.
Polynomials:
Advanced properties of polynomials, including factor theorem, remainder theorem, and polynomial division.
Geometry:
Properties of geometric figures, conic sections, and coordinate geometry.
Calculus:
Further advanced techniques of calculus, including differential equations, parametric equations, and integration.
Complex Numbers:
Advanced concepts of complex numbers, including complex algebra, roots of equations, and geometric representation.