Mathematics Advanced
Year 12 · Stage 6 · NSW Mathematics syllabus
Further graph transformations and modelling
Apply transformations (reflections, translations, dilations) to trigonometric, exponential and logarithmic functions; model real periodic and logarithmic phenomena with transformed functions.
3 sub-topics
Sequences and series
Find the th term and partial sums of arithmetic and geometric sequences; apply the limiting sum of an infinite geometric series; model growth, decay and financial situations using recurrence relations and series.
3 sub-topics
Differential calculus
Extend differentiation to exponential, logarithmic and trigonometric functions; apply the product, quotient and chain rules; find second derivatives.
3 sub-topics
Integral calculus
Develop anti-differentiation and integration skills; evaluate definite integrals using the fundamental theorem of calculus; calculate exact areas and use the trapezoidal rule.
3 sub-topics
Applications of calculus
Use differentiation and integration to sketch curves, solve optimisation problems, and analyse rates of change and motion.
3 sub-topics
Random variables
Introduce continuous random variables and probability density functions; calculate probabilities as areas under a pdf; find mean, median and mode of continuous distributions; apply the normal distribution including z-scores and the empirical rule.
2 sub-topics
Financial mathematics
Apply geometric series to calculate future and present values of annuities; analyse reducing-balance loans using recurrence relations; compare investment and loan scenarios.
2 sub-topics