HSC Maths Advanced study guide
HSC Maths Advanced · Work through your exam, one topic at a time.
Mathematics Advanced is a Board Developed Stage 6 course in New South Wales, offered as 11255 (2 units – Year 11) and 15255 (2 units – Year 12), and taught under the Mathematics Advanced Stage 6 Syllabus (2017). It is a calculus-based course built around developing mathematics as a way of viewing and modelling the world - investigating order, relation, pattern, uncertainty and generality - and it suits students who need a strong mathematical foundation for tertiary study in disciplines where mathematical thinking matters. The HSC Maths Advanced study guide has 5 sections and about 1,731 words.
01Functions: Algebra, Graphs and Transformations
A function pairs each input with exactly one output; the domain is the set of permitted inputs and the range the set of outputs. For HSC Advanced you must move fluently between algebraic and graphical forms: linear and quadratic functions, polynomials, absolute value, hyperbolas, circles and semicircles, exponentials and logarithms, and inverse functions.
359 words, about 2 min02Trigonometric Functions: Radians, Identities and Graphs
Advanced trigonometry works in radians : arc length l = rθ, sector area A = ½r²θ, and angular measure linked to the unit circle. You must know exact values in both degree and radian form, the ASTC sign pattern by quadrant, and the symmetry identities such as sin(π − θ) = sin θ and cos(π − θ) = −cos θ.
387 words, about 2 min03Calculus: Differentiation, Integration and Applications
Differentiation from first principles defines the derivative as a limit of a difference quotient; in practice you apply the power, product, quotient and chain rules, and differentiate exponentials, logarithms and trigonometric functions. The derivative gives gradient, so it drives tangents and normals, stationary points, increasing/decreasing intervals and rates of change.
312 words, about 2 min04Financial Mathematics: Sequences, Series and Loans
Financial mathematics in Advanced builds on arithmetic and geometric sequences. Simple interest grows linearly; compound interest grows geometrically with factor (1 + r) per period, where r is the rate per period as a decimal.
326 words, about 2 min05Statistical Analysis: Data, Distributions and Inference
Statistical analysis in Advanced covers describing and comparing data, the normal distribution, and drawing inferences. You must compute and interpret measures of centre (mean, median, mode) and spread (range, interquartile range, standard deviation), read and construct box plots, histograms and stem-and-leaf plots, and identify outliers using the 1.5 × IQR rule.
347 words, about 2 min