Year 12: Mathematics Advanced Stage 6 Syllabus (2017)
Listed Mathematics syllabus outcomes at Year 12, in the words of the NSW Education Standards Authority (NESA), with the practice on this site that covers it. Checked against the source on 4 September 2026.
Current for the 2026 HSC. The Mathematics Advanced 11–12 Syllabus (2024) reaches Year 12 in Term 4, 2026, so this page will need to move to outcomes MAV-12-01 to MAV-12-08 for the 2027 HSC cohort. Coverage refers to the 8 outcomes listed here; MA12-9 (technology) and MA12-10 (reasoning and justification) are not included on this page.
- 8syllabus outcomes
- 126skills mapped
- 100%have practice
Coverage is the percentage of listed syllabus outcomes with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one syllabus outcome, so some appear more than once below.
Functions
MA12-1uses detailed algebraic and graphical techniques to critically construct, model and evaluate arguments in a range of familiar and unfamiliar contexts
- Sketching polynomial functions
- Identifying transformed polynomials
- Sketching power functions
- Sketching sum, different and product of two functions
- Intersection of two graphs
- Function transformations
- Absolute value function
- Composite functions
- Level 1: Composite functions
- Domain and range of composite functions
- Level 1: Composite function equations
- Level 2: Composite function equations
- Level 1: Restricting a function to make it one-to-one
- Level 2: Restricting a function to make it one-to-one
- Level 1: Continuity and discontinuity of functions
- Level 2: Continuity and discontinuity of functions
- Domain of an inverse function
- Range of an inverse function
- Level 2: Solving inverse function equations
- Level 3: Solving inverse function equations
- Level 4: Solving inverse function equations
- Level 1: Transformations of functions
- Level 2: Transformations of functions
- Level 3: Transformations of functions
- Simplification and expansion of algebraic expressions
- Simplification of rational algebraic expressions
- Simplification of algebraic expressions involving integer indices
- Simplification of algebraic expressions involving rational indices
- Long division of polynomials
- Simultaneous linear equations in three unknowns
- Simultaneous linear equations in four unknowns
- Simultaneous nonlinear equations
- Level 1: Solving inequalities using sign charts
- Level 2: Solving inequalities using sign charts
- Evaluation of logarithms
- Simplification of logarithmic expressions
- Equations involving exponents
- Level 1: Logarithmic equations
- Level 2: Logarithmic equations
- Level 1: Logarithm laws
- Level 2: Logarithmic equations and domains
- Coordinates of points on a line
- Level 1: Coordinate of a point on a line given the length
- Level 2: Coordinate of a point on a line given the length
- Coordinates of a planar shape from a line
- Image of a point
Financial mathematics
MA12-2models and solves problems and makes informed decisions about financial situations using mathematical reasoning and techniques
- Depreciation: flat rate vs reducing balance crossover
- Depreciation: unit cost method
- Perpetuities: cumulative payments
- Compound interest: regular deposits, find the rate
- Compound interest: effective annual rate and interest earned
- Annuities: two-phase withdrawals, total years
- Making informed decisions: comparing investment options
- Making informed decisions: comparing loan offers
- Making informed decisions: break-even between payment plans
Calculus
MA12-3applies calculus techniques to model and solve problems
- Level 1: Differentiation word problems
- Level 2: Differentiation word problems
- Level 3: Differentiation word problems
- Level 1: Average and instantaneous rates of change
- Level 1: Application of differentiation to graphs
- Level 2: Application of differentiation to graphs
- Differentiation problems involving stationary points
- Differentiation problems involving the cubic function
- Level 1: Stationary points, inflection points and intervals of increase or decrease
- Level 1: Local minimum and local maximum values
- Level 2: Local minimum and local maximum values
- Level 2: Finding a curve from a stationary point
- Level 3: Finding a curve from a stationary point
MA12-6applies appropriate differentiation methods to solve problems
- Evaluation of a derivative at a point
- Identify a differentiable function
- Level 1: Differentiate using the chain rule
- Level 2: Differentiate using the chain rule
- Level 1: Apply the chain rule to composite functions
- Level 2: Apply the chain rule to composite functions
- Level 3: Apply the chain rule to composite functions
- Level 1: Apply the product rule
- Level 2: Apply the product rule
- Level 1: Indirect differentiation
- Level 1: Differentiation of indirectly defined relations
- Differentiation of fractions
- Level 1: Differentiation of logarithmic functions
- Level 2: Differentiation of logarithmic functions
- Level 1: Differentiation of mixed functions
- Level 2: Differentiation of mixed functions
- Level 3: Differentiation of mixed functions
- Level 1: Gradient and tangent of a curve at a point
- Level 1: Differentiability of piecewise functions
- Level 2: Differentiability of piecewise functions
MA12-7applies the concepts and techniques of indefinite and definite integrals in the solution of problems
Sequences and series
MA12-4applies the concepts and techniques of arithmetic and geometric sequences and series in the solution of problems
Trigonometric functions
MA12-5applies the concepts and techniques of periodic functions in the solution of problems involving trigonometric graphs
- Evaluate trigonometric functions
- General solution of trigonometric equations
- Trigonometric relations involving circles
- Trigonometric relations involving complex geometric shapes
- Level 1: Differentiation of trigonometric functions
- Level 2: Differentiation of trigonometric functions
- Level 3: Differentiation of trigonometric functions
- Level 4: Differentiation of trigonometric functions
Statistical analysis
MA12-8solves problems using appropriate statistical processes
- Summary and spread of data
- Understanding scatter plots
- Understanding stem-and-leaf plots
- Understanding frequency tables
- Understanding histograms
- Understanding box plots
- Conditional probability
- Level 1: Conditional probability
- Identify discrete probability distributions
- Calculate probabilities given a discrete probability distribution
- Level 1: Discrete random variables
- Level 1: Multi-stage probability experiments
- Level 2: Multi-stage probability experiments
- Level 1: Probabilities from polynomial probability density functions
- Level 1: Probabilities from exponential probability density functions
- Level 1: Statistics from polynomial probability density functions
- Level 1: Statistics from exponential probability density functions
- Basic set operations
- Venn diagrams involving two sets
- Venn diagrams involving three sets
Other Year 12 skills
Year 12 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.
- Basic operations on complex numbers
- Powers of complex numbers
- Rules for matrix elements
- Level 1: Transition matrices
- Level 1: Leslie matrices
- Level 1: Permutation matrices
- Level 2: Permutation matrices
- Level 1: Communication matrices
- Level 2: Communication matrices
- Level 1: Dominance matrices
- Level 1: Counting problems (permutations and combinations)
- Level 2: Counting problems (permutations and combinations)
- Level 3: Counting problems (permutations and combinations)
- Properties of vertices
- Properties of graphs
- Shortest path
Level 1: Find integer solutions to linear equations- Level 2: Find integer solutions to linear equations
- Congruences
- Divisibility
- Prime numbers
- Special functions
- Winning the tic-tac-toe
- Interpreting and using logarithmic scales
- Graph features of translated logarithmic functions
- Earth coordinates and great circles
- Distances on the Earth
- Increments formula - linear approximation
- Riemann sums - estimating area under a curve
- Displacement given velocity
- Position given acceleration and initial conditions
- Project networks and activity times
- Critical paths and float times
- Time zones
- Present value of ordinary annuities
- Future value of ordinary annuities
- Perpetuities
- Linear transformation of mean and standard deviation
- Bernoulli distribution - mean and variance
- Bernoulli distribution - modelling practical problems
- Normal distribution - qualitative graph features
- Normal distribution - probabilities and quantiles
- Least-squares regression lines
- Coefficient of determination
- Residuals, interpolation and extrapolation
- Association and causation
- Time series plots and patterns
- Moving averages and smoothing
- Seasonal indices and time series models
- Sample proportion - mean and standard deviation
- Confidence interval and margin of error for a proportion
- Rationalise a binomial surd denominator
- Simplify nested surds
- Inverse relationship of exponential and logarithmic functions
- Geometric proofs - circle theorems
- Geometric proofs - Pythagoras theorem
- Angle sum and difference identities
- Co-function identities
- The sine and cosine laws
- Limit of the exponential difference quotient
- The number e as the base giving a limit of 1
- Vector arithmetic
- Vector dot product
- Vector magnitude
- Vector direction and components
- Vector scalar multiplication and addition
- Distance between position vectors
- Contexts suitable for a normal model
- The concept of a random sample
- Sources of bias and ensuring randomness
- Approximate normality of the sample proportion
- Simulated sampling distribution of the sample proportion
- Coverage of repeated confidence intervals
- Friction on a rough surface
- Moments
- Quantities and units in mechanics
- Resultant forces
- Forces and Newton's first law
- Newton's second law
- Weight and motion under gravity
- Newton's third law and connected bodies
- Resolving forces into components
- Coefficient of friction
- The language of kinematics
- Motion graphs
- Constant acceleration formulae
- Calculus in kinematics
- Projectiles
- Pythagoras theorem
- Conversions between radians and degrees
- Evaluate the sine and cosine functions
- Find amplitude, period and range of trigonometric functions
- Sketch trigonometric functions
- Find the unknown angle using trigonometric functions
- Modulus and argument
- The Argand plane
- Complex conjugates and division
- Modulus-argument form
- Quadratics over the complex field