Year 11: Mathematics Advanced 11–12 Syllabus (2024)
Listed Mathematics syllabus outcomes at Year 11, 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.
The 2024 syllabus is implemented for Year 11 from Term 1, 2026, and is first examined in the 2027 HSC.
- 10syllabus outcomes
- 156skills 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.
Algebra and functions
MAV-11-01applies algebraic techniques and the laws of indices and surds to manipulate expressions and solve problems
- Simplification and expansion of algebraic expressions
- Factorisation
- Simplification of rational algebraic expressions
- Rewrite rational expressions
- Greatest common divisor of algebraic expressions
- Symbolic substitution in algebraic expressions
- Transposing formulas
- Solve linear equations
- Solving inequalities
- Solving simultaneous linear equations
- Simultaneous linear equations in three unknowns
- Simultaneous linear equations in four unknowns
- Simultaneous linear equations word problems
- Level 1: Integer indices
- Level 2: Integer indices
- Level 3: Integer indices
- Level 1: Rational indices
- Level 2: Rational indices
- Level 1: Solve the quadratic equation by factorisation
- Level 2: Solve the quadratic equation by factorisation
- Level 3: Solve the quadratic equation by factorisation
- Completing the square
- The general quadratic formula
- Level 1: The quadratic equation discriminant
- Level 2: The quadratic equation discriminant
- Solving quadratic inequalities
- Factorising polynomials
- Polynomial coefficients and constants
- Level 1: Long division of polynomials
- Level 2: Long division of polynomials
- Level 3: Long division of polynomials
- Level 1: Factorisation of the cubic equation
- Level 2: Factorisation of the cubic equation
- Level 1: The cubic equation
- Level 2: The cubic equation
- Solving cubic inequalities
MAV-11-02uses functions and relations to model, analyse and solve problems
- Relation type
- Domain and range of set relations
- Level 1: Domain and range of polynomial relations
- Level 2: Domain and range of polynomial relations
- Definition of functions
- Level 1: Domain and range of polynomial functions
- Level 2: Domain and range of polynomial functions
- Level 1: Domain and range of rational functions
- Level 2: Domain and range of rational functions
- Level 3: Domain and range of rational functions
- Level 4: Domain and range of rational functions
- Level 1: Domain and range of square root functions
- Level 2: Domain and range of square root functions
- Function continuity
- Even and odd polynomial functions
- Sketching polynomial functions
- Sketching the cubic function
- The cubic function of the form f(x)=a(x-h)3+k
- Inverse functions
- Sketch inverse 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
- Piecewise-defined functions
- Composite functions
- Intersection of two graphsFunctions and relations
- Linear intercepts
- The gradient of a line
- The gradient of the perpendicular to a line
- Families of straight lines
- Coordinates of points on a line
- The equation of a straight line
- Parallel and perpendicular lines
- Linear models
- The parabola
- Quadratic models
- Level 1: Quadratic turning point
- Level 2: Quadratic turning point
- Level 1: Intersection of a line and a parabola
- Level 2: Intersection of a line and a parabola
- Level 1: System of linear inequalities in two variables
- Level 2: System of linear inequalities in two variables
- Rectangular hyperbolas
- The truncus
- The circle
- The square root graph
- Intersection of two graphsCoordinate geometry
- Level 1: Distance between points on a line and the midpoint
- Level 2: Distance between points on a line and the midpoint
- 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
MAV-11-03analyses and solves algebraic and graphical problems involving transformations of functions and relations
Trigonometric functions
MAV-11-04applies trigonometry to solve problems involving geometric shapes
MAV-11-05uses periodic functions to solve trigonometric equations and prove trigonometric identities
Calculus
MAV-11-06interprets the meaning of the derivative and determines the derivative of functions to solve problems
- Evaluate limits of simple expressions
- Evaluate limits of rational functions
- Evaluate the average rate of change
- Average rate of change word problems
- Interpreting a tanget to a graph
- Evaluation of a derivative at a point
- Identify a differentiable function
- Tangents and normals
- Stationary points
- Level 1: Differentiation of polynomial functions
- Level 2: Differentiation of polynomial functions
- Differentiation of polynomials raised to a power
- Level 1: Differentiation of fractions
- Level 2: Differentiation of fractions
- Differentiation of surds
- Level 1: Applications of differentiation
- Level 2: Applications of differentiation
- Level 3: Applications of differentiation
- Level 2: Finding a curve from a stationary point
- Level 3: Finding a curve from a stationary point
Exponential and logarithmic functions
MAV-11-07applies exponential and logarithmic laws to simplify expressions, solve equations and prove results
- Evaluation of logarithms
- Simplification of logarithmic expressions
- Level 1: Equations involving exponents
- Level 2: Equations involving exponents
- Level 3: Equations involving exponents
- Level 1: Using logarithms to solve equations involving exponents
- Level 2: Using logarithms to solve equations involving exponents
- Level 1 -Solving exponential inequalities
- Level 2 -Solving exponential inequalities
MAV-11-08analyses graphs of exponential and logarithmic functions
Statistical analysis
MAV-11-09solves problems involving probability in a variety of contexts
- Sample spaces, events and outcomes
- Probability of simple events
- Estimating probabilities from data
- Level 1: Probability of simple and compound events
- Level 2: Probability of simple and compound events
- Probabilities from Venn diagrams
- The addition rule for probabilities
- Conditional probability
- Discrete probability distributions
Winning the tic-tac-toe- Basic set operations
- Venn diagrams involving two sets
- Venn diagrams involving three sets
MAV-11-10displays and analyses datasets using summary statistics and graphical representations
Other Year 11 skills
Year 11 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.
- Percentage change
- Level 1: Find integer solutions to linear equations
- Level 2: Find integer solutions to linear equations
- Numeric sequences from geometric shapes
- Divisibility
- Congruences
- Prime numbers
- Financial mathematics - Identify the best deal
- Financial mathematics - Income and tax
- Financial mathematics - Profit, loss, markup and discount
- Financial mathematics - Simple interest
- Financial mathematics - Compound interest
- Partial sums of arithmetic series
- Indefinite integration of polynomials
- Definite integration
- Application of integration for polynomial equations
- Level 1: Matrix addition and subtraction
- Level 2: Matrix addition and subtraction
- Level 3: Matrix addition and subtraction
- Level 1: Matrix multiplication
- Level 2: Matrix multiplication
- Level 3: Matrix multiplication
- Level 1: Matrix power
- Level 2: Matrix power
- Level 1: Matrix inverse
- Level 2: Matrix inverse
- Level 3: Matrix inverse
- Matrix determinant
- Vector arithmetic
- Vector dot product
- Counting addition and multiplication rules
- Level 1: Permutations
- Level 2: Permutations
- Level 3: Permutations
- Level 1: Permutations with repetition
- Permutations of digits in numbers
- Level 1: Combinations
- Level 2: Combinations
- Level 3: Combinations
- Level 4: Combinations
- Recursive sequences
- How to get home in bekomaze
- Tic-tac-toe
- Properties of vertices
- Properties of graphs
- Types of graphs
- Shortest path
- Understanding histograms
- Understanding stem-and-leaf plots
- Scientific notation and significant figures
- Personal budgeting - fixed and discretionary spending
- Currency exchange rates
- Binomial theorem problem solving and identities
- Limiting behaviour of geometric sequences
- Sum of the first n terms of a geometric sequence
- Graph features of translated exponential functions
- Similarity and scale drawings
- Area and volume scale factors
- Volume of standard three-dimensional objects
- Surface area of standard three-dimensional objects
- Co-function identities
- Angle sum and difference identities
- Simplifying the difference quotient
- Derivative from first principles - Leibniz notation
- Standard scores - z-scores
- The 68-95-99.7 empirical rule and normal graph features
- Normal distribution probabilities and quantiles
- Classify categorical variables - ordinal or nominal
- Classify numerical variables - discrete or continuous
- Box plot outlier fences
- Rationalise a binomial surd denominator
- Simplify nested surds
- Geometric proofs - circle theorems
- Geometric proofs - Pythagoras theorem
- Vector magnitude
- Vector direction and components
- Vector scalar multiplication and addition
- Distance between position vectors
- 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
- Basic operations on complex numbers
- Powers of complex numbers
- Modulus and argument
- The Argand plane
- Complex conjugates and division
- Modulus-argument form
- Quadratics over the complex field