Year 11: Mathematics Extension 1 11–12 Syllabus (2024)
Listed Mathematics 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 3 September 2026.
Implemented for Year 11 from Term 1, 2026. Mathematics Advanced Year 11 is a co-requisite.
- 5outcomes
- 72skills mapped
- 100%have practice
Coverage is the percentage of listed 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 outcome, so some appear more than once below.
Syllabus outcomes
ME1-11-01solves problems involving inequalities, functions and their inverses, graphical relationships between functions, and parametric equations
- Solving inequalities
- Solving quadratic inequalities
- Level 1 -Solving exponential inequalities
- Level 2 -Solving exponential inequalities
- Solving cubic inequalities
- 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
- Piecewise-defined functions
- Intersection of two graphsFunctions and relations
- Function transformation by translation
- Function transformation by dilation and reflection
- Composite 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: System of linear inequalities in two variables
- Level 2: System of linear inequalities in two variables
- The square root graph
- Intersection of two graphsCoordinate geometry
ME1-11-02applies the remainder and factor theorem and sums and products of zeroes to solve problems involving polynomials
- 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
ME1-11-03solves problems in three dimensions using trigonometry and simplifies expressions, proves results and solves problems involving compound angles using trigonometric identities
- Calculate the area of a compound shape
- Angles in a circle
- Pythagoras theorem
- Conversions between radians and degrees
- Evaluate the sine and cosine functions
- Evaluate trigonometric functions
- Find amplitude, period and range of trigonometric functions
- Sketch trigonometric functions
- Find the unknown angle using trigonometric functions
- General solution of trigonometric equations
- The sine and cosine laws
- Trigonometric relations involving circles
- Trigonometric relations involving complex geometric shapes
ME1-11-04uses permutations and combinations to solve problems involving counting, ordering and probability
ME1-11-05uses the binomial theorem to solve problems and prove identities
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
Challenge: Level 1: Find integer solutions to linear equations- Challenge: Level 2: Find integer solutions to linear equations
- Challenge: Numeric sequences from geometric shapes
- Challenge: Divisibility
- Congruences
- Challenge: 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
- Simplification and expansion of algebraic expressions
- Factorisation
- Simplification of rational algebraic expressions
- Symbolic substitution in algebraic expressions
- Rewrite rational expressions
- Solve linear equations
- Greatest common divisor of algebraic expressions
- Transposing formulas
- 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
- Level 1: Quadratic turning point
- Level 2: Quadratic turning point
- The general quadratic formula
- Level 1: The quadratic equation discriminant
- Level 2: The quadratic equation discriminant
- Quadratic models
- Partial sums of arithmetic series
- 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
- Combination of transformation
- Matrix transformations
- Identifying transformed polynomials
- Linear intercepts
- Level 1: Distance between points on a line and the midpoint
- Level 2: Distance between points on a line and the midpoint
- 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
- Level 1: Intersection of a line and a parabola
- Level 2: Intersection of a line and a parabola
- Rectangular hyperbolas
- The truncus
- The circle
- 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
- 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
- Indefinite integration of polynomials
- Definite integration
- Application of integration for polynomial equations
- Level 2: Finding a curve from a stationary point
- Level 3: Finding a curve from a stationary point
- 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
- Recursive sequences
- Challenge: How to get home in bekomaze
- Challenge: Tic-tac-toe
- Properties of vertices
- Properties of graphs
- Types of graphs
- Shortest path
- 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
- Challenge: Winning the tic-tac-toe
- Basic set operations
- Venn diagrams involving two sets
- Venn diagrams involving three sets
- Summary and spread of data
- Understanding bar charts
- Understanding scatter plots
- Understanding frequency tables
- Understanding histograms
- Understanding stem-and-leaf plots
- Scientific notation and significant figures
- Personal budgeting - fixed and discretionary spending
- Currency exchange rates
- Limiting behaviour of geometric sequences
- Sum of the first n terms of a geometric sequence
- Graph features of translated exponential functions
- Graph features of translated logarithmic 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