Mathematics Advanced 11–12 units and assessments (2024)
Sample units and assessments to support teachers implementing the Mathematics Advanced 11–12 Syllabus (2024).
Syllabus
Syllabus outcomes and content descriptors from Mathematics Advanced 11–12 Syllabus (2024) © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2025.
Year 11
These units and assessments for Year 11 represent ‘one way’ of designing teaching and learning experiences.
An 8-lesson unit for Year 11 with resources.
This program of learning addresses content from the focus area of Probability and data. The lessons and sequences in this program of learning are designed to allow students to explore sets, probability, and data through practical applications. Students use representations, formulas, rules and real-world contexts to represent sets, calculate probabilities, and interpret data.
Introduction
Probability and data (DOCX 6.1 MB)
Lesson 1 – organising datasets
Lesson 2 – identifying the mode and median
- Identifying the mode and median (DOCX 4.4 MB)
- Identifying the mode and median – slide deck (PPTX 1.3 MB)
Lesson 3 – sets, subsets and probability
Lesson 4 – intersections and unions
Lesson 5 – tree diagrams and arrays
Lesson 6 – complements
Lesson 7 – conditional probability
Lesson 8 – independent events
A 7-lesson unit for Year 11 with resources.
This program of learning addresses content from the focus areas of Working with functions and Exponential and logarithmic functions. The lessons and sequences in this program of learning are designed to introduce students to functions and relations and the basic graphs within the scope of the Mathematics Advanced course. Students use the vertical line test, find the domain and range, and intercepts whilst connecting equations to their corresponding graphs.
Introduction
Introduction to functions (DOCX 6.1 MB)
Lesson 1 – functions
Lesson 2 – function values and intercepts
- Function values and intercepts (DOCX 7.3 MB)
- Function values and intercepts – slide deck (PPTX 4.3 MB)
Lesson 3 – the cubic and reciprocal function
- The cubic and reciprocal function (DOCX 6.2 MB)
- The cubic and reciprocal function – slide deck (PPTX 4.2 MB)
Lesson 4 – circles and semicircles
Lesson 5 – domain and range
Lesson 6 – composite functions
Lesson 7 – odd and even functions
A 16-lesson unit for Year 11 with resources.
This program of learning addresses content from the focus areas of Working with functions. The lessons and sequences in this program of learning are designed to provide an exploration of linear and quadratic functions, their graphs, and their applications to model practical problems. Students will refine their algebraic skills while learning and applying appropriate methods for graphing quadratic functions.
Introduction
Linear and quadratic equations (DOCX 2.1 MB)
Lesson 1 – linear functions
Lesson 2 – modelling linear functions
Lesson 3 – linear inequalities
Lesson 4 – solving simultaneous equations
- Solving simultaneous equations (DOCX 3.1 MB)
- Solving simultaneous equations – slide deck (PPTX 4.5 MB)
Lesson 5 – factorising monic quadratic functions
- Factorising monic quadratic functions (DOCX 2.5 MB)
- Factorising monic quadratic functions – slide deck (PPTX 4.0 MB)
Lesson 6 – graphing monic quadratic functions
- Graphing monic quadratic functions (DOCX 3.5 MB)
- Graphing monic quadratic functions – slide deck (PPTX 4.1 MB)
Lesson 7 – factorising and graphing non-monic quadratic functions
- Factorising and graphing non-monic quadratic functions (DOCX 2.7 MB)
- Factorising and graphing non-monic quadratic functions – slide deck (PPTX 4.1 MB)
Lesson 8 – completing the square
Lesson 9 – the quadratic formula
Lesson 10 – simplifying surds
Lesson 11 – rationalising the denominator
Lesson 12 – the discriminant
Lesson 13 – finding quadratic functions from a graph
- Finding quadratic functions from a graph (DOCX 3.0 MB)
- Finding quadratic functions from a graph – slide deck (PPTX 3.5 MB)
Lesson 14 – modelling quadratic functions
Lesson 15 – simultaneous quadratic equations
- Simultaneous quadratic equations (DOCX 2.8 MB)
- Simultaneous quadratic equations – slide deck (PPTX 3.7 MB)
Lesson 16 – solving quadratic inequalities
A 12-lesson unit for Year 11 with resources.
The lessons and sequences in this program of learning are designed to allow students to explore graphical transformations of functions, including reflections, translations, and dilations.
Students will investigate how changes to equations affect graphs within the scope of the Mathematics Advanced course, and determine key features such as domain, range, intercepts, and asymptotes. Students then apply this knowledge to solve a range of problems including those involving direct and inverse variation.
Introduction
Graphing transformations (DOCX 6 MB)
Lesson 1 – piecewise-defined functions
Lesson 2 – absolute value
Lesson 3 – solving absolute value equations
- Solving absolute value equations (DOCX 6.1 MB)
- Solving absolute value equations – slide deck (PPTX 9.5 MB)
Lesson 4 – reflection
Lesson 5 – translations
Lesson 6 – further circles
Lesson 7 – further cubic functions
Further cubic functions (DOCX 6.2 MB)
Lesson 8 – dilations (enlargements and reductions)
- Dilations (enlargements and reductions) (DOCX 8.8 MB)
- Dilations (enlargements and reductions) – slide deck (PPTX 2.7 MB)
Lesson 9 – dilations (horizontal and vertical)
- Dilations (horizontal and vertical) (DOCX 9 MB)
- Dilations (horizontal and vertical) – slide deck (PPTX 3. MB)
Lesson 10 – applying graphing transformations
- Applying graphing transformations (DOCX 6.8 MB)
- Applying graphing transformations – slide deck (PPTX 2.8 MB)