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Mathematics Extension 1 11–12 units and assessments (2024)

Sample units and assessments to support teachers implementing the Mathematics Extension 1 11–12 Syllabus (2024).

Syllabus

Mathematics Extension 1 11–12 (2024) © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2024.

This 2026 Mathematics Extension 1 Stage 6 Quick Reference Guide (PDF 285 KB) provides an overview of support available to implement the Mathematics Extension 1 Stage 6 Syllabus (2024).

Year 11

These units and assessments for Year 11 represent ‘one way’ of designing teaching and learning experiences.

A 9-lesson unit for Year 11 with resources.

This program of learning addresses content from the focus area of Permutations and combinations. The lessons and sequences in this program of learning are designed to allow students to build understanding of permutations and combinations through a range of Working mathematically skills.

Introduction

Permutations and combinations (DOCX 7.5 MB)

Lesson 1 – multiplication principle

Lesson 2 – factorials

Lesson 3 – introduction to permutations

Lesson 4 – permutations with restrictions

Lesson 5 – permutations with repetition

Lesson 6 – circular permutations

Lesson 7 – introduction to combinations

Lesson 8 – combinations with restrictions

Lesson 9 – permutations and combinations

This program of learning addresses content from the focus area of The binomial theorem. The lessons and sequences in this program of learning are designed to allow students to explore using the binomial theorem to expand binomial expressions by selecting and applying appropriate algebraic techniques and prove identities involving binomial coefficients by substituting into algebraic expressions, comparing coefficients or applying a combinatorial argument.

Introduction

The binomial theorem (DOCX 7.5 MB)

Lesson 1 – Pascal's triangle

Lesson 2 – combinatorial patterns

Lesson 3 – the binomial theorem

Lesson 4 – finding coefficients and the constant term

Lesson 5 – comparing coefficients

Lesson 6 – further proofs

This program of learning addresses content from the focus area of Polynomials. The lessons and sequences in this program of learning are designed to allow students to examine the language and graphs of polynomials, applying the remainder and factor theorems and explores the sums and products of zeroes of polynomials.

Introduction

Polynomials (DOCX 6 MB)

Lesson 1 – introducing polynomials

Lesson 2 – finding zeroes

Lesson 3 – sum and product of zeroes

Lesson 4 – relationships between zereos

Lesson 5 – connecting the zeroes

Lesson 6 – dividing polynomials

Lesson 7 – remainder and factor theorems

This program of learning addresses content from the focus area of Further work with functions. The lessons and sequences in this program of learning are designed to allow students to explore methods for solving cubic inequalities, absolute value inequalities and inequalities involving rational expressions with variables in the denominator.

Introduction

Inequalities (DOCX 5.2 MB)

Lesson 1 – cubic inequalities

Lesson 2 – absolute value inequalities

Lesson 3 – rational inequalities

This program of learning addresses content from the focus area of Further work with functions. The lessons and sequences in this program of learning are designed to allow students to explore the parametric form of linear and quadratic functions and circles.

Introduction

Parametric form (DOCX 6 MB)

Lesson 1 – introduction to parametric form

Lesson 2 – linear and quadratic parametric form

Lesson 3 – circle parametric form

This program of learning addresses content from the focus area of Further work with functions. The lessons and sequences in this program of learning are designed to allow students to explore the reciprocal, inverse and absolute value functions as well as the addition and subtraction of functions.

Introduction

Further work with functions (DOCX 8.3 MB)

Lesson 1 – absolute value

Lesson 2 – reflecting in the line y=x

Lesson 3 – one-to-one functions and sketching the inverse

One-to-one functions and sketching the inverse (DOCX 11.9 MB)

Lesson 4 – finding the equation of the inverse

Lesson 5 – addition and subtraction of functions

Lesson 6 – reciprocal functions

Lesson 7 – reciprocal trigonometric graphs

Reciprocal trigonometric graphs (DOCX 9.6 MB)

This program of learning addresses content from the focus area of Further trigonometry. The lessons and sequences in this program of learning are designed to allow students to explore trigonometry in three dimensions, introduce more complex trigonometric identities and equations including sum and difference expansions, double angle formulas and their applications.

Introduction

Further trigonometry (DOCX 8.3 MB)

Lesson 1 – sum and difference expansion formulas

Lesson 2 – double angle formulas

Lesson 3 – proving results

Lesson 4 – solving trigonometric equations

Lesson 5 – simplifying sums of sine and cosine functions

Lesson 6 – using R sin (x ± a) or R cos (x ± a) to solve equations

Lesson 7 – modelling and solving problems using trigonometry

Lesson 8 – trigonometry in three dimensions

Lesson 9 – trigonometry in three dimensions further problems

Year 12

These units and assessments for Year 12 represent ‘one way’ of designing teaching and learning experiences.

This program of learning addresses content from the focus area of Introduction to vectors. The lessons and sequences in this program of learning are designed to allow students to explore vector representation and notation for both 2D and 3D vectors and develops into operating with vectors.

Introduction

Vectors (DOCX 8.3 MB)

Lesson 1 – vectors in two dimensions

Lesson 2 – vectors in three dimensions

Lesson 3 – vector notations

Lesson 4 – scalar multiples

Lesson 5 – addition and subtraction of vectors

Lesson 6 – triangle and parallelogram laws

Lesson 7 – magnitude of a vector

Lesson 8 – the unit vector

Lesson 9 – parallel and perpendicular vectors

Lesson 10 – the scalar product

Lesson 11 – magnitude using the scalar product

Lesson 12 – angles between vectors

Lesson 13 – further angles between vectors

Lesson 14 – parallel and perpendicular vectors using the scalar product

Lesson 15 – vector projection

Lesson 16 – further vector projection

This program of learning addresses content from the focus area of Inverse trigonometric functions.

The lessons and sequences in this program of learning are designed to allow students to define and graph inverse trigonometric functions, explore their properties and apply transformations to inverse trigonometric functions.

Introduction

Inverse trigonometric functions (DOCX 579 KB)

Lesson 1 – defining inverse trigonometric functions

Lesson 2 – graphs of inverse trigonometric functions

Lesson 3 – transformations of inverse trigonometric graphs

Lesson 4 – proving and applying inverse trigonometric properties

Lesson 5 – composite functions

Lesson 6 – proving inverse trigonometric results

Mathematics Advanced 11–12 units and assessments (2024)

Sample units and assessments to support teachers of Years 11–12 implementing the Mathematics Advanced 11–12 Syllabus (2024).

Category:

  • Mathematics Extension 1
  • Teaching and learning
  • Unit

Topics:

  • Classroom resources
  • HSC
  • Stage 6

Business Unit:

  • Curriculum
Page details

Last modified date
04/11/2026
Business unit contact email
mrd@det.nsw.edu.au
Executive director
Megan Kelly
Executive director’s business unit
Teaching Learning&Student Wellbeing
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