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

• Multiplication principle (DOCX 12.2 MB)
• Multiplication principle – slide deck (DOCX 8.4 MB)

Lesson 2 – factorials

• Factorials (DOCX 5.8 MB)
• Factorials – slide deck (PPTX 1.3 MB)

Lesson 3 – introduction to permutations

• Introduction to permutations (DOCX 6.5 MB)
• Introduction to permutations – slide deck (PPTX 1.2 MB)

Lesson 4 – permutations with restrictions

• Permutations with restrictions (DOCX 5.9 MB)
• Permutations with restrictions – slide deck (PPTX 2.8 MB)

Lesson 5 – permutations with repetition

• Permutations with repetition (DOCX 5.9 MB)
• Permutations with repetition – slide deck (PPTX 1.5 MB)

Lesson 6 – circular permutations

• Circular permutations (DOCX 5.9 MB)
• Circular permutations – slide deck (PPTX 1.5 MB)

Lesson 7 – introduction to combinations

• Introduction to combinations (DOCX 5.9 MB)
• Introduction to combinations – slide deck (PPTX 1.3 MB)

Lesson 8 – combinations with restrictions

• Combinations with restrictions (DOCX 5.9 MB)
• Combinations with restrictions – slide deck (PPTX 1.4 MB)

Lesson 9 – permutations and combinations

• Permutations and combinations (DOCX 6.4 MB)
• Permutations and combinations – slide deck (PPTX 1.3 MB)

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

• Pascal’s triangle (DOCX 6.3 MB)
• Pascal’s triangle – slide deck (PPTX 1.5 MB)

Lesson 2 – combinatorial patterns

• Combinatorial patterns (DOCX 6.6 MB)
• Combinatorial patterns – slide deck (PPTX 1.5 MB)

Lesson 3 – the binomial theorem

• The binomial theorem (DOCX 7.5 MB)
• The binomial theorem – slide deck (PPTX 1.6 MB)

Lesson 4 – finding coefficients and the constant term

• Finding coefficients and the constant term (DOCX 8.2 MB)
• Finding coefficients and the constant term – slide deck (PPTX 1.7 MB)

Lesson 5 – comparing coefficients

• Comparing coefficients (DOCX 7.3 MB)
• Comparing coefficients – slide deck (PPTX 8.5 MB)

Lesson 6 – further proofs

• Further proofs (DOCX 6.3 MB)
• Further proofs – slide deck (PPTX 8.8 MB)

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

• Introducing polynomials (DOCX 3 MB)
• Introducing polynomials – slide deck (PPTX 2.3 MB)

Lesson 2 – finding zeroes

• Finding zeroes (DOCX 2.2 MB)
• Finding zeroes – slide deck (PPTX 2.4 MB)

Lesson 3 – sum and product of zeroes

• Sum and product of zeroes (DOCX 3 MB)
• Sum and product of zeroes – slide deck (PPTX 1.9 MB)

Lesson 4 – relationships between zereos

• Relationships between zereos (DOCX 3 MB)
• Relationships between zereos – slide deck (PPTX 2.6 MB)

Lesson 5 – connecting the zeroes

• Connecting the zeroes (DOCX 3 MB)
• Connecting the zeroes – slide deck (PPTX 1.6 MB)

Lesson 6 – dividing polynomials

• Dividing polynomials (DOCX 4.6 MB)
• Dividing polynomials – slide deck (PPTX 1.7 MB)

Lesson 7 – remainder and factor theorems

• Remainder and factor theorems (DOCX 4.1 MB)
• Remainder and factor theorems – slide deck (PPTX 1.8 MB)

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

• Cubic inequalities (DOCX 6.9 MB)
• Cubic inequalities – slide deck (PPTX 1.8 MB)

Lesson 2 – absolute value inequalities

• Absolute value inequalities (DOCX 8.6 MB)
• Absolute value inequalities – slide deck (PPTX 2 MB)

Lesson 3 – rational inequalities

• Rational inequalities (DOCX 5.9 MB)
• Rational inequalities – slide deck (PPTX 2 MB)

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

• Absolute value (DOCX 7.4 MB)
• Absolute value – slide deck (PPTX 6.7 MB)

Lesson 2 – reflecting in the line y=x

• Reflecting in the line y=x (DOCX 9.2 MB)
• Reflecting in the line y=x – slide deck (PPTX 4.4 MB)

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

• Finding the equation of the inverse (DOCX 9.2 MB)
• Finding the equation of the inverse – slide deck (PPTX 3.5 MB)

Lesson 5 – addition and subtraction of functions

• Addition and subtraction of functions (DOCX 7.2 MB)
• Addition and subtraction of functions – slide deck (PPTX 4.8 MB)

Lesson 6 – reciprocal functions

• Reciprocal functions (DOCX 6.9 MB)
• Reciprocal functions – slide deck (PPTX 3.4 MB)

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

• Sum and difference expansion formulas (DOCX 4.1 MB)
• Sum and difference expansion formulas – slide deck (PPTX 2.2 MB)

Lesson 2 – double angle formulas

• Double angle formulas (DOCX 2.2 MB)
• Double angle formulas – slide deck (PPTX 1.6 MB)

Lesson 3 – proving results

• Proving results (DOCX 2.1 MB)
• Proving results – slide deck (PPTX 1.6 MB)

Lesson 4 – solving trigonometric equations

• Solving trigonometric equations (DOCX 2.1 MB)
• Solving trigonometric equations – slide deck (PPTX 1.5 MB)

Lesson 5 – simplifying sums of sine and cosine functions

• Simplifying sums of sine and cosine functions (DOCX 2.5 MB)
• Simplifying sums of sine and cosine functions – slide deck (PPTX 1.6 MB)

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

• Using R sin (x ± a) or R cos (x ± a) to solve equations (DOCX 3.9 MB)
• Using R sin (x ± a) or R cos (x ± a) to solve equations – slide deck (PPTX 1.6 MB)

Lesson 7 – modelling and solving problems using trigonometry

• Modelling and solving problems using trigonometry (DOCX 2.1 MB)
• Modelling and solving problems using trigonometry – slide deck (PPTX 1.9 MB)

Lesson 8 – trigonometry in three dimensions

• Trigonometry in three dimensions (DOCX 2.4 MB)
• Trigonometry in three dimensions – slide deck (PPTX 1.8 MB)

Lesson 9 – trigonometry in three dimensions further problems

• Trigonometry in three dimensions further problems (DOCX 2.6 MB)
• Trigonometry in three dimensions further problems – slide deck (PPTX 1.8 MB)