Unit 4 – graphing transformations – assessment task

Students apply their understanding of functions and relations by writing equations with domain and range restrictions to model shapes, and design an original logo using mathematical curves. Then they reflect on how mathematics can be used to create visual designs by evaluating the strengths and limitations of their work.

• Assessment task sample solutions – graphing transformations (DOCX 6.6 MB)
• Student assessment task – graphing transformations (DOCX 5 MB)
• Teacher information – graphing transformations (DOCX 3.5 MB)

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

• Organising datasets (DOCX 5.8 MB)
• Organising datasets – spreadsheet (XLSX 118 KB)

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

• Sets, subsets and probability (DOCX 7.3 MB)
• Sets, subsets and probability – slide deck (PPTX 1.7 MB)

Lesson 4 – intersections and unions

• Intersections and unions (DOCX 6 MB)
• Intersections and unions – slide deck (PPTX 2.4 MB)

Lesson 5 – tree diagrams and arrays

• Tree diagrams and arrays (DOCX 6.1 MB)
• Tree diagrams and arrays – slide deck (PPTX 2.5 MB)

Lesson 6 – complements

• Complements (DOCX 6.1 MB)
• Complements – slide deck (PPTX 1.5 MB)

Lesson 7 – conditional probability

• Conditional probability (DOCX 6.1 MB)
• Conditional probability – slide deck (PPTX 2.4 MB)

Lesson 8 – independent events

• Independent events (DOCX 5.9 MB)
• Independent events – slide deck (PPTX 2.2 MB)

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

• Functions (DOCX 8.1 MB)
• Functions – slide deck (PPTX 1 MB)

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

• Circles and semicircles (DOCX 7.5 MB)
• Circles and semicircles – slide deck (PPTX 4.2 MB)

Lesson 5 – domain and range

• Domain and range (DOCX 6.6 MB)
• Domain and range – slide deck (PPTX 4.5 MB)

Lesson 6 – composite functions

• Composite functions (DOCX 8.2 MB)
• Composite functions – slide deck (PPTX 13.3 MB)

Lesson 7 – odd and even functions

• Odd and even functions (DOCX 7.4 MB)
• Odd and even functions – slide deck (PPTX 4.3 MB)

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

• Linear functions (DOCX 4.1 MB)
• Linear functions – slide deck (PPTX 4.2 MB)

Lesson 2 – modelling linear functions

• Modelling linear functions (DOCX 3.4 MB)
• Modelling linear functions – slide deck (PPTX 6.6 MB)

Lesson 3 – linear inequalities

• Linear inequalities (DOCX 3 MB)
• Linear inequalities – slide deck (PPTX 4.5 MB)

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

• Completing the square (DOCX 5.0 MB)
• Completing the square – slide deck (PPTX 3.1 MB)

Lesson 9 – the quadratic formula

• The quadratic formula (DOCX 3.3 MB)
• The quadratic formula – slide deck (PPTX 2.8 MB)

Lesson 10 – simplifying surds

• Simplifying surds (DOCX 4.2 MB)
• Simplifying surds – slide deck (PPTX 3.9 MB)

Lesson 11 – rationalising the denominator

• Rationalising the denominator (DOCX 2.3 MB)
• Rationalising the denominator – slide deck (PPTX 5.6 MB)

Lesson 12 – the discriminant

• The discriminant (DOCX 3.0 MB)
• The discriminant – slide deck (PPTX 3.0 MB)

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

• Modelling quadratic functions (DOCX 2.2 MB)
• Modelling quadratic functions – slide deck (PPTX 3.4 MB)

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

• Solving quadratic inequalities (DOCX 3.0MB)
• Solving quadratic inequalities – slide deck (PPTX 4.7 MB)

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

• Piecewise-defined functions (DOCX 7.7 MB)
• Piecewise-defined functions – slide deck (PPTX 3.4 MB)

Lesson 2 – absolute value

• Absolute value (DOCX 7.5 MB)
• Absolute value – slide deck (PPTX 2.2 MB)

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

• Reflection (DOCX 8 MB)
• Reflection – slide deck (PPTX 7.4 MB)

Lesson 5 – translations

• Translations (DOCX 6 MB)
• Translations – slide deck (PPTX 3.8 MB)

Lesson 6 – further circles

• Further circles (DOCX 9 MB)
• Further circles – slide deck (PPTX 3.6 MB)

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)

Lesson 11 – direct variation

• Direct variation (DOCX 7.6 MB)
• Direct variation – slide deck (PPTX 2.5 MB)

Lesson 12 – inverse variation

• Inverse variation (DOCX 5.8 MB)
• Inverse variation – slide deck (PPTX 2.1 MB)

An 8-lesson unit for Year 11 with resources.

This program of learning addresses content from the focus area of Introduction to differentiation. The lessons and sequences in this program of learning are designed to allow students to explore rates of change by looking at average speed vs instantaneous speed. The lessons introduce the concept of the derivative and use first principles to find the derivative of quadratic functions.

Introduction

Foundations of differentiation (DOCX 6 MB)

Lesson 1 – average speed

• Average speed (DOCX 6.4 MB)
• Average speed – slide deck (PPTX 3.5 MB)

Lesson 2 – instantaneous speed

• Instantaneous speed (DOCX 6.1 MB)
• Instantaneous speed – slide deck (PPTX 3.2 MB)

Lesson 3 – modelling change

• Modelling change (DOCX 5 MB)
• Modelling change – slide deck (PPTX 3.1 MB)

Lesson 4 – negative and fractional indices

• Negative and fractional indices (DOCX 8.3 MB)
• Negative and fractional indices – slide deck (PPTX 3.3 MB)

Lesson 5 – introducing the derivative

• Introducing the derivative (DOCX 5.8 MB)
• Introducing the derivative – slide deck (PPTX 10.2 MB)

Lesson 6 – algebraic fractions

• Algebriac fractions (DOCX 6.1 MB)
• Algebriac fractions – slide deck (PPTX 9.2 MB)

Lesson 7 – differentiating by first principles

• Differentiating by first principles (DOCX 7.2 MB)
• Differentiating by first principles – slide deck (PPTX 2.4 MB)

Lesson 8 – parallel and perpendicular lines

• Parallel and perpendicular lines (DOCX 5.8 MB)
• Parallel and perpendicular lines – slide deck (PPTX 2 MB)

An 10-lesson unit for Year 11 with resources.

This program of learning addresses content from the focus area of Introduction to differentiation. The lessons and sequences in this program of learning are designed to allow students to differentiate using a variety of rules before applying them to describe functions and graph derivatives.

Introduction

Differentiation techniques and applications (DOCX 6 MB)

Lesson 1 – basic differentiation rules

• Basic differentiation rules (DOCX 7.5 MB)
• Basic differentiation rules – slide deck (PPTX 1.5 MB)

Lesson 2 – tangents and normals

• Tangents and normals (DOCX 8.4 MB)
• Tangents and normals – slide deck (PPTX 1.8 MB)

Lesson 3 – the chain rule, part 1

• The chain rule, part 1 (DOCX 7.2 MB)
• The chain rule, part 1 – slide deck (PPTX 2 MB)

Lesson 4 – the chain rule, part 2

• the chain rule, part 2 (DOCX 8.1 MB)
• the chain rule, part 2 – slide deck (PPTX 2.3 MB)

Lesson 5 – the product rule

• The product rule (DOCX 8.1 MB)
• The product rule – slide deck (PPTX 2.6 MB)

Lesson 6 – the quotient rule

• The quotient rule (DOCX 8.3 MB)
• The quotient rule – slide deck (PPTX 1.9 MB)

Lesson 7 – mixed differentiation

• Mixed differentiation (DOCX 7.2 MB)
• Mixed differentiation – slide deck (PPTX 460 KB)

Lesson 8 – increasing and decreasing functions

• Increasing and decreasing functions (DOCX 8.5 MB)
• Increasing and decreasing functions – slide deck (PPTX 2 MB)

Lesson 9 – graphing the derivative function

• Graphing the derivative function (DOCX 7.4 MB)
• Graphing the derivative function – slide deck (PPTX 1.5 MB)

Lesson 10 – displacement and velocity

• Displacement and velocity (DOCX 7.8 MB)
• Displacement and velocity – slide deck (PPTX 1.9 MB)

A 7-lesson unit for Year 11 with resources.

This unit focuses on exponential and logarithmic functions, exploring their properties, behaviours and interrelationships. Students will graph exponential functions, identify their characteristics, learn about Euler’s number and apply logarithmic laws to solve equations, ultimately understanding the reflection between exponential and logarithmic graphs.

Introduction

Exponential and logarithmic functions (DOCX 6 MB)

Lesson 1 – transformations of exponential functions

• Transformations of exponential functions (DOCX 3.1 MB)
• Transformations of exponential functions – slide deck (PPTX 1.8 MB)

Lesson 2 – Euler's number

• Euler's number (DOCX 4.9 MB)
• Euler's number – slide deck (PPTX 2 MB)

Lesson 3 – finding the power

• Finding the power (DOCX 4.1 MB)
• Finding the power – slide deck (PPTX 1.5 MB)

Lesson 4 – the logarithmic function

• The logarithmic function (DOCX 4.6 MB)
• The logarithmic function – slide deck (PPTX 2.4 MB)

Lesson 5 – the logarithmic laws

• The logarithmic laws (DOCX 2.1 MB)
• The logarithmic laws – slide deck (PPTX 3.1 MB)

Lesson 6 – the logarithmic laws – proofs and equations

• The logarithmic laws – proofs and equations (DOCX 3.9 MB)
• The logarithmic laws – proofs and equations – slide deck (PPTX 1.9 MB)

Lesson 7 – change of base

• Change of base (DOCX 3 MB)
• Change of base – slide deck (PPTX 1.6 KB)

An 11-lesson unit for Year 12 with resources.

This program of learning addresses content from the focus areas of further graph transformations and modelling and differential calculus. The lessons and sequences allow students to explore transformations of trigonometric functions, including reflections, translations, and dilations using graphing applications; modelling and solving practical problems with periodic phenomena and to apply differentiation techniques to exponential, logarithmic and trigonometric functions, using derivatives to analyse tangents and normals of the functions within the scope of the Mathematics Advanced course.

Introduction

Further differentiation, modelling and graphing (DOCX 7.4 MB)

Lesson 1 – reflections and translations of trigonometric functions

• Reflections and translations of trigonometric functions (DOCX 2.2 MB)
• Reflections and translations of trigonometric functions – slide deck (PPT 4.7 MB)

Lesson 2 – dilations of trigonometric functions

• Dilations of trigonometric functions (DOCX 7 MB)
• Dilations of trigonometric functions – slide deck (PPTX 3.4 MB)

Lesson 3 – trigonometric functions and modelling

• Trigonometric functions and modelling (DOCX 2.2 MB)
• Trigonometric functions and modelling – slide deck (PPTX 3.2 MB)

Lesson 4 – logarithmic scales

• Logarithmic scales (DOCX 3.9 MB)
• Logarithmic scales – slide deck (PPTX 2.6 MB)

Lesson 5 – differentiating exponential functions with base e

• Differentiating exponential functions with base e (DOCX 3 MB)
• Differentiating exponential functions with base e – slide deck (PPTX 2.8 MB)

Lesson 6 – differentiating exponential functions with base a

• Differentiating exponential functions with base a (DOCX 3 MB)
• Differentiating exponential functions with base a – slide deck (PPTX 3.2 MB)

Lesson 7 – differentiating natural logarithmic functions

• Differentiating natural logarithmic functions (DOCX 3.9 MB)
• Differentiating natural logarithmic functions – slide deck (PPTX 3.7 MB)

Lesson 8 – differentiating logarithmic functions

• Differentiating logarithmic functions (DOCX 4.1 MB)
• Differentiating logarithmic functions – slide deck (PPTX 3.3 MB)

Lesson 9 – differentiating sine and cosine functions

• Differentiating sine and cosine functions (DOCX 2.3 MB)
• Differentiating sine and cosine functions – slide deck (PPTX 2.7 MB)

Lesson 10 – differentiating tangent functions

• Differentiating tangent functions (DOCX 2.3 MB)
• Differentiating tangent functions – slide deck (PPTX 3 MB)

Lesson 11 – differentiating cosecant, secant and cotangent functions

• Differentiating cosecant, secant and cotangent functions (DOCX 4.1 MB)
• Differentiating cosecant, secant and cotangent functions – slide deck (PPTX 2.3 MB)