### Course Description

This course is the first of two that cover every dot point from MA-F1 Working with Functions the new NSW Year 11 Mathematics Advanced syllabus. The first covers F1.1: Algebraic techniques and parts of F1.2: Introduction to functions and F1.3: Linear, quadratic and cubic functions.

The course goes into greater detail than the textbooks so that teachers will be more comfortable in their ability to deliver the content. All 133 examples have been recorded, so that you can watch an experienced maths teacher talk through the examples and any important points to note.

New and existing content is explored in detail, including interesting and more efficient techniques that experienced teachers may not have seen before. Important points to be covered with students are noted, and the limits of the syllabus are discussed. As more detail on the syllabus is released by NESA any changes required will be made. Also included are related skills that are beyond the syllabus that you can use to extend more capable students.

Each lesson includes a section for Extension Students, that covers work that can help them develop skills and techniques that helps prepare them for content they will cover in the Extension 1 or Extension 2 courses.

The course includes:

• 133 recorded examples
• 225 page course handout
• 133 optional practice questions, matching the examples from the course
• 76 mixed questions, all with fully worked solutions

The remainder of the Year 11 Advanced syllabus is be covered in four more courses:

ADV#2 covers the remainder of MA-F1 Working with Functions.

ADV#3 covers MA-T1 Trigonometry and Measure of Angles and MA-T2 Trigonometric Functions and Identities

ADV#4 covers MA-C1 Introduction to Differentiation.

ADV#5 will cover MA-E1 Logarithms and Exponentials and MA-S1 Probability and Discrete Probability Distributions

### Audience

Mathematics teachers of any experience level who are preparing to teach the new Advanced syllabus.

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### Complete Subject:

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#### Do you teach in NSW? If so, this is relevant to you:

Completing Mathematics In Depth - Year 11 Advanced - Functions Part A - ADV#1 will contribute 10 hours of NSW Education Standards Authority (NESA) Accredited PD in the priority area of f Delivery and assessment of NSW Curriculum/Early Years Learning Framework addressing standard descriptors 2.1.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.

## Course curriculum

• 1

### Introduction

• Introduction to the Mathematics Advanced Year 11 In Depth Series

• Introduction to In Depth ADV#1

• 2

### Functions

• Introduction to Functions

• Relevant Parts of the Syllabus

• 3

### Lesson 1 Basic Index Laws

• Lesson Overview

• Indices

• Index Laws

• Extension Students

• Practice Exercises

• 4

### Lesson 2 Negative, Fractional & Combined Index Laws

• Lesson Overview

• Negative and Fractional Indices

• Further Index Laws

• Extension Students

• Practice Exercises

• 5

### Lesson 3 Surds

• Lesson Overview

• Surds

• Surd Rules

• Simplifying Surds

• Extension Students

• Practice Exercises

• 6

### Lesson 4 Surds - Rationalising the denominator

• Lesson Overview

• Rationalising the Denominator

• Extension Students

• Practice Exercises

• 7

### Lesson 5 Quadratic Equations I – Factorisation

• Lesson Overview

• Quadratic Functions - Background Information

• Solving Quadratic Equations by Factorising

• Factorising Monic Trinomials

• Factorising Non-monic Trinomials - PSF Method

• Extension Students

• Practice Exercises

• 8

### Lesson 6 Quadratic Equations II – Completing the Square and the Quadratic Formula

• Lesson Overview

• Completing the Square

• Extension Students

• Practice Exercises

• 9

### Lesson 7 Algebraic Fractions

• Lesson Overview

• Algebraic Fractions

• Operations with Fractions

• Extension Students

• Practice Exercises

• 10

### Lesson 8 Relations and Functions, Types of Relations

• Lesson Overview

• Preamble

• Relations and Functions

• Functions

• Why do we care whether a Relation is also a Function?

• Types of Relations

• Extension Students

• Practice Exercises

• 11

### Lesson 9 Independent/Dependent, Function notation, Graphs

• Lesson Overview

• Dependent and Independent Variables

• Function Notation

• Graphing Functions

• Extension Students

• Practice Exercises

• 12

### Lesson 10 Domain and Range; Odd & Even Functions

• Lesson Overview

• Interval Notation

• Domain and Range

• Odd and Even Functions

• Extension Students

• Practice Exercises

• 13

### Lesson 11 Linear Functions - Direct Variation, Gradient/Intercept Form

• Lesson Overview

• How to approach teaching Linear Functions

• Constant Functions

• Linear Functions

• Standard Forms of a Line

• Direct Variation

• Extension Students

• Practice Exercises

• 14

### Lesson 12 Linear Functions - Point Gradient and Two Point Forms

• Lesson Overview

• Determining the Equation of a Linear Function

• Two Point Formula

• Intercept Formula

• Extension Students

• Practice Exercises

• 15

### Lesson 13 Linear Functions - Parallel and Perpendicular

• Lesson Overview

• Parallel Lines

• Perpendicular Lines

• Extension Students

• Practice Exercises

• 16

### Questions from the HSC

• Advanced Year 11 Functions Part A in the HSC Exams

• 17

### Appendix 1: Factorising Non-monic Trinomials - Alternative Methods

• Alternative Methods for Factorising Non-monic Trinomials

• Magic Method

• Cross Method

• 18

### Appendix 2: Mixed Revision Exercises

• Mixed Revision

• 19

### Conclusion

• Highlights of Functions Part A

• Conclusion to In Depth ADV#1

• 20

### Course Feedback

• Feedback form

## Presented by:

Steve Howard

Steve Howard has inspired and equipped hundreds of Maths teachers with his In-Depth Senior Mathematics courses, providing all the tips, examples and resources to teach the HSC syllabus with confidence. He loves to discover the most efficient techniques for solving mathematical problems, by analysing other experts' solutions or by developing his own approaches when he finds a better way. As a student, Steve did Unit 4 Mathematics, gaining a mark of 198/200, before training as an actuary. After retraining as a teacher, Steve has taught Maths at Cowra High School, NSW, for 28 years. He has also taught gifted and talented students online through Xsel and Aurora College, and developed all student course material for TTA's Year 12 Extension Maths Portal.

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