### Course Description

This course covers every dot point of ME-F2 Polynomials and the remainder of  ME-F1 Further Work with Functions from the new NSW Year 11 Mathematics Extension 1 syllabus (F1.1 Graphical Relationships was covered in course EXT1#1).

The course goes into greater detail than the textbooks, so that teachers become comfortable in their ability to deliver the content. All 127 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.

The course includes:

• 127 recorded examples

• 139 page course handout

• 127 optional practice questions matching the examples from the course, with fully worked solutions

A suggested scope and sequence for Year 11 Advanced and Extension 1 for combined classes is provided, plus a lesson by lesson breakdown of the Advanced, Extension 1 and Extension 2 courses for Year 11 and 12 to help you create your own scope and sequences.

The remainder of the Mathematics Extension 1 syllabus, is covered in four other courses:

EXT1#1 of the series covers  ME-A1 Working with Combinatorics and ME-F1 Further Work with Functions (F1.1: Graphical Relationships)

Ext1#3 covers ME-T1 Inverse Trigonometric Functions, ME-T2 Further Trigonometric Identities & ME-C1 Rates of Change.

Ext1#4 (Year 12) covers ME-P1 Proof by Mathematical Induction and ME-V1 Introduction to Vectors.

Ext1#5 (Year 12) covers ME-T3 Trigonometric Equations, ME-C2 Further Calculus Skills, ME-C3 Applications of Calculus and ME-S1 The Binomial Distribution.

### Audience

Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.

### Teaching Standards

2.1.2 Proficient Level - Know the content and how to teach it - Content and teaching strategies of the teaching area:  Apply knowledge of the content and teaching strategies of the teaching area to develop engaging teaching activities

### This Course:

Further Work with Functions Part B & Polynomials - EXT1#2

Order Course

### Complete Subject:

Extension 1 Mathematics (5 courses)

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

Completing Mathematics Extension 1 Year 11: Further Work with Functions Part B & Polynomials - EXT1#2 will contribute 10 hours of NSW Education Standards Authority (NESA) Accredited PD in the priority area of 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 (5 mins)

• Introduction to the Mathematics Extension 1 In Depth Year 11 Series

• Introduction to Part II

• 2

### Further Work with Functions (Part B) (5 mins)

• Further Work with Functions (Part B)

• Relevant Part of the Syllabus: Further Work with Functions

• 3

### FWwF(B) 1: Quadratic Inequalities (25 mins)

• Lesson 1 Overview

• Method 1 - Number Line and Testing Points

• Method 2 - Parabola and Concavity

• FWwF(B) Lesson 1 Quiz

• 4

### FWwF(B) 2: Further Inequalities (35 mins)

• Lesson 2 Overview

• Understanding the Inequality

• Why Can’t we Multiply the Denominator to the Other Side?

• Graphical Method

• Critical Values Method

• Multiplying by the Square of the Denominator

• Case Method

• Mixed Examples

• FWwF(B) Lesson 2 Quiz

• 5

### FWwF(B) 3: Absolute Value Inequalities (8 mins)

• Lesson 3 Overview

• Absolute Value and the Number Line

• FWwF(B) Lesson 3 Quiz

• 6

### FWwF(B) 4: Inverse Relations (25 mins)

• Lesson 4 Overview

• Inverse Operations

• Inverse Relations

• Finding Inverse Relations Algebraically

• Finding Inverse Relations Geometrically

• FWwF(B) Lesson 4 Quiz

• 7

### FWwF(B) 5: Inverse Functions (20 mins)

• Lesson 5 Overview

• One-to-One Functions and the Horizontal Line Test

• Restricting the Domain

• Inverse Functions as Composite Functions

• FWwf(B) Lesson 5 Quiz

• 8

### FWwF(B) 6: Parametric Form - Background and Lines (10 mins)

• Lesson 6 Overview

• Cartesian and Parametric Forms

• What is the Use of Parametric Form?

• Converting Between Cartesian and Parametric Forms

• Parametric Form of a Line

• FWwF(B) Lesson 6 Quiz

• 9

### FWwF(B) 7: Parametric Form - Quadratics and Circles (15 mins)

• Lesson 7 Overview

• Parametric Form of a Parabola

• Parametric Form of a Circle

• FWwF(B) Lesson 7 Quiz

• 10

### Polynomials (2 mins)

• Introduction to Polynomials

• Relevant Part of the Syllabus: Polynomials

• 11

### Polynomials 1: Division - Solving by Inspection (20 mins)

• Lesson 1 Overview

• Polynomial Definitions

• Division of Integers and Polynomials

• Methods of Division of Integers and Polynomials

• Splitting the Numerator

• The Grid Method

• Polynomials Lesson 1 Quiz

• 12

### Polynomials 2: Long Division (20 mins)

• Lesson 2 Overview

• Long Division

• Long Division of Integers

• Long Division of Polynomials

• Synthetic Division

• Polynomials Lesson 2 Quiz

• 13

### Polynomials 3: Remainder and Factor Theorems (15 mins)

• Lesson 3 Overview

• Remainder Theorem

• Factor Theorem

• Polynomials Lesson 3 Quiz

• 14

### Polynomials 4: Sum and Product of Roots I (20 mins)

• Lesson 4 Overview

• Relationship Between Roots and Coefficients

• Shortcuts for Algebraic Manipulations

• Polynomials Lesson 4 Quiz

• 15

### Polynomials 5: Sum and Product of Roots II (20 mins)

• Lesson 5 Overview

• Examples with Cubics and Quartics

• Sums of Powers of Roots Equal to the Degree or Higher

• Polynomials Lesson 5 Quiz

• 16

### Polynomials 6: Multiplicity of Roots (20 mins)

• Lesson 6 Overview

• Background to Multiplicity of Roots

• Determining Multiplicity Using Factorisation

• Determining Multiplicity Using Differentiation

• Polynomials Lesson 6 Quiz

• 17

### Polynomials 7: Solving Polynomial Equations by Factorising (30 mins)

• Lesson 7 Overview

• Solving Polynomial Equations by Factorising

• Useful Results

• Basic Factorising

• Finding Linear Factors of the Polynomial

• Non-integral Roots, Irreducible Quadratic Factors or Multiple Roots

• Standard Method of Finding Linear Factors

• Polynomials Lesson 7 Quiz

• 18

### Polynomials 8: Graphing Polynomials (15 mins)

• Lesson 8 Overview

• Graphing Polynomials

• Change of Sign Around Roots

• Graphing Polynomials in General Form

• Polynomials Lesson 8 Quiz

• 19

### Polynomials 9: Beyond the Syllabus (Optional) (40 mins)

• Lesson 9 Overview

• The Grid Method

• Synthetic Division

• Transforming Polynomials

• 20

### Conclusion to Part II (1 min)

• Highlights of Further Work with Functions Part B and Polynomials

• Conclusion to Part II

• 21

### Course Feedback

• Course Feedback

## Presenter

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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