Mathematics Extension 1 Year 11: In Depth Part II - Functions (Part B) & Polynomials

Steve Howard
Passionate about Mathematics
A comprehensive guide to the knowledge & techniques needed to teach the remainder of Further Work with Functions & Polynomials from the new Maths Extension 1 Year 11 sy...
Target Audience
Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.
2 reviews

Learning Areas

Teaching Standards

General Description

I created this course to provide teachers with a comprehensive guide to the knowledge and techniques required to teach the new NSW Mathematics Extension I Year 11 syllabus. The course covers every dot point from the new NSW Year 11 Mathematics Extension 1 syllabus, both old and new content. Please note that only Extension 1 content is covered, not Mathematics Advanced.

The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 111 examples have been recorded, so that you can watch an experienced maths teacher talk through the examples and any important points to note.

Part II of the series covers the remainder of ME-F1 Further Work with Functions (F1.1 Graphical Relationships was covered in Part I) plus ME-F2 Polynomials. These two topics can be taught with a few prerequisites from the Advanced course. Teachers of classes that include Extension and Advanced students may choose to start their Extension students with one of these topics.

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 111 recorded examples, with a 143 page course handout. There are also 111 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.

Part I of the series covers ME-A1 Working with Combinatorics and ME-F1 Further Work with Functions (Part A) F1.1: Graphical relationships.

Part III of the series will cover ME-T1 Inverse Trigonometric Functions, ME-T2 Further Trigonometric Identities & ME-C1 Rates of Change.


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

Available Delivery Formats

Format Description

Course Access - This course is available 24/7. Begin the course when it suits you. After completing the course you will still have ongoing access to review content.

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Teaching Standards
2.1.2 Proficient Level – Content and teaching strategies of the teaching area
6.2.2 Proficient Level – Engage in professional learning and improve practice
Are you in NSW? If so, this is relevant for you
Completing this course will contribute 6 hours of NESA Registered PD addressing 2.1.2 & 6.2.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.

This course contributes to 6.0 professional development hours.


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5 minutes

Course Administration
Introduction to the Mathematics Extension 1 In Depth Year 11 Series
Introduction to Part I

Further Work with Functions (Part B)

5 minutes

Introduction to Further Work with Functions

Lesson 1 Quadratic Inequalities

25 minutes

Quadratic Inequalities
Method 1 – Number line and testing points
Method 2 – Parabola and Concavity

Lesson 2 Further Inequalities

35 minutes

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

Lesson 3 Absolute Value Inequalities

8 minutes

Absolute Value and the Number line

Lesson 4 Inverse Relations

25 minutes

Inverse Operations
Inverse Relations
Finding Inverse Relations Algebraically
Finding Inverse Relations Graphically

Lesson 5 Inverse Functions

20 minutes

One-to-one Functions and the Horizontal line test
Restricting the Domain
Inverse Functions as Composite Functions

Lesson 6 Parametric Form - Background and Lines

10 minutes

Cartesian and Parametric Forms
What is the use of Parametric Form
Converting Between Cartesian and Parametric Form
Parametric Form of a Line

Lesson 7 Parametric Form - Quadratics and Circles

15 minutes

Parametric Form of a Parabola
Parametric Form of a Circle


2 minutes

Introduction to Polynomials

Lesson 1 - Division - Solving by Inspection

20 minutes

Polynomial Definitions
Division of Integers and Polynomials
Methods of Division of Integers and Polynomials
Splitting the Numerator
The Grid Method

Lesson 2 - Long Division of Integers and Polynomials

20 minutes

Long Division
Long Division of Integers
Long Division of Polynomials
Synthetic Division

Lesson 3 - Remainder and Factor Theorems

15 minutes

Remainder Theorem
Factor Theorem

Lesson 4 - Sum and Product of Roots I

20 minutes

Relationship Between Roots and Coefficients
Shortcuts for Algebraic Manipulations
Examples with Quadratics

Lesson 5 - Sum and Product of Roots II

20 minutes

Examples with Cubics and Quartics
Sums of Powers of Roots Equal to the Degree or Higher

Lesson 6 - Multiplicity of Roots

20 minutes

Background to Multiplicity of Roots
Determining Multiplicity Using Factorisation
Determining Multiplicity Using Differentiation

Lesson 7 Solving Polynomial Equations by Factorising

30 minutes

Solving Polynomial Equations by Factorising
Useful Results
Basic Factorising
Finding Linear Factors of the Polynomial
Non-integral, Irreducible Quadratic Factors or Multiple Roots
Standard Method of finding Linear Factors

Lesson 8 - Graphing Polynomials

15 minutes

Graphing polynomials given the roots and their multiplicity
Change of sign around Roots
Graphing Polynomials in General Form

Lesson 9 - Beyond the Syllabus

40 minutes

The Grid Method
Synthetic Division
Transforming Polynomials


1 minute

Conclusion to Part II

User Rating


Latest Reviews

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Mathematics Extension 1 Year 11: In Depth Part II - Functions (Part B) & Polynomials - Steve Howard

Quality and relevance both good, covered exactly what it needed to.

Mathematics Extension 1 Year 11: In Depth Part II - Functions (Part B) & Polynomials - Steve Howard

very relevant and will be used in class

About the team

Steve Howard


Steve is a Mathematics Teacher at Cowra High School, a medium sized rural high school in Central West NSW, where he has taught for 25 years. He has also taught gifted and talented students online through xsel and Aurora College. He has a particular love and passion for Mathematics Extension 2, writing his own textbook and study resources for the old syllabus, to be updated for the new syllabus. He also creates study resources for Mathematics and Extension 1. He loves finding more efficient techniques for solving mathematical questions, by trawling through other teachers' solutions or making up his own approaches when there must be a better way. Steve did 4 Unit Mathematics as a student, gaining a mark of 198/200 and training as an actuary. Working in an office in the city wasn’t for him, so he went back to uni to retrain as a teacher then headed to the country, where he lives in an owner built mud house, with chickens, goats and rescued native birds (which you will sometimes hear in his recordings)!!