General Description

The course covers every dot point from the new NSW Year 11 Mathematics Extension 1 syllabus, both old & new content. (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 topics can be taught with a few prerequisites from the Advanced course. Teachers of classes that include Extension & Advanced students may choose to start their Extension students with one of these topics.

New & existing content is explored in detail, including interesting & 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 & sequence for Year 11 Advanced & 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.

 

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,

6.2.2 Proficient Level - Engage in Professional Learning - Engage in professional learning and improve practice:   Participate in learning to update knowledge and practice targeted to professional needs and school and/or system priorities

 

Are you in NSW? If so, this is relevant for you

Completing “Mathematics Extension 1 Year 11: In Depth Part II - Functions (Part B) & Polynomials” before 4th February 2022 under NESA’s interim arrangements will contribute 6 hours of NSW Education Standards Authority (NESA) Accredited PD in the priority area of Delivery and assessment of NSW curriculum addressing standard descriptors  2.1.2, 6.2.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.

 

Course curriculum

  • 1

    Introduction (5 mins)

    • Course Administration

    • 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

    • Quadratic Inequalities

    • 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

    • Examples with Quadratics

    • 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)

    • Conclusion to Part II

  • 21

    Course Feedback

    • Course Feedback

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