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 syllabus. The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 101 examples have been recorded, so that you can watch an experienced maths teacher talk through the examples and any important points to note.


Part I covers Proof and Vectors (ME-P1 and ME-V1), two topics that are paired with topics in Extension 2 and so need to be taught early in the Extension 1 course if students are also taking Extension 2.


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 101 recorded examples, with a 226 page course handout including 101 optional practice questions matching the examples from the course, with fully worked solutions. A suggested scope and sequence for Year 12 Advanced, Extension 1 and Extension 2 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.



Mathematics teachers who are preparing to teach the new Extension 1 syllabus. This course is suitable for teachers with any level of previous experience.


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 12: In Depth Part I – Proof and Vectors” before 4th February 2022 under NESA’s interim arrangements will contribute 10 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


    • Course Administration

    • Introduction to the Mathematics Extension 1 In Depth Year 12 Series

    • Introduction to Part I

  • 2


    • Introduction to Proof

  • 3

    Proof 1: A Background to Proof

    • Lesson 1 Overview

    • Proof - The Art of Clear and Logical Argument

    • Writing a Good Proof

    • The different types of proof

    • Lesson 1 Quiz

  • 4

    Proof 2: Mathematical Induction I - Theory & Proofs involving series

    • Lesson 2 Overview

    • The changes to Induction in Extension 1 and Extension 2

    • An Introduction to Mathematical Induction

    • Analogies

    • Looking at the Two Steps in Depth

    • Setting out a Mathematical Induction Proof

    • Proving results with Sums

    • Lesson 2 Quiz

  • 5

    Proof 3: Mathematical Induction II - Proofs involving Divisibility, False Proofs & Inappropriate Situations

    • Lesson 3 Overview

    • Simple divisibility proofs by induction

    • Cases where proof by induction is not appropriate

    • False proof by induction

    • Lesson 3 Quiz

  • 6

    Proof 4: Appendix - Setting out a Mathematical Induction Proof (Optional)

    • Lesson 4 Overview

    • Setting Out an Induction Proof

  • 7


    • Introduction to Vectors

  • 8

    Vectors 1: Scalars and Vectors - Geometric Representation

    • Lesson 1 Overview

    • Definition and Uses

    • Notation and Geometric Representation

    • Special Vectors

    • Scalar Multiplication & Parallel Vectors

    • Perpendicular Vectors

    • Addition and Subtraction of Vectors

    • Vectors in Terms of Other Vectors

    • Splitting Vectors

    • Lesson 1 Quiz

  • 9

    Vectors 2: Vectors and the Number Plane

    • Lesson 2 Overview

    • Vectors on the Cartesian Plane

    • Unit Vectors

    • Algebraic Representation of a Vector

    • Addition and Subtraction of Vectors (algebraically)

    • Scalar Multiplication

    • Collinear Points

    • Splitting Vectors (algebraically)

    • Magnitude of Vectors

    • Direction of Vectors

    • Special Vectors

    • Lesson 2 Quiz

  • 10

    Vectors 3: Scalar (Dot) Product of Vectors and its applications

    • Lesson 3 Overview

    • Unit Vectors

    • Scalar (Dot) Product of Vectors

    • Angle Between Two Vectors

    • Projection of One Vector onto Another

    • Lesson 3 Quiz

  • 11

    Vectors 4: Problem Solving and Geometric Proofs

    • Lesson 4 Overview

    • Problems involving displacement, force and velocity

    • Geometric Proofs

    • Lesson 4 Quiz

  • 12

    Vectors 5: Projectile Motion - Definitions, Equations of Motion & Horizontal and Vertical Components of Velocity

    • Lesson 5 Overview

    • Projectile Motion

    • Projectile Motion and Vectors

    • Equations of Horizontal Motion

    • Equations of Vertical Motion

    • Use of Vector Notation

    • Lesson 5 Quiz

  • 13

    Vectors 6: Projectile Motion - Harder Examples

    • Lesson 6 Overview

    • HSC Standard Questions & The Role of Formula

    • Time of flight, Range, Maximum Range and Greatest Height

    • Cartesian Equation of Motion (Moved to Extension 2)

    • Lesson 6 Quiz

  • 14


    • Highlights of Proof and Vectors

    • Conclusion to Part I

  • 15

    Course Feedback

    • Course Feedback

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