Course Description

This course provides teachers with a comprehensive guide to the knowledge and techniques required to teach the new NSW Mathematics Extension I syllabus. It covers every dot point of ME-P1 Proof by Mathematical Induction and ME-V1 Introduction to Vectors. These two topics 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.

The course goes into greater detail than the textbooks, so that teachers become 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. 

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

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#2  of the series covers the remainder of ME-F1 Further Work with Functions plus ME-F2 Polynomials.

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

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


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

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

Completing Mathematics Extension 1 Year 12: Proof And Vectors - EXT1#4 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 Descriptor 2.1.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher 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


Steve Howard

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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