#### 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 2 syllabus. The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 179 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 (MEX-P1, MEX-P2, V1.1, V1.2 and V1.3), two topics that are paired with topics in Extension 1. They are best taught early in the course, once the equivalent topics in Extension 1 have been taught.

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 179 recorded examples, with a 306 page course handout including 179 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.

#### Audience

Mathematics teachers who are preparing to teach the new Extension 2 syllabus. This course is suitable for teachers with any level of previous experience.

#### Available Delivery Formats

#### Format Description

**24/7 course access****IMPORTANT INFORMATION:**

- If you have a TTA subscription or membership please ignore the pricing when enrolling. Rest assured if your school has a subscription you will not be charged and for Memberships, your invoice will be adjusted accordingly to reflect your discount.

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- For more details on our Unlimited Online Subscription packages Click here .

- Money-Back Guarantee – If you complete less than 25% of an online course and aren’t impressed, simply visit tta.edu/go/refund to let us know what happened, and we will cancel your enrolment and provide a full refund.

**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**

**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.

This course contributes to 15.0 professional development hours.

#### Occurrences

#### Sessions

##### Introduction

5 minutes

Course Administration

Introduction to the Mathematics Extension 2 In Depth Year 12 Series

Introduction to Part I

##### Proof

5 minutes

Introduction to Proof

##### Proof 1 - Language of Proof & Simple Proofs

1 hour

Lesson 1 Overview

How should we use the Language of Proof?

Terms and Symbols

Implication

Quantifiers

Other Terminology

Symbols and Set Notation

Simple Proofs Involving Numbers

##### Proof 2 - Proof by Contradiction & Contrapositive

1 hour

Lesson 2 Overview

Converse

Negation

Contrapositive

Proof by Contrapositive

Proof by Contradiction

##### Proof 3 - Equivalence & Disproofs

1 hour

Lesson 3 Overview

Equivalent Statements (If and Only If)

Proving Equivalence

Disproof, Examples and Counterexamples

##### Proof 4 - Inequality Proofs

1 hour and 30 minutes

Lesson 4 Overview

Inequalities

Setting Out the Proof

The Basics of Inequalities

Equality

Properties of Positive Numbers

Geometrical Analogies

Miscellaneous Tips

Triangle Inequality

The Square of a Real Number is Non-negative

##### Proof 5 - Arithmetic Mean - Geometric Mean Inequality

1 hour and 30 minutes

Lesson 5 Overview

The Four Means

Arithmetic Mean – Geometric Mean Inequality

Proving the AM-GM Inequality for 3 or 4 Variables

##### Proof 6 - Induction I - Initial Value other than 1; Step other than 1; Sigma Notation; Inequalities; Harder Divisibility

1 hour and 30 minutes

Lesson 6 Overview

Mathematical Induction in Extension 2

The Initial Value and Step Not 1

Sigma Notation

Divisibility Proofs in Extension 2

Inequality Proof by Induction

##### Proof 7 - Induction II - Calculus; Probability; Geometry; First Order Recursive

1 hour and 30 minutes

Lesson 7 Overview

Choosing a Method in Unusual Questions

Calculus

Probability

Geometry

Classic Induction Questions

First Order Recursive Formula

##### Proof 8 - Beyond the Syllabus (Optional)

1 hour

Lesson 8 Overview

Fibonacci Sequence and Induction

Finding the Conjecture

##### Vectors

5 minutes

Introduction to Vectors

##### Vectors 1 - Three Dimensional Vectors

1 hour and 30 minutes

Lesson 1 Overview

Typing Vectors in Microsoft Office (Word, PowerPoint etc)

Vectors in Three Dimensions

Three Dimensional Coordinate System

Standard Unit Vectors

Addition, Subtraction and Scalar Multiplication

Magnitude of Vectors

Unit Vectors

Scalar (Dot) Product of Vectors

Angle Between Two Vectors

##### Vectors 2 - Geometric Proofs

1 hour and 30 minutes

Lesson 2 Overview

Geometric Proofs

##### Vectors 3 - Straight Lines

1 hour and 30 minutes

Lesson 3 Overview

Vector Equation of a Line in Two Dimensions

Lines in Three Dimensions

Sketching a Vector Equation

Finding the Vector Equation of a Line Through Two Points

Parallel and Perpendicular Lines

Does a Point Lie on a Line?

Point of Intersection of Two Lines

Converting Between Cartesian and Vector Equations

##### Vectors 4 - Spheres & Curves

1 hour and 30 minutes

Lesson 4 Overview

Spheres

Curves in Two Dimensions

Transformations

Restrictions

Spirals

Miscellaneous Curves

Curves in Three Dimensions

Helixes

Unusual Curves

##### Vectors 5 - Beyond the Syllabus (Optional)

30 minutes

Lesson 5 Overview

Curves Involving Sine and Cosine

Roulettes

Other Curves

##### Conclusion

1 minute

Conclusion to Part I

#### User Rating

4.9#### Latest Reviews

Please note the feedback listed here is unfiltered, and includes all comments and ratings collected.

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Very good content, some of it quite hard.

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Excellent course with great resources and covered all the syllabus dot points in depth

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Great content

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Excellent course

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Awesome

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Great explanations, however would have been better if there were more difficult examples of each e.g the style of questions found in the enrichment sections in the cambridge textbooks

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

excellent and very relevant

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Course was very worthwhile

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

As always, the quality works in sync with the simplicity of delivery so that the relevance of the course content is not hidden behind bells and whistles :)

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Very clear instructions with carefully graded examples. Some great examples used, the notes are also very useful.

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

- All content related to the to the HSC Ext 2 Mathematics syllabus involving the topics of Proof and Vectors are very well explained. Gurdeep Mankoo

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Outstanding!

##### Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

This course was outstanding and I have already recommended it to others.... Steve’s explanations and sequencing of content were easy to follow and well thought out. The resources provided will be very useful when teaching and assisting students. This was one of the best online PD sessions I have ever done. Thanks Steve.

##### Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Excellent

##### Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

The course follows the syllabus and the quality of notes and examples are great.

##### Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Excellent and thorough course.

##### Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Quality well explained course

##### Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

This has been a really great source of information. Especially with the vectors

##### Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

Very informative and thank you Anthony Condous

##### Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard

An excellent, detailed course. This detailed, well presented course helped me prepare to teach the new Extension 1 course.

#### About the team

#### Steve Howard

##### Creator

Steve is a Mathematics Teacher at Cowra High School, a medium sized rural high school in Central West NSW, where he has taught for over 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 new syllabus, which you can access from any of his courses. 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 maths 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)!!