Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors

Steve Howard
Passionate about Mathematics
A comprehensive guide to the knowledge and techniques needed to teach Proof and Vectors from the new Mathematics Extension 2 Year 12 syllabus.
Target 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.
32 reviews
164

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


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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 Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors before 31 July 2021 under NESA’s interim arrangements will contribute 15 hours and 0 minutes 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.


This course contributes to 15.0 professional development hours.

Occurrences

  Start Date Location Availability Price    
Enrol Now Now Online Places available $269 + GST Enrol Now

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
08/10/2020

Very good content, some of it quite hard.

Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
08/10/2020

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
08/10/2020

Great content

Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
08/10/2020

Excellent course

Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
08/10/2020

Awesome

Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
08/10/2020

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
08/10/2020

excellent and very relevant

Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
08/10/2020

Course was very worthwhile

Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
08/10/2020

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
08/10/2020

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
08/10/2020
  • 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
27/04/2020

Outstanding!

Mathematics Extension 2 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
27/04/2020

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
18/04/2020

Excellent

Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
18/04/2020

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
18/04/2020

Excellent and thorough course.

Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
18/04/2020

Quality well explained course

Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
18/04/2020

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
18/04/2020

Very informative and thank you Anthony Condous

Mathematics Extension 1 Year 12: In Depth Part I – Proof and Vectors - Steve Howard
18/04/2020

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)!!