Course Description

This course provides teachers with a comprehensive guide to the knowledge and techniques required to teach Mathematics Extension 1 11-12 Syllabus (2024). It covers all of the dot points in Proof by mathematical induction and Inverse trigonometric functions.


The course goes into greater detail than the textbooks, so that teachers become more comfortable in their ability to deliver the content. All 51 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.


The course includes:
  • 51 recorded examples
  • A total of 25 quiz questions at the end of each lesson
  • A 182 page course handout in two formats – one with blank space for you to complete the examples and a second with completed solutions to the examples.
  • A 23 page exercise booklet with 51 optional practice questions matching the examples from the course, with fully worked solutions.


The Mathematics Extension 1 11-12 Syllabus (2024) will be covered in seven courses. The courses are:

Extension 1 Course 1 - Year 11 

Permutations and combinations

The binomial theorem

Extension 1 Course 2 - Year 11

Polynomials

Further work with functions

Extension 1 Course 3 - Year 11

Further trigonometry

Extension 1 Course 4 - Year 12

Proof by mathematical induction

Inverse trigonometric functions

Extension 1 Course 5 - Year 12

Introduction to vectors

Extension 1 Course 6 - Year 12

Further calculus skills

Further applications of calculus

Extension 1 Course 7 - Year 12

The binomial distribution and sampling
Distribution of the mean


Audience

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

Course curriculum

  • 1

    Course information

    • Course information and introduction
  • 2

    Part 1a Preparing to teach the 2024 Mathematics syllabuses

    • 2024 Syllabuses

    • Extension 1 scopes and sequences
  • 3

    Part 1b How is teaching Advanced different to teaching Standard?

    • How is teaching Extension 1 different to teaching Advanced?

    • General hints for student success in Extension 1
  • 4

    Part 2a Introduction to Proof by mathematical induction & Inverse trigonometric functions

    • Summary of the content in this course

    • What has changed from the 2017 syllabus?

  • 5

    Part 2b Lessons

    • List of lessons

  • 6

    Lesson 1 – A background to proof

    • Lesson introduction

    • Introduction to proof

    • Direct proofs

    • Proof by cases

    • Practice exercises

    • Lesson 1 Quiz
  • 7

    Lesson 2 – Mathematical induction theory and proofs involving sums

    • Lesson introduction

    • The changes to mathematical induction in the 2024 syllabus

    • Analogies for mathematical induction

    • The principle of mathematical induction

    • Setting out an induction proof

    • Mathematical induction - proving results with sums

    • Step value of 2

    • Practice exercises

    • Lesson 2 Quiz
  • 8

    Lesson 3 – Proofs involving divisibility and false proofs

    • Lesson introduction

    • Mathematical induction - proving results involving divisibility

    • Initial value and/or the step value is not 1

    • Harder applications

    • When can we use mathematical induction?

    • False proof by mathematical induction

    • Practice exercises

    • Lesson 3 Quiz
  • 9

    Lesson 4 – Inverse trigonometric functions

    • Lesson introduction

    • Angles, arcs and intervals around the unit circle

    • Finding inverse trig functions using the trig functions

    • Using graphing applications to understand inverse trig functions

    • Graphing inverse trigonometric functions

    • Properties of inverse trigonometric functions

    • Practice exercises

    • Lesson 4 Quiz
  • 10

    Lesson 5 – Composite trigonometric functions

    • Lesson introduction

    • Trigonometric function of an inverse trigonometric function

    • Inverse trigonometric function of a trigonometric function

    • Practice exercises

    • Lesson 5 Quiz
  • 11

    Conclusion

    • Conclusion
  • 12

    Course Feedback

    • Course Feedback

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