Course Description

This course provides teachers with a comprehensive guide to the knowledge and techniques required to teach Mathematics Extension 2 11-12 Syllabus (2024). It covers all of the dot points in Introduction to complex numbers.


The course goes into greater detail than the textbooks, so that teachers become more comfortable in their ability to deliver the content. All 130 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:

  • 130 recorded examples
  • A total of 45 quiz questions at the end of each lesson
  • A 217 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 49 page exercise booklet with 130 optional practice questions matching the examples from the course, with fully worked solutions.


The Mathematics Extension 2 11-12 Syllabus (2024) will be covered in five courses. The courses are:

Extension 2 Course 1 - Year 12 Introduction to complex numbers

Extension 2 Course 2 - Year 12 The nature of proof

Extension 2 Course 3 - Year 12 Further work with vectors

Extension 2 Course 4 - Year 12 Further integration

Extension 2 Course 5 - Year 12 Applications of calculus to mechanics


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 2 scopes and sequences

  • 3

    Part 1b How is teaching Extension 2 different to teaching Extension 1?

    • How is teaching Extension 2 different to teaching Extension 1?

    • General hints for student success in Extension 2

  • 4

    Part 2a Introduction to Introduction to complex numbers

    • 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 complex numbers

    • Lesson introduction

    • How complex numbers fit with other number systems

    • Imaginary numbers

    • The complex plane

    • Powers of 𝑖

    • Harder examples

    • Practice exercises

    • Lesson 1 Quiz
  • 7

    Lesson 2 – Cartesian form of a complex number

    • Lesson introduction

    • Forms of a complex number

    • Addition, subtraction and multiplication in Cartesian form

    • Conjugate of a complex number and division in Cartesian form

    • Mixed calculations

    • Equal complex numbers

    • Harder examples

    • Practice exercises

    • Lesson 2 Quiz
  • 8

    Lesson 3 – Modulus and square roots in Cartesian form

    • Lesson introduction

    • Modulus of a complex number in Cartesian form

    • Square roots of a complex number in Cartesian form

    • Harder examples

    • Practice exercises

    • Lesson 3 Quiz
  • 9

    Lesson 4 – Modulus-argument form of a complex number

    • Lesson introduction

    • Modulus, argument and modulus-argument form of a complex number

    • Calculations in modulus-argument form

    • Harder examples

    • Practice exercises

    • Lesson 4 Quiz
  • 10

    Lesson 5 – Conjugate theorems

    • Lesson introduction

    • Conjugate rules

    • Operations with conjugates

    • Conjugate root theorem

    • Harder examples

    • Practice exercises

    • Lesson 5 Quiz
  • 11

    Lesson 6 – Complex numbers as vectors

    • Lesson introduction

    • Complex numbers as vectors

    • Rotation and dilation

    • Midpoint

    • Triangle inequality

    • Harder examples

    • Practice exercises

    • Lesson 6 Quiz
  • 12

    Lesson 7 – Lines, curves and regions

    • Lesson introduction

    • Lines on the complex plane

    • Circles

    • Rays and sectors

    • Miscellaneous examples

    • Arcs and intervals using arguments

    • Harder examples

    • Practice exercises

    • Lesson 7 Quiz
  • 13

    Lesson 8 – de Moivre’s theorem

    • Lesson introduction

    • de Moivre’s theorem

    • Trigonometrical applications of de Moivre’s theorem

    • Harder examples

    • Practice exercises

    • Lesson 8 Quiz
  • 14

    Lesson 9 – 𝑛th roots of complex numbers

    • Lesson introduction

    • Complex numbers to a fractional power

    • Complex roots of unity

    • Complex roots of minus one

    • Complex roots of other complex numbers

    • Harder examples

    • Practice exercises

    • Lesson 9 Quiz
  • 15

    Conclusion

    • Conclusion

Features of TTA Online PD

  • Availabilty

    Online courses are available 24/7. Designed to be done in your own time at your own pace.

  • Money back Guarantee

    If you complete less than 25% of an online course and aren't completely satisfied, let us know, and we will cancel your enrolment and provide a full refund.