Course Description

This course provides teachers with a comprehensive guide to the knowledge and techniques required to teach Mathematics Advanced 11-12 Syllabus (2024). It covers all of the dot points in the two focus areas Polynomials & Further work with functions.

The course goes into greater detail than the textbooks, so that teachers become more comfortable in their ability to deliver the content. All 125 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:
  • 125 recorded examples
  • A total of 65 quiz questions at the end of each lesson
  • A 240 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 71 page exercise booklet with 125 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 1a Preparing to teach the 2024 Mathematics syllabuses

    • How is teaching Extension 1 different to teaching Advanced?

    • General hints for student success in Extension 1
  • 4

    Part 2a Introduction to Polynomials & Further work with 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 – Polynomials and sketching polynomials

    • Lesson introduction

    • Polynomial definitions and terminology

    • Sketching polynomials

    • Practice exercises

    • Lesson 1 Quiz
  • 7

    Lesson 2 – Division of polynomials

    • Lesson introduction

    • Division of integers by inspection

    • Division of polynomials by inspection

    • Long division of integers

    • Long division of polynomials

    • Practice exercises

    • Lesson 2 Quiz
  • 8

    Lesson 3 – Remainder and factor theorems

    • Lesson introduction

    • Remainder and factor theorems

    • Factorising polynomials

    • Harder applications of the remainder and factor theorems

    • Practice exercises

    • Lesson 3 Quiz
  • 9

    Lesson 4 – Sum and product of zeroes

    • Lesson introduction

    • Relationships the between the zeroes and coefficients of quadratics

    • Relationships the between the zeroes and coefficients of cubics and quartics

    • Practice exercises

    • Lesson 4 Quiz
  • 10

    Lesson 5 – Graphing the reciprocal of a function

    • Lesson introduction

    • Introduction to graphical relationships

    • The graph of a reciprocal of a function

    • Sketching the curves of the reciprocal trig functions

    • Practice exercises

    • Lesson 5 Quiz
  • 11

    Lesson 6 – Graphing the absolute value of a function

    • Lesson introduction

    • The graph of the absolute value of a function

    • The graph of the function of an absolute value

    • Other variations

    • Practice exercises

    • Lesson 6 Quiz
  • 12

    Lesson 7 – Graphing sums and differences of functions

    • Lesson introduction

    • The graph of the sum of two functions

    • The graph of the difference of two functions

    • Find the domain and range of the sum and difference algebraically

    • Practice exercises

    • Lesson 7 Quiz
  • 13

    Lesson 8 – Inverse relations

    • Lesson introduction

    • Inverse operations

    • Inverse relations

    • Practice exercises

    • Lesson 8 Quiz
  • 14

    Lesson 9 – Inverse functions

    • Lesson introduction

    • One-to-one functions and the horizontal line test

    • Restricting the Domain

    • Inverse functions as composite functions

    • Practice exercises

    • Lesson 9 Quiz
  • 15

    Lesson 10 – Parametric form of a line

    • Lesson introduction

    • Cartesian and parametric forms

    • Converting between Cartesian and parametric forms

    • Parametric form of a line

    • Practice exercises

    • Lesson 10 Quiz
  • 16

    Lesson 11 – Parametric form of parabolas and circles

    • Lesson introduction

    • Parametric form of a parabola

    • Parametric form of a circle

    • Practice exercises

    • Lesson 11 Quiz
  • 17

    Lesson 12 – Cubic and absolute value inequalities

    • Lesson introduction

    • Cubic inequalities

    • Absolute value inequalities

    • Practice exercises

    • Lesson 12 Quiz
  • 18

    Lesson 13 - Inequalities with the unknown in the denominator

    • Lesson introduction

    • Understanding inequalities with the unknown in the denominator

    • Practice exercises

    • Lesson 13 Quiz
  • 19

    Conclusion

    • Conclusion
  • 20

    Course Feedback

    • Course Feedback

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