Course curriculum

  • 1

    Changes to this content in the 2024 syllabus

    • Induction intro
  • 2

    3.0A Introduction to Mathematical Induction (Ext 1)

    • Principle of Mathematical Induction

    • Example 1

    • Analogies

    • Example 2

    • Example 3

    • Exercise 3.0A

    • Exercise 3.0A Recorded Solutions
  • 3

    3.0B Other Mathematical Induction (Ext 1)

    • Divisibility Proofs

    • Example 1

    • A Note on Ext 1 Divisibility & When Can We Use Induction?

    • Example 2

    • Can We Prove a False Result?

    • Example 3

    • Example 4

    • Exercise 3.0B

    • Exercise 3.0B Recorded Solutions
  • 4

    3.1 Further Algebraic Induction Proofs

    • 2024 syllabus changes for this lesson

    • Initial Value and Step Not Equal to 1

    • Example 1

    • Sigma Notation

    • Example 2

    • Divisibility Proofs in Extension 2

    • Example 3

    • Inequality Proofs by Induction

    • Example 4

    • Exercise 3.1

    • Exercise 3.1 Recorded Solutions
  • 5

    3.2 Other Induction Proofs

    • 2024 syllabus changes for this lesson

    • 3.2 ex1

    • Lesson 3.2a

    • Lesson 3.2b

    • 3.2 ex4

    • 3.2 q4

    • 3.2 q5

    • 3.2 q6

    • 3.2 q3

    • 3.2 ex3

    • 3.2 ex2

    • 3.2 q9

    • 3.2 q7

    • 3.2 q8

    • 3.2 q12

    • 3.2 q11

    • 3.2 q10

    • Choosing a Method in Unusual Questions

    • Example 1

    • Example 2

    • Example 3

    • First Order Recursive Formula

    • Example 4

    • Exercise 3.2

    • Exercise 3.2 Recorded Solutions

Bonus Textbook

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Instructor

Steve Howard

Steve Howard has inspired and equipped hundreds of Maths teachers with his In-Depth Senior Mathematics courses, providing all the tips, examples and resources to teach the HSC syllabus with confidence. He loves to discover the most efficient techniques for solving mathematical problems, by analysing other experts' solutions or by developing his own approaches when he finds a better way. As a student, Steve did Unit 4 Mathematics, gaining a mark of 198/200, before training as an actuary. After retraining as a teacher, Steve has taught Maths at Cowra High School, NSW, for 28 years. He has also taught gifted and talented students online through Xsel and Aurora College, and developed all student course material for TTA's Year 12 Extension Maths Portal.