Course curriculum

  • 1

    Changes to this content in the 2024 syllabus

    • The nature of proof intro
  • 2

    1.1 The Language of Proof and Simple Proofs

    • 2024 syllabus changes for this lesson

    • Implication, Quantifiers and Simple Proofs Involving Numbers

    • Example 1

    • Example 2

    • Example 3

    • Example 4

    • Example 5

    • Exercise 1.1

    • Exercise 1.1 Recorded Solutions
  • 3

    1.2 Proof by Contrapositive

    • 2024 syllabus changes for this lesson

    • Converse and Negation

    • Example 1

    • Example 2

    • Example 3

    • Proof by Contrapositive

    • Example 4

    • Example 5

    • Exercise 1.2

    • Exercise 1.2 Recorded Solutions
  • 4

    1.3 Proof by Contradiction

    • 2024 syllabus changes for this lesson

    • Proof by Contradiction

    • Example 1

    • Example 2

    • Exercise 1.3

    • Exercise 1.3 Recorded Solutions
  • 5

    1.4 Equivalence and Disproofs

    • 2024 syllabus changes for this lesson

    • Equivalence Statements

    • Example 1

    • Disproof, Examples and Counterexamples

    • Example 2

    • Example 3

    • Example 4

    • Example 5

    • Example 6

    • Exercise 1.4

    • Exercise 1.4 Recorded Solutions
  • 6

    1.5 Inequality Proofs

    • 2024 syllabus changes for this lesson

    • Setting Out the Proof and Properties of Positive Numbers

    • Example 1

    • Example 2

    • Triangle Inequailty

    • Example 3

    • Example 4

    • Example 5

    • Exercise 1.5

    • Exercise 1.5 Recorded Solutions
  • 7

    1.6 Arithmetic Mean - Geometric Mean Inequality

    • 2024 syllabus changes for this lesson

    • AM-GM Inequality

    • Example 1

    • Example 2

    • Example 3

    • Example 4

    • Example 5

    • Exercise 1.6

    • Exercise 1.6 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.