Course curriculum

  • 1

    1.1 The Language of Proof and Simple Proofs

    • 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
  • 2

    1.2 Proof by Contrapositive

    • Converse and Negation

    • Example 1

    • Example 2

    • Example 3

    • Proof by Contrapositive

    • Example 4

    • Example 5

    • Exercise 1.2

    • Exercise 1.2 Recorded Solutions
  • 3

    1.3 Proof by Contradiction

    • Proof by Contradiction

    • Example 1

    • Example 2

    • Exercise 1.3

    • Exercise 1.3 Recorded Solutions
  • 4

    1.4 Equivalence and Disproofs

    • 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
  • 5

    1.5 Inequality Proofs

    • 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
  • 6

    1.6 Arithmetic Mean - Geometric Mean Inequality

    • AM-GM Inequality

    • Example 1

    • Example 2

    • Example 3

    • Example 4

    • Example 5

    • Exercise 1.6

    • Exercise 1.6 Recorded Solutions

Bonus Textbook

Download HSC Extension 2 Mathematics Textbook FREE

Click to Download

Instructor

Steven Howard

Steve is a Mathematics Teacher at Cowra High School, a medium sized rural high school in Central West NSW, where he has taught for over 25 years. He has also taught gifted and talented students online through xsel and Aurora College. He has a particular love and passion for Mathematics Extension 2, writing his own textbook and study resources for the new syllabus, which you can access from any of his courses. He loves finding more efficient techniques for solving mathematical questions, by trawling through other teachers' solutions or making up his own approaches when there must be a better way. Steve did 4 Unit Mathematics as a student, gaining a mark of 198/200 and training as an actuary. Working in an office in the city wasn't for him, so he went back to uni to retrain as a maths teacher then headed to the country, where he lives in an owner built mud house, with chickens, goats and rescued native birds (which you will sometimes hear in his recordings)!!