Course curriculum

  • 1

    Changes to this content in the 2024 syllabus

    • Integration intro
  • 2

    4.1 Standard Integrals & Completing the Square

    • 2024 syllabus changes for this lesson

    • Integration in Extension 2

    • Completing the Square

    • Example 1

    • Example 1 Video

    • Example 2

    • Example 2 Video

    • Example 3

    • Example 3 Video

    • Example 4

    • Example 4 Video

    • Exercise 4.1

    • Exercise 4.1 Recorded Solutions
  • 3

    4.2 The Reverse Chain Rule and U Substitutions

    • 2024 syllabus changes for this lesson

    • The Reverse Chain Rule and U Substitutions

    • Example 1

    • Example 1 Video

    • Example 2

    • Example 2 Video

    • Example 3

    • Example 3 Video

    • Example 4

    • Example 4 Video

    • Example 5

    • Example 5 Video

    • Exercise 4.2

    • Exercise 4.2 Recorded Solutions
  • 4

    4.3 Splitting the Numerator

    • Splitting the Numerator

    • Example 1

    • Example 1 Video

    • Example 2

    • Example 2 Video

    • Example 3

    • Example 3 Video

    • Splitting the Numerator (Part II)

    • Example 4

    • Example 4 Video

    • Partial Fractions by Inspection

    • Example 5

    • Example 5 Video

    • Example 6

    • Example 6 Video

    • Exercise 4.3

    • Exercise 4.3 Recorded Solutions

    • 2024 syllabus changes for this lesson
  • 5

    4.4 Partial Fractions

    • 2024 syllabus changes for this lesson

    • Partial Fractions (Equating Coefficients)

    • Example 1

    • Example 1 Video

    • Partial Fractions (Elimination by Substitution)

    • Example 2

    • Example 2 Video

    • Notes on Substitution Method

    • Partial Fractions (Cover Up Method)

    • Example 3

    • Example 3 Video

    • Partial Fractions (Cover Up Method II)

    • Example 4

    • Example 4 Video

    • Partial Fractions (Cover Up Method III)

    • Example 5

    • Example 5 Video

    • Exercise 4.4

    • Exercise 4.4 Recorded Solutions
  • 6

    4.5 Other Algebraic Substitutions

    • 2024 syllabus changes for this lesson

    • Simplifying Integrands

    • Example 1

    • Example 1 Video

    • Example 2

    • Example 2 Video

    • Example 3

    • Example 3 Video

    • Simplifying Integrands (Part II)

    • Example 4

    • Example 4 Video

    • Exercise 4.5

    • Exercise 4.5 Recorded Solutions
  • 7

    4.6 Trigonometric Functions I

    • 2024 syllabus changes for this lesson

    • Powers of Sine and Cosine

    • Example 1

    • Example 1 Video

    • Powers of Tangent and Secant

    • Example 2

    • Example 2 Video

    • Example 3

    • Example 3 Video

    • Example 4

    • Example 4 Video

    • Powers of Cotangent and Cosecant

    • Product to Sum Identities

    • Example 5

    • Example 5 Video

    • Exercise 4.6

    • Exercise 4.6 Recorded Solutions
  • 8

    4.7 Trigonometric Functions II

    • 2024 syllabus changes for this lesson

    • Integrating with t-formulae

    • Example 1

    • Example 1 Video

    • Trig Substitutions

    • Example 2

    • Example 2 Video

    • Exercise 4.7

    • Exercise 4.7 Recorded Solutions
  • 9

    4.8 Integration by Parts

    • 2024 syllabus changes for this lesson

    • Integration by Parts (inc DETAIL)

    • Example 1

    • Example 1 Video

    • Example 2

    • Example 2 Video

    • Integration by Parts (Reverse Chain Rule)

    • Example 3

    • Example 3 Video

    • Exercise 4.8

    • Exercise 4.8 Recorded Solutions
  • 10

    4.9 Recurrence Relationships

    • 2024 syllabus changes for this lesson

    • Recurrence Relationships

    • Example 1

    • Example 1 Video

    • Example 2

    • Example 2 Video

    • Example 3

    • Example 3 Video

    • Exercise 4.9

    • Exercise 4.9 Recorded Solutions
  • 11

    4.10 Definite Integrals

    • Definite Integrals

    • Example 1

    • Example 1 Video

    • Example 2

    • Example 2 Video

    • Example 3

    • Example 3 Video

    • Example 4

    • Example 4 Video

    • Exercise 4.10

    • Exercise 4.10 Recorded Solutions

    • 2024 syllabus changes for this lesson

Bonus Textbook

Download HSC Extension 2 Mathematics Textbook FREE

Click to Download

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.