Course Description

The course covers every dot point from MA-C4 Integral Calculus in the new NSW Year 12 Mathematics Advanced syllabus.Β 

The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 158 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. As more detail on the syllabus is released by NESA any changes required will be made. Also included are related skills that are beyond the syllabus that you can use to extend more capable students.

Each lesson includes a section for Extension Students, that covers work that can help them develop skills and techniques that helps prepare them for content they will cover in the Extension 1 or Extension 2 courses.

The course includes:

  • 158 recorded examples

  • 303 page course handout

  • 158 optional practice questions matching the examples from the course

  • 84 mixed questions, all with fully worked solutions.
    Β 

The remainder of the Year 12 Advanced syllabus is covered in four other courses:

ADV#6Β Further Differentiation (MA-C2 Differential Calculus and MA-C3 Applications of Differentiation)

ADV#8Β Functions and Trigonometric Functions (MA-F2 Graphing Techniques and MA-T3 Trigonometric Functions and Graphs)Β 

ADV#9Β Statistics (MA-S2 Descriptive Statistics and Bivariate Data Analysis and MA-S3 Random Variables)

ADV#10Β Financial Mathematics (MA-M1 Modelling Financial Situations)


Audience

Mathematics teachers of any experience level who are preparing to teach the new Advanced syllabus.


Teaching StandardsΒ 

2.1.2 Proficient LevelΒ - 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

Do you teach in NSW? If so, this is relevant to you:

Completing Year 12 Advanced Mathematics: Integration - ADV#7 will contribute 10 hours of NSW Education Standards Authority (NESA) Accredited PD in the priority area of Delivery and Assessment of NSW Curriculum/Early Years Learning Framework, addressing Standard Descriptor 2.1.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher in NSW.

Course curriculum

  • 1

    Course Administration

    • Course Administration

    • Introduction to the Mathematics Advanced Year 12 In Depth Series

    • Introduction to In Depth ADV#7
  • 2

    Integration

    • Introduction to Integration

    • Relevant Part of the Advanced Syllabus
  • 3

    Lesson 1 – Anti-derivatives of Polynomials

    • Lesson Overview

    • Anti-differentiation

    • Understanding Anti-differentiation of Polynomials

    • Standard Integrals for Polynomials

    • Additivity and Linearity of Integration

    • Simplifying Integrands

    • The Reverse Chain Rule

    • Reverse Chain Rule with Power Functions

    • Harder Reverse Chain Rule

    • Solving for the Constant

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 1 Quiz
  • 4

    Lesson 2 – Anti-derivatives of Trigonometric Functions

    • Lesson Overview

    • Understanding Anti-differentiation of Trigonometric Functions

    • Standard Integrals for Trigonometric Functions

    • Reverse Chain Rule with Trigonometric Functions

    • Simplifying the Integrand

    • Solving for the Constant

    • Other Trigonometric Integrands

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 2 Quiz
  • 5

    Lesson 3 – Anti-derivatives of Exponential Functions

    • Lesson Overview

    • Understanding Anti-differentiation of Exponentials with Base 𝑒

    • Standard Integrals for Exponentials with Base 𝑒

    • Simplifying the Integrand

    • Reverse Chain Rule for Exponentials with Base 𝑒

    • Solving for the Constant

    • Understanding Anti-differentiation of Exponentials with Other Bases

    • Standard Integrals for Exponentials with Other Bases

    • Simplifying the Integrand

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 3 Quiz
  • 6

    Lesson 4 – Anti-derivatives of Reciprocal Functions

    • Lesson Overview

    • Understanding Anti-differentiation of Natural Logarithms

    • Standard Integrals for Natural Logarithms

    • Why do we Add the Absolute Value Signs?

    • Why doesn’t ∫π‘₯^(βˆ’1) 𝑑π‘₯ Follow the Rule for the Anti-derivative of other Power Functions?

    • Solving for the Constant

    • Harder Applications

    • Understanding Anti-differentiation of Logarithms with Other Bases

    • Solving for the Constant

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 4 Quiz
  • 7

    Lesson 5 – Area Under a Curve Using Geometric Shapes

    • Lesson Overview

    • The Area Under a Curve

    • Integral Notation

    • Exact Area Under a Curve Using Geometric Shapes

    • Estimating the Area Under a Curve Using Geometric Shapes

    • Trapezoidal Rule

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 5 Quiz
  • 8

    Lesson 6 – Definite Integrals

    • Lesson Overview

    • Background to The Fundamental Theorem of Calculus

    • The Fundamental Theorem of Calculus

    • Finding the Total Change by Integrating the Instantaneous Rate of Change

    • The Arguments For and Against Using a Dummy Variable

    • Using The Fundamental Theorem of Calculus

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 6 Quiz
  • 9

    Lesson 7 – Areas Enclosed by the x-axis

    • Lesson Overview

    • Areas and Definite Integrals

    • Odd and Even Functions

    • Areas Enclosed by the π‘₯-axis

    • Sum or Difference of Areas

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 7 Quiz
  • 10

    Lesson 8 – Areas Enclosed by the y-axis or Between Two Curves

    • Lesson Overview

    • Areas Enclosed by the 𝑦-axis

    • Areas Enclosed by Two Curves

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 8 Quiz
  • 11

    Lesson 9 – Applications of Integration

    • Lesson Overview

    • Applications of Integration

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 9 Quiz
  • 12

    Lesson 10 – Motion and Integration

    • Lesson Overview

    • Motion and Integration

    • Extension Students

    • Practice Exercises

    • ADV#7 Lesson 10 Quiz
  • 13

    Questions from the HSC

    • Advanced Year 12 Integration in the HSC Exams
  • 14

    Appendix 1: Mixed Revision Exercises

    • Mixed Exercises
  • 15

    Conclusion

    • Highlights of Integration

    • Conclusion to In Depth ADV#7
  • 16

    Course feedback

    • Please take a few minutes to give us your feedback.

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