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NSW Syllabuses

Mathematics Extension 2 Stage 6 - Year 12 Extension 2 - Calculus MEX-C1 Advanced Calculus Skills

Outcomes

A student:

  • MEX12-1

    understands and uses different representations of numbers and functions to model, prove results and find solutions to problems in a variety of contexts

  • MEX12-5

    applies techniques of integration to structured and unstructured problems

  • MEX12-7

    applies various mathematical techniques and concepts to model and solve structured, unstructured and multi-step problems

  • MEX12-8

    communicates and justifies abstract ideas and relationships using appropriate language, notation and logical argument

Subtopic Focus

The principal focus of this subtopic is extending students’ knowledge, understanding and skills to a broader range of integration techniques, such as integration of rational functions, integration using partial fractions and integration by parts.

Students develop the ability to recognise and apply this knowledge in a variety of contexts and multi-step problems.

Content

  • Students:
  • integrate rational functions involving a quadratic denominator by completing the square or otherwise CCT
  • integrate rational functions whose denominators have simple linear or quadratic factors or a combination of both
  • use partial fractions to integrate functions of the form \(\frac{f(x)}{g(x)}\), where \(f(x)\) and \(g(x)\) are polynomials and \(g(x)\) is expressed in simple linear or quadratic factors (ACMSM122) CCT
  • evaluate integrals using the method of integration by parts  (ACMSM123)
  • develop the method for integration by parts, \(\int uv'\,dx = uv - \int vu' \,dx\), where \(u\) and \(v\) are both functions of \(x\) CCT
  • apply these techniques of integration to practical and theoretical situations AAM CCTICT