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11–12Mathematics Extension 2 11–12 Syllabus (2024)

Record of changes
Implementation from 2026
Expand for detailed implementation advice
OverviewRationaleAimOutcomesContentAssessmentGlossaryTeaching and learning support

Content

Year 12

Further integration
  • Derive the identities for trigonometric products as sums and differences for cos⁡Acos⁡B=12cos⁡A-B+cos⁡A+B, sin⁡Asin⁡B=12cos⁡A-B-cos⁡A+B, sin⁡Acos⁡B=12sin⁡A+B+sin⁡A-B and cos⁡Asin⁡B=12sin⁡A+B-sin⁡A-B

  • Use the identities for trigonometric products as sums and differences to solve problems and prove results

  • Solve trigonometric equations by applying the formulas for trigonometric products as sums and differences for cos⁡Acos⁡B, sin⁡Asin⁡B and sin⁡Acos⁡B over restricted domains
  • Use identities relating the trigonometric products as sums and differences to solve problems involving integrals of the form ∫sin⁡mxcos⁡nxdx, ∫sin⁡mxsin⁡nxdx or ∫cos⁡(mx)cos⁡(nx)dx
  • Derive the expressions sin⁡A=2t1+t2, cos⁡A=1-t21+t2 and tan⁡A=2t1-t2 where t=tan⁡A2 (the t-formulas) and use them to solve trigonometric equations over restricted domains

  • Find Loading  and evaluate definite integrals using the method of Loading  by substitution, where the Loading  may or may not be given

  • Decompose rational Loading  whose Loading  can be expressed as a product of Loading  Loading  factors, distinct irreducible quadratic factors and perfect square factors into Loading 

  • Integrate rational functions whose denominators can be expressed as a product of distinct linear factors, distinct irreducible quadratic factors and perfect square factors, using partial fraction decomposition

  • Integrate rational functions by completing the square on a quadratic denominator

  • Integrate rational functions where the degree of the Loading  is not less than the degree of the denominator

  • Integrate functions by changing an Loading  into an appropriate form using algebraic manipulation

  • Derive the method for Loading 

  • Find indefinite integrals and evaluate definite integrals using the method of integration by parts, including problems where more than one application is required

  • Derive and use Loading  involving integration by parts

  • Solve theoretical problems involving multiple techniques of integration

  • Solve practical problems involving multiple techniques of integration

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