SACE Specialist Mathematics Stage 2 Notes

These are the 20 revision notes inside the SACE Specialist Mathematics Mastery Pack. Open any note to see what it covers before you buy.

1. Proof by mathematical inductionTopic 1: Mathematical induction · Subtopic 1.1: Proof by mathematical induction

   Proof by mathematical induction

2. Cartesian and polar forms and de Moivre's theoremTopic 2: Complex numbers · Subtopic 2.1: Cartesian and polar forms

   Cartesian and polar forms and de Moivre's theorem

3. The Argand plane: geometry, loci and regionsTopic 2: Complex numbers · Subtopic 2.2: The complex (Argand) plane

   The Argand plane: geometry, loci and regions

4. Roots of complex numbers and the roots of unityTopic 2: Complex numbers · Subtopic 2.3: Roots of complex numbers

   Roots of complex numbers and the roots of unity

5. Factorisation of real polynomials over the complex numbersTopic 2: Complex numbers · Subtopic 2.4: Factorisation of polynomials

   Factorisation of real polynomials over the complex numbers

6. Composition of functions and its domainTopic 3: Functions and sketching graphs · Subtopic 3.1: Composition of functions

   Composition of functions and its domain

7. One-to-one functions and inverse functionsTopic 3: Functions and sketching graphs · Subtopic 3.2: One-to-one functions

   One-to-one functions and inverse functions

8. Sketching absolute value, reciprocal and rational graphsTopic 3: Functions and sketching graphs · Subtopic 3.3: Sketching graphs

   Sketching absolute value, reciprocal and rational graphs

9. The algebra of vectors in three dimensionsTopic 4: Vectors in three dimensions · Subtopic 4.1: The algebra of vectors in three dimensions

   The algebra of vectors in three dimensions

10. Lines in three dimensions and closest-point problemsTopic 4: Vectors in three dimensions · Subtopic 4.2: Vector and Cartesian equations

    Lines in three dimensions and closest-point problems

11. Scalar and vector products, planes and vector proofTopic 4: Vectors in three dimensions · Subtopic 4.2: Vector and Cartesian equations

    Scalar and vector products, planes and vector proof

12. Systems of linear equations and the geometry of planesTopic 4: Vectors in three dimensions · Subtopic 4.3: Systems of linear equations

    Systems of linear equations and the geometry of planes

13. Trigonometric identities, substitution and inverse trigonometric integralsTopic 5: Integration techniques and applications · Subtopic 5.1: Integration techniques

    Trigonometric identities, substitution and inverse trigonometric integrals

14. Partial fractions and integration by partsTopic 5: Integration techniques and applications · Subtopic 5.1: Integration techniques

    Partial fractions and integration by parts

15. Areas between curves and volumes of solids of revolutionTopic 5: Integration techniques and applications · Subtopic 5.2: Applications of integral calculus

    Areas between curves and volumes of solids of revolution

16. Implicit differentiationTopic 6: Rates of change and differential equations · Subtopic 6.1: Implicit differentiation

    Implicit differentiation

17. Related rates, separable differential equations and slope fieldsTopic 6: Rates of change and differential equations · Subtopic 6.2: Differential equations

    Related rates, separable differential equations and slope fields

18. Polynomial parameterisations, uniform motion and free flightTopic 6: Rates of change and differential equations · Subtopic 6.3: Pairs of varying quantities — polynomials

    Polynomial parameterisations, uniform motion and free flight

19. Velocity, tangents, speed and arc length of parametric curvesTopic 6: Rates of change and differential equations · Subtopic 6.4: Related rates, velocity, and tangents

    Velocity, tangents, speed and arc length of parametric curves

20. Trigonometric parameterisations and circular motionTopic 6: Rates of change and differential equations · Subtopic 6.5: Trigonometric parameterisations

    Trigonometric parameterisations and circular motion