WACE Mathematics Specialist Year 12 Notes

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

1. Modulus, argument, polar form and de Moivre's theorem for integral powersComplex numbers · Topic 3.1: Complex numbers

   Complex arithmetic using polar form

2. Addition as vector addition, multiplication as rotation and dilation, and complex-number geometryComplex numbers · Topic 3.1: Complex numbers

   The complex plane (the Argand plane)

3. Loci and regions in the complex plane: circles, rays, perpendicular bisectors and |z - a| = k|z - b|Complex numbers · Topic 3.1: Complex numbers

   The complex plane (the Argand plane)

4. nth roots of unity and of complex numbers; factor and remainder theorems, conjugate roots and polynomial equationsComplex numbers · Topic 3.1: Complex numbers

   Roots of complex numbers; factorisation of polynomials

5. Composition of functions: when f(g(x)) is defined, its domain and rangeFunctions · Topic 3.2: Functions and sketching graphs

   Functions

6. One-to-one functions, inverse functions and the reflection propertyFunctions · Topic 3.2: Functions and sketching graphs

   Functions

7. Absolute value, y = 1/f(x), y = |f(x)|, y = f(|x|) and rational functions with vertical, horizontal and oblique asymptotesFunctions · Topic 3.2: Functions and sketching graphs

   Sketching graphs

8. 3D vector algebra, scalar product and vector proofs of geometric resultsVectors · Topic 3.3: Vectors in three dimensions

   The algebra of vectors in three dimensions

9. Lines, line segments, spheres and parametric curves; do the paths cross or do the particles meet?Vectors · Topic 3.3: Vectors in three dimensions

   Vector and Cartesian equations

10. Cross product, planes and systems of three linear equations with their geometric interpretationVectors · Topic 3.3: Vectors in three dimensions

    Vector and Cartesian equations; systems of linear equations

11. Vector functions of time: velocity, acceleration, distance travelled, projectile and circular motionVectors · Topic 3.3: Vectors in three dimensions

    Vector calculus

12. Integration with trigonometric identities and the substitution u = g(x), including exact definite integralsCalculus · Topic 4.1: Integration and applications of integration

    Integration techniques

13. Integral of 1/x, f'(x)/f(x) and partial fractionsCalculus · Topic 4.1: Integration and applications of integration

    Integration techniques

14. Areas between curves in x and in y, volumes of solids of revolution about either axis, and numerical integrationCalculus · Topic 4.1: Integration and applications of integration

    Applications of integral calculus

15. Implicit differentiation, related rates and the increments formulaCalculus · Topic 4.2: Rates of change and differential equations

    Applications of differentiation

16. Separable differential equations and slope fieldsCalculus · Topic 4.2: Rates of change and differential equations

    Applications of differentiation

17. Formulating differential equations: exponential, logistic and other growth-rate modelsCalculus · Topic 4.2: Rates of change and differential equations

    Applications of differentiation

18. Rectilinear motion with variable acceleration, v dv/dx, and simple harmonic motionCalculus · Topic 4.2: Rates of change and differential equations

    Modelling motion

19. The sample mean as a random variable: distribution of X-bar and the central limit theoremStatistics · Topic 4.3: Statistical inference

    Sample means

20. Confidence intervals for a population mean: construction, sample size, width and interpretationStatistics · Topic 4.3: Statistical inference

    Confidence intervals for means