VCE Specialist Mathematics Units 3&4 Notes

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

1. Implications, equivalence and proof structures (direct, cases, contradiction, contrapositive)3 · AOS1

   Unit 3 AOS1 — Discrete mathematics: Logic and proof

2. Proof by mathematical induction (sums, divisibility, inequalities)3 · AOS1

   Unit 3 AOS1 — Discrete mathematics: Logic and proof

3. Rational functions: partial fractions and asymptotic behaviour3 · AOS2

   Unit 3 AOS2 — Functions, relations and graphs

4. Stationary points, inflection and the second-derivative test for curve sketching3 · AOS2

   Unit 3 AOS2 — Functions, relations and graphs

5. Complex numbers: Cartesian and polar form, the Argand plane and complex regions3 · AOS3

   Unit 3 AOS3 — Algebra, number and structure: Complex numbers

6. De Moivre's theorem and the nth roots of complex numbers3 · AOS3

   Unit 3 AOS3 — Algebra, number and structure: Complex numbers

7. Factorisation over C: the conjugate root theorem and solving polynomial equations3 · AOS3

   Unit 3 AOS3 — Algebra, number and structure: Complex numbers

8. Vector algebra, the dot product, resolutes and the angle between vectors3 · AOS5

   Unit 3 AOS5 — Space and measurement: Vectors

9. The cross product, normals to planes and vector proofs of geometric results3 · AOS5

   Unit 3 AOS5 — Space and measurement: Vectors

10. Vector, parametric and Cartesian equations of lines and planes3 · AOS5

    Unit 3 AOS5 — Space and measurement: Vectors

11. Inverse circular derivatives, second derivatives and implicit/related rates4 · AOS4

    Unit 4 AOS4 — Calculus: advanced differentiation

12. Anti-differentiation: recognising inverse-circular and log forms, and the four core techniques4 · AOS4

    Unit 4 AOS4 — Calculus: integration techniques

13. Areas, arc length of parametric curves, and solids of revolution4 · AOS4

    Unit 4 AOS4 — Calculus: applications of integration

14. Solving dy/dx = f(x), dy/dx = g(y), separation of variables and second-order by antidifferentiation4 · AOS4

    Unit 4 AOS4 — Calculus: differential equations

15. Logistic growth, direction (slope) fields and Euler's method4 · AOS4

    Unit 4 AOS4 — Calculus: differential equations

16. Rectilinear motion: velocity-time graphs, calculus links and the acceleration forms4 · AOS4

    Unit 4 AOS4 — Calculus: kinematics

17. Vector functions of time: paths, meeting/colliding particles and velocity/acceleration vectors4 · AOS4

    Unit 4 AOS4 — Calculus: vector calculus

18. Expectation and variance of sums and linear combinations of random variables4 · AOS6

    Unit 4 AOS6 — Data analysis, probability and statistics: linear combinations of random variables

19. The sample mean as a random variable and the central limit behaviour4 · AOS6

    Unit 4 AOS6 — Data analysis, probability and statistics: distribution of the sample mean

20. Confidence intervals for a mean and one- and two-tailed hypothesis tests4 · AOS6

    Unit 4 AOS6 — Data analysis, probability and statistics: confidence intervals & hypothesis testing