SACE Mathematical Methods Stage 2 Notes

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

1. Rates of change, first principles and derivatives of power functionsTopic 1 · Topic 1: Further differentiation and applications

   Subtopic 1.1 Introductory differential calculus

2. The chain, product and quotient rulesTopic 1 · Topic 1: Further differentiation and applications

   Subtopic 1.2 Differentiation rules

3. Differentiating e^x and e^f(x) and exponential modelsTopic 1 · Topic 1: Further differentiation and applications

   Subtopic 1.3 Exponential functions

4. Derivatives of sine, cosine and tangent and periodic modelsTopic 1 · Topic 1: Further differentiation and applications

   Subtopic 1.4 Trigonometric functions

5. Second derivatives, concavity, stationary points and points of inflectionTopic 1 · Topic 1: Further differentiation and applications

   Subtopic 1.5 The second derivative

6. Discrete probability distributions, expected value and standard deviationTopic 2 · Topic 2: Discrete random variables

   Subtopic 2.1 Discrete random variables

7. Bernoulli random variables and their mean and standard deviationTopic 2 · Topic 2: Discrete random variables

   Subtopic 2.2 The Bernoulli distribution

8. The binomial distribution: conditions, probabilities, mean and standard deviationTopic 2 · Topic 2: Discrete random variables

   Subtopic 2.3 Repeated Bernoulli trials and the binomial distribution

9. Indefinite integrals, integration rules and the constant of integrationTopic 3 · Topic 3: Integral calculus

   Subtopic 3.1 Anti-differentiation

10. Upper and lower rectangle sums and the definite integral as areaTopic 3 · Topic 3: Integral calculus

    Subtopic 3.2 The area under curves

11. The fundamental theorem of calculus and exact areasTopic 3 · Topic 3: Integral calculus

    Subtopic 3.3 Fundamental theorem of calculus

12. Integrating rates of change and motion problemsTopic 3 · Topic 3: Integral calculus

    Subtopic 3.4 Applications of integration

13. Natural logarithms, logarithm laws and solving exponential equationsTopic 4 · Topic 4: Logarithmic functions

    Subtopic 4.1 Using logarithms for solving exponential equations

14. The graph of y = ln(x) and its transformationsTopic 4 · Topic 4: Logarithmic functions

    Subtopic 4.2 Logarithmic functions and their graphs

15. Differentiating and integrating logarithmic functionsTopic 4 · Topic 4: Logarithmic functions

    Subtopic 4.3 Calculus of logarithmic functions

16. Probability density functions, mean and standard deviation of continuous random variablesTopic 5 · Topic 5: Continuous random variables

    Subtopic 5.1 Introduction to continuous random variables

17. The normal distribution, z-scores and inverse-normal calculationsTopic 5 · Topic 5: Continuous random variables

    Subtopic 5.2 Normal distributions

18. Sampling distributions of the sample sum and sample mean and the central limit theoremTopic 5 · Topic 5: Continuous random variables

    Subtopic 5.3 Sampling

19. Confidence intervals for a population meanTopic 6 · Topic 6: Sampling and confidence intervals

    Subtopic 6.1 Confidence intervals for a population mean

20. Sample proportions and confidence intervals for a population proportionTopic 6 · Topic 6: Sampling and confidence intervals

    Subtopic 6.2 Population proportions / Subtopic 6.3 Confidence intervals for a population proportion