Lessons

BONUS GIFT: The Ultimate Maths Methods Overview v1.0

MATHS METHODS IN 2.5 HOURS

IMPORTANT: Read this first

1. Functions and Relations

2. Logs, Powers, Sin, Cos and Tan

3. Calculus

4. Probability and Statistics

MATHS METHODS: IN DETAIL

LINEAR EQUATIONS

1. Really Basic Stuff

2. How to Draw Linear Equations

3. Parallel, Perpendicular and Literal Lines

4. Linear – Midpoints, Length, Line Segments and Angles

5. Simultaneous Equations

MATRIX

1. Really Basic Stuff

2. Determinant and Inverse

3. Simultaneous Equations

PARABOLAS & QUADRATICS

1. Really Basic Stuff

2. Simple Transformations

3. Quadratic Formula and Square Roots

4. Three Main Ways to Draw Parabolas

5. How to Factorise Quadratics

BASICS OF FUNCTIONS & RELATIONS

1. How to Read Relations

2. Domain and Range

3. How to Read Functions

4. Transformations – Functions and Points

5. Transformations – Using Matrices

6. Transformations – Series of Transformations

HOW TO SKETCH ANY FUNCTION

1. Translation – Moving Functions

2. Stretching and Reflecting

3. Sketching in Intercept Form

4. Summary

5. How to Find Any Domain

6. Cubics, Quartics and Other Polynomials

7. How to Factorise Polynomials

8. Sketching Fraction Powers

COMPOSITE FUNCTIONS f(g(x))

1. Introduction to Composite Functions

2. Finding the Domain of f(g(x))

3. Restricting f(g(x)) so it Works

4. Working Out f(g(x)) in Full

TYPES OF FUNCTIONS

1. One to One, Many to One, Hybrid, Odd and Even

2. Sum and Product

3. Inverse Functions

4. Summary

LOGS AND EXPONENTIALS

1. Exponential Laws (Power Laws)

2. What are Logarithms?

3. Log Laws

4. Using Log Laws

5. Sketching Logs and Exponentials

6. Understanding Euler’s Number (e)

SIN, COS & TAN

1. Definitions of Sin and Cos

2. The Unit Circle

3. What are Radians?

4. Using Radians

5. Proving Exact Values

6. How to Find Exact Values

7. Finding θ

8. Example of finding θ

9. Understanding the Graphs of Sin, Cos & Tan

10. Sketching Sin, Cos & Tan

11. Example of Sketching Cosθ

CALCULUS

1. What You Need to Know Before Calculus

2. Definition of Calculus

3. The First Principle

4. How to Graph f'(x)

5. Finding the derivitive – f'(x) of x, e, Log, Cos, Sin and Tan

6. f'(x) Graphs for Parabolas, Cubics and Quartics

7. Symbols and Terminology

8. Chain Rule

9. Product and Quotient Rules

10. Continuous, Differentiable and Limits

11. Equation of the Tangent and Normal

12. Rates of Change

SKETCHING ANY GRAPH (using calculus)

1. Types of Stationary Points

2. How to Find Stationary Points

3. How to Sketch Any Graph Using Calculus

ANTIDIFFERENTIATION

1. Definition of Antidifferentiation

2. Symbols of Antidiff

3. Basics Ways to Antidiff Stuff

4. Tougher Antidiffs

5. Approximate Area

6. Understanding Exact Area

7. Integration – Finding Exact Area

8. Area Between Curves and Average Value

9. Kinematics – Velocity, Acceleration and stuff

PROBABILITY BASICS

1. Probability Basics

2. Conditional Probability Basics

DISCRETE RANDOM VARIABLES

1. Random Variables

2. Discrete Random Variables

3. Discrete Random Variables – Measuring Centre

4. Discrete Random Variables – Measuring Spread

5. Binomial Random Variables – Bernoulli and Binomial Distribution

6. Binomial Random Variables – More complex Binomials

7. Binomial Random Variables – Expected Value, Variance and Standard Deviation

CONTINUOUS RANDOM VARIABLES

1. Basics of Continuous Random Variables

2. Conditional Probability and Using Limits

3. Measures of Center

4. Measuring Spread

5. Normal Distribution

6. Normal Distribution – Using Standard Normal Distributions

7. Normal Distribution – Z-Value Formula

8. Normal Distribution – Using the Calculator

9. Normal Distribution – A More Complex Question

10. Normal Distribution – Conditional Probability

STATISTICS

1. What are statistics?

2. Sampling Distibutions

3. Mean and Standard Deviation

4. Large Populations

5. Normal Approximations of Binomials

6. Confidence Intervals

7. Margin of Error

VCAA-Style Questions

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