Year 12 Maths Methods (Units 3 & 4)

Maths Methods Video Tutorials

Year 12 Maths Methods (Units 3 & 4)

Maths Methods Video Tutorials

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Functions and Relations

LINEAR EQUATIONS

1. Really Basic Stuff

2. How to Draw Linear Equations

3. Parallel, Perpendicular and Literal Lines

4. Midpoints, Length, Line Segments and Angles

5. 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

6. Completing the Square

7. Simultaneous Equations & Inequalities

BASICS OF FUNCTIONS & RELATIONS

1. How to Read Relations

2. Domain and Range

3. How to Read Functions

4. Transformations – Functions and Points

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. Sketching Circles

6. How to Find Any Domain

7. Cubics, Quartics and Other Polynomials

8. How to Factorise Polynomials

9. 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

Algebra

LOGS AND EXPONENTIALS

1. Exponential Laws (Power Laws)

2. What are Logarithms?

3. Understanding 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

Basic Calculus

1. What You Need to Know Before Calculus

2. Definition of Calculus

Finding the Derivative

1. The First Principle

2. How to Graph f'(x)

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

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

5. Symbols and Terminology

6. More on First Principle & Approximating the Derivative

Chain, Product and Quotient Rules

1. The Chain Rule

2. Product and Quotient Rules

Applications of Calculus

1. Continuous, Differentiable and Limits

2. Equation of the Tangent and Normal

3. Rates of Change

4. Types of Stationary Points

5. How to Find Stationary Points

6. How to Sketch Any Graph Using Calculus

7. Bisection & Newton's Method

8. Pseudocode and Algorithms

Antidifferentiation

1. Definition of Antidifferentiation

2. Symbols of Antidiff

3. How to Antidiff anything

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 (Old Curriculum)

Probability

Probability Basics

1. Probability Basics

2. Conditional and Independent Probability

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 Distributions

3. Mean and Standard Deviation

4. Large Populations

5. Normal Approximations of Binomials

6. Confidence Intervals

7. Margin of Error

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Year 12 Maths Methods Video Tutorials

104 Lessons

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Functions and Relations

6 Chapters

LINEAR EQUATIONS

5 Lessons

1. Really Basic Stuff

2. How to Draw Linear Equations

3. Parallel, Perpendicular and Literal Lines

4. Midpoints, Length, Line Segments and Angles

5. Simultaneous Equations

PARABOLAS & QUADRATICS

7 Lessons

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

6. Completing the Square

7. Simultaneous Equations & Inequalities

BASICS OF FUNCTIONS & RELATIONS

5 Lessons

1. How to Read Relations

2. Domain and Range

3. How to Read Functions

4. Transformations – Functions and Points

6. Transformations – Series of Transformations

HOW TO SKETCH ANY FUNCTION

9 Lessons

1. Translation – Moving Functions

2. Stretching and Reflecting

3. Sketching in Intercept Form

4. Summary

5. Sketching Circles

6. How to Find Any Domain

7. Cubics, Quartics and Other Polynomials

8. How to Factorise Polynomials

9. Sketching Fraction Powers

COMPOSITE FUNCTIONS f(g(x))

4 Lessons

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

4 Lessons

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

2. Sum and Product

3. Inverse Functions

4. Summary

Algebra

2 Chapters

LOGS AND EXPONENTIALS

6 Lessons

1. Exponential Laws (Power Laws)

2. What are Logarithms?

3. Understanding Log Laws

4. Using Log Laws

5. Sketching Logs and Exponentials

6. Understanding Euler’s Number (e)

SIN, COS & TAN

11 Lessons

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

5 Chapters

Basic Calculus

2 Lessons

1. What You Need to Know Before Calculus

2. Definition of Calculus

Finding the Derivative

6 Lessons

1. The First Principle

2. How to Graph f'(x)

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

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

5. Symbols and Terminology

6. More on First Principle & Approximating the Derivative

Chain, Product and Quotient Rules

2 Lessons

1. The Chain Rule

2. Product and Quotient Rules

Applications of Calculus

8 Lessons

1. Continuous, Differentiable and Limits

2. Equation of the Tangent and Normal

3. Rates of Change

4. Types of Stationary Points

5. How to Find Stationary Points

6. How to Sketch Any Graph Using Calculus

7. Bisection & Newton's Method

8. Pseudocode and Algorithms

Antidifferentiation

9 Lessons

1. Definition of Antidifferentiation

2. Symbols of Antidiff

3. How to Antidiff anything

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 (Old Curriculum)

Probability

3 Chapters

Probability Basics

2 Lessons

1. Probability Basics

2. Conditional and Independent Probability

Discrete Random Variables

7 Lessons

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

10 Lessons

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

7 Lessons

1. What are statistics?

2. Sampling Distributions

3. Mean and Standard Deviation

4. Large Populations

5. Normal Approximations of Binomials

6. Confidence Intervals

7. Margin of Error

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About the teacher

Alex Bell

Hey guys! It's Alex, I'm the creator of MathsMethods.com.au with degrees in Mathematics/Astrophysics. I've educated students for my entire career, spent several years rewriting the Maths Methods textbook to create my popular video tutorials that focus on a solid understanding the fundamentals, as this is the key to making Maths Methods easier for all students.

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