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Pre-Calculus

Functions

What are Functions? (9:20)
Types of Function (9:01)
Maximum and Minimum Values of a Function (10:17)
Domain and Range of a Function (15:56)
Writing the Domain and Range of a Function (12:06)
Average Rate of Change of a Function (10:40)
Practice Questions

Graphs of Functions

Starting Graphs of Functions (10:51)
Graphs of Common Functions (12:44)
Sketching Graphs of Functions (14:17)
Sketching Graphs of Functions . . . More Advanced (17:19)
Behaviour of Functions (12:25)
Practice Questions

Composite and Inverse Functions

Determining Inverse Functions (8:38)
The Graph of an Inverse Function (14:23)
The Domain & Range of an Inverse Function (12:49)
Determining Composite Functions (9:14)
The Domain & Range of a Composite Function (11:05)
Composite and Inverse Functions Together (9:16)
Practice Questions

Linear & Quadratic Equations

Starting Linear Equations (7:15)
Solving Linear Equations (13:29)
Solving Equations with Parentheses (10:09)
Solving Equations with Fractions (11:44)
Practice Questions

Polynomials

Polynomial Expressions (8:01)
Factorising Polynomial Expressions (8:47)
Factorising Polynomial Expressions with a Given Factor (9:06)
Factorising Polynomial Expressions without a Given Factor (9:19)
Starting Polynomial Equations (8:15)
Solving Polynomial Equations Already Factorised (8:38)
Solving Polynomial Equations Not Factorised (14:23)
Practice Questions

Exponential & Logarithmic Functions

Exponential Functions (5:01)
Graphs of Exponential Functions (8:01)
Logarithmic Functions (5:42)
Graphs of Logarithmic Functions (6:57)
Switching Between Exponential & Logarithmic Form (7:02)
Rules (Laws) of Logarithms (7:22)
Practice Questions

Trigonometric Functions

Starting Radians (6:10)
Using Radians (10:24)
The Unit Circle Definitions of the Trig Functions (12:17)
The Graph of the Sine Function (9:52)
The Graph of the Cosine Function (9:30)
The Graph of the Tangent Function (8:21)
The CAST Diagram (10:07)
The CAST Diagram in Radians (7:38)
Practice Questions

Trigonometric Identities

The Double Angle Formulas (8:49)
The Addition Formulas (9:43)
The Wave Function (13:27)
Practice Questions

Polar Co-ordinates

What are Polar Co-ordinates? (7:16)
Converting Between Polar & Cartesian Co-ordinates (16:28)
Sketching Curves Given in Polar Form (10:33)
Further Curve Sketching in Polar Form (15:55)
Practice Questions

The Binomial Expansion

Starting the Binomial Expansion (9:09)
Pascal’s Triangle (14:06)
Factorial Notation and Combinatorics (12:51)
Binomial Expansion Using Factorial Notation (17:44)
Binomial Expansion for (1 + x)^n (10:28)
Practice Questions

Series

Starting Sequences (6:47)
From Sequences to Series (5:58)
Arithmetic Sequences (9:46)
Arithmetic Series (10:05)
Geometric Sequences (12:55)
Geometric Series (9:11)
Sums to Infinity (11:18)
Summation (Sigma) Notation (13:35)
Practice Questions

Proof by Induction

What is a Mathematical Proof? (12:28)
Starting Proof by Induction (8:13)
Examples of Proof by Induction (26:50)
Practice Questions

Additional Resources

Formula List
Trigonometric Function Graphs

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Formula List

Formula list for the Pre-Calculus course.

Pre-Calculus Formula List.pdf

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