Precalculus - A Complete Course

Master key function techniques and get ready for Calculus

What you'll learn

Mathematical Functions

Trigonometry

Polar Co-ordinates

Binomial Expansions

Series

Mathematical Proof

Requirements

Students should have some algebra experience

Description

Pre-Calculus is a key gateway course in Math, helping you build core Mathematical skills while preparing you for Calculus and beyond. The Precalculus course focuses on Mathematical functions which are used in a wide variety of disciplines in the real world. We start by looking at some important concepts about functions and move onto studying specific functions such as Polynomials, Exponential, Logarithmic, and Trigonometric. We then turn to additional key techniques such as Polar Coordinates, Binomial Expansions, and Series. This Course is For YouI created this course to help you master Precalculus through clear instructional videos and relevant practice questions. There are many reasons why you might want to take this course:To learn Precalculus from scratch For additional support if you're taking Precalculus in school or collegeTo help you prep for a Precalculus assessment To review key techniques To access more than 300 relevant practice questions with full solutions As prep for taking further Math courses such as Calculus 1 or Calculus 2To access 11 hours of instructional videoWhatever your reason this course will help you build key skills and confidence quickly. What You'll Take Away From This CoursePrecalculus is a challenging but rewarding course with a lot of content. By mastering some core techniques you'll be able to answer a wide variety of questions both in class and in the real-world. Each instructional video teaches one primary skill and mixes a small amount of theory with example problems. You will then practice what you've learnt in the end of section review exercise. I've also included step-by-step solutions so you can check your work as you go. Take this course and you will learn:The foundations of Mathematical functionsCore function techniques such as composite / inverse functions, function graphs, and domain / rangeEquation solving skills - a fundamental Math skill at all levels Polynomials - one of the most common types of functionSpecific functions such as exponentials / logarithms / trigonometric Mathematical series - a key concept / techniques for more advanced Math courses

Overview

Section 1: Functions

Lecture 1 What are Functions?

Lecture 2 Types of Function

Lecture 3 Maximum and Minimum Value of a Function

Lecture 4 Domain and Range of a Function

Lecture 5 Writing the Domain and Range of a Function

Lecture 6 Average Rate of Change of a Function

Lecture 7 Test Your Knowledge

Section 2: Graphs of Functions

Lecture 8 Starting Graphs of Functions

Lecture 9 Graphs of Common Functions

Lecture 10 Sketching Graphs of Functions

Lecture 11 Sketching Graphs of Functions . . . More Advanced

Lecture 12 Behaviour of Functions

Lecture 13 Test Your Knowledge

Section 3: Composite and Inverse Functions

Lecture 14 Determining Inverse Functions

Lecture 15 The Graph of an Inverse Function

Lecture 16 The Domain and Range of an Inverse Function

Lecture 17 Determining Composite Functions

Lecture 18 The Domain and Range of a Composite Function

Lecture 19 Composite and Inverse Functions Together

Lecture 20 Test Your Knowledge

Section 4: Linear and Quadratic Equations

Lecture 21 Starting Linear Equations

Lecture 22 Solving Linear Equations

Lecture 23 Solving Equations with Parentheses

Lecture 24 Solving Equations with Fractions

Lecture 25 Test Your Knowledge

Section 5: Polynomials

Lecture 26 Polynomial Expressions

Lecture 27 Factorising Polynomial Expressions

Lecture 28 Factorising Polynomial Expressions with a Given Factor

Lecture 29 Factorising Polynomial Expressions without a Given Factor

Lecture 30 Starting Polynomial Equations

Lecture 31 Solving Polynomial Equations Already Factorised

Lecture 32 Solving Polynomial Equations Not Factorised

Lecture 33 Test Your Knowledge

Section 6: Exponential and Logarithmic Functions

Lecture 34 Exponential Functions

Lecture 35 Graphs of Exponential Functions

Lecture 36 Logarithmic Functions

Lecture 37 Graphs of Logarithmic Functions

Lecture 38 Switching Between Exponential and Logarithmic Form

Lecture 39 Rules (Laws) of Logarithms

Lecture 40 Test Your Knowledge

Section 7: Trigonometric Functions

Lecture 41 Starting Radians

Lecture 42 Using Radians

Lecture 43 The Unit Circle Definition of the Trigonometric Functions

Lecture 44 The Graph of the Sine Function

Lecture 45 The Graph of the Cosine Function

Lecture 46 The Graph of the Tangent Function

Lecture 47 The CAST Diagram

Lecture 48 The CAST Diagram in Radians

Lecture 49 Test Your Knowledge

Section 8: Trigonometric Identities

Lecture 50 The Double Angle Formulas

Lecture 51 The Addition Formulas

Lecture 52 The Wave Function

Lecture 53 Test Your Knowledge

Section 9: Polar Coordinates

Lecture 54 What are Polar Coordinates?

Lecture 55 Converting Between Polar and Cartesian Coordinates

Lecture 56 Sketching Curves Given in Polar Form

Lecture 57 Further Curve Sketching in Polar Form

Lecture 58 Test Your Knowledge

Section 10: The Binomial Expansion

Lecture 59 Starting the Binomial Expansion

Lecture 60 Pascal's Triangle

Lecture 61 Factorial Notation and Combinatorics

Lecture 62 Binomial Expansion Using Factorial Notation

Lecture 63 Binomial Expansion for (1 + x)^n

Lecture 64 Test Your Knowledge

Section 11: Series

Lecture 65 Starting Sequences

Lecture 66 From Sequences to Series

Lecture 67 Arithmetic Sequences

Lecture 68 Arithmetic Series

Lecture 69 Geometric Sequences

Lecture 70 Geometric Series

Lecture 71 Sums to Infinity

Lecture 72 Summation (Sigma) Notation

Lecture 73 Test Your Knowledge

Section 12: Proof by Induction

Lecture 74 What is a Mathematical Proof?

Lecture 75 Starting Proof by Induction

Lecture 76 Example of Proof by Induction

Lecture 77 Second Example of Proof by Induction

Lecture 78 Test Your Knowledge

Section 13: Additional Resources

Lecture 79 Formula List

Lecture 80 Trigonometric Function Graphs

Students who need to learn Precalculus,Students who need to prep for Calculus,Students who want to review Precalculus topics for an assessment,Students looking for Precalculus practice questions with full step-by-step solutions,Students who want clear instruction on all aspects of Precalculus