## Pre-Calculus

Total Units: 13

Pre-Calculus plays a crucial role in preparing students for calculus and post-secondary mathematics. This course focuses on more abstract and theoretical concepts, allowing students to improve their critical thought processes. The primary goal of this course is for students to own a thorough understanding of all types of functions and prepare them for Calculus.

### Review of Functions and Quadratics

- 1.1 Introduction to Functions
- 1.2 Domain of a Function and Interval Notation
- 1.3 Range of a Function and Interval Notation
- 1.4 Composition of Functions
- 1.5 Inverse of Functions
- 1.6 Introduction to Quadratic Functions
- 1.7 Graphing Quadratic Functions in Vertex Form
- 1.8 Solving Quadratic Equations with Square Roots
- 1.9 Solving Quadratics by Completing the Square
- 1.10 Converting to Vertex Form by Completing the Square
- 1.11 Graphing Quadratic Inequalities

### Polynomial Functions

- 2.1 Introduction to Polynomials
- 2.2 Finding a Polynomial Given the Roots
- 2.3 Dividing Polynomials Using Long Division
- 2.4 Dividing Polynomials Using Synthetic Division
- 2.5 Remainder Theorem/Factor Theorem
- 2.6 Location principle & Multiplicity of Zeros
- 2.7 Rational Root Theorem
- 2.8 Complex Conjugate Root Theorem
- 2.9 Fundamental Theorem of Algebra & Descartes Rule of signs
- 2.10 Graphing Polynomials

### Rational Functions

- 3.1 Introduction to Rational Functions
- 3.2 Graphing Rational Functions
- 3.3 Graphing Rational Functions Part II
- 3.4 Slant Asymptotes
- 3.5 Parabolic Asymptotes
- 3.6 Multiplying and Dividing Rational Expressions
- 3.7 Solving Rational Equations

### Exponential & Logarithmic Functions

- 4.1 Introduction to Exponential & Logarithmic Functions
- 4.2 Graphing Exponential Functions
- 4.3 Logarithmic Functions and Change of Base Formula
- 4.4 Properties of Logarithms
- 4.5 Exponential/Logarithmic Inverse Property
- 4.6 Natural Exponentials & Logarithms
- 4.7 Solving Exponential Equations
- 4.8 Solving Logarithmic Equations
- 4.9 Fitting Log Functions to Data

### Vectors

- 5.1 Introduction to Vectors
- 5.2 Vectors in Two Dimensions
- 5.3 Adding & Subtracting Vectors
- 5.4 Multiplying Vectors by a Scalar
- 5.5 Vector Components
- 5.6 Vector Notation
- 5.7 Operations in Vector Noation
- 5.8 Dot Product

### Matrices

- 6.1 Introduction to Matrices
- 6.2 Basic Matrix Operations
- 6.3 Matrix Multiplication
- 6.4 Determinant of 2x2 Matrices
- 6.5 Determinant of 3x3 Matrices
- 6.6 Inverse of Matrices
- 6.7 Elementary Row Operations & Augmented Matrices
- 6.8 Using Matrices to Solve 2x2 Systems
- 6.9 Using Matrices to Solve 3x3 Systems

### Complex Numbers

- 7.1 Introduction to Complex
- 7.2 Adding and Subtracting Complex Numbers
- 7.3 Multiplying Complex Numbers
- 7.4 Complex Conjugate & Dividing
- 7.5 The Complex Plane
- 7.6 Modulus of Complex Numbers
- 7.7 Distance in the Complex Plane
- 7.8 Midpoint in the Complex Plane

### Trigonometric Functions

- 8.1 Introduction to Trigonometric Functions
- 8.2 Radian Measure
- 8.3 Standard Position & Reference Angles
- 8.4 Special Triangles and Exact Ratios
- 8.5 Graphing the Sine and Cosine Functions
- 8.6 Graphing the Tangent and Cotangent Functions
- 8.7 Graphing the Secant and Cosecant Functions
- 8.8 Applications of Trigonometric Functions
- 8.9 Modelling Trigonometric Functions
- 8.10 Inverse Trigonometric Functions

### Analytic Trigonometry

- 9.1 Introduction to Analytic Trigonometry
- 9.2 Cofunction, Periodicity and Negative Angle Identities
- 9.3 Addition and Subtraction Identities
- 9.4 Double and Half-Angle Identities
- 9.5 Product to Sum Identities
- 9.6 Solving Trigonometric Equations Algebraically
- 9.7 Solving Trigonometric Equations with Identities

### Conic Sections

- 10.1 Introduction to Conic Sections
- 10.2 Parabolas
- 10.3 Parabolas Part II
- 10.4 Circles
- 10.5 Circles Part II
- 10.6 Ellipses
- 10.7 Ellipses Part II
- 10.8 Hyperbolas
- 10.9 Hyperbolas Part II
- 10.10 Solving Non Linear Systems
- 10.11 Parametric Equations
- 10.12 Parametric Equations of Conic Sections

### Polar Coordinates

- 11.1 Introduction to Polar Coordinates
- 11.2 Converting Rectangular to Polar Coordinates
- 11.3 Converting Polar to Rectangular Coordinates
- 11.4 Polar Equations and Graphs
- 11.5 Eccentricity of Conic Sections
- 11.6 Polar Equations of Conic Sections
- 11.7 Complex Numbers in Polar Notation
- 11.8 Multiplication and Division with Polar Notation
- 11.9 DeMoivre's Theorem

### Sequence & Series

- 12.1 Introduction to Sequences and Series
- 12.2 Sequences & Series
- 12.3 Arithmetic Sequences
- 12.4 Arithmetic Series
- 12.5 Geometric Sequences
- 12.6 Finite Geometric Series
- 12.7 Infinite Geometric Series
- 12.8 Permutations and Combinations
- 12.9 Pascal's Triangle
- 12.10 Binomial Theorem

### Introduction to Calculus

- 13.1 Introduction to Calculus
- 13.2 Limits and Continuity
- 13.3 Limits Involving Infinity
- 13.4 Slope of a Tangent Line
- 13.5 The Power Rule
- 13.6 The Product and Quotient Rules
- 13.7 The Chain Rule
- 13.8 Applications of Derivatives
- 13.9 Antiderivatives
- 13.10 Integrals and the Area Under a Curve