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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.

Unit 1

Review of Functions and Quadratics

  1. 1.1 Introduction to Functions
  2. 1.2 Domain of a Function and Interval Notation
  3. 1.3 Range of a Function and Interval Notation
  4. 1.4 Composition of Functions
  5. 1.5 Inverse of Functions
  6. 1.6 Introduction to Quadratic Functions
  7. 1.7 Graphing Quadratic Functions in Vertex Form
  8. 1.8 Solving Quadratic Equations with Square Roots
  9. 1.9 Solving Quadratics by Completing the Square
  10. 1.10 Converting to Vertex Form by Completing the Square
  11. 1.11 Graphing Quadratic Inequalities

Unit 2

Polynomial Functions

  1. 2.1 Introduction to Polynomials
  2. 2.2 Finding a Polynomial Given the Roots
  3. 2.3 Dividing Polynomials Using Long Division
  4. 2.4 Dividing Polynomials Using Synthetic Division
  5. 2.5 Remainder Theorem/Factor Theorem
  6. 2.6 Location principle & Multiplicity of Zeros
  7. 2.7 Rational Root Theorem
  8. 2.8 Complex Conjugate Root Theorem
  9. 2.9 Fundamental Theorem of Algebra & Descartes Rule of signs
  10. 2.10 Graphing Polynomials

Unit 3

Rational Functions

  1. 3.1 Introduction to Rational Functions
  2. 3.2 Graphing Rational Functions
  3. 3.3 Graphing Rational Functions Part II
  4. 3.4 Slant Asymptotes
  5. 3.5 Parabolic Asymptotes
  6. 3.6 Multiplying and Dividing Rational Expressions
  7. 3.7 Solving Rational Equations

Unit 4

Exponential & Logarithmic Functions

  1. 4.1 Introduction to Exponential & Logarithmic Functions
  2. 4.2 Graphing Exponential Functions
  3. 4.3 Logarithmic Functions and Change of Base Formula
  4. 4.4 Properties of Logarithms
  5. 4.5 Exponential/Logarithmic Inverse Property
  6. 4.6 Natural Exponentials & Logarithms
  7. 4.7 Solving Exponential Equations
  8. 4.8 Solving Logarithmic Equations
  9. 4.9 Fitting Log Functions to Data

Unit 5

Vectors

  1. 5.1 Introduction to Vectors
  2. 5.2 Vectors in Two Dimensions
  3. 5.3 Adding & Subtracting Vectors
  4. 5.4 Multiplying Vectors by a Scalar
  5. 5.5 Vector Components
  6. 5.6 Vector Notation
  7. 5.7 Operations in Vector Noation
  8. 5.8 Dot Product

Unit 6

Matrices

  1. 6.1 Introduction to Matrices
  2. 6.2 Basic Matrix Operations
  3. 6.3 Matrix Multiplication
  4. 6.4 Determinant of 2x2 Matrices
  5. 6.5 Determinant of 3x3 Matrices
  6. 6.6 Inverse of Matrices
  7. 6.7 Elementary Row Operations & Augmented Matrices
  8. 6.8 Using Matrices to Solve 2x2 Systems
  9. 6.9 Using Matrices to Solve 3x3 Systems

Unit 7

Complex Numbers

  1. 7.1 Introduction to Complex
  2. 7.2 Adding and Subtracting Complex Numbers
  3. 7.3 Multiplying Complex Numbers
  4. 7.4 Complex Conjugate & Dividing
  5. 7.5 The Complex Plane
  6. 7.6 Modulus of Complex Numbers
  7. 7.7 Distance in the Complex Plane
  8. 7.8 Midpoint in the Complex Plane

Unit 8

Trigonometric Functions

  1. 8.1 Introduction to Trigonometric Functions
  2. 8.2 Radian Measure
  3. 8.3 Standard Position & Reference Angles
  4. 8.4 Special Triangles and Exact Ratios
  5. 8.5 Graphing the Sine and Cosine Functions
  6. 8.6 Graphing the Tangent and Cotangent Functions
  7. 8.7 Graphing the Secant and Cosecant Functions
  8. 8.8 Applications of Trigonometric Functions
  9. 8.9 Modelling Trigonometric Functions
  10. 8.10 Inverse Trigonometric Functions

Unit 9

Analytic Trigonometry

  1. 9.1 Introduction to Analytic Trigonometry
  2. 9.2 Cofunction, Periodicity and Negative Angle Identities
  3. 9.3 Addition and Subtraction Identities
  4. 9.4 Double and Half-Angle Identities
  5. 9.5 Product to Sum Identities
  6. 9.6 Solving Trigonometric Equations Algebraically
  7. 9.7 Solving Trigonometric Equations with Identities

Unit 10

Conic Sections

  1. 10.1 Introduction to Conic Sections
  2. 10.2 Parabolas
  3. 10.3 Parabolas Part II
  4. 10.4 Circles
  5. 10.5 Circles Part II
  6. 10.6 Ellipses
  7. 10.7 Ellipses Part II
  8. 10.8 Hyperbolas
  9. 10.9 Hyperbolas Part II
  10. 10.10 Solving Non Linear Systems
  11. 10.11 Parametric Equations
  12. 10.12 Parametric Equations of Conic Sections

Unit 11

Polar Coordinates

  1. 11.1 Introduction to Polar Coordinates
  2. 11.2 Converting Rectangular to Polar Coordinates
  3. 11.3 Converting Polar to Rectangular Coordinates
  4. 11.4 Polar Equations and Graphs
  5. 11.5 Eccentricity of Conic Sections
  6. 11.6 Polar Equations of Conic Sections
  7. 11.7 Complex Numbers in Polar Notation
  8. 11.8 Multiplication and Division with Polar Notation
  9. 11.9 DeMoivre's Theorem

Unit 12

Sequence & Series

  1. 12.1 Introduction to Sequences and Series
  2. 12.2 Sequences & Series
  3. 12.3 Arithmetic Sequences
  4. 12.4 Arithmetic Series
  5. 12.5 Geometric Sequences
  6. 12.6 Finite Geometric Series
  7. 12.7 Infinite Geometric Series
  8. 12.8 Permutations and Combinations
  9. 12.9 Pascal's Triangle
  10. 12.10 Binomial Theorem

Unit 13

Introduction to Calculus

  1. 13.1 Introduction to Calculus
  2. 13.2 Limits and Continuity
  3. 13.3 Limits Involving Infinity
  4. 13.4 Slope of a Tangent Line
  5. 13.5 The Power Rule
  6. 13.6 The Product and Quotient Rules
  7. 13.7 The Chain Rule
  8. 13.8 Applications of Derivatives
  9. 13.9 Antiderivatives
  10. 13.10 Integrals and the Area Under a Curve