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Pre-Calculus Curriculum Table of Contents

Unit 0 – Preparing for Pre-Calculus

0-1 Sets

0-2 Operations with Complex Numbers

0-3 Quadratic Functions and Equations

0-4 nth Roots and Real Exponents

0-5 Systems of Linear Equations and Inequalities

0-6 Matrix Operations

0-7 Probability with Permutations and Combinations

0-8 Statistics

Unit 1 – Functions and Relations

1-1 Functions

1-2 Analyzing Graphs of Functions and Relations

1-3 Continuity, End Behavior, and Limits

1-4 Extrema and Average Rates of Change

1-5 Parent Functions and Transformations

1-6 Function Operations and Composition of Functions

1-7 Inverse Relations and Functions

Unit 2 – Power, Polynomial, and Rational Functions

2-1 Power and Radical Functions

2-2 Polynomial Functions

2-3 The Remainder and Factor Theorems

2-4 Zeros of Polynomial Functions

2-5 Rational Functions

2-6 Nonlinear Inequalities

Unit 3 – Exponential and Logarithmic Functions

3-1 Exponential Functions

3-2 Logarithmic Functions

3-3 Properties of Logarithms

3-4 Exponential and Logarithmic Equations

3-5 Modeling with Nonlinear Regression

Unit 4 – Trigonometric Functions

4-1 Right Triangle Trigonometry

4-2 Degrees and Radians

4-3 Trigonometric Functions on the Unit Circle

4-4 Graphing Sine and Cosine Functions

4-5 Graphing Other Trigonometric Functions

4-6 Inverse Trigonometric Functions

4-7 The Law of Sines and the Law of Cosines

Unit 5 – Trigonometric Identities and Equations

5-1 Trigonometric Identities

5-2 Verifying Trigonometric Identities

5-3 Solving Trigonometric Equations Exercises

5-4 Sum and Difference Formulas

5-5 Multiple-Angle and Product-to-Sum Identities

Unit 6 – Systems of Equations and Matrices

6-1 Multivariable Linear Systems and Row Operations

6-2 Matrix Multiplication, Inverses, and Determinants

6-3 Solving Linear Systems Using Inverses and Cramer’s Rule

6-4 Partial Fractions

6-5 Linear Optimization

Unit 7 – Conic Sections and Parametric Equations

7-1 Parabolas

7-2 Ellipses and Circles

7-3 Hyperbolas

7-4 Rotations of Conic Sections

7-5 Parametric Equations

Unit 8 – Vectors

8-1 Introduction to Vectors

8-2 Vectors in the Coordinate Plane

8-3 Dot Products and Vector Projections

8-4 Vectors in Three-Dimensional Space

8-5 Dot and Cross Products of Vectors in Space

Unit 9 – Polar Coordinates and Complex Numbers

9-1 Polar Coordinates

9-2 Graphs of Polar Equations

9-3 Polar and Rectangular Forms of Equations

9-4 Polar Forms of Conic Sections

9-5 Complex Numbers and DeMoivre’s Theorem

Unit 10 – Sequences and Series

10-1 Sequences, Series, and Sigma Notation

10-2 Arithmetic Sequences and Series

10-3 Geometric Sequences and Series

10-4 Mathematical Induction

10-5 The Binomial Theorems

10-6 Functions as Infinite Series

Unit 11 – Inferential Statistics

11-1 Descriptive Statistics

11-2 Probability Distributions

11-3 The Normal Distribution

11-4 The Central Limit Theorem

11-5 Confidence Intervals

11-6 Hypothesis Testing

11-7 Correlation and Linear Regression

Unit 12 – Limits and Derivatives

12-1 Estimating Limits Graphically

12-2 Evaluating Limits Algebraically

12-3 Tangent Lines and Velocity

12-4 Derivatives

12-5 Area Under a Curve and Integrations

12-6 The Fundamental Theorem of Calculus