# Pre-Calculus Curriculum Map

Pre-Calculus Curriculum Map with CCS

## Unit 0 – Preparing for Pre-Calculus

0-1   Sets

0-2   Operations with Complex Numbers

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

2-2   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

4-3   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