The content, assignments, and assessments for Precalculus are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Precalculus Learning Outcomes.

## Module 1: Introduction to Functions

### Describe properties of functions and their relationships

- Identify and evaluate functions
- Calculate the domain and range of a function
- Describe change behaviors of graphs
- Evaluate composite functions
- Transform functions
- Solve absolute value functions
- Find inverse functions

## Module 2: Linear Functions

### Understand linear functions, their graphs, and how they relate to data

- Evaluate linear functions
- Graph linear functions
- Model real world scenarios with linear functions
- Use linear models of data to make predictions

## Module 3: Polynomial and Rational Functions

### Evaluate polynomial and rational functions and their graphs

- Simplify complex number expressions
- Understand quadratic functions
- Identify power functions and polynomial functions
- Graph polynomial functions
- Divide polynomial functions
- Find the zeros of polynomial equations
- Graph rational functions
- Find inverse functions
- Solve direct, indirect, and joint variation problems

## Module 4: Exponential and Logarithmic Functions

### Model growth and decay patterns with exponential and logarithmic functions

- Evaluate exponential functions
- Graph exponential functions
- Use logarithmic functions
- Graph logarithmic functions
- Expand and condense logarithmic expressions
- Solve exponential and logarithmic equations
- Use exponential and logarithmic models
- Fit exponential models to data

## Module 5: Systems of Equations and Inequalities

### Evaluate systems of linear and non-linear equations with both two and three variables

- Solve systems of linear equations in two variables
- Solve systems of linear equations in three variables
- Solve and graph systems of nonlinear equations and inequalities
- Decompose partial fractions
- Evaluate matrices and matrix operations
- Write and solve systems with Gaussian Elimination
- Solve systems with inverses
- Solve systems with Cramer’s rule

## Module 6: Sequences, Probability, and Counting Theory

### Solve sequence and counting problems

- Write the terms of a sequence
- Evaluate arithmetic sequences
- Evaluate geometric sequences
- Find the terms of a series
- Solve counting problems
- Use the binomial theorem
- Compute probabilities

## Module 7: Trigonometric Functions

### Evaluate trigonometric functions using angles and right triangles

- Find and use angles
- Evaluate sine and cosine functions
- Understand other trigonometric functions
- Use right triangle trigonometry

## Module 8: Periodic Functions

### Analyze the graphs of trigonometric functions

- Graph sine and cosine functions
- Analyze and graph other trigonometric functions
- Use inverse trigonometric functions

## Module 9: Trigonometric Identities and Equations

### Solve trigonometric equations using identities

- Solve trigonometric equations with identities
- Use sum and difference formulas
- Use double-angle, half-angle, and reduction formulas
- Use sum-to-product and product-to-sum formulas
- Solve trigonometric equations
- Model trigonometric equations

## Module 10: Further Applications of Trigonometry

### Apply trigonometric rules to evaluate more complex graphs and equations

- Solve non-right triangles using the Law of Sines
- Solve non-right triangles using the Law of Cosines
- Identify and use polar coordinates
- Graph polar equations
- Evaluate the polar form of complex numbers
- Find parametric equations
- Graph parametric equations
- Perform vector operations

## Module 11: Analytic Geometry

### Analyze the graphs and equations of conic sections

- Evaluate ellipses
- Evaluate hyperbolas
- Evaluate parabolas
- Evaluate the rotation of axes
- Evaluate conic sections in polar coordinates

## Module 12: Introduction to Calculus

### Describe how to find limits and derivatives of functions

- Find limits using graphs and tables
- Find limits using properties
- Determine continuity of functions
- Find the derivative of a function