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