Learning Outcomes

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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