Learning Outcomes

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

Module 1: Algebra Essentials

• Review topics needed for success in Algebra Essentials
• Identify types of real numbers and use them in algebraic expressions
• Evaluate expressions involving exponents and perform calculations with numbers in scientific notation
• Simplify radical expressions and solve equations with rational exponents

Module 2: Polynomial and Rational Expressions

• Review topics needed for success in Polynomial and Rational expressions
• Create and evaluate expressions involving polynomials
• Use a variety of methods to factor polynomial expressions
• Evaluate and simplify rational expressions

Module 3: The Rectangular Coordinate System and Equations of Lines

• Review topics needed for success in The Rectangular Coordinate System and Equations of Lines
• Plot points and lines on the coordinate plane and calculate distances based on their locations
• Evaluate linear equations

Module 4: Equations and Inequalities

• Review topics needed for success in Equations and Inequalities
• Solve special types of equations that involve radicals, absolute value, and polynomials
• Write linear equations to model real world scenarios
• Factor to solve quadratic equations and use the quadratic formula
• Use properties of inequalities to solve linear and absolute value inequalities

Module 5: Function Basics

• Review topics needed for success in Function Basics
• Identify characteristics of common functions and their graphs
• Find the domain and range of a function from its equation or its graph
• Find rates of change of a function and identify behaviors of various graphs

Module 6: Algebraic Operations on Functions

• Review topics needed for success in Algebraic Operations on Functions
• Create and evaluate compositions of functions
• Graph and evaluate transformations of functions
• Find and evaluate the inverse of a function

Module 7: Linear and Absolute Value Functions

• Review topics needed for success in Linear and Absolute Value Functions
• Write and interpret a linear function
• Graph, write, and analyze equations of linear functions
• Model problems with linear functions and draw conclusions from those results

Module 8: Quadratic Functions

• Review topics needed for success in Quadratic Functions
• Make calculations with complex numbers
• Identify characteristics of quadratic functions and their resulting parabolas
• Solve problems involving quadratic roots, intercepts, and maximums/minimums

Module 9: Power and Polynomial Functions

• Review topics needed for success in Power and Polynomial Functions
• Identify degrees and describe behaviors of polynomial functions
• Create graphs and write equations for polynomial functions
• Use multiple techniques to divide polynomials
• Use multiple methods for finding zeros of polynomial equations

Module 10: Rational and Radical Functions

• Review topics needed for success in Rational and Radical Functions
• Analyze and graph rational functions
• Evaluate the inverse of polynomial and radical functions
• Solve variation functions

Module 11: Exponential and Logarithmic Functions

• Review topics needed for success in Exponential and Logarithmic Functions
• Find and evaluate exponential functions
• Graph exponential functions and evaluate the results
• Evaluate logarithms and covert between logarithmic to exponential form
• Graph logarithmic functions and evaluate the results

Module 12: Exponential and Logarithmic Equations and Models

• Review topics needed for success in Exponential and Logarithmic Equations and Models
• Rewrite logarithmic expressions using a combination of logarithm rules and formulas
• Solve exponential and logarithmic equations both algebraically and graphically
• Graph and solve real world problems involving data that follow logarithmic or exponential growth and decay trends

Module 13: Systems of Equations and Inequalities

• Review topics needed for success in Systems of Equations and Inequalities
• Solve systems of linear equations with two variables
• Use various techniques to solve systems of nonlinear equations
• Solve equations involving three variables
• Use systems of equations to decompose rational expressions

Module 14: Solve Systems With Matrices

• Review topics needed for success in Solve Systems With Matrices
• Make calculations with matrices
• Use matrices to solve a system of equations
• Use inverses to solve systems of equations

Module 15: Conic Sections

• Review topics needed for success in Conic Sections
• Evaluate, graph, and solve problems involving ellipses
• Evaluate, graph, and solve problems involving hyperbolas
• Evaluate, graph, and solve problems involving parabolas

Module 16: Sequences and Series

• Review of topics needed for success in Sequences and Series
• Identify the terms of a sequence and use factorial notation
• Use formulas to make calculations for an arithmetic sequence or find a term in the sequence
• Use formulas to make calculations for an geometric sequence or find a term in the sequence
• Use summation notation and other formulas to make calculations for a series

Module 17: Probability and Counting Principles

• Review of topics needed for success in Probability and Counting Principles
• Use counting principles to solve real world scenarios
• Construct probability models and compute probability to solve problems