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Study Guides > College Algebra CoRequisite Course

Learning Outcomes

icon of a magnifying glass over a list The content, assignments, and assessments for College Algebra are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: College Algebra Learning Outcomes COMING SOON.

Module 1: Algebra Essentials

Evaluate and simplify expressions that contain both real numbers and variables

  • Classify a real number
  • Perform calculations using order of operations.
  • Use the properties of real numbers
  • Evaluate and simplify algebraic expressions.
  • Use the rules of exponents to simplify exponential expressions
  • Use scientific notation
  • Evaluate and simplify square roots
  • Rationalize a denominator that contains a square root
  • Rewrite a radical expression using rational exponents

Module 2: Polynomial and Rational Expressions

  • Identify the degree, leading coefficient, and leading term of a polynomial expression
  • Perform algebraic operations on polynomial expressions
  • Identify the greatest common factor of a polynomial expression
  • Factor a wide variety of polynomials including those with fractional or negative exponents
  • Simplify and perform algebraic operations on rational expressions

Module 3: The Rectangular Coordinate System and Equations of Lines

  • Plot ordered pairs, and graph equations by plotting points
  • Use a graphing utility to graph equations
  • Find the x and y intercepts of a graphed equation
  • Use the distance and midpoint formulas
  • Write equations of lines in slope-intercept, point-slope, and standard forms
  • Identify the equations and graphs of horizontal and vertical lines
  • Determine whether two lines are parallel, perpendicular, or neither
  • Write equations of lines that are parallel or perpendicular to another line
  • Develop a problem solving method
  • Write an equation to model an application
  • Solve distance, rate and time problems
  • Solve perimeter, area, and volume problems

Module 4: Equations and Inequalities

  • Solve equations involving rational exponents
  • Solve equations using factoring
  • Solve radical equations
  • Solve absolute value equations
  • Set up a linear equation to solve a real-world application
  • Use a formula to solve a real-world application
  • Solve quadratic equations by factoring
  • Solve quadratic equations by the square root property
  • Solve quadratic equations by completing the square
  • Solve quadratic equations by using the quadratic formula
  • Use interval notation
  • Use properties of inequalities
  • Solve inequalities in one variable algebraically
  • Solve absolute value inequalities

Module 5: Function Basics

  • Determine whether a relation represents a function
  • Find the value of a function
  • Determine whether a function is one-to-one
  • Use the vertical line test to identify functions
  • Graph the functions listed in the library of functions
  • Find the domain of a function defined by an equation
  • Write Domain and Range Using Standard Notations
  • Find Domain and Range from a Graph
  • Define Domain and Range of Toolkit Functions
  • Graph Piecewise-Defined Functions
  • Find the average rate of change of a function
  • Use a graph to determine where a function is increasing, decreasing, or constant
  • Use a graph to locate local maxima and local minima
  • Use a graph to locate the absolute maximum and absolute minimum

Module 6: Algebraic Operations on Functions

  • Combine functions using algebraic operations
  • Create a new function by composition of functions
  • Evaluate composite functions
  • Find the domain of a composite function
  • Decompose a composite function into its component functions
  • Graph functions using vertical and horizontal shifts
  • Graph functions using reflections about the [latex]x[/latex] -axis and the [latex]y[/latex] -axis
  • Determine whether a function is even, odd, or neither from its graph
  • Graph functions using compressions and stretches
  • Combine transformations
  • Verify inverse functions
  • Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
  • Find or evaluate the inverse of a function
  • Use the graph of a one-to-one function to graph its inverse function on the same axes

Module 7: Linear and Absolute Value Functions

  • Represent a linear function with an equation, words, a table and a graph
  • Determine whether a linear function is increasing, decreasing, or constant.
  • Write and interpret a linear function.
  • Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations
  • Write the equation of a linear function given it's graph, including vertical and horizontal lines, match linear equations with their graphs
  • Find the equations of vertical and horizontal lines
  • Graph an absolute value function, find it's intercepts
  • Identify steps for modeling and solving.
  • Build linear models from verbal descriptions.
  • Draw and interpret scatter plots.
  • Find the line of best fit using an online graphing calculator calculator.
  • Distinguish between linear and nonlinear relations.
  • Use a linear model to make predictions.

Module 8: Quadratic Functions

  • Express square roots of negative numbers as multiples of i
  • Plot complex numbers on the complex plane
  • Add and subtract complex numbers
  • Multiply and divide complex numbers
  • Recognize characteristics of parabolas
  • Understand how the graph of a parabola is related to its quadratic function
  • Use the quadratic formula and factoring to find both real and complex roots (x-intercepts) of quadratic functions
  • Use algebra to find the y-intercepts of a quadratic function
  • Solve problems involving the roots and intercepts of a quadratic function
  • Use the discriminant to determine the nature (real or complex) and quantity of solutions to quadratic equations
  • Determine a quadratic function’s minimum or maximum value
  • Solve problems involving a quadratic function’s minimum or maximum value

Module 9: Power and Polynomial Functions

  • Identify power functions.
  • Identify end behavior of power functions.
  • Identify polynomial functions.
  • Identify the degree and leading coefficient of polynomial functions.
  • Identify local behavior of polynomial functions.
  • Identify zeros of polynomial functions with even and odd multiplicity
  • Use the degree of a polynomial to determine the number of turning points of its graph
  • Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem
  • Write the equation of a polynomial function given it's graph
  • Use long division to divide polynomials.
  • Use synthetic division to divide polynomials.
  • Evaluate a polynomial using the Remainder Theorem.
  • Use the Factor Theorem to solve a polynomial equation.
  • Use the Rational Zero Theorem to find rational zeros.
  • Find zeros of a polynomial function.
  • Use the Linear Factorization Theorem to find polynomials with given zeros.
  • Use Descartes’ Rule of Signs.
  • Solve real-world applications of polynomial equations

Module 10: Rational and Radical Functions

  • Use arrow notation to describe end behavior of rational functions
  • Solve applied problems involving rational functions.
  • Find the domains of rational functions.
  • Identify vertical and horizontal asymptotes of graphs of rational functions
  • Graph rational functions.
  • Find the inverse of a polynomial function.
  • Restrict the domain to find the inverse of a polynomial function.
  • Solve direct variation problems.
  • Solve inverse variation problems.
  • Solve problems involving joint variation.

Module 11: Exponential and Logarithmic Functions

  • Evaluate an exponential growth function with different bases
  • Use a compound interest Formula
  • Write an exponential function
  • Find an exponential function given a graph
  • Use a graphing calculator to find an exponential function
  • Find an exponential function that models continuous growth or decay
  • Graph exponential functions, determine whether a graph represents exponential growth or decay
  • Graph exponential functions using transformations.
  • Convert from logarithmic to exponential form.
  • Convert from exponential to logarithmic form.
  • Evaluate common and natural logarithms.
  • Identify the domain of a logarithmic function.
  • Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote
  • Identify why and how a logarithmic function is an inverse of an exponential function

Module 12: Exponential and Logarithmic Equations and Models

  • Use power, product, and quotient rules to expand and condense logarithms
  • Use the change-of-base formula for logarithms.
  • Use like bases to solve exponential equations.
  • Use logarithms to solve exponential equations.
  • Use the definition of a logarithm to solve logarithmic equations.
  • Use the one-to-one property of logarithms to solve logarithmic equations.
  • Solve applied problems involving exponential and logarithmic equations.
  • Model exponential growth and decay.
  • Use Newton’s Law of Cooling.
  • Use logistic-growth models.
  • Choose an appropriate model for data.
  • Express an exponential model in base e.
  • Build an exponential model from data.

Module 13: Systems of Equations and Inequalities

  • Solve systems of equations by graphing, substitution, and addition.
  • Identify inconsistent systems of equations containing two variables.
  • Express the solution of a system of dependent equations containing two variables using standard notations.
  • Solve a system of nonlinear equations using substitution or elimination.
  • Graph a nonlinear inequality.
  • Graph a system of nonlinear inequalities.
  • Solve systems of three equations in three variables.
  • Identify inconsistent systems of equations containing three variables.
  • Express the solution of a system of dependent equations containing three variables using standard notations.
  • Decompose   [latex]\frac{{P( x )}}{{ Q( x )}}[/latex] ,  where  Q( x )  has only nonrepeated linear factors.
  • Decompose  [latex]\frac{{P( x )}}{{ Q( x )}}[/latex] ,  where  Q( x )  has repeated linear factors.
  • Decompose  [latex]\frac{{P( x )}}{{ Q( x )}}[/latex] ,  where  Q( x )  has a nonrepeated irreducible quadratic factor.
  • Decompose  [latex]\frac{{P( x )}}{{ Q( x )}}[/latex] ,  where  Q( x )  has a repeated irreducible quadratic factor.

Module 14: Solve Systems With Matrices

  • Find the sum and difference of two matrices.
  • Find scalar multiples of a matrix.
  • Find the product of two matrices.
  • Write the augmented matrix of a system of equations.
  • Write the system of equations from an augmented matrix.
  • Perform row operations on a matrix.
  • Solve a system of linear equations using matrices.
  • Find the inverse of a matrix.
  • Solve a system of linear equations using an inverse matrix.

Module 15: Conic Sections

  • Write equations of ellipses in standard form
  • Graph ellipses centered at the origin
  • Graph ellipses not centered at the origin
  • Solve applied problems involving ellipses
  • Locate a hyperbola’s vertices and foci
  • Write equations of hyperbolas in standard form
  • Graph hyperbolas centered at the origin
  • Graph hyperbolas not centered at the origin
  • Solve applied problems involving hyperbolas
  • Graph parabolas with vertices at the origin
  • Write equations of parabolas in standard form
  • Graph parabolas with vertices not at the origin
  • Solve applied problems involving parabolas

Module 16: Sequences and Series

  • Write the terms of a sequence defined by an explicit formula
  • Write the terms of a sequence defined by a recursive formula
  • Use factorial notation
  • Find the common difference for an arithmetic sequence
  • Write terms of an arithmetic sequence
  • Use a recursive formula for an arithmetic sequence
  • Use an explicit formula for an arithmetic sequence
  • Find the common ratio for a geometric sequence
  • List the terms of a geometric sequence
  • Use a recursive formula for a geometric sequence
  • Use an explicit formula for a geometric sequence
  • Use summation notation
  • Use the formula for the sum of the first [latex]n[/latex] terms of an arithmetic series
  • Use the formula for the sum of the first [latex]n[/latex] terms of a geometric series
  • Use the formula for the sum of an infinite geometric series
  • Solve annuity problems

Module 17: Probability and Counting Principles

  • Solve counting problems using the Addition Principle and the Multiplication Principle
  • Solve counting problems using permutations and combinations  involving n distinct objects
  • Find the number of subsets of a given set
  • Solve counting problems using permutations involving n non-distinct objects
  • Apply the Binomial Theorem
  • Construct probability models
  • Compute probabilities of equally likely outcomes
  • Compute probabilities of the union of two events
  • Use the complement rule to find probabilities
  • Compute probability using counting theory

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