The content and assignments for this College Algebra course are aligned with the following learning goals and outcomes. 

Lesson I: Algebra Essentials and Polynomial and Rational Expressions - Learners will be able to evaluate and simplify expressions that contain real numbers and variables, classify a real number, conduct calculations using order of operations, use the properties of real numbers, evaluate algebraic expressions, simplify exponential expressions, use scientific notation, evaluate and simplify square roots, rationalize a denominator that contains a square root, and write a radical expression using rational exponents.

In addition, they can 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 range of polynomials with fractional or negative exponents, and perform algebraic operations on rational expressions.

Lesson II: The Rectangular Coordinate System, Equations of Lines, and Equations and Inequalities - Learners will be able to 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, and 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.

Also, they were able to 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, and solve absolute value inequalities.

Lesson III: Function Basics, Algebraic Operations on Functions - Participants in this course would be able to determine whether a relation represents a function, find the value of a function, use the vertical line test to identify 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, 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, and use a graph to locate the absolute maximum and absolute minimum.

In addition, they will be able to 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 x-axis and the y-axis, graph functions using compressions and stretches, combine transformations, verify inverse functions, find or evaluate the inverse of a function, and use the graph of a one-to-one function to graph its inverse function on the same axes.

Lesson IV: Linear, Absolute Value Functions, and Quadratic Functions - They would be able to represent a linear function with an equation, words, a table, and a graph, determine whether a linear function is increasing, decreasing, or constant, and 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 its graph, including vertical and horizontal lines, match linear equations with their graphs, find the equations of vertical and horizontal lines, and use a linear model to make predictions.

Also, they can 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, determine a quadratic function’s minimum or maximum value, solve problems involving a quadratic function’s minimum or maximum value.

Lesson V: Power, Polynomial Functions, Rational, and Radical Functions - Learners will be able to identify power functions, the behavior of power functions, polynomial functions, the degree and leading coefficient of polynomial functions, local behavior of polynomial functions, zeros of polynomial functions with even and odd multiplicity, use the degree of a polynomial to determine the number of turning points in 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 its graph, use long division to divide polynomials, use synthetic division to divide polynomials, 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.
 
Also, they will learn how to use arrow notation to describe the 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, and solve problems involving joint variation.

Lesson VI: Exponential, Logarithmic Functions, Exponential, Logarithmic Equations, and Models - Learners should be able to 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, and convert from exponential to logarithmic form.

Also, will be able to 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 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, and build an exponential model from data.

Lesson VII: Systems of Equations, Inequalities, and Solve Systems With Matrices - Learners should be able to 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, and express the solution of a system of dependent equations containing three variables using standard notations.

In addition, they should be able to 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, and find the inverse of a matrix

Lesson VIII: Conic Sections, Sequences, and Series - They will be able to 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, write equations of parabolas in standard form, and graph parabolas with vertices, not at the origin.

Also, they will be able to 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 an explicit formula for a geometric sequence, use summation notation.

Lesson IX: Probability, Counting Principles, Rectangular Coordinates, and  Graphs - They will understand the Ordered Pairs, The Rectangular Coordinate System  The Distance Formula, The Midpoint formula, and Graphing Equations. They can 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, compute probabilities of equally likely outcomes, compute probabilities of the union of two events, use the complement rule to find probabilities, and compute probability using counting theory.

Lesson X: Quadratic Equations - Participants will learn how to solve a Quadratic Equation, Complete the Square, The Quadratic Formula, Solve for a Specified Variable, and The Discriminant.

Session XI: Exponential and Logarithmic Functions - Exponential Functions, Compound Interest Formula, The Number 𝑒, Exponential Model, Continuous Growth/Decay Formula, Continuous Growth/Decay, Graphs of Exponential Functions, Graphing a Vertical or Horizontal Shift, Horizontal and Vertical Translations, Vertical Stretch and Compression, Reflections of Exponential Functions, Natural Logarithms.

Session XII: Exponential and Logarithmic Equations and Models - Product Rule for Logarithms, Quotient Rule for Logarithms, Power Rule for Logarithms, Condense Logarithmic Expressions, Change of Base for Logarithms, Exponential Equations, Exponential Equations with a Common Base, Equations Containing 𝑒, Extraneous Solutions.