Dual Enrollment Program DE Course: Math 1021 College Algebra
Dual Enrollment Program DE Course: Math 1021 College Algebra
Math 1021 College Algebra provides an in-depth treatment of solving equations and inequalities; function properties and graphs with transformations; inverse functions; linear, quadratic, polynomial, rational, exponential, and logarithmic functions with applications; systems of equations.
This is an LSU Integrative Learning Core (ILC) course that awards general education credit.
Note: Math 1021 is designed primarily to prepare students for success in subsequent courses in trigonometry and calculus. It is usually offered in the fall semester followed by Math 1022 Trigonometry in the spring semester. Math 1021 can also be offered in the spring semester for students who are not deemed prepared for Math 1021 in the fall. For the fall preceding Math 1021 in the spring, an LSU-created one-semester course for high school credit only titled Algebra III is available to be used as preparation for Math 1021. Students will need only one MyLab Math access code for either sequence.
Topics and Objectives
Chapter and section numbers refer to Algebra & Trigonometry, 4th edition
1.1 Linear and Rational Equations
(67 exercises)
- Determine whether equations are linear or nonlinear
- Solve linear equations with integer coefficients
- Solve linear equations involving fractions
- Solve linear equations involving decimals
- Identify rational equations
- Solve rational equations that lead to linear equations
1.4 Quadratic Equations
(62 exercises)
- Solve quadratic equations by factoring
- Solve quadratic equations using the square root property
- Solve quadratic equations using the quadratic formula
- Use the discriminant to determine the type of solutions of a quadratic equation
1.6 Other Types of Equations
(58 exercises)
- Solve higher-order polynomial equations
- Solve equations that are quadratic in form
- Solve equations involving single radical
1.7 Linear Inequalities
(39 exercises)
- Solve linear inequalities in one variable
- Solve three-part inequalities in one variable
1.8 Absolute Value Equations and Inequalities
(16 exercises)
- Solve absolute value equations
2.1 The Rectangular Coordinate System
(29 exercises)
- Plot ordered pairs
- Determine if an ordered pair lies on a graph
- Find intercepts of graphs from equations
- Find the midpoint of a line segment using the midpoint formula
- Find the distance between two points using the distance formula
2.2 Circles
(42 exercises)
- Write the standard form of an equation of a circle
- Find the center, radius, and intercepts and sketch the graph of circles given equations in standard form
- Find the center, radius, and intercepts and sketch the graph of circles given equations in general form
2.3 Lines
(60 exercises)
- Find the slopes of lines that pass through two given points
- Sketch the graph of a line given a point and the slope
- Find the equation of a line in point-slope form
- Find the equation of a line in slope-intercept form
- Find the equation of a line in standard form
- Find the slope and the y-intercept of a line in standard form and sketch the graph
- Sketch the graphs of lines given in standard form by plotting intercepts
- Find equations of horizontal lines and vertical lines
2.4 Parallel and Perpendicular Lines
(39 exercises)
- Determine whether two lines are parallel, perpendicular, or neither
- Find the equations of lines parallel to given lines
- Find the equations of lines perpendicular to given lines
3.1 Relations and Functions
(65 exercises)
- Find the domain and range of relations, and determine if relations represent functions
- Determine whether equations represent functions
- Use function notation to identify points that lie on graphs of functions
- Evaluate functions at given values
- Determine difference quotients
- Use the vertical line test to determine if graphs represent functions
- Classify functions as polynomials, rational functions, or root functions, and find their domains
3.2 Properties of a Function’s Graph
(54 exercises)
- Determine the intercepts of a function
- Determine the domain and range of functions from their graphs
- Determine where functions are increasing, decreasing, or constant
- Determine relative maximum and relative minimum values of a function
- Determine whether a function is even, odd, or neither
- Use graphs to evaluate or compare functions
- Identify function properties from graphs
3.3 Graphs of Basic Functions; Piecewise Functions
(41 exercises)
- Sketch the graphs of the basic functions
- Sketch graphs of basic functions with restricted domains
- Determine functions and their domains from graphs of piecewise-defined functions
- Graph and determine properties of piecewise-defined functions
3.4 Transformations of Functions
(54 exercises)
- Use vertical shifts to graph functions
- Use horizontal shifts to graph functions
- Use reflections to graph functions
- Use vertical stretches and compressions to graph functions
- Use combinations of transformations to graph functions
- Use transformations to sketch the graphs of piecewise-defined functions
3.5 Composite Functions
(23 exercises)
- Find composite functions
- Evaluate composite functions at a given point
3.6 One-to-One Functions; Inverse Functions
(46 exercises)
- Determine if functions are one-to-one
- Determine whether a function is one-to-one using the horizontal line test
- Determine if functions are inverses of one another
- Find inverses of one-to-one functions
- Sketch the graphs of inverse functions
- Use the graph of a function to determine properties of its inverse
4.1 Quadratic Functions
(39 exercises)
- Determine whether the graph of a quadratic function opens up or down
- Determine properties of quadratic function in vertex form and graph the function
- Determine properties of quadratic function using the vertex formula and graph the function
- Determine the equation of a quadratic function given its graph
4.2 Applications of Quadratic Functions
(14 exercises)
- Solve applications involving the maximum of projectile motion functions
- Solve applications involving the maximum of functions in economics
4.3 Graphs of Polynomial Functions
(47 exercises)
- Identify polynomial functions and their degree, leading coefficient, and constant term
- Sketch the graphs of power functions using transformations
- Use the end behavior of polynomial functions to describe the equation of the function
- Determine the intercepts of a polynomial function
- Determine the real zeros of polynomial functions and their multiplicities
- Sketch the graph of a polynomial function using the four-step process
- Determine a possible equation of a polynomial function given its graph
4.6 Rational Functions and Their Graphs
(40 exercises)
- Find the domain and intercepts of rational functions
- Identify vertical asymptotes of rational functions
- Identify horizontal asymptotes of rational functions
- Use transformations to sketch the graphs of rational functions
- Find removable discontinuities, intercepts, and asymptotes and sketch graphs of rational functions
5.1 Exponential Functions
(62 exercises)
- Evaluate exponential expressions
- Sketch the graphs of exponential functions
- Determine possible equations of exponential functions given their graphs
- Sketch the graphs of exponential functions using transformations
- Solve exponential equations by relating the bases
- Solve applications involving exponential functions
5.2 Logarithmic Functions
(62 exercises)
- Change equations between exponential form and logarithmic form
- Evaluate logarithmic expressions
- Use properties of logarithms to evaluate expressions
- Use common and natural logarithms
- Sketch the graphs of logarithmic functions
- Find the domain of logarithmic functions
5.3 Properties of Logarithms
(40 exercises)
- Expand and evaluate logarithmic expressions using properties of logarithms
- Condense and evaluate logarithmic expressions using properties of logarithms
- Solve logarithmic equations using the logarithm property of equality
- Use the change of base formula to approximate logarithmic expressions
- Use the change of base formula to solve logarithmic equations
5.4 Exponential and Logarithmic Equations
(48 exercises)
- Solve exponential equations
- Solve logarithmic equations
5.5 Applications of Exponential and Logarithmic Functions
(19 exercises)
- Solve applications involving compound interest
- Solve exponential growth and decay applications
12.1 Systems of Linear Equations in Two Variables
(20 exercises)
- Determine whether ordered pairs are solutions to systems of linear equations in two variables
- Solve systems of linear equations using the substitution method
- Solve systems of linear equations using the elimination method
- Solve systems of linear equations in two variables using either method
- Solve applications using a system of linear equations
Syllabus & Pacing Guide
| Name | Last Modified |
|---|---|
| S26 Math 1021 DE Syllabus [docx] | 2025-12-10 |
| S26 Math 1021 DE Pacing Guide [docx] | 2025-12-10 |
| F25 Math 1021 DE Syllabus [docx] | 2025-04-23 |
| F25 Math 1021 DE Pacing Guide [docx] | 2025-04-23 |
Course Profile
| Name | Last Modified |
|---|---|
| Math 1021 College Algebra COURSE PROFILE 6-10-2024 [docx] | 2025-12-10 |