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
Linear Equations
- Recognizing linear equations
- Solving linear equations with integer coefficients
- Solving linear equations involving fractions
- Solving linear equations involving decimals
- Recognizing rational equations
- Solving rational equations that lead to linear equations
Quadratic Equations
- Solving quadratic equations by factoring and the zero product property
- Solving quadratic equations using the square root property
- Solving quadratic equations using the quadratic formula
- Using the discriminant to determine the type of solutions of a quadratic equation
Other Types of Equations
- Solving higher-order polynomial equations
- Solving equations that are quadratic in form
- Solving equations involving single radicals
Linear Inequalities
- Solving linear inequalities
- Solving three-part inequalities
Absolute Value Equations and Inequalities
- Solving an absolute value equation
- Solving an absolute value “less than” inequality
- Solving an absolute value “greater than” inequality
The Rectangular Coordinate System
- Plotting ordered pairs
- Finding intercepts of a graph given an equation
- Finding the midpoint of a line segment using the midpoint formula
- Finding the distance between two points using the distance formula
Circles
- Writing the standard form of an equation of a circle
- Sketching the graph of a circle
- Converting the general form of a circle into standard form
Lines
- Determining the slope of a line
- Sketching a line given a point and the slope
- Finding the equation of a line using the point-slope form
- Finding the equation of a line using the slope-intercept form
- Writing the equation of a line in standard form
- Finding the slope and the y-intercept of a line in standard form
- Sketching lines by plotting intercepts
- Finding the equation of a horizontal line and a vertical line
Parallel and Perpendicular Lines
- Understanding the definition of parallel lines
- Understanding the definition of perpendicular lines
- Determining whether two lines are parallel, perpendicular, or neither
- Finding the equations of parallel and perpendicular lines
Relations and Functions
- Understanding the definitions of relations and functions
- Determining whether equations represent functions
- Using function notation; evaluating functions
- Using the vertical line test
- Determining the domain of a function given the equation
Properties of a Function’s Graph
- Determining the intercepts of a function
- Determining the domain and range of a function from its graph
- Determining whether a function is increasing, decreasing, or constant
- Determining relative maximum and relative minimum values of a function
- Determining whether a function is even, odd, or neither
- Determining information about a function from a graph
Graphs of Basic Functions; Piecewise Functions
- Sketching the graphs of the basic functions
- Sketching the graphs of basic functions with restricted domains
- Analyzing piecewise-defined functions
Transformations of Functions
- Using vertical shifts to graph functions
- Using horizontal shifts to graph functions
- Using reflections to graph functions
- Using vertical stretches and compressions to graph functions
- Using combinations of transformations to graph functions
Composite Functions
- Forming and evaluating composite functions
- Determining the domain of composite functions
One-to-One Functions; Inverse Functions
- Understanding the definition of a one-to-one function
- Determining whether a function is one-to-one using the horizontal line test
- Understanding and verifying inverse functions
- Sketching the graphs of inverse functions
- Finding the inverse of a one-to-one function
Quadratic Functions
- Understanding the definition of a quadratic function and its graph
- Graphing quadratic functions written in vertex form
- Graphing quadratic functions using the vertex formula
- Determining the equation of a quadratic function given its graph
Applications and Modeling of Quadratic Functions
- Maximizing projectile motion functions
- Maximizing functions in economics
The Graphs of Polynomial Functions
- Understanding the definition of a polynomial function
- Sketching the graphs of power functions
- Determining the end behavior of polynomial functions
- Determining the intercepts of a polynomial function
- Determining the real zeros of polynomial functions and their multiplicities
- Sketching the graph of a polynomial function
- Determining a possible equation of a polynomial function given its graph
Rational Functions and Their Graphs
- Finding the domain and intercepts of rational functions
- Identifying vertical asymptotes
- Identifying horizontal asymptotes
- Using transformations to sketch the graphs of rational functions
- Finding removable discontinuities, intercepts, asymptotes and sketch graphs of rational functions
Exponential Functions
- Understanding the characteristics of exponential functions
- Sketching the graphs of exponential functions using transformations
- Solving exponential equations by relating the bases
- Solving applications of exponential functions
Logarithmic Functions
- Understanding the definition of a logarithmic function
- Evaluating logarithmic expressions
- Understanding the properties of logarithms
- Using the common and natural logarithms
- Understanding the characteristics of logarithmic functions
- Sketching the graphs of logarithmic functions using transformations
- Finding the domain of logarithmic functions
Properties of Logarithms
- Using the product rule, quotient rule, and power rule for logarithms
- Expanding and condensing logarithmic expressions
- Solving logarithmic equations using the logarithm property of equality
- Using the change of base formula
Exponential and Logarithmic Equations
- Solving exponential equations
- Solving logarithmic equations
Applications of Exponential and Logarithmic Functions
- Solving compound interest applications
- Solving exponential growth and decay applications
Systems of Equations
- Verifying solutions to a system of linear equations in two variables
- Solving a system of linear equations using the substitution method
- Solving a system of linear equations using the elimination method
- Solving applied problems 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 |