Math 1021 College Algebra

Math 1021 College Algebra provides an in-depth treatment of solving equations and inequalities; function properties and graphs; inverse functions; linear, quadratic, polynomial, rational, exponential and logarithmic functions with applications; systems of equations.

Course Eligibility

To enroll in Math 1021 Coreq (linked with Math 1020), you must meet one of the following requirements:

  • Math ACT at least 17 but less than 21; or,
  • ALEKS at least 30 but less than 41; or,
  • Math SAT at least 470 but less than 530.

To enroll in regular Math 1021, you must meet one of the following requirements:

  • Math ACT at least 21 but less than 25; or,
  • ALEKS at least 41 but less than 61; or,
  • Math SAT at least 530 but less than 590.

Incoming freshmen with a Math ACT score of 25 or greater receive automatic credit for Math 1021.

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

Math 1021 College Algebra Syllabus
NameLast Modified

Daily Schedule

Math 1021 College Algebra Daily Schedule
NameLast Modified

Class Notes

Math 1021 College Algebra Class Notes
NameLast Modified
Section 1.1a Linear and Rational Equations [docx]2024-08-05
Section 1.1a Linear and Rational Equations [pdf]2024-08-05
Section 1.7 Linear Inequalities in One Variable [docx]2024-08-05
Section 1.7 Linear Inequalities in One Variable [pdf]2024-08-05
Section 1.4a Quadratic Equations [docx]2024-08-05
Section 1.4a Quadratic Equations [pdf]2024-08-05
Section 1.4b Quadratic Equations [docx]2024-08-05
Section 1.4b Quadratic Equations [pdf]2024-08-05
Section 1.1b Linear and Rational Equations [docx]2024-08-05
Section 1.1b Linear and Rational Equations [pdf]2024-08-05
Section 1.6a Other Types of Equations [docx]2024-08-05
Section 1.6a Other Types of Equations [pdf]2024-08-05
Section 1.6b Other Types of Equations [docx]2024-08-05
Section 1.6b Other Types of Equations [pdf]2024-08-05
Section 1.8 Absolute Value Equations [docx]2024-08-05
Section 1.8 Absolute Value Equations [pdf]2024-08-05
Section 2.1 The Rectangular Coordinate System [docx]2024-08-06
Section 2.1 The Rectangular Coordinate System [pdf]2024-08-06
Section 2.2 Circles [docx]2024-08-06
Section 2.2 Circles [pdf]2024-08-06
Section 2.3 Lines [docx]2025-06-09
Section 2.3 Lines [pdf]2025-06-09
Section 2.4 Parallel and Perpendicular Lines [docx]2024-08-06
Section 2.4 Parallel and Perpendicular Lines [pdf]2024-08-06
Section 12.1 Systems of Linear Equations in Two Variables [docx]2024-08-06
Section 12.1 Systems of Linear Equations in Two Variables [pdf]2024-08-06
Section 3.1 Relations and Functions [docx]2024-08-06
Section 3.1 Relations and Functions [pdf]2024-08-06
Section 3.2 Properties of a Function's Graph [docx]2024-08-06
Section 3.2 Properties of a Function's Graph [pdf]2024-08-06
Basic Functions Summary [docx]2023-05-21
Basic Functions Summary [pdf]2023-05-21
Section 3.3 Graphs of Basic Functions; Piecewise Functions [docx]2024-10-07
Section 3.3 Graphs of Basic Functions; Piecewise Functions [pdf]2024-10-07
Section 3.4 Transformations of Functions [docx]2024-08-06
Section 3.4 Transformations of Functions [pdf]2024-08-06
Section 3.5 Composite Functions [docx]2024-08-06
Section 3.5 Composite Functions [pdf]2024-08-06
Section 3.6 One-to-one Functions; Inverse Functions [docx]2024-08-06
Section 3.6 One-to-one Functions; Inverse Functions [pdf]2024-08-06
Section 4.1 Quadratic Functions [docx]2024-08-09
Section 4.1 Quadratic Functions [pdf]2024-08-09
Section 4.2 Applications of Quadratic Functions [docx]2024-10-07
Section 4.2 Applications of Quadratic Functions [pdf]2024-10-07
Section 4.3 The Graphs of Polynomial Functions [docx]2024-08-09
Section 4.3 The Graphs of Polynomial Functions [pdf]2024-08-09
Section 4.6 Rational Functions and Their Graphs [docx]2024-08-09
Section 4.6 Rational Functions and Their Graphs [pdf]2024-08-09
Section 5.1a Exponential Functions [docx]2024-08-09
Section 5.1a Exponential Functions [pdf]2024-08-09
Section 5.2 Logarithmic Functions [docx]2024-08-09
Section 5.2 Logarithmic Functions [pdf]2024-08-09
Section 5.3 Properties of Logarithms [docx]2024-08-09
Section 5.3 Properties of Logarithms [pdf]2024-08-09
Section 5.4 Exponential and Logarithmic Equations [docx]2024-08-09
Section 5.4 Exponential and Logarithmic Equations [pdf]2024-08-09
Section 5.1b Exponential Functions (Objective 4) [docx]2024-08-09
Section 5.1b Exponential Functions (Objective 4) [pdf]2024-08-09
Section 5.5 Applications of Exponential and Logarithmic Functions [docx]2024-08-09
Section 5.5 Applications of Exponential and Logarithmic Functions [pdf]2024-08-09

Videos

Section 1.1: Linear Equations

Section 1.4: Quadratic Equations

Section 1.6: Radical Equations; Quadratic-Type Equations; Factorable Equations

Section 1.7: Linear Inequalities

Section 1.8: Absolute Value Equations and Inequalities

Section 2.1: Rectangular Coordinates

Graphs of Equations--Intercepts and Tests for Symmetry

Section 2.2: Circles

Sections 2.3 and 2.4: Lines

Sections 3.1 and 3.2: Functions

Sections 3.3 and 3.4: Basic Functions, Piecewise Functions, and Transformations of Functions

Section 3.5: Composite Functions

Section 3.6: One to One Functions; Inverse Functions

Sections 4.1 and 4.2: Quadratic Functions

Section 4.3: Polynomial Functions

Section 4.6: Rational Functions

Section 5.1a: Exponential Functions

Section 5.2: Logarithmic Functions

Section 5.3: Logarithmic Properties

Section 5.4: Logarithmic and Exponential Equations

Sections 5.5 and 5.1b: Compound Interest Applications

Section 5.5: Exponential Growth and Decay Applications

Section 12.1: Systems of Linear Equations

Course Coordinator

Photo of Stephanie H. Kurtz

Stephanie H. Kurtz
Math 1020/1021 Coordinator
Office: 274 Lockett Hall
Office hours: M 10:30am–11:25am, 1:00pm–3:00pm (LSU Math Lab); Tu 10:30am–12:00pm, 12:30pm–2:30pm (LSU Math Lab); W 12:30pm–1:25pm; Th 12:00pm–2:00pm (LSU Math Lab)
Telephone: +1 225 578 1653
Email: skurtz1@lsu.edu