# Math 1021 College Algebra

## Precalculus Program

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

• Solving quadratic equations by factoring and the zero product property
• Solving quadratic equations using the square root property
• 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

• 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
F23 Math 1021 Syllabus for Sections 1 - 30 [pdf]2023-08-15
F23 Math 1021 Syllabus for Section 51 Online [pdf]2023-08-15
F23 Math 1021 Syllabus for Sections 101 - 144 [pdf]2023-08-15

## Daily Schedule

Math 1021 College Algebra Daily Schedule
F23 Math 1021 Monday Schedule Sections 1 - 6 [pdf]2023-08-15
F23 Math 1021 Tuesday Schedule Sections 7 - 11 updated 8_22 [pdf]2023-08-22
F23 Math 1021 Wednesday Schedule Sections 13 - 18 [pdf]2023-08-15
F23 Math 1021 Thursday Schedule Sections 19 - 24 [pdf]2023-08-15
F23 Math 1021 Friday Schedule Sections 25 - 30 [pdf]2023-08-15
F23 Math 1021 Online Schedule Section 51 [pdf]2023-08-15
F23 Math 1020 1021 Monday Wednesday Schedule Sections 101 - 114 and 140 - 144 [pdf]2023-08-15
F23 Math 1020 1021 Tuesday Thursday Schedule Sections 115 - 139 [pdf]2023-08-15

## Class Notes

Math 1021 College Algebra Class Notes
Section 1.1 Linear and Rational Equations [docx]2019-07-10
Section 1.1 Linear and Rational Equations [pdf]2023-05-19
Section 1.7 Linear Inequalities in One Variable [docx]2019-07-10
Section 1.7 Linear Inequalities in One Variable [pdf]2023-05-19
Section 1.8 Absolute Value Equations and Inequalities [docx]2019-07-10
Section 1.8 Absolute Value Equations and Inequalities [pdf]2023-05-19
Section 1.6 Other Types of Equations [docx]2023-05-21
Section 1.6 Other Types of Equations [pdf]2023-05-21
Section 2.1 The Rectangular Coordinate System [docx]2019-07-10
Section 2.1 The Rectangular Coordinate System [pdf]2023-05-19
Section 2.2 Circles [docx]2019-07-10
Section 2.2 Circles [pdf]2023-05-19
Section 2.3 Lines [docx]2019-07-10
Section 2.3 Lines [pdf]2023-05-20
Section 2.4 Parallel and Perpendicular Lines [docx]2019-07-10
Section 2.4 Parallel and Perpendicular Lines [pdf]2023-05-19
Section 3.1 Relations and Functions [docx]2019-07-10
Section 3.1 Relations and Functions [pdf]2023-05-19
Section 3.2 Properties of a Function's Graph [docx]2019-07-10
Section 3.2 Properties of a Function's Graph [pdf]2023-05-19
Basic Functions Summary [docx]2023-05-21
Basic Functions Summary [pdf]2023-05-21
Section 3.3 Graphs of Functions; Piecewise Functions [docx]2019-07-10
Section 3.3 Graphs of Functions; Piecewise Functions [pdf]2023-05-19
Section 3.4 Transformations of Functions [docx]2019-07-10
Section 3.4 Transformations of Functions [pdf]2023-05-19
Section 3.5 Composite Functions [docx]2019-07-10
Section 3.5 Composite Functions [pdf]2023-05-19
Section 3.6 One-to-One Functions; Inverse Functions [docx]2019-07-10
Section 3.6 One-to-One Functions; Inverse Functions [pdf]2023-05-19
Section 4.2 Applications and Modeling of Quadratic Functions [docx]2019-07-10
Section 4.2 Applications and Modeling of Quadratic Functions [pdf]2023-05-19
Section 4.3 The Graphs of Polynomial Functions [docx]2019-07-10
Section 4.3 The Graphs of Polynomial Functions [pdf]2023-05-19
Section 4.6 Rational Functions and Their Graphs [docx]2019-07-10
Section 4.6 Rational Functions and Their Graphs [pdf]2023-05-19
Section 5.1a Exponential Functions [docx]2019-07-10
Section 5.1a Exponential Functions [pdf]2023-05-20
Section 5.1b Applications of Exponential Functions [docx]2019-07-10
Section 5.1b Applications of Exponential Functions [pdf]2023-05-20
Section 5.2 Logarithmic Functions [docx]2023-05-19
Section 5.2 Logarithmic Functions [pdf]2023-05-19
Section 5.3 Properties of Logarithms [docx]2019-07-10
Section 5.3 Properties of Logarithms [pdf]2023-05-19
Section 5.4 Exponential and Logarithmic Equations [docx]2019-07-10
Section 5.4 Exponential and Logarithmic Equations [pdf]2023-05-19
Section 5.5 Applications of Exponential and Logarithmic Functions [docx]2019-07-10
Section 5.5 Applications of Exponential and Logarithmic Functions [pdf]2023-05-19
Section 12.1 Solving Systems of Linear Equations in Two Variables [docx]2019-07-10
Section 12.1 Solving Systems of Linear Equations in Two Variables [pdf]2023-05-19

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