# 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

Name | Last Modified |
---|---|

Su23 Session B May 22 - June 24 Math 1021 Syllabus for Section 1 [pdf] | 2023-05-18 |

Su23 Session C July 3 - August 5 Math 1021 Syllabus for Section 2 [pdf] | 2023-05-20 |

Su23 Session C July 3 - August 5 Math 1021 with Corequisite Support Syllabus for Section 101 [pdf] | 2023-05-20 |

## Daily Schedule

Name | Last Modified |
---|---|

Su23 Session B May 22 - June 24 Math 1021 Section 1 Daily Schedule [pdf] | 2023-05-18 |

Su23 Session C July 3 - August 5 Math 1021 Sec 2 Schedule [pdf] | 2023-05-20 |

## Class Notes

## 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

Stephanie H. Kurtz

Math 1020/1021 Coordinator

Office: 274 Lockett Hall

Telephone: +1 225 578 1653

Email: skurtz1@lsu.edu