Math 1021 College Algebra with Math 1020 Coreq Support
Math 1021 College Algebra (with Math 1020 Corequisite Support) 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.
Math 1020 provides corequisite materials designed to promote mastery of the specific skills and knowledge required for success in Math 1021 College Algebra.
Math 1020 is taken concurrently with Math 1021. Registration in Math 1020 is linked with registration in Math 1021 using the same section number.
Course Eligibility
Students enroll in two separate courses: Math 1020 Corequisite Support and Math 1021 College Algebra. Students first enroll in Math 1020 and subsequently enroll in the corresponding section of Math 1021. To enroll in Math 1020 (and then the corresponding section of Math 1021), 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.
Math 1020 Review Topics
Math topics:
- properties of real numbers;
- order of operations;
- operations with fractions and decimals;
- evaluating and simplifying polynomial expressions;
- factoring polynomials;
- working with integer and rational exponents;
- solving simple linear equations and inequalities;
- solving rational and quadratic equations;
- using function notation;
- finding intercepts;
- sketching the graphs of basic functions.
Learning support topics:
- reframing an academic mindset;
- empowerment for independent math learners;
- reflecting and adapting after testing;
- planning for finals and beyond.
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
Syllabi
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Daily Schedule
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Class Notes
Math 1020 Review Videos
Adding and Subtracting Polynomials
Compound Inequalities
Exponents
Factoring Binomials
Factoring Trinomials of the Form $ax^2+bx+c$
Factoring Trinomials of the Form $x^2+bx+c$
Functions
Graphing Piecewise-Defined Functions; Shifting and Reflecting Graphs of Functions
Greatest Common Factor and Factoring by Grouping
Multiplying Polynomials
Negative Exponents
Perfect Square Trinomials
Properties of Equality
Quadratic Functions and Their Graphs
Rational Exponents
Simplifying Algebraic Expressions
Simplifying Square Roots and Rationalizing Denominators
Solving Systems of Linear Equations by Graphing
Special Products
Math 1021 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
Office hours: M 1:00pm–3:00pm (LSU Math Lab), 10:30am–11:25am; TuW 12:30pm–2:30pm (LSU Math Lab); Tu 9:30am–10:25am, 11:30am–12:00pm; Th 10:30am–11:30am
Telephone: +1 225 578 1653
Email: skurtz1@lsu.edu