About this course: This course covers mathematical topics in college algebra, with an emphasis on functions. The course is designed to help prepare students to enroll for a first semester course in single variable calculus. Upon completing this course, you will be able to: 1. Solve linear and quadratic equations 2. Solve some classes of rational and radical equations 3. Graph polynomial, rational, piece-wise, exponential and logarithmic functions 4. Find integer roots of polynomial equations 5. Solve exponential and logarithm equations 6. Understand the inverse relations between exponential and logarithm equations 7. Compute values of exponential and logarithm expressions using basic properties
Created by: University of California, Irvine
Taught by: Dr. Sarah Eichhorn, Associate Dean, Distance Learning & Tenured Lecturer
Taught by: Dr. Rachel Cohen Lehman
| Level | Intermediate |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
Course Overview and Algebra Review
We begin with an overview of the course and an opportunity to review and practice some of the prerequisite algebra skills needed for success in this course.
11 videos, 3 readings
- Reading: Syllabus
- Reading: Quiz Notation
- Video: Introduction to Algebra and Geometry
- Reading: Algebra Review: Readings and Exercises
- Video: Properties of Integer Exponents
- Video: Adding and Subtracting Polynomials
- Video: Multiplication of Binomials
- Video: Multiplication of Polynomials
- Video: Multiple Operations with Polynomials
- Video: Rational Exponents
- Video: Simplified Radical Form
- Video: Square Root Addition and Subtraction
- Video: Multiplication Involving Square Roots
- Video: Rationalizing a Denominator
WEEK 2
Linear Equations and Inequalities. Absolute Value Equations and Inequalities.
In this module, we will learn to solve linear and absolute value equations and inequalities. We will also explore a range of story problems which can be solved utilizing linear equations.
13 videos, 3 readings
- Reading: Linear Equations and Inequalities I: Reading and Exercises
- Video: Solving Linear Equations
- Video: Algebraic Symbol Manipulation
- Video: Linear Word Problems
- Video: Percentage Word Problems
- Video: Area and Perimeter Word Problems
- Reading: Linear Equations and Inequalities II: Readings and Exercises
- Video: Distance-Rate-Time
- Video: Mixture Problems Using Linear Equations
- Video: Solving a Linear Inequality
- Video: Compound Inequalities
- Video: Linear Inequality Word Problems
- Reading: Absolute Value Equations and Inequalities: Readings and Exercises
- Video: Absolute Value Equations
- Video: Absolute Value Inequalities
- Video: Inequalities Involving Radicals
Graded: Linear Equations and Inequalities I
Graded: Linear Equations and Inequalities II
Graded: Absolute Value Equations and Inequalities
WEEK 3
Quadratic Equations.
In this module, we explore a variety of methods for solving quadratic equations.
9 videos, 1 reading
- Reading: Quadratic Equations: Readings and Exercises
- Video: Introduction to Polynomials and Rational Functions
- Video: Factoring a Quadratic Expression
- Video: Special Factoring Formulas
- Video: Factoring by Grouping
- Video: Solving a Quadratic Equation
- Video: Discriminant
- Video: Quadratic Formula
- Video: Solving a Quadratic Equation - Completing the Square
- Video: Quadratic Equation Word Problems
Graded: Quadratic Equations I
Graded: Quadratic Equations II
WEEK 4
Rational and Radical Equations.
We begin this module by practicing manipulations of rational expressions using basic properties. We then utilize these manipulations to solve rational and radical equations.
10 videos, 1 reading
- Reading: Rational Expressions: Readings and Exercises
- Video: Simplifying Fractions
- Video: Simplifying a Ratio of Polynomials
- Video: Adding and Subtracting Rational Expressions
- Video: Multiplying Rational Expressions
- Video: Dividing Rational Expressions
- Video: Square Root Property
- Video: Solving Rational Equations, Part 1
- Video: Solving Rational Equations, Part 2
- Video: Solving an Equation Quadratic in Form
- Video: Solving Equations Involving Radicals
Graded: Rational Expressions
Graded: Rational and Radical Equations
WEEK 5
Functions. Graphs of Functions. Transformations of Functions.
In this module, we define the notion of "function". We learn to distinguish between functions and non-functions in graphical, symbolic and tabular form. Finally, we will explore graphs of functions and how these graphs behave under linear transformations.
13 videos, 3 readings
- Reading: Functions: Readings and Exercises
- Video: Introduction to Functions & Graphs
- Video: Relations versus Functions
- Video: Functions and the Vertical Line Test
- Video: Domain
- Video: Evaluating Functions
- Reading: Graphs of Functions
- Video: Finding the Domain and Range from a Graph
- Video: Domain and Intercepts
- Video: Difference Quotient
- Video: Piecewise-Defined Functions
- Reading: Transformation of Functions: Readings and Exercises
- Video: Increasing/Decreasing/Constant
- Video: Graph Transformations, Part 1
- Video: Graph Transformations, Part 2
- Video: Odd and Even Functions
Graded: Functions
Graded: Graphs of Functions
Graded: Transformations of Functions
WEEK 6
Quadratic Functions. Inverse Functions. Polynomials.
In this module, we explore quadratic equations and graphs. We also introduce the notion of inverse functions. Finally, we will learn about polynomial properties and practice some methods for polynomial root finding.
14 videos, 3 readings
- Reading: Quadratic Functions: Readings and Exercises
- Video: Equations of Quadratic Functions
- Video: Converting a Quadratic Function from Standard to Vertex Form
- Video: Graphing a Parabola, Part 1
- Video: Graphing a Parabola, Part 2
- Video: Maximum/Minimum Quadratic Function Word Problems
- Video: Quadratic Inequalities
- Reading: Inverse Functions: Readings and Exercises
- Video: Finding the Inverse of a Function
- Video: Inverse Functions
- Video: Verifying Inverse Functions
- Reading: Polynomials: Readings and Exercises
- Video: Polynomial Long Division
- Video: Synthetic Division
- Video: Properties of Polynomials
- Video: Remainder Theorem
- Video: Factor Theorem
Graded: Quadratic Functions
Graded: Inverse Functions
Graded: Polynomials
WEEK 7
Exponential and Logarithmic Equations.
Exponential and logarithmic functions are two important functions that are useful in applications of calculus. We will discuss properties and graphs of these special functions. We will also learn to solve equations involving exponential and logarithmic functions.
9 videos, 2 readings
- Reading: Exponentials and Logarithms: Readings and Exercises
- Video: Introduction to Exponential & Logarithmic Functions
- Video: Solving Exponential Equations
- Video: Change of Base Formula for Logarithms
- Video: Converting Between Logarithmic and Exponential Equations
- Video: Properties of Logarithms
- Reading: Exponential and Logarithmic Equations and Graphs: Readings and Exercises
- Video: Evaluating Logarithmic Expressions
- Video: Solving Logarithmic Equations
- Video: Exponential Graphs
- Video: Logarithmic Graphs
Graded: Exponentials and Logarithms
Graded: Exponential and Logarithmic Equations and Graphs
WEEK 8
Pre-Calculus Functions Final Exam
Now is your opportunity to review the topics from this course. The comprehensive final exam is your chance to demonstrate your conceptual understandings of functions and algebraic computational skills.
Graded: Pre-Calculus Final Exam
FAQs
How It Works
Coursework
Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.
Help from Your Peers
Connect with thousands of other learners and debate ideas, discuss course material, and get help mastering concepts.
Certificates
Earn official recognition for your work, and share your success with friends, colleagues, and employers.
Creators
University of California, Irvine
Since 1965, the University of California, Irvine has combined the strengths of a major research university with the bounty of an incomparable Southern California location. UCI’s unyielding commitment to rigorous academics, cutting-edge research, and leadership and character development makes the campus a driving force for innovation and discovery that serves our local, national and global communities in many ways.
Pricing
| Audit | Purchase Course | |
|---|---|---|
| Access to course materials | Available | Available |
| Access to graded materials | Not available | Available |
| Receive a final grade | Not available | Available |
| Earn a shareable Course Certificate | Not available | Available |
Ratings and Reviews
I really learned a ton from the course and thought it was challenging. Plus, I think the instructors presented it in a great way, and I enjoyed watching their videos.
Teachers are great, very good material.
It is a very useful course
Coursera provides universal access to the world’s best education, partnering with top universities and organizations to offer courses online.
© 2017 Coursera Inc. All rights reserved.
Good for a quick refresher on functions before college