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COLLEGE ALGEBRA

SELF-PACED COURSE


1. About this Course

This course reviews the fundamentals taught in Algebra during one semester in college. The goal of the creator of this course – Modern States Education Alliance, a non-profit organization – is to prepare you to pass the College Board's CLEP examination and obtain college credit for free.


Through the guidance of Dr. James Murphy from Johns Hopkins University, this course will provide you with the basic algebraic skills and knowledge on key concepts, including vocabulary, symbols, and notation. 

This course is organized into four topical chapters or modules that contain short video lessons, exercises and readings. The material covered includes basic algebra, equations and inequalities, functions, and number systems.

"After studying these lectures, understanding the presented exercises, and working the practice questions, you will be well positioned to pass this exam", says Professor Murphy.

This exam contains approximately 60 questions to be answered in 90 minutes. An online scientific (nongraphing) calculator function will be available as part of the testing software. Students are expected to know how and when to make appropriate use of the calculator.

The Algebra course is completely self-paced. There are no prerequisites to take this course, and it is entirely free. Any student who wants to save time and money while completing freshman year in college can take it.

2. About James Murphy

Dr. James Murphy is an applied mathematician. His research interests include harmonic analysis, machine learning, and the analysis of remote sensing data. Recent work has focused on fast algorithms for unsupervised learning and development of distance metrics for stochastic data models, with applications to hyperspectral imagery.

Dr. Murphy has taught at some of the world’s finest academic institutions, including the University of Chicago, the University of Maryland College Park, Duke University, and most recently at the Johns Hopkins University. His courses range from introductory statistics and precalculus to research topics courses for Ph.D. students. He was honored with the Aziz/Osborn Gold Medal in Teaching Excellence at the University of Maryland in 2013. He also works closely with undergraduates on research projects in both pure and applied mathematics. Several of his students are currently working on Ph.D.s at top universities. Dr. Murphy earned his Ph.D. in mathematics at the University of Maryland College Park in 2015. He earned his B.S. in mathematics from the University of Chicago in 2011, where he was a Student Marshal and Phi Beta Kappa.

3. Required Knowledge and Skills

Questions on the College Algebra examination require candidates to demonstrate the following abilities in the approximate proportions indicated:

  • Solving routine, straightforward problems (about 50 percent of the examination)

  • Solving nonroutine problems requiring an understanding of concepts and the application of skills and concepts (about 50 percent of the examination)

4. Course Modules

Following are the main topics and percentages of the exam’s questions, mostly based on the College Board's description of the course:

Module 1: Algebraic operations (25%)

  1.1 Factoring and expanding polynomials

1.1.1 Algebraic Operations

1.1.2 Manipulating Fractions

1.1.3 Powers and Roots

  1.2 Operations with algebraic expressions

1.2.1 Factoring and Expanding Polynomials

1.2.2 First Order Polynomials

1.2.3 Second Degree Polynomials

1.2.4 Roots of Quadratics

1.2.5 Higher Order Polynomials

1.2.6 Expanding Polynomials

  1.3 Operations with exponents

1.3.1 Introduction to Exponentials

1.3.2 Properties of Exponents

1.3.3 Plots of Exponentials

  1.4 Properties of logarithms

1.2.1 Logarithms

1.2.2 Properties of Logarithms

1.2.3 Logarithm as Inverse of Exponential

1.2.4 Roots of Quadratics

1.2.5 Higher Order Polynomials

1.2.6 Expanding Polynomials


Module 2: Equations and inequalities 
(25%)

  2.1 Linear equations and inequalities

2.1.1 Linear Equations and Inequalities

2.1.2 Linear Inequalities

  2.2 Quadratic equations and inequalities

2.2.1 Quadratic Equations

2.2.2 Quadratic Formula

2.2.3 Quadratic Inequalities

  2.3 Absolute value equations and inequalities

2.3.1 Exponential and Logarithmic Equations

  2.4 Systems of equations and inequalities

2.4.1 Introduction to Absolute Value

2.4.2 Equations with Absolute Values

2.4.3 Inequalities Involving Absolute Values

  2.5 Exponential and logarithmic equations

2.5.1 Systems of Equations and Inequalities

2.5.2 Systems of Linear Equations

2.5.3 Higher Order Systems


Module 3: Functions and their properties 
(30%)

  3.1 Definition and interpretation

3.1.1 What is a Function?

3.1.2 Function or not?

3.1.3 Vertical Line Test

 3.2 Representation/modeling (graphical, numerical, symbolic, and verbal representations of functions)

3.2.1 Representing with Functions

3.2.2 Linear Modeling

3.2.3 Exponential Modeling

  3.3 Domain and range

3.3.1 Domain and Range of a Function

3.3.2 Intrinsic Domain Limitations

3.3.3 Visualizing Domain and Range

  3.4 Algebra of functions

3.3.1 Algebra of Functions

3.3.2 Composition of Functions 

 3.5 Graphs and their properties (including intercepts, symmetry, and transformations)

3.5.1 Plotting Functions

3.5.2 Symmetry of Functions

3.5.3 Transformation of Functions

  3.6 Oxidation-Reduction Reactions

3.6.0 Inverse Functions

3.6.1 Remarks on Inverse Functions

3.6.2 Horizontal Line Test


Module 4: Number systems and operations (20%)

  4.1 Ionic and Molecular Species Present in Chemical Systems; Net-Ionic Equations

4.1.1 Real Numbers

4.1.2 Integers

4.1.3 Rational Numbers

4.1.4 Irrational Numbers

  4.2 Complex numbers

4.2.1 Complex Numbers

4.2.2 Arithmetic with Complex Numbers

4.2.3 Division of Complex Numbers

  4.3 Sequences and series

4.3.1 Sequences and Series

4.3.2 Notation

4.3.3 Arithmetic Series

4.3.3.1 Arithmetic Series

4.3.4 Geometric Series

  4.4 Factorials and Binomial Theorem

4.4.1 Factorials and Binomial Theorem

4.4.2 Factorial!

4.4.3 Counting with Factorials

4.4.3.1 Counting with Factorials

4.4.4 Binomial Theorem

  4.5 Determinants of 2-by-2 matrices

4.5.1 Matrices

4.5.2 Matrix Algebra

4.5.3 Determinant

5. How CLEP Works

Developed by the College Board, CLEP (College-Level Examination Program®) is the most widely accepted credit-by-examination program.

CLEP’s credits are accepted by 2,900 colleges and universities, according to the College Board. These tests assess college-level knowledge in 33 subject areas.

On average, a college course costs $700 while a CLEP exam costs $80.

Modern States Education Alliance is the non-profit organization behind these edX-style courses. Its project is called “Freshman Year for Free” and its mission is to make college more accessible and affordable through free, high-quality online education.

• CLEP® College Algebra: at a Glance

• 'Passing the CLEP and Learning with Modern States' orientation course