College Algebra

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College Algebra Course Description
By Rochelle Connery, eHow Contributor updated: April 27, 2010

College algebra consists of basic and advanced algebraic concepts. College algebra courses consist of algebra refresher lessons and advanced algebraic concepts. Most college algebra courses cover one semester, or three to five credit hours. Some schools offer college algebra courses online and others allow proficient students to test out of college algebra with an Advanced Placement (AP) or College Level Examination Program (CLEP) test. College algebra courses teach students to master algebra fundamentals and help prepare them for advanced mathematics such as calculus and trigonometry.

Prerequisites
1. Students should grasp fundamental math concepts before attempting college algebra classes. Most college algebra courses necessitate prerequisites such as intermediate or high school algebra. Some colleges, such as West Texas A&M University, offer online tutorials for students and nonstudents that help prepare them for college-level algebra courses. Students should possess a basic understanding of addition, subtraction, multiplication and division of fractions and rational expressions in addition to an understanding of quadratic equations, inequalities and graphing. Some schools also cite geometry as a prerequisite.

Functions
2. College algebra courses include many problems that involve functions. Linear, graphing, exponential, polynomial and logarithmic functions comprise a good portion of college algebra. Students graph solutions to linear functions by solving for a letter and placing it on a grid using coordinates. At Oklahoma City Community College, students use exponential functions to solve problems relating to compound interest, population and other statistical results. Logarithmic

functions typically require scientific calculators and employ exponential expressions to form statements for a solution.

Formulas
3. College algebra courses include problems that necessitate formulas. One of the most popular, the quadratic formula, challenges students to properly arrange numbers and their coefficients. According to Elizabeth Stapel of the Purplemath online algebra help center, this formula comes from the process of completing a square and involves the square root sign and the "ax(squared) + bx + c = 0" equation. Students sometimes graph the results.

Rational Expressions
4. Finding the domain is a common process in college algebra that involves solving or simplifying rational expressions. According to Stapel, a rational expressional is a polynomial fraction containing polynomials and letter variables. This process employs the quadratic formula in some instances. Students must simplify the expression by canceling factors in situations where rational expressions contain no solution.

Analytical Geometry
5. Students learn to draw lines, angles and planes on graphs using graphing calculators during the precalculus and geometric portions of college algebra. Problems begin with rational expressions which, when solved, provide coordinate solutions for students to graph on a grid. Results create geometric figures, such as parabolas, ellipses and hyperbolas, which students use to calculate the axis of architectural structures such as bridges and nuclear towers. Boost Grades- Algebra DVDMathTutorDVD.com/Algebra+DVD 10 Hour Algebra Tutor DVD - Guaranteed to Raise Grades! MSc Marketing&ManagementLSBF.org.uk/Marketing-Management Top Marketing Masters Degrees, Flexible Modes of Study Worldwide! Where can I study?www.globalcampus.com College costs, entry requirements, rankings and more- all for free Get HomeWork Helpwww.MilaCoach.Com Post requirement, Select Tutor according to your Budget. Ads by Google

References
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West Texas A&M University: College Algebra Tutorials Oklahoma City Community College: Logarithmic Functions Elizabeth Stapel, Purple Math: The Quadratic Formula Elizabeth Stapel, Purple Math: Rational Expressions M. Bourne, Interactive Math: Parabolas

Read more: College Algebra Course Description | eHow.com http://www.ehow.com/about_6392164_college-algebra-coursedescription.html#ixzz12XFzcLkV How to Get Extra Help With College Algebra Read more: How to Get Extra Help With College Algebra | eHow.com http://www.ehow.com/how_2300209_get-extra-help-collegealgebra.html#ixzz12XFJWJbd

College Algebra
By Kimberley Jace, eHow Contributor So you've found yourself in a college algebra class and it's a little tougher than you expected. Many highly intelligent people have a hard time with mathematics and anyone who has been out of school for a few years is likely to discover that they've forgotten everything they once knew about algebra. Think of college algebra as a series of complex number "tricks" you can learn, because that's what it is. Contrary to what teens shout at their parents, you really DO use algebra in real life, so passing this class will give you skills that will come in handy--plus, it's impossible to get a bachelor's degree without this credit. Where can you turn? From Essentials: Algebra Answers Tutorial



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Difficulty: Moderately Easy

Instructions Things You'll Need:
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Class textbook Other college algebra textbooks Other college students Your college's free tutoring staff Internet access High school honors students

1. 1 When you first look at your class textbook, algebra can seem truly overwhelming, even if you once knew this stuff. So get your class textbook early--even the day you register for the class. Spend some free hours before your first class looking through the chapters and find out if any of it looks familiar, whether there are "inclass" instead of "homework" problems, whether there are supplementary practice problems and if there is an answer key. Practice problems with answers will be the most helpful, because they'll give you a chance to study at home and test yourself once class starts. 2. 2 Some textbooks are much better than others in explaining mathematics topics. Especially beware the textbooks written by the college staff itself; even math geniuses can write confusing textbooks. Because all the topics are the same, you can use any college algebra book to help you understand. Ask friends for old textbooks, advertise on freecycle sites, haunt used bookstores and resale shops, check your local library. Anything that says "college algebra" might be useful. 3. 3

You don't have to go it alone. If you're struggling in your class, there are probably others in the same situation. Go to class early and informally ask the other earlyarrivers if they are interested in forming a study group. There's probably somewhere at the school (such as their resource center/library) where you can meet and go over the homework, compare test answers, etc. Most colleges also offer free tutoring of some kind; if you can fit that into your schedule, sign up early, since math spots tend to fill up quickly. 4. 4 The Internet can also be a great source of college algebra help. Search by topic (i.e., "factoring polynomials") in any search engine, or go to the homework helper sites. Youtube.com has many video clips of math teachers explaining algebra concepts, and it's often helpful to hear a few different teachers explain the same concept. 5. 5 College algebra is taught to high school honor students, and many high schools require seniors to do some type of community service. Ask your friends and neighbors with smart high school students, or call your local high school's principal and explain that you're looking for free, higher-mathematics tutoring and will sign off on community service forms. Young people can be surprisingly patient at explaining algebra. If you can't find someone who needs the community service hours, the student will probably be happy to accept a modest fee. Marketing&Business Degreewww.LSBF.org.uk/Marketing-Masters From Top London School, Expert Tutors. Full-time,Part-time&Online Algebra DVD TutorialMathTutorDVD.com/Algebra+DVD 10 Hour Algebra Tutor DVD - Guaranteed to Raise Grades! Where can I study?www.globalcampus.com College costs, entry requirements, rankings and more- all for free Improve Teaching Skillsinternational.mq.edu.au/distance Earn a Degree or Masters in Education Leadership online Ads by Google

Tips & Warnings


Maybe it goes without saying, but attend every one of your college algebra classes, take good notes, copy down sample problems from the board and ask questions about anything you don't understand.

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Be willing to spend an hour a day or so at home solving practice problems in your current topic. Be willing to talk to your instructor about how you're doing in the class and take his suggestions seriously. Some instructors are willing to meet early/stay late with a small group of students to give extra help (but don't count on this). Don't be tempted to use the answer key to do your homework. Eventually, you'll have to pass the test without the benefit of supplied answers, so there's no way around learning this stuff.

Read more: How to Get Extra Help With College Algebra | eHow.com http://www.ehow.com/how_2300209_get-extra-help-collegealgebra.html#ixzz12XF2EVPF

College Algebra Tutorial on Linear Equations in One Variable
By Steph Ellen, eHow Contributor updated: April 29, 2010 A linear equation produces a straight line when graphed. Some equations contain just a single variable (an unknown like x or y). In college algebra, you'll need to know how to graph linear equations of one variable. Graphing in college algebra is usually accomplished on a graphing calculator, but you'll also need to know how to interpret the results from those graphs. Difficulty: Challenging

Instructions
1. 1 Enter the Y Editor on your calculator. Most graphing calculators will have a "Y=" button that you can press to enter the editor. 2. 2 Enter the expression using the alphanumeric keypad, without typing the "Y=." For example, y= 2x + 2 would be entered on the calculator as 2x + 2. (The ^ symbol normally has its own key.)

3. 3 Graph the equation. Most graphing calculators have a "Graph" button. 4. 4 Press the "Trace" button on your calculator. This slides along the length of the graph, giving you every possible output for the function. To find an output for a specific value of X, just enter the number into the calculator. For example, if you want to know what the Y value is for an input of 2, enter "2" into your calculator after pressing the "Trace" button. Math Quick Guidesquickstudy.com Study guides outlining mathematics, inexpensive & durably laminated. Marketing&Business Degreewww.LSBF.org.uk/Marketing-Masters From Top London School, Expert Tutors. Full-time,Part-time&Online Award Winning Algebra DVDMathTutorDVD.com/Algebra+DVD 10 Hour Algebra DVD Tutor - Guaranteed to Raise Grades! Need the best summary?trynow.topicmarks.com Generate your own. Topicmarks reads and summarizes any text in minutes. Ads by Google

Tips & Warnings


Make sure your equation is in the form "Y=" to enter it into your calculator. For example, if your expression is 21 = 5 - x, you'll need to convert to the form y = 16 - x before entering it into the calculator.

References


"Functions and Change"; Bruce Crauder & Benny Evans; 2007

Read more: College Algebra Tutorial on Linear Equations in One Variable | eHow.com http://www.ehow.com/how_6399512_college-linear-equations-onevariable.html#ixzz12XH0xb00

How to Use Matrices to Solve Linear Equations
By Sky Smith, eHow Contributor updated: May 5, 2010

A matrix consists of a block of numbers representing a vector. Linear algebra is the division of math concerned with vectors and the rules applied to vectors. It focuses on matrices, which are mathematical structures used to represent vector transformations. The most basic and important application of linear algebra is solving systems of linear equations, which include any problem that seeks a solution to more than one variable for a series of two or more linear equations. Difficulty: Moderately Challenging

Instructions Things You'll Need:


TI-83, TI-84 or another matrix-performing calculator

1. 1 Align your system of linear equations so that the same variables occupy the same space so that all constants are on the right side of the equation. If a variable does not exist for one of the linear equations, make its coefficient zero. For example, consider the following system of linear equations: 3x + 5z -- y = 10 x -- y + 1 = -1 2y -- 3z + x = 1

becomes ... 3x -- y + 5z = 10 x -- y + 0z = -2 x + 2y -- 3z = 1 Note: If a term does not change its side of the equation, its sign does not change. 2. 2 Create the matrices that you will store into your calculator. [A] = the coefficients (multipliers) of the variables in order. | 3 -1 5 | | 1 -1 0 | | 1 2 -3 | [B] = the solutions to the equations in order of their correspondence to the coefficients. | 10 | | -2 | |1| 3. 3 Store the matrices into your calculator. On most graphing calculators, you will hit the "2nd" key and then "MATRX" to access the matrix program. Scroll to "EDIT," choose matrix [A]. Hit "ENTER." Matrices are built as rows x columns. In this case, put in 3 x 3. Then fill in the information corresponding to the numbers of matrix [A] from Step 2. Once finished, quit the MTRX program and then restart the MTRX program, this time building matrix [B], which will be a 3 x 1 matrix. 4. 4 Once your matrices are built, go to the MTRX program and choose matrix [A] under "NAMES." It will show up as [A] on your home screen. Hit the "X^-1" key, or inverse key, which should appear under the "MATH" program key. Then go back to the "MTRX" program and choose [B] under "NAMES." Hit "ENTER" and then hit "ENTER" again on the home screen to calculate the answers. 5. 5 Interpret your results. Based on the order you put our variables, the solutions will be in the form of x = first entry, y = second entry and z = third entry. In this case, the solution on the home screen should read as follows:

|1| |3| |2| Where x = 1, y = 3 and z = 2 are the solutions to our linear equations. Algebra DVD TutorialMathTutorDVD.com/Algebra+DVD 10 Hour Algebra Tutor DVD - Guaranteed to Raise Grades! MBA, Top Business Collegewww.LSBF.org.uk/MBA FT Listed MBA Programme From London School of Business & Finance Mathematica Add-Onwww.smartcae.de Easy to Use Interactive Graphics Legends, Options, Zoom, Scaling MathType - Download Todaywww.dessci.com/MathType The premier Math authoring tool for MS Word, Web, and more! Ads by Google

Tips & Warnings
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The matrix inverse method works for systems of equations of any dimension so long as there are the same number of equations as there are variables. Taking inverse matrices by hand, while possible, is extremely tedious and not recommended as a way of solving linear equations. Resort to a calculator or do not attempt this method of reaching a solution.

References


University of Wisconsin: Matrix Inverse Method

Read more: How to Use Matrices to Solve Linear Equations | eHow.com http://www.ehow.com/how_6018015_use-matrices-solve-linearequations.html#ixzz12XHUyaXc

How to Use Matrices to Solve Simultaneous Equations
By Serm Murmson, eHow Contributor

updated: May 5, 2010

A TI-83 graphing calculator, useful for matrix calculations Matrices are potentially intimidating mathematical concepts to learn, but they have countless uses. Matrices are essentially just grid-based representations of numeric data and can be used to organize and solve problems that might otherwise take much longer. They are especially useful in solving a system of linear equations. Difficulty: Moderate

Instructions Things You'll Need:


Calculator

1. 1 Rewrite your equations so that all similar variables are aligned. For example, for the equations x + 2y = 5 and 5y = 26 - 3x, write the following; x + 2y = 5 3x + 5y = 26 2. 2 Write a matrix using the coefficients of each equation as the rows of the matrix. The coefficients are the numbers by which the variables are multiplied. For example, for x + 2y = 5 and 3x + 5y = 26, write the following: [12 35]

3. 3 Enter this matrix into your calculator. For example, on a TI-83, press the "matrix" button and enter the relevant numbers into the desired matrix. 4. 4 Construct a similar matrix for the answers to your equations. For example, for x + 2y = 5 and 3x + 5y = 26, write the following: [5 26 ] Enter this matrix into another slot on your calculator. 5. 5 Multiply the inverse of your first matrix by the second. Select the first matrix and raise it to the -1 power, and multiply that by the second. The resulting matrix consists of the solutions to your equations. For example, for x + 2y = 5 and 3x + 5y = 26 [ 1 2 ^ -1 * [ 5 = [ 27 3 5 ] 26 ] -11 ] The solutions to the equations are x = 27 and y = -11. Award Winning Algebra DVDMathTutorDVD.com/Algebra+DVD 10 Hour Algebra DVD Tutor - Guaranteed to Raise Grades! Algebra Equation Graphingwww.WebGraphing.com Plot and graph equations online; lines, circles, parabolas, cubics. Need the best summary?trynow.topicmarks.com Generate your own. Topicmarks reads and summarizes any text in minutes. For International StudentInternational.Cuhk.Edu.hk Seeking undergraduate programmes? Chinese University of Hong Kong! Ads by Google

References


Algebra Lab; Solving Systems of Equations with Matrices

Read more: How to Use Matrices to Solve Simultaneous Equations | eHow.com http://www.ehow.com/how_6022635_use-matrices-solve-simultaneousequations.html#ixzz12XHrMozm

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