You will need to be fully familiar with the following material before classes start. All the material with blue and pink background is taken from a fairly extensive online Interactive Algebra Review page. Please go to that excellent page if you find that the brief summary below is too fast for you or that you need more practice. I also highly recommend that you visit the following Algebra 1 and Algebra 2 websites. These web sites have detailed online explanations and practice problems. A link with lots of student-written examples is mathpower.com. Another online source with detailed explanations is this site in British Columbia. You can download most of it in Word or PDF format.

Chapters 1 of the textbook Introduction to Mathematical Economics provides more examples and chapter 2 some applications to economics. If chapter 1 of the textbook is much too brief for your taste, then you should consider another Schaum Outline text by the same author that proceeds much more slowly: Mathematical Methods for Business and Economics.

Interval Notation

Exponents

Rules of Exponents with integers

Negative and Zero Exponents

Roots of Products and Quotients

Root versus Exponential Notation

Rules of Exponents when the exponents are rational numbers rather than integers

Check your knowledge of the rules relating to exponents

Basic Rules of Algebra

Multiplying Algebraic Expressions

Factoring Algebraic Expressions

Factoring Quadratic Equations by Trial and Error

Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Completing the Square

Algebra of Rational Expressions

Solving Algebraic Equations

Check your knowledge of the rules relating to basic algebra

Solving Inequalities with the Sign Diagram

Check your knowledge of the solving inequalities with the sign diagram

Interval Notation

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Exponents

Rules of Exponents with integers

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Negative and Zero Exponents

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Roots of Products and Quotients

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Root versus Exponential Notation

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Rules of Exponents when the exponents are rational numbers rather than integers

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Check your knowledge of the rules relating to exponents

Simplify each of the following by hand. If you cannot do these without error, you will need to study the above rules for exponents in more detail. The online tutorials 2a and 2b would be helpful in this respect. In addition, or alternatively, check out this webpage for Algebra 1, which has more detailed explanations and practice problems. Concentrate on sections 1 and 2 of this page.

a.                

b.                    

c.                     

d.                     

e.                

f.                  

g.        

h.        

i.              

j.          

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Basic Rules of Algebra

Multiplying Algebraic Expressions

The Maple commands to solve two of the above examples

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Factoring Algebraic Expressions

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Factoring Quadratic Equations by Trial and Error

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Solving Quadratic Equations by Factoring

The Maple command to factor the above equation

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Solving Quadratic Equations by Completing the Square

The Maple commands and the Maple solution to the above two examples are

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Algebra of Rational Expressions

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Solving Algebraic Equations

The Maple commands and the Maple solution to the above two examples are

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Check your knowledge of the rules relating to basic algebra

If your algebra is rusty, please study in some detail the algebra material above before you try the examples below. If you still cannot do the problems below without error, please take a look at the online tutorials 3 to 5. If you are still lost, work through sections 3, 8, 10, and 13 of this Algebra 1 web site. If you find you really have no time for this, I would stronly suggest that you reconsider your decision to go through a graduate program in economics.

a. Simplify                

b. Factor                                         

c. Solve for x                         

d. Simplify                                  

e. Solve for x                           

f. Solve for x             

g. Solve by completing the square                    

h. Solve for p                         

i. Solve for z             

j. Solve for x and y   

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Solving Inequalities with the Sign Diagram

The Maple commands and the Maple solution to the above two examples are

To practice solving inequalities without a graph go through sections 4 and 5 or this Algebra 1 site.

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Check your knowledge of solving inequalities with the sign diagram

For which interval does this inequality hold?      

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Author: Joachim Zietz, jzietz@mtsu.edu
Original file location: http://www.mtsu.edu/~jzietz/module2/page-2.html