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Course Syllabus for Intermediate Algebra
After completing each chapter the student should be able to accomplish the following:
Chapter Ten – Polynomials: Factoring
1. Factor monomials
2. Factor the greatest common factor from polynomials
3. Factor four term polynomials by grouping
4. Factor trinomials
5. Factor special products
6. General strategy for factoring
7. Solving Quadratic Equations by factoring
8. Applications of Quadratic Equations
Chapter Eleven - Rational Expressions and Expressions
1. Evaluate rational expressions
2. Simplify rational expressions.
3. Multiply and divide rational expressions
4. Add or subtract expressions with the same denominator.
5. Add or subtract expressions with different denominators.
6. Simplify complex fractions .
7. Solve equations containing rational expressions.
8. Use tables to solve problems involving work and motion.
9. Solve problems involving direct and inverse variation.
Chapter Fifteen - Radicals, Rational Exponents and Complex numbers
1. Find the square, cube and roots.
2. Graph square and cube root functions.
3. Use the rules for exponents to simplify expressions that contain rational exponents.
4. Simplify radicals.
5. Use product and quotient rules to simplify radicals.
6. Simplify radical expressions and then add, subtract or multiply them.
7. Rationalize denominators.
8. Solve radical equations.
9. Add, Subtract, Multiply and Divide complex numbers.
10. Raise the complex number “i” to its powers .
Chapter Sixteen - Solving Quadratic Equations
1. Use the Square Root Property to solve quadratic equations...
2. Solve quadratic equations by completing the square.
3. Use the Quadratic Formula to solve quadratic equations.
4. Graph quadratic equations of the form y = ax^2 + bx + c.
5. Determine the number and types of solutions by using the discriminate.
6. Solve polynomial inequalities of degree 2 or greater.
7. Solve problems involving variation.
Chapter Seventeen - Exponential and Logarithmic Functions (Optional)
1. 1. Add, subtract, multiply and divide functions
2. Construct composite functions
3. Find the inverse of a relation and a function
4. Graph a function and its inverse on the same axis.
5. Graph an exponential and logarithmic function.
6. Convert between logarithmic and exponential functions
8. Solve logarithmic and exponential equations
Students will be able to:
1. Perform factoring of all types
2. Solve applied problems by writing the appropriate equation and solving it appropriately.
3. Simplifying rational expressions.
4. Perform operations with radicals, and rational exponents.
5. Solve quadratic equations.
REVIEW SHEET FOR THE FINAL EXAMINATION
The final examination for this course consists of fifty computational questions. The problems are similar to those that you have worked to complete each unit and similar to the questions you experienced on each quiz. One way to review all the material from this course is to work the Chapter Review located at the end of each chapter. Further, you may find it beneficial to review the Chapter Highlights at the end of each chapter. There you will find an example of each of the concepts. If you have any difficulties you should review that section of the chapter more thoroughly. If you have any questions, be sure to ask before you take the final examination.
A suggested list of topics that you should review includes, but is not necessarily limited to:
1. Add, subtract, multiply and divide rational expressions
2. Solve rational equations
3. Solve all types of equations.
4. Solve absolute value equations and inequalities.
5. Graph linear, nonlinear and quadratic equations.
6. Solve systems of linear equations by various methods.
7. Solve applications problems that involve systems of linear equations.
8. Simplify radicals.
9. Add, subtract, multiply, and divide radicals.
10. Simplify expressions containing fractional exponents.
11. Solve radical equations.
12. Solve quadratic equations by various methods.
13. Solve application problems that contain quadratic equations.
14. Find the inverse of a function
15. Solve an elementary exponential equation
16. Solve an elementary logarithmic equation
17. Apply the properties of logarithms
18. Solve an application involving logarithms