# Exam 2 - Study Guide

A description of the problems on the chapters 3 and 4 Intermediate Algebra exam follow. In each case, a reference is given to study other problems of a similar nature.

Here's a major study aid. All of the problems on the test, with the exception of the story problems, come directly from the odd problems listed as a study reference.

1. In the lecture on section 3.1 and 3.2, there were 2 properties of exponents which were starred as being the only way to multiply two quantities. You need to know what to do with the base and the exponent in each of these cases.
2. There is a guideline to factoring polynomials. There are three general steps, and some methods under step 2. You will need to reproduce this chart for the exam. There is a similar chart in section 3.8 of your textbook, but I have combined their steps 2 - 4 into one step (number 2). There is also one additional method under a trinomial that isn't mentioned in the book. You do not need to show examples for these methods, only list the name of the method.
3. Simplify an expression involving exponents. Leave only positive exponents. Look at problems 37 - 57 in section 3.2.
4. Multiply two polynomials together. The column (vertical) method would be appropriate here. Look at problems 11 - 29 in section 3.4.
5. Expand a special product. Look at problems 49 - 57 in section 3.4.
6. Factor a polynomial completely. Look at problems 1 - 71 in section 3.8.
7. Factor a polynomial completely. Look at problems 1 - 71 in section 3.8.
8. Solve an equation by factoring. Look at problems 1 - 37 in section 3.9.
9. Solve an equation by factoring. Look at problems 1 - 37 in section 3.9.
10. Height of a freely falling body. Look at problems 51 - 57 in section 3.9. Hint, an object hits the ground when the height is zero (0). You don't need a definition statement because the variables are defined in the problem.
11. Divide two polynomials by factoring and dividing out common factors. Look at problems 13 - 25 in section 4.2.
12. Divide using synthetic division. Look at problems 1 - 19 in Appendix A.
Warning! I will not give credit for the correct answer if the technique is wrong. You must use synthetic division.
13. Simplify a problem involving multiplication of rational expressions. You need to factor, and divide out common factors. You do not need to expand the final answer, you may leave it in factored form (please do). Look at problems 13 - 31 in section 4.3
14. Combine rational expressions. Reduce your answer to lowest terms. Look at problems 11 - 63 in section 4.4 with a special emphasis on problems where you need to factor a negative one (-1) out of one of the factors.
15. Simplify a complex fraction as much as possible. Look at problems 17 - 31 in section 4.5.
16. Solve a rational equation. Be sure to list the values that x cannot be after you have determined your LCD and then don't use those numbers. Look at problems 23 - 41 in section 4.6.
17. Solve a rational equation. Be sure to list the value that x cannot be after you have determined your LCD (it is possible that there are no restrictions). Look at problems 1 - 9 in section 4.6.
18. Work problem. If Sam can do a job in 3 days while it takes Fred 6 days to the same job, how long will it take them working together to do 10 jobs? Look at problems 15 - 21 in section 4.7 Don't forget the definition statement. A box like you will be shown in class is very useful.
Problem 1 is 8 points (4 points for each type of multiplication)
Problem 2 is 5 points (1/2 point for every blank you need to complete)
Problems 3 - 17 are 5 points each
Problem 18 is 8 points (2 or 4 for a defintion statement (2 if wrong, 4 if correct) and 4 for the correct answer)
Total - 96 points, so everyone gets 4 free points (no, it's not 4 points for putting your name on the paper).