# Math 160: Study Guide - Chapters 3&4

1. Identify which type of problem (simple interest, compound interest, future value annuity, or present value annuity) is applicable. Do not attempt to answer the question, only identify the type of problem you would need to answer the question. Ten parts.
2. Financial problem. I'm being purposely vague here. It could be any of the simple interest, compound interest, future value, or present value problems.
3. Financial problem
4. Retirement problem: Find the present value needed to retire, then find the payment needed under a future value to reach that goal. Find out how much money there is after so many years. Determine what happens if an inheritence is applied. Look at the first part of the chapter 3 project.
5. Financial problem.
6. Write the solution to the system of linear equations from the augmented matrix. Four parts ... including the special cases. Look at problems 4.3.11-20.
7. Multiply the matrices by hand and simplify the result. Look at problems 4.4.11-14 and 55-58, but practice on larger matrices.
8. Perform the row operations on the matrix. Two parts. Look at problems 4.2.13-24.
9. One elementary row operation has been performed to a matrix. Determine what that row operation is. Two parts. Look at problems 4.2.25-34.
10. Solve the matrix equation for X. Two parts. Look at the first part of the chapter 4 project.
11. Leontief Input-Output Analysis. Write the input-output matrix and find the output. Look at problems 4.7.27-34.

## Group Portion

1. Incidence Matrix (shipping / airline / network traffic). Look at problems 4.4.67-68 and also part 2 of the chapter 4 project.
2. Traffic Flow application problem (map of one-way streets). Look at problems 4.3.89-90.
3. Dominance Relation (players winning and losing indirectly). Look at problems 4.4.73-74.

## Notes

• There is a group portion of this exam worth 34 points. You may work with a partner (or alone), but each person must submit answers for the problems.
• The group portion involves loading matrices into wxMaxima and working with them. This is because the matrices are larger and this will save you time and mistakes since you won't have to enter them yourself. Use matrix calculations to answer the questions on the group test. Do not perform the calculations by adding rows or columns in a matrix by hand.
• You will need your calculator for the test. The test is designed so that much of the work is performed on the calculator. If you sit there and do it by hand, you're going to have trouble getting through the test in the given time.
• The computer may not be used during the individual portion of the exam.
• Show enough work so that I can give partial credit if you're wrong. That may mean just writing down what you're looking for and what you entered into the calculator for some problems, but if there's nothing but an answer, you better make sure it's right.
• Have you act together when you come in to take the test. Know your material. Go through and work the easiest problems first, not necessarily the order they're given to you on the test.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 G1 G2 G3 Total 20 3 6 21 8 8 4 4 6 6 5 12 11 11 125