# 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.
2. Stock transaction problem. Find the amount of principal and commission at buying and selling time. Identify the duration of the investment and compute the annual rate of return for the investment.
3. Find out how much money will be saved if regular deposits are made.
4. Find out how much money will be saved after a certain time period using compound interest. Determine how long it will take to accumulate a certain amount if regular deposits are made.
5. Retirement problem: Find the present value needed to retire, then find the payment needed under a future value to reach that goal.
6. Future value: Find the future value. Find the effective rate.
7. Home loan: Find the down payment, how much is financed, what the monthly payment will be, what the total payments are, and how much interest will be paid.
8. Home loan: Find the remaining balance after a fixed time, the equity in the house after so many years, the time to pay off the loan if extra is paid, and the amount of money saved by paying extra.
9. Solve the equation for X. Three parts. Know how to handle factoring of matrices and scalar multiplication. Look at problems 4.6.37-42 and the project for chapter 4.
10. Write the solution to the system of linear equations from the augmented matrix. Four parts ... including the special cases. The matrices may be in either row echelon form or reduced row echelon form. Look at problems 4.3.11-20.
11. Multiply the matrices by hand and simplify the result. Look at problems 4.4.11-14, but practice on larger matrices.
12. Use your calculator to solve the 3x3 system of linear equations. Be aware of the special cases of no solution or many solutions and be able to write the answer in parametric form. Three parts. Look at problems 4.3.31-50.
13. Find the values of x1, x2, and x3 using matrix inverses. Look at problems 4.6.13-16.
14. Perform the row operations on the matrix. Four parts. Look at problems 4.2.13-24.
15. Dominance Relation. Look at problem 4.4.73-74.
16. Construct a mathematical model for problem and use the inverse of a matrix to find the solution. Look at problems 4.6.49-56.
17. Leontief Input-Output Analysis. Write the input-output matrix and find the output. Look at problems 4.7.27-34.
18. Traffic flow. Create and solve the system of linear equations necessary to find the network flow. Give the limitations on the parameter. Find the traffic flow for a particular value of the parameter. Look at problems 4.3.81-82.

## Notes

• The test is individual, there are no groups allowed.
• You will need your calculator for the test. The test is designed so that much of the work is performed on the calculator.
• 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.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Total 8 6 5 6 6 6 8 8 6 4 4 3 2 4 6 6 6 6 100