Mat 119 Test 1A: S. TakahashiPage 1 of 5

Arizona State UniversityMath 119 Finite Mathematics Test 2 A

Graded test will be returned on 11/4/02.

Dr. S. Takahashi

Place your name label here:

Your Predicted Score:______

Your Actual Score: ______

Read the following before you take this test.

1)Maximum total points for this test is 100.

2)You have ninety minutes to complete. Your score is reduced by one point per each minute exceeded.

3)Show all of your work. No work No credit

4)No need to show work for true-or-false questions.

5)Use only Casio CFX-9850GB, TI-81, 83, 86 or ordinary non-graphing calculators, if needed.

6)Use scratch paper provided by the proctor and attach to the test.

7)Make sure you indicate your solutions by circling or boxing your final answers.

8)Before you start, make sure you have all questions.

9)No rubber-necking.

Good luck.

Honor Statements: (Standard ASU math dept. version)

By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam. This includes any use of a graphing calculator beyond those uses specifically authorized by the Mathematics Department and your instructor. Furthermore, you agree not to discuss this exam with anyone until thetesting period is over. In addition, your calculator’s program memory and menus may be checked at any time and cleared by any testing center proctor or Mathematics Department instructor.

SignatureDate

Show All Work, except for True or False Questions.

  1. True or False:(15 points total)

ア）Let and be two arbitrary sets. Then ______

イ）A Power set of the set is:

______

ウ）Cardinal number of a finite set is the number of distinct elements in the set.

______

エ）Let and be two sets. If, and ,

then

______

オ) {φ}φ

______

  1. Suppose the price of the house you have purchased was $140,000 and you made a down payment of $30, 000. You are able to amortize the balance at 6% for 30 years from the bank. (10 points)

ア) Calculate the monthly mortgage payment.

イ) Calculate the total interest.

ウ) Calculate the equity of the house after 20 years.

  1. If you decide to establish a sinking fund to accumulate one million dollars by depositing $8000 every year to a bank account that is paying 7% per annum interest, how long will it take for you to do so? (10 pts.)
  1. Calculate each amount if:

a)$1000 is invested at simple interest rate of 8 % for 3 years.

b)$1000 is invested at 8 % compounded monthly for 3 years.

  1. Calculate:

ア)The effective annual yield for 9% compounded quarterly.

イ)The principal needed to get $4000 in 3 years at 10 % compounded semiannually.

  1. Calculate the time required to empty an IRA account of $350,000 if you withdraw $4500 every month.

The IRA is accumulating an interest of 5 % compounded monthly.

Ch 5.4 #32

  1. You are contributing $5000 per year to an retirement account paying 10 % compounded annually for

25 years.

ア) Calculate the value of your retirement account.

イ) Calculate the amount you can withdraw each year for 20 years at 10 % compounded annually.

Ch 5.4 #7

  1. You are to solve the following problem using the Simplex Method. Ch 4.2 Eg

Maximize:

Subject to constraints:

ア)Set up an initial Simplex Tableau.

イ)Apply pivoting as many times as needed to obtain the final Simplex Tableau.

ウ)Finally, maximize . What is the value of each of the basic and non-basic variables that yield this maximum?

  1. Answer the following questions. (points total)

ア）How many license plates can you generate using three letters followed by four numbers, if

① You can repeat letters and digits.

② You must place the letter “A” first and the digit “0” at the end.

③ You are not allowed to repeat letters but digits can be repeated.

④ You are not allowed to repeat letters nor digits.

イ）Let , , and

① Calculate (Find) the set

② Calculate the set

  1. Using the Simplex method, solve the following linear programming problem.

Copyright: S. Takahashi Arizona State University