MATH Final Exam Review Sheet

8/14/2019 MATH Final Exam Review Sheet

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Math 1324 Final Examination Review

1. Find the slope of the line between the two points(2, 3) and (5, 7).

2. Plot the line: y = 3x 2Label the y-intercept and show the slope with 2 stair steps.

3. Solve the simultaneous linear equations x + 2y = 42x + y = 3

4. Add the following two matrices:

2103

2035 =


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5. Do the following scalar multiplication:

20

353 =

6. Do the vector multiplication:

5

2

1

312 =

7. Do the matrix multiplication:

5 3 2 3

0 2 0 1

8. Graph the inequality: 1232 y x


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12. Setup the initial simplex tableau for the optimization problem,including slack variables:

Maximize: 3 4 Subject to:

3,2,1,0

18432

12542

321

321

i x x x x

x x x

i

13. Given this simplex tableau, circle the next pivot value identifyrow and column.

x1 x2 x3 s 1 s 2 z2 3 1 1 0 0 3005 2 2 0 1 0 200

-7 -5 -1 0 0 1 0

14. Give the solution for this simplex tableau:

x1 x2 x3 s 1 s 2 z2 2 1 1 0 0 200 1 2 -2 1 0 100 5 1 3 0 1 50

x1 = , x 2 = , x 3 = , s 1 = , s 2 = , z =

15. State the transpose of the matrix:

T

345

010

321

=


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Round to nearest dollar in the next three problems.

16. Find the maturity value of a loan of $2,000 at the end of 9months with simple interest of 13.2%.

17. Find the maturity value of a deposit of $4,000 paying 7.4%compounded annually after 4 years.

18. A note will pay $12,000 in 6 years. Assuming an interest of6%, compounded annually, what is the present value of thenote?

19. Draw a Venn diagram showing two sets overlapping that show

a) B A b) B A

20. For U = {1,2,3,4,5,6,7,8,9} , X = { 1,3,5,7,9) and Y = {2,3,4,5} ,state:

a) X = b) Y X =

21. A jar contains 3 white, 6 orange, 5 yellow, and 6 black marbles.If one marble is drawn at random, what is the probability it isyellow?


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22. Given 5 different letters, {a,b,c,d,e}, how many arrangements of2 letters are possible?

23. A menu offers 3 salads, 2 main dishes, and 6 desserts. Howmeals are possible consisting of a salad, a main dish, and a

dessert?

24. A club has 15 members. In how many ways can a committeeof 3 be created?

25. A bowl contains 6 red apples and 4 yellow apples. If the applesare indistinguishable (same shape, hardness), what is theprobability of a blindfolded person picking a red apple?

26. If the probability of selecting a defective item is p = 0.2 and ifthe number of items is large enough that independent trials canbe assumed, what is the probability of getting 3 defective itemsin a sample of 5 items?

27. Find the Expected Value of x given: E(x) = ____

x 2 3 4 5P(x) .2 .4 .3 .1

28. Using the standard normal curve, find P(0.25< z < 1.36) =

29. If a binomial distribution has p = 0.10 and n = 30, what are themean and standard deviation of the binomial distribution?(Answer to 2 decimal places.)

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MATH Final Exam Review Sheet