mth507-mathematics for social science (1)

7/24/2019 Mth507-Mathematics for Social Science (1)

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COLLEGE OF ENGINEERING, SCIENCE AND TECHNOLOGY

SCHOOL OF MATHEMATICAL AND COMPUTING SCIENCES

M T H 5 7 M A T H E M A T I C S F O R S O C I A L S C I E N C E S

FINAL EXAMINATION

TRIMESTER 2, 2015

Time allowed: 3 hours + 10 minutes reading time

Instructions:

1. There are two sections in the paper. Section A (40 marks is compulsory) and choose 3 out of the 4questions in Section B (3 x 20 = 60 marks)

2. Start each Section on a new page.3. Show all working as partly correct answers may be rewarded.4. Programmable calculators are not allowed.5. This exam is worth 50% of your overall mark.6. If you use extra sheets of paper, attach it securely to the Answer Booklet.


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MTH507 Final Examination , Trimester 2, 2015,

Page 2

SECTION A [COMPULSORY] [40 marks]

1. Determine the inverse of matrix A below:

2154A

[4marks]

2. A straight line passes through the point ()and ( ). It also passes through point( ). Find

the value of .

[5marks]

3. Graph the following inequalities and shade the feasible region.

123

2054

yx

yx

[5marks]

4.

For the given data, find the mode, median, mean and standard deviation.

[1+2+2+4 = 9marks]

5. How many terms of an arithmetic sequence with first term as 10 and common difference of 6 isneeded to give a sum of 520.

[4marks]

6. Evaluate 6

0

3554 dxxx

[4marks]


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7. Standardized mathematic scores for two forms are given below;

Score Form A Form B

Over 80% 8 12

Under 80% 32 48

a)

What is the probability that a randomly selected mark is of a student from Form Ab)

What is the probability that a randomly selected mark is of a student from Form B given he/she scoredabove 80%?

[2+3=5marks]

8. Jone, at age 35, decides to invest in an investment account in a local bank. He will put $2500 peryear for the next 40 years. How much will he have at age 75 if his rate of return is assumed to be12% per annum?

Hint: The annuity amount after n payment periods is given byi

iPA

n 1)1(

[4marks]


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SECTION B Answer any THREE of the FOUR questions available Clearly label on the answer booklet the numbers you have chosen.

QUESTION B1

1) The fourth term of an arithmetic sequence is 47 and the eight term is 35. Solve for the first termand the common difference using Elimination method.

[5marks]

2) A company produces two types of Steel. Type 1 requires 2 hours of melting, 4 hours of cutting, and10 hours of rolling per ton. Type 2 requires 5 hours of melting, 1 hour of cutting and 5 hours ofrolling per ton. Forty hours is available for melting, twenty hours for cutting, and sixty hours forrolling. Each ton of Type 1 steel produces $240 profit, and each ton of Type 2 produces $80 profit.

Find the maximum profit and the production schedule that will produce this profit. Clearly state theobjective function and constraints. Use the graph paper provided for plotting and attach it to theanswer booklet.

[15marks]

QUESTION B2

1)Suppose that a store has three sizes of cans of nuts. Thestandard size conatins 2 pounds of peanutsand 1 pound of cashews. The largesize contains 1 pound of walnuts, 6 pounds of peanuts and 2pounds of cashews. Thegiant size conatins 1 pound of walnuts, 4 pounds of peanuts, and 2 poundsof cashews. Suppose that the store recieves an order for 5 pounds of walnuts, 26 pounds of peanutsand 12 pounds of cashews. How will it fill this order with the given sizes of cans?You may any method you wish to solve this system.

[10marks]

2) Given below are Examination scores of a group of Mathematics students;

a)Group this data into classes. Keep the class width same and use the starting interval as

b)Find the mean, standard deviaition and variance of the grouped data obtained in (a).

[3+2+4+1=10marks]


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Page 5

QUESTION B3

1)

A farmer with 3000 meters of fencing wants to enclose a rectangular plot that borders on a straighthigway. If the farmer does not want to fence the side along the highway, what is the largest areathat can be enclosed?

[6marks]

2) Compute the following limits:

a)25

103lim

2

2

5

x

xx

x

b)13

46lim3

2

x

x

x

[3+3=6marks]

3) The weight of 100 college students closely follow a normal distribution with a mean of 130 poundsand standard deviation of 5.2 pounds.

a) How many of these students would you expect to weigh at least 138 pounds?b)What range of weight would you expect the middle 70% of the students in the group?

[4+4=8marks]


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Page 6

QUESTION B4

1) Evaluate the following:

40

1

2 )42(k

kk

[4marks]

2) A tank is filled at a rate of 24)(' ttv where v(t) is the volume of the tank and t is time in

minutes. Initially there is 1000 L of water already present.a) How much water will the tank hold after 3 minutes?

b) If the capacity of the tank is 5000L , how long will it take for the tank to overflow?

[4+3=7marks]

3) Sera took $12 000 to a local bank with a view of putting it into a savings account. The bank givesSera the three options of interest rates with their different compounding times.

Option 1 Option 2 Option 3

Interest type , rate Simple , 8.4% Compound , 8.2% Compound, 8.3%Method Annually Monthly Daily

Compute her total amount after 24 months for all the three options, and hence conclude on whichoption she should take in order to get maximum return on her investment. Show all relevantworking.

[9marks]

THE EN


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mth507-mathematics for social science (1)

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