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ARAB OPEN UNIVERSITY
FACULTY OF COMPUTER STUDIES
INFORMATION TECHNOLOGY AND COMPUTING
MST 121 : USING MATHEMATICS
SPRING- 2003-2004
FIRST PRESENTATION-PART-1I
EXAM PERIOD: 150 MINUTES
This exam is in two parts and is worth a total of 122 points.
FINAL EXAM
(FORM A)
Student ID:
Student Name:
Group Number:
Tutor Name:
Grade for Part I is out of 42 Points.
Grade for Part II is out of 80 Points.
Total Grade is out of 122 Points.
Exam Period: 150 Minutes.
PART I :(This part is worth a maximum of 42 points).
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In this part, please do answer only fourteen (14) questions from the
available sixteen (16). Each question is worth 3 points. From the given
choices (a), (b),(c) and (d), select the correct answer.
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Question - 1: The area represented by the definite integral:
(a) 28
(b) 16
(c) 15

2
1
4 x3dx
(d) 10
The answer is:
……………………………………………………………………………………..
Question - 2: The number of different Tennis ball teams made of 2
persons that can be chosen from a group of 5 people is:
(a)10
(b) 15
(c) 120
(d) 20
The answer is:
……………………………………………………………………………...
Question - 3: The median of the grade list: 70, 60, 100, 90, is:
(a)60
(b) 70
(c) 80
(d) 100
The answer is:
……………………………………………………………………………………..
Question - 4: The final grades for all MST 121 students group of size 100,
in an AOU branch, has a mean of 63 and a standard deviation of 25.5, which
is the 95% confidence interval for all MST 121 students in AOU.
(a)(55.5, 70.5)
(b) (60, 66)
(c) (58, 68)
(d)(43,83)
The answer is:
……………………………………………………………………………….
Question - 5:A box contains17 balls numbered 1,2,..17. If one ball is drawn
at random, the probability that the number on the ball is not divisible by 3 is:
(a) 12/17
(b) 17/3
(c) 1/ 3
(d) 5/17
The answer is:
……………………………………………………………………………………..
Question-6:The velocity v of a moving particle is given by v = 5t -0.10 e10 t .
The time t at which the particle has a zero acceleration is:
(a)t = ln (5)
(b)t= ln(5)/10
(c) t = 5- e
2
(d) t is infinite
The answer is:
………………………………………………………………………………..
Question - 7: The integral  (cos 2 ( x)  1 / 2)dx , is equal to:
(a) cos( 2 x)  C
(b) C  sin( 2 x) / 4
(c) 1
(d) C  sin 2 (2 x)
The answer is:
……………………………………………………………………………………..
Question - 8: The sample standard deviation of the list: 70, 60, 100, 90, is:
(a)5 10
(b) 18.26
(c) 80
(d) 1000
The answer is:
……………………………………………………………………………………..
Question - 9: A mode for the function, P(x) = x in [-1, 1] is:
(a)-1/2
(b) 0
(c) 1
(d)1/2
The answer is:
……………………………………………………………………………………..
Question - 10: If y = 20 x2 + sin (-3x)
3
(a) 40 x + cos (3 x)
(b) 40 x + 3 cos (3x)
(c) 40 x – 3 cos (3 x)
(d) 2 x – 1/3 cos(3x)
1
5
The answer is:
……………………………………………………………………………………..
Question -11: The mean for the density, P(x) = x in [-1, 1], is:
(a)-1/2
(b) 0
(c) 1
(d)1/2
The answer is:
……………………………………………………………………………………..
Question -12: Two AOU Branches A and B have 100 and 90 MST students.
If the student mean grade in branch A is 63 with standard deviation 24, and
the mean grade in Branch B is 60 with standard deviation of 30, then the test
statistic, for the null hypothesis H0 that" The Branches means are equal" is:
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(a)0.74
(b) 1.5
(c) 2.75
(d)9.47
The answer is:
……………………………………………………………………………………..
Question -13: The minimum for the function, f(x) = x ln(x), ( x  0 ) is at: .
(a)(1/e, 1/e)
(b) (e, e)
(c) 1/e
(d) (1/e, -1/e)
The answer is:
………………………………………………………………………………………
Question - 14: The solution of the differential equation dy/dt = 2y, is:
(a) c  e 2t
(b) ce 2t
(d) ce2 x
(c) πt + c
The answer is:
………………………………………………………………………………
Question-15: An inflection point of the function f (x)=1/3 x3-5/2 x2 + 6x,
is:
(a) x = 3
(b) x =2
(c) x = 5/2
(d) no inflection point
The answer is:
………………………………………………………………………………..
Question - 16: The second derivative f ″ (x), for f (x) = e 3x + ln (2x+1), is:
(a) 9 e3x – 4/ (2x +1)2
(b) 3 e3x +2/ (2x +1)
(c) 9 e3x + 4/ (2x +1)2
(d) 9 e3x + 4ln (2x +1)
The answer is:
PART II :(This part is worth a maximum of 80 points).
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In this part, please answer only four (4) questions from the available six
(6) questions. Please do write down your solution neatly in the space
provided directly below each sub- part of a question. Each sub- part of
a question is worth 5 points, for a total 20 points for each question.
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……………………………………………………………………………...
Question -1: Before the final, the grades of a student taking MST121 are:
95, 75, 70, 60, 80, 95, 95, 65, 85, 80.
a) Find the Mode and the Median of the grades data set.
b) Find the average grade of the student so far.
c) Find the standard deviation of the grade data set.
d) Based on the list, predict the grade this student will get on the final exam
within 99% confidence interval. (Recall z =2.8 for 1% significance level).
……………………………………………………………………………..
Question -2: Two AOU Branches A and B have 100 and 90 MST students.
If the sample mean grade in branch A is 63 with standard deviation 25, and
the sample mean grade in Branch B is 60 with standard deviation of 30,
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a) Find the Estimated Standard Error (ESE) for the sampling distribution of
the difference of the grade means.
b) Find the test statistic, Z, for the null hypothesis H0 that" the Branches A
and B MST grades means are equal" .
c) Decide whether we should accept or reject the null hypothesis H0 at the
10% significance level. (Recall z = 1.64 for 10% significance level).
d) If another AOU Branch C has 100 MST 121 students with a sample mean
grade of 68, find the minimum standard deviation that will allow us to
accept the null hypothesis H0: "The grades means of Branch A and Branch
C are equal" at the 5% significance level.
……………………………………………………………………………..
Question -3: In an experiment of tossing a fair die with faces numbered 1
through 6, and two fair coins, each with faces numbered 0 and 1, the triplet
(x, y, z) where x=1,2..6, and y, z = 0 or 1, is recorded for each toss.
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a) Find the size of the sample space (the set of outcomes), and the
probability P(A) of the event A= {(x, y, z) such that: x = y = z}.
b) List all outcomes in the event B= {(x, y, z) such that: x + y + z = 6}, and
find P(B).
c) In any particular toss, given that x + y + z = 6, what is the probability that
y = z, (i.e. if C={(x, y, z) such that y=z}, then find P(C/B)).
d)Find the probability P(D), with D = {(x, y, z), such that: x+ y + z  6}.
……………………………………………………………………………..
Question – 4: For t  0, a particle is moving through a path y (t) (in m).
The velocity v (t) (in m/s) of the moving particle is given by:
v (t) = 10 - 2 t , (t  0) .
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a) Find the particle path function y (t), if y (0) = 4.
b) Find the acceleration a (t) of the particle (in m/s2). What relation exists
between a(t), and y(t). What can you say about the concavity of the path?.
c) Find the critical points of y(t) if any, and classify them.
d) Find the equation of the tangent to the path function y(t), when t = 3 s..
……………………………………………………………………………
Question – 5: Consider the function f(x) = 12 - 2e - 2 x in [0,  ).
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a)Find the area A under the function in the given interval [0,3].
b) Show that f(x) satisfies the differential equation: y' + 2y = 24.
c) Find the Second Derivative of the function f(x) when x = 1.
What happens to f(x), f ' (x) and f " (x) as x goes to  (infinity).
d) Consider the function G (x) =

x
0
f (t )dt . Find G(0), G(3) and G' (x).
……………………………………………………………………………..
Question – 6: Consider the functions f (x) = 2  (x-1) + cos (2  x), ( x  0) ,
and g(x) = 2 + x ln (x) – x , (x  0).
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a) Find the extreme values of f (x), in [0,1], and classify them.
b) Find the second derivative, g " (x), of g(x), at x= 1/2.
c) Knowing that both f and g are differentiable for x  1, find the derivative
the product function h(x) = f(x )g(x) for x  1. Show that in [1,  ), h(x)
is continuous.
d) Use the fundamental theorem of calculus to give an explicit expression
x
for the function W (x) = 1 ( g ' (t )  f ' (t ))dt . What is W(1) equal to?.
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