# FirstExam

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Kingdom of Saudi Arabia
Ministry of Higher Education
Majmaah University
College of Engineering
Department: Basic Engineering Sciences
Exam Information
First Exam
Course code:
Math 254
Course Title: Numerical Methods
Instructor:
Dr. Mukhtar Salah
Section number:
1
Exam date:
Mon. 27/10/2014
Exam time:
From:
4:00 pm
To: 6:00
pm
Exam hall:
3D40-41
Number of pages: 5
Total score:
20 points
Student’s Information
Name:
ID:
Exam Instructions:
 Read the questions carefully and several times. Writing clearly will make
it possible to assess your answers correctly.
 Any form of cheating, intention to cheating, or disruption of the exam will
subject you to a disciplinary action as specified by the university’s
regulations.
 Carrying or using the mobile phone during the exam is not allowed. Using
the phone during the exam will carry a disciplinary action.
 The calculator is only permitted by the exam supervisor.
 No student can leave the exam room during the first half hour of the
exam. Any student coming after the first half hour of the exam will not be
permitted to enter the exam.
 A student leaving the exam, even for legitimate reasons, may not be given
a makeup exam.
Points Earned:
Question
Score
1
2
3
4
Total score in the exam:
Dear student, we encourage you to answer the exam the best you can and we
wish you all success.
1
Question 1:( 5pts)
You are working for a start-up computer assembly company and have
been asked to determine the minimum number of computers that the shop
will have to sell to make a profit. The equation that gives the minimum
number of computers n to be sold after considering the total costs and the
total sales is
f (n)  40 n3  875n  35000  0
Use the bisection method of finding roots of equations to find the
minimum number of computers that need to be sold to make a profit.
Conduct three iterations to estimate the root of the above equation. Find
the absolute relative approximate error at the end of each iteration.
2
Question 2:( 5pts)
To find the inverse of a number a , one can use the equation
f (c )  a 
1
0
c
where c is the inverse of a .
Use the Newton-Raphson method of finding roots of equations to find the
inverse of a  2.5 . Conduct three iterations to estimate the root of the
above equation. Find the absolute relative approximate error at the end of
each iteration.
3
Question3 : (5pts)
Thermistors are used to measure the temperature of bodies. Thermistors
are based on materials’ change in resistance with temperature. To
measure temperature, manufacturers provide you with a temperature vs.
resistance calibration curve. If you measure resistance, you can find the
temperature. A manufacturer of thermistors makes several observations
with a thermistor, which are given in the following Table 1.
Table 1 Temperature as a function of resistance.
R ohm 
T C
910
630
450
30
40
50
Determine the temperature corresponding to 754.8 ohms using Newton’s
divided difference method of interpolation and a second order
polynomial.
4
Question4 : (5pts)
Solve the following set of equations with LU decomposition:
2x1 − x2 + x3 = 1
3x1 + 3x2 +9x3 = 2
3x1 + 3x2 + 5x3 = 1
=============================================================
End of the Exam
Good Luck
Dr. Mukhtar Salah
5
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