APM3715 MAJOR TEST 01 – 06/09/ 2023-Sem 2
UNIVERSITY OF SOUTH AFRICA
SCHOOL OF ENGINEERING
CONTINUOUS ASSESSMENT
Major Test 1
APM3715
Numerical Methods for Civil Engineers I
Examiner: LC Maselela
Marks: 100
Internal Moderator: Walied Elsaigh
Weight of Assessment: 30 %
External Moderator: Landry Omalanga
Duration: 2H00
Graduate Attribute being assessed: None
Open- Book Examination
This paper consists of 3 Pages, including this cover page.
Instructions:
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Please tick the Honor Pledge and answer ALL three (3) questions.
Please note this is IRIS invigilated exam. Your microphone and camera should be on for
the duration of the exam.
Your script must be saved with file named as student no, subject code (For Example:
72111986_APM3715) and uploaded on MyExams, under assessment #3.
If the information given is not complete, please assume, specify the required value, and
continue with the exam paper. Provide answers to three (3) decimal points.
For all calculation purposes, use radians.
Additional student instructions:
1. Students must upload their answer scripts in a single PDF file (answer scripts must not be
password protected or uploaded as “read only” files)
2. NO emailed scripts will be accepted.
3. Students are advised to preview submissions (answer scripts) to ensure legibility and that the
correct answer script file has been uploaded.
4. Students are permitted to re-submit their answer scripts, within the given time frame, should
their initial submission be unsatisfactory.
5. Incorrect file format and uncollated answer scripts will not be considered.
6. Incorrect answer scripts and/or submissions made on unofficial examinations platforms
(including the invigilator cellphone application) will not be marked and no opportunity will be
granted for resubmission.
7. Mark awarded for incomplete submission will be the student’s final mark. No opportunity for resubmission will be granted.
8. Mark awarded for illegible scanned submission will be the student’s final mark. No opportunity
for resubmission will be granted.
9. Submissions will only be accepted from registered student accounts.
10. Students who have not utilized invigilation or proctoring tools will be subjected to disciplinary
processes.
11. Students suspected of dishonest conduct during the examinations will be subjected to
disciplinary processes. UNISA has a zero tolerance for plagiarism and/or any other forms of
academic dishonesty.
12.Students are provided 30 MINUTES to submit their answer scripts after the official
examination time. Submissions made after the official examination time will be rejected.
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APM3715 MAJOR TEST 01 – 06/09/ 2023-Sem 2
Question 1
1.1 State the significance of numerical methods in Civil Engineering.
(2)
1.2 Briefly discuss the following statement: “numerical methods can merge to an
adequate approximation but not an exact solution”.
(3)
1.3 A simply supported beam is subjected to non-uniform distributed load. The
maximum vertical deflection position (x) is given by a non-linear equation f(x). The
Secant method has been used with an initial guess to determine the root of the equation.
The following results came out.
Table 1: Absolute and relative error calculations.
Iteration no
Root estimate
Absolute error
Initial value
X0
15.000
1
X1
14.557
2
X2
14.572
3
X3
14.572
Relative error
Do the necessary calculations and fill in the last two columns of Table 1.
(10)
1.4 Find the LU Decomposition of the following matrix:
3 −7 −2
�−3 5
1�
6 −4 0
(15)
[ 30 Marks]
Question 2
Write a user defined Octave function for the following math function:
𝑧𝑧(𝑥𝑥, 𝑦𝑦) = 𝑒𝑒 𝑦𝑦 cos(𝑥𝑥) + sin (𝑥𝑥 2 − 𝑦𝑦)
Where: x and y are input arguments and z is the output argument.
Write a main script that call the function to make a 3D plot of the function for 𝜋𝜋 ≤ 𝑥𝑥 ≤ 𝜋𝜋
and −𝜋𝜋/2 ≤ 𝑦𝑦 ≤ 𝜋𝜋/2
Note: Your answer must include two (2) parts, user defined function and a script. The
screenshot must include student’s details, date, time, and module code.
[20 Marks]
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APM3715 MAJOR TEST 01 – 06/09/ 2023-Sem 2
Question 3
A Civil Engineer involved in construction requires 4800,5810, and 5690 cubic meters of
sand, fine gravel, and coarse gravel, respectively, for a building project. There are three
(3) borrow pits from which these materials are obtained. The material composition of
these pit is given in the Table 2:
Table 2: Percentage material composition of Pit 1, Pit 2, and Pit 3.
Borrow Pit no.
Sand (%)
Fine Gravel (%)
Coarse Gravel (%)
Pit 1
52
30
18
Pit 2
20
50
30
Pit 3
25
20
55
3.1 Generate the system of equations to represent the relationship of material required
by the engineer at the construction site.
(9)
3.2 How many cubic meters must be hauled from each pit to meet the engineer’s
needs? Use the Gaussian Elimination Method.
(18)
3.3 Do the calculations in 3.2 by using the Gauss-Seidel method. Do five (5) iterations
and assume initial values of (2000, 2000, 2000). Make use of an EXCEL® sheet to do
your calculations. Work to at least five (5) decimal places for more accurate results. The
EXCEL® sheet must show student’s details.
(17)
3.4 Use the results of Q3.2 to find the relative error related to the results of the 5th
iteration in Q3.3.
(6)
[ 50 Marks]
TOTAL MARKS [100]
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UNISA 2023
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