100% correct workings
APM2616 EXAM
PACK 2025/2026 –
QUESTION &
ANSWERS
QUESTIONS & ANSWERS
, lOMoARcPSD|18998289
UNIVERSITY EXAMINATIONS
OCTOBER/NOVEMBER 2024
APM2616
Computer Algebra
Welcome to the APM2616 examination
Date: 18 November 2024
Time: 08:00
Hours: 2
Examiner name: Mr M KGAROSE
Internal moderator name: Prof JMW MUNGANGA
This paper consists of 7 pages (including the cover page).
Total marks: 100
Instructions:
• Include reference to additional information sheets if applicable.
• You are NOT allowed to use a pocket or a non-programming calculator.
• You need to declare your honesty regarding writing this paper.
• This exam is IRIS invigilated. You must have your camera on for entire duration of the
exam. Failure to have your camera on for the duration of the exam, will lead to disciplinary
action taken against you.
• Answer All Questions and Submit within the stipulated timeframe.
• Late submissions will not be accepted.
• ALL COMPUTATIONS MUST BE SHOWN.
Additional student instructions
• Students must upload their answer scripts in a single PDF file (answer scripts must not be
password protected or uploaded as “read only” files)
• Incorrect file format and uncollated answer scripts will not be considered.
• NO emailed scripts will be accepted.
• Students are advised to preview submissions (answer scripts) to ensure legibility and that
the correct answer script file has been uploaded.
• Incorrect answer scripts and/or submissions made on unofficial examinations platforms
(including the invigilator cell phone application) will not be marked and no opportunity will
be granted for resubmission. Only the last answer file uploaded within the stipulated
submission duration period will be marked.
• Mark awarded for incomplete submission will be the student’s final mark. No opportunity for
resubmission will be granted.
• Mark awarded for illegible scanned submission will be the student’s final mark. No
opportunity for resubmission will be granted.
• Submissions will only be accepted from registered student accounts.
• Students who have not utilised the proctoring tool will be deemed to have transgressed
Unisa’s examination rules and will have their marks withheld. If a student is found to have
been outside the proctoring tool for a total of 10 minutes during their examination session,
Open Rubric
Downloaded by Syokstech ()
, lOMoARcPSD|18998289
they will be considered to have violated Unisa’s examination rules and their marks will be
withheld. For examinations which use the IRIS invigilator system, IRIS must be recording
throughout the duration of the examination until the submission of the examinations scripts.
• Students have 48 hours from the date of their examination to upload their invigilator results
from IRIS. Failure to do so will result in students deemed not to have utilized the proctoring
tools.
• Students suspected of dishonest conduct during the examinations will be subjected to
disciplinary processes. Students may not communicate with any other person or request
assistance from any other person during their examinations. Plagiarism is a violation of
academic integrity and students who plagiarise, copy from published work or Artificial
Intelligence Software (e.g. ChatGPT) or online sources (e.g. course material), will be in
violation of the Policy on Academic Integrity and the Student Disciplinary Code and may be
referred to a disciplinary hearing. Unisa has a zero tolerance for plagiarism and/or any
other forms of academic dishonesty.
• Listening to audio (music) and making use of audio-to-text software is strictly prohibited
during your examination session unless such usage of the software is related to a student’s
assistive device which has been so declared. Failure to do so will be a transgression of
Unisa’s examination rules and the student's marks will be withheld.
• Students are provided 30 minutes to submit their answer scripts after the official
examination time. Students who experience technical challenges should report the
challenges to the SCSC on 080 000 1870 or their College exam support centres (refer to
the Get help during the examinations by contacting the Student Communication Service
Centre [unisa.ac.za]) within 30 minutes. Queries received after 30 minutes of the official
assessment duration time will not be responded to. Submissions made after the official
assessment time will be rejected according to the examination regulations and will not be
marked. Only communication received from your myLife account will be considered.
• Non-adherence to the processes for uploading assessment responses will not qualify the
student for any special concessions or future assessments.
• Queries that are beyond Unisa’s control include the following: a. Personal network or
service provider issues
b. Load shedding/limited space on personal computer
c. Crashed computer
d. Non-functioning cameras or web cameras
e. Using work computers that block access to the myExams site (employer firewall
challenges)
f. Unlicensed software (e.g. license expires during exams)
Postgraduate students experiencing the above challenges are advised to apply for an
aegrotat and submit supporting evidence within ten days of the examination session.
Students will not be able to apply for an aegrotat for a third examination opportunity.
Postgraduate/undergraduate students experiencing the above challenges in their second
examination opportunity will have to reregister for the affected module.
• 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.
Downloaded by Syokstech ()
, lOMoARcPSD|18998289
APM2616
3 October/November 2024
QUESTION 1
(a) Given that a function f maps x to x sin(x), find the function that represents the derivative of f , and (10)
evaluate it at π.
(b) Given the following series, (15)
N
X 1 + sin(x)
HN (x) = ,
k
k=1
with partial sums for some values N . Plot in the same graph, H1 , H2 , . . . , H15 , where x ∈ [−8, 5].
[25]
QUESTION 2
Given that the following have been defined in a MuPAD session as:
n is a positive integer;
x as an array of n identifiers;
g as an n × n matrix.
Write a MuPAD procedure called mygam that takes the above as input and outputs n × n × n array defined by
n
1X ∂gai ∂gbi ∂gab
Cabc = hci + −
2 i=1 ∂xb ∂xa ∂xi
where h is the matrix inverse of g.
[25]
Downloaded by Syokstech ()
APM2616 EXAM
PACK 2025/2026 –
QUESTION &
ANSWERS
QUESTIONS & ANSWERS
, lOMoARcPSD|18998289
UNIVERSITY EXAMINATIONS
OCTOBER/NOVEMBER 2024
APM2616
Computer Algebra
Welcome to the APM2616 examination
Date: 18 November 2024
Time: 08:00
Hours: 2
Examiner name: Mr M KGAROSE
Internal moderator name: Prof JMW MUNGANGA
This paper consists of 7 pages (including the cover page).
Total marks: 100
Instructions:
• Include reference to additional information sheets if applicable.
• You are NOT allowed to use a pocket or a non-programming calculator.
• You need to declare your honesty regarding writing this paper.
• This exam is IRIS invigilated. You must have your camera on for entire duration of the
exam. Failure to have your camera on for the duration of the exam, will lead to disciplinary
action taken against you.
• Answer All Questions and Submit within the stipulated timeframe.
• Late submissions will not be accepted.
• ALL COMPUTATIONS MUST BE SHOWN.
Additional student instructions
• Students must upload their answer scripts in a single PDF file (answer scripts must not be
password protected or uploaded as “read only” files)
• Incorrect file format and uncollated answer scripts will not be considered.
• NO emailed scripts will be accepted.
• Students are advised to preview submissions (answer scripts) to ensure legibility and that
the correct answer script file has been uploaded.
• Incorrect answer scripts and/or submissions made on unofficial examinations platforms
(including the invigilator cell phone application) will not be marked and no opportunity will
be granted for resubmission. Only the last answer file uploaded within the stipulated
submission duration period will be marked.
• Mark awarded for incomplete submission will be the student’s final mark. No opportunity for
resubmission will be granted.
• Mark awarded for illegible scanned submission will be the student’s final mark. No
opportunity for resubmission will be granted.
• Submissions will only be accepted from registered student accounts.
• Students who have not utilised the proctoring tool will be deemed to have transgressed
Unisa’s examination rules and will have their marks withheld. If a student is found to have
been outside the proctoring tool for a total of 10 minutes during their examination session,
Open Rubric
Downloaded by Syokstech ()
, lOMoARcPSD|18998289
they will be considered to have violated Unisa’s examination rules and their marks will be
withheld. For examinations which use the IRIS invigilator system, IRIS must be recording
throughout the duration of the examination until the submission of the examinations scripts.
• Students have 48 hours from the date of their examination to upload their invigilator results
from IRIS. Failure to do so will result in students deemed not to have utilized the proctoring
tools.
• Students suspected of dishonest conduct during the examinations will be subjected to
disciplinary processes. Students may not communicate with any other person or request
assistance from any other person during their examinations. Plagiarism is a violation of
academic integrity and students who plagiarise, copy from published work or Artificial
Intelligence Software (e.g. ChatGPT) or online sources (e.g. course material), will be in
violation of the Policy on Academic Integrity and the Student Disciplinary Code and may be
referred to a disciplinary hearing. Unisa has a zero tolerance for plagiarism and/or any
other forms of academic dishonesty.
• Listening to audio (music) and making use of audio-to-text software is strictly prohibited
during your examination session unless such usage of the software is related to a student’s
assistive device which has been so declared. Failure to do so will be a transgression of
Unisa’s examination rules and the student's marks will be withheld.
• Students are provided 30 minutes to submit their answer scripts after the official
examination time. Students who experience technical challenges should report the
challenges to the SCSC on 080 000 1870 or their College exam support centres (refer to
the Get help during the examinations by contacting the Student Communication Service
Centre [unisa.ac.za]) within 30 minutes. Queries received after 30 minutes of the official
assessment duration time will not be responded to. Submissions made after the official
assessment time will be rejected according to the examination regulations and will not be
marked. Only communication received from your myLife account will be considered.
• Non-adherence to the processes for uploading assessment responses will not qualify the
student for any special concessions or future assessments.
• Queries that are beyond Unisa’s control include the following: a. Personal network or
service provider issues
b. Load shedding/limited space on personal computer
c. Crashed computer
d. Non-functioning cameras or web cameras
e. Using work computers that block access to the myExams site (employer firewall
challenges)
f. Unlicensed software (e.g. license expires during exams)
Postgraduate students experiencing the above challenges are advised to apply for an
aegrotat and submit supporting evidence within ten days of the examination session.
Students will not be able to apply for an aegrotat for a third examination opportunity.
Postgraduate/undergraduate students experiencing the above challenges in their second
examination opportunity will have to reregister for the affected module.
• 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.
Downloaded by Syokstech ()
, lOMoARcPSD|18998289
APM2616
3 October/November 2024
QUESTION 1
(a) Given that a function f maps x to x sin(x), find the function that represents the derivative of f , and (10)
evaluate it at π.
(b) Given the following series, (15)
N
X 1 + sin(x)
HN (x) = ,
k
k=1
with partial sums for some values N . Plot in the same graph, H1 , H2 , . . . , H15 , where x ∈ [−8, 5].
[25]
QUESTION 2
Given that the following have been defined in a MuPAD session as:
n is a positive integer;
x as an array of n identifiers;
g as an n × n matrix.
Write a MuPAD procedure called mygam that takes the above as input and outputs n × n × n array defined by
n
1X ∂gai ∂gbi ∂gab
Cabc = hci + −
2 i=1 ∂xb ∂xa ∂xi
where h is the matrix inverse of g.
[25]
Downloaded by Syokstech ()
