MAT1501
EXAM PACK
Recent exam questions and answers
Summarised study notes
Exam tips and guidelines
+27 81 278 3372
DISCLAIMER & TERMS OF USE
1. Educational Aid: These study notes are designed to serve as educational aids and should not be considered as a
substitute for individual research, critical thinking, or professional guidance. Students are encouraged to
conduct their own extensive research and consult with their instructors or academic advisors for specific
assignment requirements.
2. Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the
information provided in these study notes, the seller cannot guarantee the completeness or correctness of all
the content. It is the responsibility of the buyer to verify the accuracy of the information and use their own
judgment when applying it to their assignments.
3. Academic Integrity: It is crucial for students to uphold academic integrity and adhere to their institution's
policies and guidelines regarding plagiarism, citation, and referencing. These study notes should be used as a
tool for learning and inspiration, but any direct reproduction of the content without proper acknowledgment and
citation may constitute academic misconduct.
4. Limited Liability: The seller of these study notes shall not be held liable for any direct or indirect damages,
losses, or consequences arising from the use of the notes. This includes, but is not limited to, poor grades,
academic penalties, or any other negative outcomes resulting from the application or misuse of the information
provide
]
, lOMoARcPSD|22437965
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
university
of south africa
October/November 2024
MAT1501 -FUNDAMENTAL MATHEMATICS
Duration : 3 Hours 100 Marks
EXAMINERS :
FIRST : PROF AR ADEM
SECOND : MR TW SEKGOBELA
EXTERNAL : PROF B MUATJETJEJA
Closed book and online examination, which you have to write within 3 hours and submit online.
Use of any calculator is NOT allowed.
This web based examination remains the property of the University of South Africa and may not be distributed
from the Unisa platform.
This examination allows typed in text and/or attached documents as part of your submission.
Save frequently while working.
Declaration: I have neither given nor received aid on this examination.
The examination will take place on the Online Assessment tool located in your module examination site on
myModules in myUnisa.
Once you finish click on the submit for grading button to submit your exam
This examination question paper consists of 6 pages.
Answer All Questions and Submit within the stipulated timeframe.
Late submission will not be accepted.
This paper consists of 6 pages.
Downloaded by Corona Virus ()
, lOMoARcPSD|22437965
QUESTION 1
Suppose A = {x ∈ R : x > −3} and B = (−4; 5].
(a) Sketch each of A and B on separate number lines. (1)
(b) Write A ∪ B in set builder notation. (1)
(c) Sketch A ∪ B on a separate number line. (1)
(d) Write A ∩ B in set builder notation. (1)
(e) Write A ∩ B on a separate number line. (1)
[5]
QUESTION 2
The sketch shows a circle, a parabola, which is the graph of f , and a straight line, which is the graph of g. The
parabola has xintercepts -2 and 6, and y-intercept 6. Its turning point is C. The circle has its centre at the origin
and it passes through the point A, which has coordinates (−2, 0). At point B both the circle and the straight line
cut the x-axis. The straight line has y-intercept 1.
[TURN OVER]
Downloaded by Corona Virus ()
, lOMoARcPSD|22437965
(a) What are the coordinates of B? (1)
(b) What is the equation of g (2)
(c) Write down the equation of the line that is perpendicular to the graph of g and passes through B. (2)
(d) Find the equation that defines f . (2)
(e) Show that C has coordinates (2, 8). (1)
(f ) What is the distance between A and C? (1)
(g) Find the midpoint D of AC: (1)
(h) Write down the equation of the circle that has AC as diameter. (2)
(i) Find the maximum vertical distance between the graphs of f and g on the interval x ∈ [0, 6]. (2)
[14]
QUESTION 3
(a) Obtain the sum of the series 8 + 11 + 14 + · · · + 56. (2)
(b) A geometric sequence of positive terms has first term 2, and the sum of the first three terms is 266. (3)
Calculate the common ratio.
(c) An arithmetic sequence, A, has first term a and common difference 2, and a geometric sequence, B, has (3)
first term a and common ratio 2. The first four terms of each sequence have the same sum. Obtain the
value of a.
[8]
QUESTION 4
Evaluate the following limits:
3
(a) lim sin(x2 ) + x 3ex + 6 (2)
x→2
p
(b) lim u3 + 3u4 + 6 + cos(u) (2)
u→π
x2 − 4
(c) Let f (x) =
|x − 2|
(i) Find lim− f (x). (3)
x→2
(ii) Find lim f (x). (2)
x→2+
(iii) Discuss lim f (x). (3)
x→2
[12]
[TURN OVER]
Downloaded by Corona Virus ()
EXAM PACK
Recent exam questions and answers
Summarised study notes
Exam tips and guidelines
+27 81 278 3372
DISCLAIMER & TERMS OF USE
1. Educational Aid: These study notes are designed to serve as educational aids and should not be considered as a
substitute for individual research, critical thinking, or professional guidance. Students are encouraged to
conduct their own extensive research and consult with their instructors or academic advisors for specific
assignment requirements.
2. Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the
information provided in these study notes, the seller cannot guarantee the completeness or correctness of all
the content. It is the responsibility of the buyer to verify the accuracy of the information and use their own
judgment when applying it to their assignments.
3. Academic Integrity: It is crucial for students to uphold academic integrity and adhere to their institution's
policies and guidelines regarding plagiarism, citation, and referencing. These study notes should be used as a
tool for learning and inspiration, but any direct reproduction of the content without proper acknowledgment and
citation may constitute academic misconduct.
4. Limited Liability: The seller of these study notes shall not be held liable for any direct or indirect damages,
losses, or consequences arising from the use of the notes. This includes, but is not limited to, poor grades,
academic penalties, or any other negative outcomes resulting from the application or misuse of the information
provide
]
, lOMoARcPSD|22437965
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
university
of south africa
October/November 2024
MAT1501 -FUNDAMENTAL MATHEMATICS
Duration : 3 Hours 100 Marks
EXAMINERS :
FIRST : PROF AR ADEM
SECOND : MR TW SEKGOBELA
EXTERNAL : PROF B MUATJETJEJA
Closed book and online examination, which you have to write within 3 hours and submit online.
Use of any calculator is NOT allowed.
This web based examination remains the property of the University of South Africa and may not be distributed
from the Unisa platform.
This examination allows typed in text and/or attached documents as part of your submission.
Save frequently while working.
Declaration: I have neither given nor received aid on this examination.
The examination will take place on the Online Assessment tool located in your module examination site on
myModules in myUnisa.
Once you finish click on the submit for grading button to submit your exam
This examination question paper consists of 6 pages.
Answer All Questions and Submit within the stipulated timeframe.
Late submission will not be accepted.
This paper consists of 6 pages.
Downloaded by Corona Virus ()
, lOMoARcPSD|22437965
QUESTION 1
Suppose A = {x ∈ R : x > −3} and B = (−4; 5].
(a) Sketch each of A and B on separate number lines. (1)
(b) Write A ∪ B in set builder notation. (1)
(c) Sketch A ∪ B on a separate number line. (1)
(d) Write A ∩ B in set builder notation. (1)
(e) Write A ∩ B on a separate number line. (1)
[5]
QUESTION 2
The sketch shows a circle, a parabola, which is the graph of f , and a straight line, which is the graph of g. The
parabola has xintercepts -2 and 6, and y-intercept 6. Its turning point is C. The circle has its centre at the origin
and it passes through the point A, which has coordinates (−2, 0). At point B both the circle and the straight line
cut the x-axis. The straight line has y-intercept 1.
[TURN OVER]
Downloaded by Corona Virus ()
, lOMoARcPSD|22437965
(a) What are the coordinates of B? (1)
(b) What is the equation of g (2)
(c) Write down the equation of the line that is perpendicular to the graph of g and passes through B. (2)
(d) Find the equation that defines f . (2)
(e) Show that C has coordinates (2, 8). (1)
(f ) What is the distance between A and C? (1)
(g) Find the midpoint D of AC: (1)
(h) Write down the equation of the circle that has AC as diameter. (2)
(i) Find the maximum vertical distance between the graphs of f and g on the interval x ∈ [0, 6]. (2)
[14]
QUESTION 3
(a) Obtain the sum of the series 8 + 11 + 14 + · · · + 56. (2)
(b) A geometric sequence of positive terms has first term 2, and the sum of the first three terms is 266. (3)
Calculate the common ratio.
(c) An arithmetic sequence, A, has first term a and common difference 2, and a geometric sequence, B, has (3)
first term a and common ratio 2. The first four terms of each sequence have the same sum. Obtain the
value of a.
[8]
QUESTION 4
Evaluate the following limits:
3
(a) lim sin(x2 ) + x 3ex + 6 (2)
x→2
p
(b) lim u3 + 3u4 + 6 + cos(u) (2)
u→π
x2 − 4
(c) Let f (x) =
|x − 2|
(i) Find lim− f (x). (3)
x→2
(ii) Find lim f (x). (2)
x→2+
(iii) Discuss lim f (x). (3)
x→2
[12]
[TURN OVER]
Downloaded by Corona Virus ()
