MAT1501
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Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
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responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
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UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
university
of south africa
October/November 2025
MAT1501 -FUNDAMENTAL MATHEMATICS
Duration : 3 Hours 100 Marks
EXAMINERS :
FIRST : DR K SEBOGODI
SECOND : PROF AR ADEM
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 7 pages.
Answer All Questions and Submit within the stipulated timeframe.
Late submission will not be accepted.
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QUESTION 1
Choose the correct answer. Write only the letter that corresponds to your choice.
1. Which of the following functions are increasing everywhere on their domains: (1)
√
(i) y = x (ii) y = e−x (iii) y = x2 (iv) y = x3
(a) (i) and (ii) only
(b) (i), (iii) and (iv) only
(c) (i) and (iv) only
(d) (ii) and (iv) only
(e) None of the above combinations are correct.
2. Which of the following functions are one-to-one: (1)
( (
4 x if x < 0 x2 if x < 0
(i) y = x (ii) y = 2
(iii) y = (iv) y = x3
x if x ⩾ 0 x if x ⩾ 0
(a) (i), (ii) (iii) and (iv)
(b) (ii) and (iv) only
(c) (i) only
(d) (iii) and (iv) only
(e) None of the above combinations are correct.
d99
3. Find (sin x) (1)
dx99
(a) cos x
(b) − cos x
(c) sin x
(d) − sin x
(e) None of the above.
d
cos−1 (ex ) =
4. (1)
dx
ex
(a) √
1 − e2x
−ex
(b) √
1 − e2x
−ex
(c) √
e2x − 1
ex
(d) √
e2x − 1
(e) None of the above.
[TURN OVER]
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r
x2 + 1
5. ln = (1)
2x3
p
(a) (x2 + 1) − 2x3
(b) 12 ln(x2 + 1) − ln 2 − 3 ln x
(c) ln x + 21 ln 1 − ln x3
r
2x3
(d)
x2 + 1
(e) None of the above
2x2 + 1
6. Find the vertical asymptotes of the function y = . (1)
3x − 2x2
(a) x = 0 only
2
(b) x = only
3
2
(c) x = 0, x =
3
3
(d) x = ,x=0
2
(e) None of the above
" 5
#− 34
+ 16a− 6
7. Let a ∈ R . Select the correct simplification of the expression √ . (1)
81 a
27
(a)
8a
27a
(b)
8
8
(c)
27a
8a
(d)
27
(e) None of the above.
1
8. Find the domain of f (x) = √ . (1)
3−x
(a) [3, ∞)
(b) (3, ∞)
(c) (−∞, 3]
(d) (−∞, 3)
(e) None of the above.
9. A function f is continuous at a number a if (1)
(a) lim− f (x) = f (a)
x→a
(b) lim+ f (a) = f (x+ )
x→a
(c) lim f (a) = f (x)
x→a
(d) lim f (x) = f (a)
x→a
(e) None of these
[TURN OVER]
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EXAM PACK
Recent exam questions and answers
Summarised study notes
Exam tips and guidelines
+27 81 278 3372
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the information in
these study notes, the seller does not guarantee the completeness or correctness of all content. The buyer is
responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
, lOMoARcPSD|53028991
UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS
university
of south africa
October/November 2025
MAT1501 -FUNDAMENTAL MATHEMATICS
Duration : 3 Hours 100 Marks
EXAMINERS :
FIRST : DR K SEBOGODI
SECOND : PROF AR ADEM
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 7 pages.
Answer All Questions and Submit within the stipulated timeframe.
Late submission will not be accepted.
Downloaded by Edger Tutora ()
, lOMoARcPSD|53028991
QUESTION 1
Choose the correct answer. Write only the letter that corresponds to your choice.
1. Which of the following functions are increasing everywhere on their domains: (1)
√
(i) y = x (ii) y = e−x (iii) y = x2 (iv) y = x3
(a) (i) and (ii) only
(b) (i), (iii) and (iv) only
(c) (i) and (iv) only
(d) (ii) and (iv) only
(e) None of the above combinations are correct.
2. Which of the following functions are one-to-one: (1)
( (
4 x if x < 0 x2 if x < 0
(i) y = x (ii) y = 2
(iii) y = (iv) y = x3
x if x ⩾ 0 x if x ⩾ 0
(a) (i), (ii) (iii) and (iv)
(b) (ii) and (iv) only
(c) (i) only
(d) (iii) and (iv) only
(e) None of the above combinations are correct.
d99
3. Find (sin x) (1)
dx99
(a) cos x
(b) − cos x
(c) sin x
(d) − sin x
(e) None of the above.
d
cos−1 (ex ) =
4. (1)
dx
ex
(a) √
1 − e2x
−ex
(b) √
1 − e2x
−ex
(c) √
e2x − 1
ex
(d) √
e2x − 1
(e) None of the above.
[TURN OVER]
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r
x2 + 1
5. ln = (1)
2x3
p
(a) (x2 + 1) − 2x3
(b) 12 ln(x2 + 1) − ln 2 − 3 ln x
(c) ln x + 21 ln 1 − ln x3
r
2x3
(d)
x2 + 1
(e) None of the above
2x2 + 1
6. Find the vertical asymptotes of the function y = . (1)
3x − 2x2
(a) x = 0 only
2
(b) x = only
3
2
(c) x = 0, x =
3
3
(d) x = ,x=0
2
(e) None of the above
" 5
#− 34
+ 16a− 6
7. Let a ∈ R . Select the correct simplification of the expression √ . (1)
81 a
27
(a)
8a
27a
(b)
8
8
(c)
27a
8a
(d)
27
(e) None of the above.
1
8. Find the domain of f (x) = √ . (1)
3−x
(a) [3, ∞)
(b) (3, ∞)
(c) (−∞, 3]
(d) (−∞, 3)
(e) None of the above.
9. A function f is continuous at a number a if (1)
(a) lim− f (x) = f (a)
x→a
(b) lim+ f (a) = f (x+ )
x→a
(c) lim f (a) = f (x)
x→a
(d) lim f (x) = f (a)
x→a
(e) None of these
[TURN OVER]
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