MAT1501
EXAM PACK
FOR ASSISTANCE WITH THIS MODULE +27 67 171 1739
, 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.
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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]
Downloaded by Edger Tutora ()
EXAM PACK
FOR ASSISTANCE WITH THIS MODULE +27 67 171 1739
, 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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, lOMoARcPSD|53028991
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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