MAT1501 EXAM PACK 2026 |Past Papers With Possible Solutions|

MAT1501
EXAM
PACK

2026

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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 distribu
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 willtake place on the Online Assessment toollocated 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
4. cos−1 (ex ) = (1)
dx
ex
(a) √
1−e 2x
x
−e
(b) √
1−e 2x
x
−e
(c) √
e2x − 1
ex
(d) √
e2x − 1
(e) None of the above.




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r
x2 + 1
5. ln = (1)
2x3
p
(a) (x2 + 1) − 2x
3

1
(b) 2
ln(x2 + 1) − ln 2 − 3 ln x
(c) ln x + 12 ln 1 − ln 3x
r
2x3
(d)
x2 + 1
(e) None of the above
2x2 + 1
6. Find the vertical asymptotes of the function y = 2 . (1)
3x − 2x
(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


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