Dr. Doaa Ezzat
Dr. Esraa Abdelraouf
Program: Software Engineering, Bioinformatics, Cyber
Security, Multimedia, Artificial Intelligence, Robotics
Academic year: 2024 - 2025
Examiners:
FCIS – Ain Shams University
Subject: BSC122 – Calculus 1
Exam: (Mid-Term) 13/11/2024
Year: (1st term) 1st undergraduate
Duration: 45 minutes
Exam Pages: 2 pages
Name in Arabic: -------------------------------------------------------------------------------------------- ID: ---------------------------------------------------------
NO SCIENTIFIC CALCULATORS ALLOWED
(Total marks: 15)
Choose the Correct Answer: (Use the solution Table)
1. If 𝒙𝟐 − 𝟕𝒙 + 𝟏𝟐 ≤ 𝟎 , then ……………
a) x ∈ (-∞, 3] ⋃ [4, ∞)
b) x ∈ [3, 4]
c) x ∈ (3, 4)
d) x ∈ (-∞, 3] ⋃ [4, ∞)
2.
If f o g(x) =
a) f(x) =
3.
4.
𝟏
√𝒙𝟓 +𝟔
1
and g(x) = 𝒙𝟓 , then ………..
b) f(x) =
x
1
√𝑥
The domain of f(x) = √𝟐 − 𝒙 + √𝒙 + 𝟓
a) (-∞, -5]
b) [-5, 2]
The graph of y =
𝟏
𝟐
𝒙−𝟐𝟓
𝒙→𝟐𝟓 √𝒙− 𝟓
1
d) f(x) =
√x+6
c) (-∞, 2]
1
√𝑥 5 +6
d) [-2, 5]
f(x)+6 is the graph of f(x) but ……………..
a) narrower and shift horizontally by 6
c) wider and shift vertically by 6
5. 𝐥𝐢𝐦
c) f(x) =
b) wider and shift horizontally by 6
d) narrower and shift vertically by 6
=⋯
a) 0
c) - ∞
b) 10
6. The domain of f(x)= sin x is………
a) R
c) [-1,1]
d) ∞
b) (-1,1)
d) [0, ∞ )
7. sec(𝑡𝑎𝑛−1 𝑥) = …………..
a)
1
b)
√𝑥 2 +1
𝑥
√𝑥 2 +1
c) √𝑥 2 + 1
d)
√𝑥 2 +1
𝟐
𝑥
8. Using the intermediate value theorem, the function 𝑓(𝑥) = 4𝒙 + 𝟐𝒙 − 6 has at least
one zero between: ……
a) -1 and 0
b) 0 and 2
c) 2 and 3
d) 3 and 4
9. The function f(x) =
a) -2
10. f (x) =
𝟔𝒙𝟑 +𝟑𝒙+𝟏
√𝟗𝒙𝟔 +𝟐𝒙𝟑
b) 2
𝒙
√𝒙 − 𝟒
has a horizontal asymptote at y = …..
c) 6
d) a and b
is continuous on the interval
a) ( 4, ∞ )
c) [ 4, ∞ )
𝑠𝑖𝑛 𝑥+2𝑥
11. 𝑙𝑖𝑚 𝑥 2 = ……
b) ( - ∞, 4)
d) ( - ∞, 4]
𝑥→∞
a) 0
b) ∞
c) 1
d) 2
Given f(x) = √𝒙 and g(x) = 𝟗 − 𝒙𝟐 answer the questions 12-15
12. f o g (x) =……..
a) √𝟗 − 𝒙𝟐
c) 𝟗 − 𝒙
13. Domain of f o g =……….
a) ( 3, ∞ )
c) [ -3, 3 ]
14. g o f (x) =……….
a) √9 − 𝑥 2
c) 9 − 𝑥
15. Domain of g o f = …………..
a) (0, ∞ )
b) ( - ∞, 0]
b) 𝟗 − 𝒙𝟐
d) √𝒙𝟐 − 𝟗
b) ( - ∞, 3)
d) R
b) 9 − 𝑥 2
d) 𝑥 − 9
c) [ 0, ∞ )
d) 𝑅
Answer:
#
Choice
1
B
2
C
3
B
4
C
5
B
6
A
7
C
8
B
9
D
10
A
11
A
12
A
13
C
14
C
15
C
Draft if needed
With Our Best Regards,
Dr. Doaa Ezzat
Dr. Esraa Abdelraouf