midterm Preparatory engineering, Exams of Mathematics

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Typology: Exams

2022/2023

Uploaded on 11/20/2023

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ج
Q1. Complete the following questions using the shown figure for the function
( )
fx
. [10 Mark]
(a) The domain of
( )
fx
[……… , ………)
(b) The range of
( )
fx
(………. , )
(c) the domain of
()fx
………………………..
(d)
( )
2f−=
…………..
(e)
( )
fx
is discontinuity at
x=
.... , …. , …. , ….
(f)
( )
fx
is one to one in the interval
(……., ..……)
(g)
…………...
(h) If
( ) ( )
( )
22, then 2g x x f g=+
…………...
(k) Sketch the inverse of
( )
fx
in the interval
(-2,2)
\
Ministry of Higher Education
Higher Institute for Engineering and Technology at Manzala
Date: 11/11/2023
First Semester: 2023/2024
Level: 0
Midterm Exam
Time allowed: 60 min
Department: Basic Science
Code: BS 011
Total Marks: 40
Examiner: Dr. Hamouda Abueldahab
Course title: Mathematics 1
:بلاطلا مسا
لسلسملا مقر
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ج

Q1. Complete the following questions using the shown figure for the function

f x. [1 0 Mark]

(a) The domain of

f x

[……… , ………)

(b) The range of

f x

(c) the domain off ( x ) ………………………..

(d)

f − 2 = …………..

(e)

f x is discontinuity at x =

(f)

f x is one to one in the interval

(g)

1

f 0

(h) If ( ) ( ( ))

2

g x = x +2, then f g 2

(k) Sketch the inverse of

f x

in the interval

\

Ministry of Higher Education

Higher Institute for Engineering and Technology at Manzala

First Semester: 2023/2024 Date: 11 /1 1 /

Midterm Exam Level: 0

Department: Basic Science Time allowed: 6 0 min

Total Marks: 40 Code: BS 011

Course title: Mathematics 1 Examiner: Dr. Hamouda Abueldahab

رقم المسلسل اسم الطالب:

Page 2 / 2

Q 2. Answer by True or False [ 3 Mark]

N 0 True (T) or False (F)

1 cos (cos

− 1

2 The range of the function 𝑦 =

equal 𝑦 ∈

[

]

5 csc

− 1

4 = sin

− 1

9 sin (sin

− 1

10 𝑇ℎ𝑒 𝑝𝑒𝑟𝑖𝑜𝑑𝑒 𝑜𝑓 𝑦 = |𝑠𝑖𝑛𝑥| is 𝑝 = 2 𝜋

Q 3. Expand 4 + x , if it's known that x 4

[ 3 Mark]

Q 4. Complete [ 3 Mark]

sin 5 x sin 3 x =................................

Q 5. Solve this equation: [ 3 Mark]

1

cos(2sin ( ))

x

Q 6. If the roots of the equation

3 2

x − 3 x +  x + 1 = 0 are in arithmetic progress, find the

roots and the value of

. [ 5 Mark]

Q 7. Calculate

f g (1)

where

2

f ( x ) = x − 1 , g x = x + 1

[ 3 Mark]

Q 8. Prove that

1

2

tan

d

x

dx x

, then find the first derivative of [ 5 Mark]

1

y tan sin x

Q 9. Sketch the function

f x = 5 cos2 x + 1 , then complete the table. [ 5 Marks]

Domain

Range

Symmetry

Zeros

Period