AIN SHAMS UNIVERSITY
FACULTY OF ENGINEERING
All Programs
I – Credit Hours Engineering Programs (ICHEP)
Midterm Exam
Fall Semester 2018
Course Code: PHM 012
Mathematics (1)
Time allowed: 75 Minutes.
The Exam Consists of FIVE questions in FIVE pages.
Maximum Marks: 25 Marks
General Instructions:
 Please read the examination paper carefully.
 Be sure to write each question number and part number ahead of your answer.
 Programmable & Graphical Calculators are NOT Allowed.
Student’s Name:
ID #:
Instructor’s Name:
Sec:
1/5
Group:
Question (1): (5 Marks)
(A)
Given y  sin 3 t
&
x  cos 3 t .
Find the equations of the tangent and normal lines to the given curve at t   4 .
[3 Marks]
(B)
Find
1
d y
if x y  3sin x  1 . (Simplify as much as you can).
dx
[2 Marks]
AIN SHAMS UNIVERSITY, FACULTY OF ENGINEERING
All Programs. I – credit Hours Engineering Programs.
Fall Semester 2018
Course Code: PHM 012
Mathematics (1)
Time allowed: 75 Minutes.
The Exam Consists of FIVE questions in FIVE pages.
Question (2): (5 Marks)
x
(A)
If f ( x ) is a continuous function such that
 f ( t ) dt
x
 x sin x  
0
f (t )
2
0 1t
dt for all x . Find an
explicit form for f ( x ) .
[3 Marks]
(B)
Find
d y
if y  log e x ( x 2  1 ) . (Simplify as much as you can).
dx
[2 Marks]
Page 2 of 5
AIN SHAMS UNIVERSITY, FACULTY OF ENGINEERING
All Programs. I – credit Hours Engineering Programs.
Fall Semester 2018
Course Code: PHM 012
Mathematics (1)
Time allowed: 75 Minutes.
The Exam Consists of FIVE questions in FIVE pages.
Question (3): (5 Marks)
(A)
Find the domain of the function f ( x ) 
3  x and find its inverse function f 1( x ) . Hence,
sketch both f ( x ) and f 1( x ) on the same graph.
[3 Marks]
(B)
Given g ( x )  5  x  x 2
,
 

x  0 . Hence, find g 1 ( 5 ) .
[2 Marks]
Page 3 of 5
AIN SHAMS UNIVERSITY, FACULTY OF ENGINEERING
All Programs. I – credit Hours Engineering Programs.
Fall Semester 2018
Course Code: PHM 012
Mathematics (1)
Time allowed: 75 Minutes.
The Exam Consists of FIVE questions in FIVE pages.
Question (4): (4 Marks)
(A)
Given ln x 2  y 2  tan1  y x  . Evaluate
d y
at the point
dx
1 , 0 .
[2 Marks]
(B)
Evaluate


dx
x tan x  cot
x

.
[2 Marks]
Page 4 of 5
AIN SHAMS UNIVERSITY, FACULTY OF ENGINEERING
All Programs. I – credit Hours Engineering Programs.
Fall Semester 2018
Course Code: PHM 012
Mathematics (1)
Time allowed: 75 Minutes.
The Exam Consists of FIVE questions in FIVE pages.
Question (5): (6 Marks)
Evaluate the following integrals:
dx
1) 
x 5 x
[2 Marks]
2)

( x  1 ) e x dx
cos 2 ( x e x )
[2 Marks]
3)

ln
3
x
x2
dx
[2 Marks]
Best Wishes.
Examination Committee
Exam. Date : November 12, 2018.
Prof. Niveen Badra, Prof. Aziz Mina, Dr. Hussein Abdelsalam, Dr. Nadia Anwer & Dr. Makram Roshdy.
Page 5 of 5