Philadelphia University
Dept. of Basic Sciences and Math.
Final Exam
General Mathematics (0210105)
Student Name:………………………………….
Date: 03/06/2010
Time: Two Hours
Student Number:……………..……...
Question 1: (15 Points)
Choose the correct answer:
1) The solution of
A)
33 x 1  9
5
3
B)
2) The solution of
A) x  3,3
3) Let
is:
1
3
C)
log 3 ( x 2  2 x  1)  0
0
1 0

A  2 11 0 
3  1  2
A) 11
then
D)
:
C) x  1
B) x  0,2
25
3
D) x  1,1
det( A) =
B) -11
C) 22
D) -22
4) If 5x  2 and 5y  3 then 5x y 
A) 5
log x
5) If y  2 2 then
2
A) 2 ln x e
C) 6
B) 8
2 ln x 1
dy
dx
=
B)
6) If the marginal cost is
then the total cost is:
A) TC  12  3Q  2 Q
x
2
C)
MC  3  4Q
2
C) TC  12  3Q  4 Q
D) 9
2
x
and the fixed cost is 12$
B) TC  3Q  4 Q
2
D) TC  4
1
D) 2x
2
1 2
0
A
B

and
3 4
0
 3 5
3
A) 
B) 

7 9 
7
1
1 then B+2A=
7) If
4
8
 2 4
C) 

6 8 
 2 5
D) 

6 9
8) Let A be a matrix of order 4x4 and det(A)=1 the det(2A)=
A) 2
B) 4
C) 8
D) 16
9) The critical point(s) for the function
A) 0,1
B) 4,1
C)
4  20
2
 2  2
1  4
A
,B  

 then AB=
1 3 
0 5 
2  18
2 8 
10 8 
A) 
B) 
C) 



1 11 
0 15
15 15
is(are):
D) 3,4
10) If
 2  14
D) 
15 
5
Question 2: (3 Points)
Find the first derivative
(1)
y  x 2 ln( 2 x  1)
(2)
x3  1
y
x2
dy
dx
for the following functions:
2
Question 3: (6 Points)
Evaluate the following integrals:
1)  (3x  5) 5 dx
2
2)  (4 x 5  3 x 2  5) dx
1
3)  (4e 2 x  32 )dx
x
4) 
x 1
dx
x
3
Question 4: (8 Points)
The demand equation of a good is 4P Q-16 0 and the total cost
function is TC  4  2Q 
3Q
10
2
3
Q

20 .
Find expressions for TR, , MR and MC in terms of Q.
4
Question 5: (9 Points)
Given that the demand equation of a good is P  50  2 Qd and the supply
function is P  2 QS  10 .
(a) Find the equilibrium point (Q0 , P0) .
(b) Find the producer's surplus (PS).
(c) Find the consumer’s surplus (CS).
5
Question 6: (10 Points)
Consider the following system:
x  y  z  0
3x  z  6
x  4 y  2 z  1
a) Write the above system in matrix form.
b) Use Cramer's Rule to solve the above system.
6