Philadelphia University
Faculty Of Science Dep. of Basic Science and Math
Business Mathematics (250105)
Final exam
Student Name : ------------------Student Number : ----------------‫المجموع‬
4
3
2
1
‫رقم السؤال‬
‫العالمة‬
Q1 : Choose the correct answer:
1. If A=
a) 8/7
2
7
x
8 and │A│=8, find x
b) 7/2
c) 14
d) -6/5
2. Find the set of solutions of log(x2-2x+1)=0
3
a) {-3,3}
b) {0,2}
c) {1}
d) {-1,1}
3. Solve the equation 2x=8x-1
a) x= 3
b) x= -4
c) x= 7/3
2 1
3 3
4. If A= 3 2
& B= 2 2 , find AB
d) x= 3/2
a) 8
8
d) 15 8
10 6
13
13
5. If A=
a) 3/8 -1/4
-1/4 1/2
b) 8 8
13 13
2 3
4 2
c) 6 3
6 4
find A-1
b) 1/4 -3/8
-1/2 1/4
c) -1//4
1/2
3/8
-1/4
6. Which of the following is increasing function
a) 2x+y= -7
b) 2x+3y= 3
c) -2x-y= 10
d) -1/4 1/2
3/8 -1/4
d) 5x-4y= 8
7. Let f(x)=3x2-3x+1. Find the equation of the tangent line of the curve f(x) at x=2
a) y=9x-11
b) y=3(3x+1)
c) y=9x+3
d) y=3x+4
8. Find the critical point of f(x)=3x2+6x+1 which is minimum
a) (1,2)
b) (-1,-2)
c) (0,1)
d) (1,10)
Q2 : Complete each of the following:
Log x5
1) If f(x)=(10)
, then f ′(x)= 5x4
8
3
8
2) If ∫ f(x)dx=6 and ∫ f(x)dx=- 8 then ∫ f(x)dx= 6- (-8) =14
2
2
3
3) ∫ e8lnx dx= x9/9+ C
4) If ex=7 and ey=3, then ex+y= 21
5) If f(x)=3x-5,then f - 1(1)= 2
6) If MR=18-4Q, then TR= 18Q-2Q2+C
3
7) ∫(4/x)dx= ln 81
1
8) If f(x)= (3x2-8)3, then f ′(x)= 18x(3x2-8)2
9) ∫ 2e-3x dx= (2e-3x)/(-3)+C
10) If f(x,y)= 4xy3-x3y+7, then fx at(1,2)= 26
2 3
11) If A = 4 2
and B=
3 7
5 6
12) If x = ln3 – ln5 , then ex= 3/5
T
, then A+B =
5 8
11 8
Q3 : The demand and the supply function of a good are given by P=-Q2-4Q+68 ,
P=Q2+2Q+12 respectively Find :
1) The equilibrium point
2) The Producer’s surplus (PS)
assuming pure competition.
Answer:
1) Q = (4,36)
4
2) PS= 144 - ∫ (Q2+2Q+12) dQ
0
= 144-85.33
= 58.77
Q4 : Put the following system in a matrix form and solve it by Cramer’s Rule
3x + y - z = 0
2x – y + z = 1
-x + 3z = 2
Answer:
3 1 -1
2 -1 1
-1 0 3
x = 1/5
y = 2/15
z = 11/15
x
y
z
=
0
1
2