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Econ1078 Math Tools for Economists I
Midterm1
February 21st, 2005
There are 6 problems. Answer the questions in the spaces provided.
You must show all the steps to get full credit. You have 50 minutes to finish the exam.
1.State whether the following statements are Multiple choice and Fill in the blanket
(24 points)
a. If a line, A, is perpendicular to 4x-2y=10, and the y-intercept of this line is 7. Write out
the equation of line A.
___________________________________________________________________.
_________ b. The result of simplifying (7m  5n)(7m  5n)  2(m  5n) 2 is
A. 38m 2  20mn  41n 2
B. 38m 2  50n 2
D. 51m2  20mn  25n 2
C. 8m 2  20mn  47n 2
__________ c. What is the domain of the function: f ( x)  x 2  3 ?
A. All the real number
B. x  -3
C. x  3
D. x  0
__________ d. Solve for the value of x: ( x  1)2  49
A. 8
B. 6
C. 6, -8
D. -6, 8
__________ e. What’s the vertex coordinate of the quadratic function: m( x)  2 x 2  12 x  7
A. (3, 25)
B. (25,3)
C. (0,7)
D.(7,0)
__________ f. What’s the x-intercept of the quadratic function: m( x)  2 x 2  12 x  10
A. 2, 3
B. 0, -10
C. –10, 0
D. 1, 5
_________ g. Which of the following expression gives the value 4.
A. 25
1
2
B.  8
2
3
C. 16
3
4
x7
?
x2  6x
B. x  7
D. x  0 and x  6
 1 
D.  
 64 

1
3
__________ h. What is the domain of the function: f ( x) 
A. All the real number
C. x  6
1
___________i. The supply and demand equations for a certain product are s  1, 000 p  2,500
and d 
1,500
where p is the price in dollars. Find the price where supply equal demand:
p
A. p=$1
B. p=$2
C. p=$3
D. p=$4
__________ j. The linear equation is 2x+3y = 12. What is the x-intercept and y-intercept
respectively?
A. 2, 3
B. 4, 6
C. 6, 4
D. 12, 12
__________ k. What is the slope of linear line 8x+3y=24?
A. 3
B. 8
C.
8
3
2. Perform the indicated operations and reduce the answer to lowest terms.
x3  8
x 2  49

2 x 2  10 x  28 x 2  14 x  49
points)
D. -
8
3
(10
2
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ID:___________________
3. Rationalizing radicals
(a) Rationalize the denominator:
(16 points)
a 2 b
a 2 b
(10 points)
(b) Simplify the expression and write answer using positive exponents only
1/ 3
 8 x 4 y 3 
A). 
2 3 
 27 x y 
(6 points)
4. Simplify the expression and write the answer using positive exponents only.
 3 x 0 y 3 
 5 4 5 
3 x y 
1
(10 points)
3
5. Combine into a simple fraction and simplify to the lowest term.
1
1
3
 2
 2
2
y  y  12 y  16 y  6 y  9
( Hint : 1. Factor all of polynomials
( 6 points)
2. Find the least common denominator
( 3 points)
3. Multiply and combine terms
( 6 points))
(15 points)
4
Name: ________________________________
ID:___________________
6. Solving equations and inequalities in one variable.
1
2
(a) Solve for x : x  1  x  3
2
3
(25 points)
(b) Solve for y in terms of x: ( y  3x)2  25x 2
(8 points)
(8 points)
(c). The supply for broccoli is described by the equation Q = P/6 where P is the price of
broccoli and Q is the amount that will be supplied at price P. The demand equation is
described by Q = 330-9P where P is the price of broccoli and Q is the amount that will
be demanded. What is the equilibrium PRICE of broccoli where demand equals supply?
(9 points)
5
Part 1,
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
y = 2x + 7
D
A
C
A
D
D
D
C
C
D
Part 2:
x2  2 x  4
2.
2( x  7)
3. a) Not required
1/ 3
 8 x 4 y 3 
b) 
2 3 
 27 x y 

a 2 b
( a  2 b )2
a  4 ab  4b


a  4b
a  2 b ( a  2 b )( a  2 b )
2 y2
3x 2
1
 3x 0 y 3 
81 y 8
4.  5 4 5   4
x
3 x y 
5.
1
1
3
 2
 2
y  y  12 y  16 y  6 y  9
1
1
3



( y  3)( y  4) ( y  4)( y  4) ( y  3)( y  3)
( y  4)( y  3)
( y  3)( y  3)
3( y  4)( y  4)



( y  3)( y  4)( y  4)( y  3) ( y  3)( y  4)( y  4)( y  3) ( y  3)( y  4)( y  4)( y  3)
( y  4)( y  3)  ( y  3)( y  3)  3( y  4)( y  4)

( y  3)( y  4)( y  4)( y  3)
( y  4)( y  3)  ( y  3)( y  3)  3( y  4)( y  4)

( y  3)( y  4)( y  4)( y  3)
2

3 y 2  y  45
( y  3)( y  4)( y  4)( y  3)
6
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ID:___________________
6.a)
1
2
x 1  x  3
2
3
1
2
x  x  3  1
2
3
1
 x  4
6
x  24
6.b)
( y  3x ) 2  25 x 2
y  3x  5 x or
y  2 x or
y  3x  5 x
y  8 x
6.c)
Qsupply = P/6
Qdemand = 330-9P
Let Qsupply= Qdemand
P/6= 330-9P
 p=36
7