MATH 1280 Spring 2016
Exam 2
Mike McCraith
March 8, 2016
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Write your name below on the space provided.
This test has a total of
144
+ 2 pages.
3
Work the problem in the space provided. If you need more space, write on the back of the test.
To insure maximum credit, show your work. In general, full credit will not be given for unsupported
answers.
Look only at your test. Don’t give me the impression that you are cheating.
Be sure to write neatly in pencil. If I cannot read what was written, do not expect the problem to
be graded.
If you finish early, go over the test again.
Good luck!
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Total
Maximum
9
4
4
15
12
2
12
8
5
5
2
6
2
12
2
100
Score
Name _________________________________
1
1) (3 points each) Simplify completely.
a)
25 (You’re welcome)
b)
x2 + 4x + 4
c)
3
−125
2) (2 points each) For the function f ( x ) = 4 x − 7 , find the following or say why they don’t exist.
Write answers as an ordered pair:
 1
a) f (2)
b) f − 
 2 
3) (2 points each) For the function f ( x ) = x − 2 + 3 …
a) Explain how to find the domain algebraically and then state the domain:
b) Explain how to use transformations of the graph of y = x to sketch the graph of f:
2
4) (3 points each) Simplify. Write answers using positive exponents. For part a only, assume
variables can represent any real number:
a) ( 25x 2 y
d)
4
−
 125 x 3 y 9 

b) −
z 3 

1
8 2
)
x 2 y 3 z ⋅ 4 x 3 yz
2
3
c)
(
)(
)
d)
25 ⋅ 3 25
27 x3 y 5
e)
9x2 y3
5) (3 points each) Perform the indicated operation:
a) 9 3 + 11 3
b)
c) 2 + 3 1− 5
3
72 − 32
(
3x − y
2
)
6) (1 point each) What must be true in order to…
a) Add two radical expressions?
b) Multiply two radical expressions?
3
7) (3 points each) Rationalize the denominator. Simplify as needed:
3
4
a)
b)
2
25x 3
c)
8x2
5
d)
2x4
5
2+ 7
8) (4 points each) Solve the equation for the variable:
1
a)
b) ( x − 3)2 + 16 = 32
x + 12 − x = −6
9) (5 points) Standing 40 feet from a building, you can look up 60° and see the top of the building.
If you are 6 feet tall, how tall is the building? Draw a picture and find the exact value.
10) (5 points) Consider a cube where the diagonal of one of the sides is 5 inches. Find the surface
area of the cube.
11) (2 points) How is this pronounced?
3
x 4 + 5 = ____________________________________
4
12) (3 points each) For the given ordered pairs ( 4, −3) and (10, −11) , find…
a) The distance between them:
b) Their midpoint:
13) (2 points) Referring to #12 above, explain how to find the distance between the point ( 4, −3)
and the answer you found in part b without using the distance formula.
14) (3 points each) Perform the indicated operation. Write answer in the form a + bi :
a) ( 4 + 5i ) + (7 − 2i )
b) (8 −12i ) − (−4 − 4i )
2
c) (3 − 5i )
d)
2 + 3i
5 − 4i
15) (2 points) Explain how to find i1025 :
16) (1 point each) Extra Credit. Fill in the blank:
a) a − n = __________
b) a 0 = __________
c) a m + n = __________
n
e)
(a )
g)
an
= __________
bn
m
1
n
= __________
i) a = _____________
d) a m − n = __________
m
f)
( ab )
h)
( a)
j)
n
1
a
m
n
= __________
m
= __________
= _____________
5