Midterm 1 Review for Math 4-40
1. Simplify:
a. i 47
a.
a

1/ 2 1/ 2 2
b
 2 x 2 y 

b. 
3 
 6y 
c.
6. Solve:
a. 3x  5  2x  1
2
3

b.
x x 1
x3 x7

c.
x 8 x 4
2
3x y   4 x
2
3
2
y 5 
1
2. Write the following expression in the
form a  bi where a and b are real
numbers
2  3i
a.
i
4  2i
b.
2  3i
c.  16   25
3 i 2  3 i 2
d.



3. Simplify the following expressions
a. 2 6  3  4 6  3
2
b.
3 5

c.


1 2
2 3
4. Factor completely:
a. 6 xy  3 y  10 x  5
b. 6 x 2  7 x  5
c. v 2  9t 2
d. a 3  8
e. 8  2 y 3
f.  6 x 4  x 3  15 x 2
5. Perform the indicated operations then
simplify
2x 9 y
a.

3 y 2 14 x 2
6x 2  x  1 9x 2  1

6x  3
15
3
1

c.
x x 1
5
2x

d. 2
x 4 x2
7. Sketch the graph of each equation.
For the circles, state the center and the
radius. For the line state the intercepts.
a. y  2 x  1
b. y  2 x  5
c x  2  y 2  1
2
d x2  4x  2 y  y 2
8. Find the equation of the line that
passes through (3,-1) and is
perpendicular to the line: 3x + y = 6.
9. Find the equation of the line that
passes through (0.7, -1) and (-3, -1)
10. Find the equation of the line that
passes through (1, 4) and is parallel to
the line: y  5 x  4
11. Find the equation of the line that
passes through (-2, 30) and (-2, 420)
12. Solve and simplify your answer:
a. x 2  5  0
2
b. x  2   17  0
c. 4 x 2  16 x  17  0
d. 3x  4  2
e. 5x  1  1
13. Solve the following inequalities.
a. x  4  4
b. 7  5x  5
b.
14. State the domain and range of each
relation. Determine whether each set is
a function.
a. 0, 0, 1,1,  3,  3 
b. 0, 3,  1, 1,  1,  3, 2, 5 
15. Graph and state the domain and range
of each relation. Determine whether each
relation is a function.
a. x 2  y 2  4
b. y  x  3
c. x 
y 2
16. State the domain of each function:
a. f ( x )  5 x  7 x 2
x3
a. f ( x ) 
x2
6
b. f ( x )  x  4
17. Sketch the graph then state its domain
and range.
x2
for x  0
a. f ( x )  
for 0  x  4
x
 1
b. f ( x )  
 x
21. Solve the following inequalities:
1
a.  x 2  2  0
2
2
b. x  5 x  14  0
22. Sketch the graph of the following
functions.
2
a. y  x  2   6
b. y  x  2  4
c. y  x  3  5
23. Postage costs 39 cents. If the mark
up percentage at UCR postal service is
20%, how much more do we have to
pay?
24. A Fuzzy Navel is a drink with 1 shot
of vodka and 2 shots of Peach Schnapps.
for  1  x  1
Vodka is 40% alcohol, Schnapps is 25%
for  2  x  2
alcohol. What is the percentage of
18. Let f ( x )  x 2  1 , and g ( x )  2 x  3 .
Find and simplify the following expressions:
a. f (3)
b. g  f 2
c. f  g
f ( x  h)  f ( x)
d.
h
1
e. g ( x )
19. Determine whether the function is even,
odd, or neither.
a. f ( x )   x  1
b. f ( x )  16  x 2
c. f ( x )   x 3  5x
20. Determine if the following functions are
inverse of each other.
1
a. f ( x )  2 x  4, g ( x )  x  2
2
3
3
b. f ( x )  x  2, g ( x )  x  2 
alcohol in one Fuzzy Navel drink?
25. If the initial cost of an item is C and
after n years its value is S, then the
annual depreciation rate r is given by :
S
r  1  
C 
1n
So if a new Nissan 350Z coupe sells for
$27,100 while a 4-year old model sells
for $16,000, then what is the annual
depreciation rate of this car?
Midterm exam is on Thursday 02/01/07.
Keep in mind that a make-up exam will
not be given, unless there is a verifiable
documented emergency (as defined by
UCR).