Download Math 004 Winter 2007 Final Review

Math4-40 Final Review
Name:_____________________
1. Simplify each expression. Assume that all
variables represent positive real numbers.
6  (3  x)
a.
2  (1)
27
b. i
c. 3  8
 31 2 3
d.
2 1
 2 x 2 y 

e. 
3 
 6y 
2
5. Solve and simplify your answer if possible.
a. 3x  5  2x  1
2
3

b.
x x 1
x3 x7

c.
x 8 x 4
d. x 2  5  0
2
e. x  2   17  0
f. 4 x 2  16 x  17  0
g. 3x  4  2
f. 3x 2 y 3    4 x 2 y 5 
1
28x 3
2
h.
6 2
1 2
j.
2 3
g.
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.


4. Factor each polynomial completely:
a. 6 xy  3 y  10 x  5
b. 6 x 2  7 x  5
c. x 2  9y 2
d. a 3  8
e. 8  2 y 3
f.  6 x 4  x 3  15 x 2

h. 5x  1  1
6. Solve each inequality. State the solution set
using interval notation and graph the solution set.
a. 4x  1  3x  2
x3
5
b.  2 
2
c.  3x  6 and 5  3x  8
d.  2 x  8 or 3x  3
e. x  4  4
3. Perform the indicated operations
a. 3x 2  x  2  ( x 2  2 x  5)

b.
c.
d.
e.
f.
2
2


3
6 3  4 6 3
5
2
3x  6x   3x
6x  x  2  2x  1
3
2
2
2x 9 y

3 y 2 14 x 2
6x 2  x  1 9x 2  1

6x  3
15
3
1

h.
x x 1
5
2x

j. 2
x 4 x2
f. 7  5x  5

7. Sketch the graph of each equation. For the
circles, state the center and the radius. For the
line state the slope and the intercepts.
a. y  2 x  1
b. y  2 x  5
c.  x  2   y 2  1
d. x 2  4 x  2 y   y 2
2
g.
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  5x  4
11. Find the equation of the line that passes
through (-2, 30) and (-2, 420)
12. State the domain and range of each relation.
Determine whether each relation is a
function.
a. 0, 0, 1,1,  3,  3 
b. 0, 3,  1, 1,  1,  3, 2, 5 
c. y  x  3
d. x 2  y 2  4
e. y  x  9
f. y  x  3x  2 x  1
3
2
13. Sketch the graph then state its domain and
range.
x2
for x  0
a. f ( x )  
for 0  x  4
x
for  1  x  1
 1
b. f ( x )  
for  2  x  2
 x
14. 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 )
15. Sketch the graph of each function. Identify
all asymptotes and intercepts.
5 x
a. f ( x ) 
x5
1
b. f ( x )  2
x
2x  1
c. f ( x ) 
x
x2
d. f ( x )  2
x 4
3
e. f ( x )  2
x 1
16. 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 
17. Solve the following inequalities:
1
a.  x 2  2  0
2
2
b. x  5 x  14  0
18. Sketch the graph of the following functions.
a. y  x  2  4
b.
y
x35
c. y  16  x 2
19. A Fuzzy Navel is a drink with 1 shot of
vodka and 2 shots of Peach Schnapps.
Vodka is 40% alcohol, Schnapps is 25% alcohol.
What is the percentage of alcohol in one Fuzzy
Navel drink
20. Write the following function in the form
y  a( x  h) 2  k and sketch its graph.
a. y  x 2  4 x
b. y  3x 2  12 x  1
c. y  2 x 2  4 x  8
21. Solve the following equations:
a. x  1  x  6
b. x 2  1  1
c. x  1  x  3
d.
x7 6
22. Solve the following inequality. State the
solution using interval notation.
a. 3x 2  4 x  4  0
b. ( x  3)( x  1)( x  4)  0
x3
0
c.
x5
1
2

d.
x 1 x 1
23. Sketch the graph of each function.
a. y  5 x
x
1
b. y   
4
c. y  log 2 ( x)
d. y  log 1 3 ( x )
31. Find the partial fraction decomposition for
each rational expression.
7x  5
2x  5
a. 2
b.
x x2
x  2x  4
24. Solve the following equations
a.  3 x  27
b. 10 x 1  0.01
1
c. 4 x 3  x
2
d. log 2 ( x)  log 2 (3x  1)  0
e. 2 ln( x  2)  3 ln( 4)
f. x log( 4)  6  x log( 25)
25. Determine the amplitude, period, and phase
shift for each function, and sketch one cycle of
the graph. Label 5 points.
a. y  3 sin 2 x
b. y  cos 2 x  1
c. y  3 sin( 2 x )  1

d. y  cos( x  )  2
4
26. Find the exact value:
a. sin( 30 )
b. cos 2 3
c. sin 7 6
d. cos(135 )
e. sin( 0 )
f. cos( 0 )
g. sin(  2 )

34. Find the sum of each series.
3
a.
2
10
i
b.
0
3
0
35. Find the first 5 terms of he infinite sequence
whose nth term is:
a. an  (2n)!
b. an  (n  1)!
36. Find values of sin  , cos  for the angle
 of the below right triangle:

3
, and x is in quadrant III, find
5
the exact value of sin x.
28. If cos x  
29. Solve the following system of equations.
3x  y  6
a.

6 x  5 y  23
y  x2

5 x  y  6
32. Sketch the graph of the solution set to each
system of inequalities
y  x  4
2 x  y  1
a. 
b. 
 y  x  2
 y  2x  3
33. Find a formula for the nth term of each
arithmetic sequence.
a. 1, 6, 11, 16, …
b. 2, 5, 8, 11, …
c. 0, 2, 4, 6, ….
d. 5, 1, -3, -7, ….
h. cos( 2 )
27. Simplify: 1  sin x1  cos x
b.
30. Nancy has a higher income than John. Their
total income is $82,000. If their salaries differ by
$16,000, then what is the income of each?
1

4
37. Review your class notes and quizzes.
Final exam is on Thursday, 03/22/2007
from 7:00-10:00pm. You must take the
final exam to pass the course. You will
be required to show your ID at the final
exam.