Math 125 Practice Final Exam pg.1
Math 125
Instructor: Butler
Practice Final Exam
Chapters 1 - 11
Expressions. Perform the indicated operation and simplify.
 45 x 3 yz
1.
5x 2 z 3
9 xy x 2  4 x  12
2.

3x  6
x 2  6x
3.
10
2

x  5x x
7 xy
14 y
 2
x  4x  4 x  4
6.
3 2 7
 
5n 3 3n
4.
 30 x 2 y 2 z 2
 35 xz3
7.
8a  4b 5a  5b
a 2  ab

 2
a  b 20a  10b 2a  2ab
5.
2
8.
2
5
3
1
 2
7 n 4n 14n
Simplify the complex fractions.
3 5

9. 2 x x
4 3

y 4y
3 5

2x y
10.
4 3

x 4y
3 1

11. 2 x 6
2 3

3x 4
Rationalize the denominators.
12.
3
5 2
13.
5
2 7
14.
3 2
4 3 8
Solving Equations. Solve for x.
x
3
2
 
x2 2 x2
x2  x
16.
2
18. x  6 x  10  0
19.
21. 3x 2  2 x  3  0
22. 5 x 2  2 x  1
24. log 4 x  5  3
25. e x  10
15.
3x  1  2
17. x 2  8 x  4  0
20.
23.
3
3x  2  2
2 x  1 3x  1 1


3
5
10
Math 125 Practice Final Exam pg.2
26. The width of a rectangle is 2 cm more than one-third of the length. The perimeter of the
rectangle is 44 cm. Find the length and width of the rectangle.
27. On a baseball diamond, the bases are 90 feet apart. Find to the nearest tenth of a foot the distance
from home plate diagonally across the diamond to second base.
Functions.
28. Let f ( x)  2 x 2  4 . Find f (3)
29. Let f ( x)  3 x  5 .
b) Find f (10)
a). Find f (3)
30. Find the domain for the following.
a) f ( x ) 
x3
2x  6
b) f ( x)  log 2 x
c) f ( x)  x 2  3x  2
d) f ( x) 
x4
x  12
e) f ( x) 
f) f ( x)  log 4 x
x3
31. Find the composition function  f  g x and simplify your answer.
f ( x)  x 2  x and g ( x)  x  2
32. If f x  2x  5 and g x   2 x 2  x  3 Then find
33. Let f ( x)  4 x  1 . Find the inverse function f
1
34. Let f ( x)  3 x  5 . Find the inverse function f
1
 f  g x
and
g  f x
( x)
( x)
35. If y is directly proportional to x, and y = 42 when x = 28 , find the value of y when x = 38.
Math 125 Practice Final Exam pg.3
Graphs. Label all points.
36. Graph f ( x)  2 x and g ( x)  log 2 x on the same set of axes.
37. Graph 4 x 2  y 2  16
38. Graph y  ( x  1)2  1
39. Graph
y 2 x2

1
9 16
40. Find the center and radius of the circle x 2  y 2  4 x  6 y  4  0 .
(First use completing the square to write it in standard form.)
41. Given the two points: 6,1 and  3,4
a) Find the distance between the two points (simplify your radical, do not approximate)
b) Find the slope between the two points.
c) Write the equation of the line passing through the two points in slope-intercept form.
42. Given the two points: 5,2 and  4,4
a) Find the distance between the two points. (simplify your radical, do not approximate)
b) Write the equation of the line passing through the two points in standard form.
43. Find the vertex of this parabola
y  x2  2x  6
44. Solve the system of equations using any method.
a) x  5 y  7
b)  5 x  4 y  35
4 x  9 y  28
45. Evaluate the determinant
x  3 y  18
3
5
2
1 4
2 0
6
0
Factor completely
46. 20 x 2  5
47. x 2  4 x  32
49. 12 x 2  3
3
50. x  64
48. x 2  11x  24
Math 125 Practice Final Exam pg.4
51. Solve for b2
53. Solve
A
1
hb1  b2 
2
3x 3  21x 2  54 x  0
52. Solve the inequality
54. Solve
3x  4  5x  1
1
x2
7
 2

3x  1 9 x  1 6 x  2
 2 x 1 


 3y 
54. Simplify and express the answer using positive exponents
2
55. Find the equation of the line that is parallel to the line 5 x  2 y  7 and contains the point  2,4 .
56. Use the properties of Logarithms to expand as much as possible.
Evaluate log expressions where possible.
57. Evaluate
log log 7 7
 x

log 

100


58. Solve
log 9x  2  log x  4  1
59. Evaluate log 3 32 by using the change of base property. Approximate to 3 decimal places.
60. How long will it take $5000 to be worth $12,500 if it is invested at 7% compounded annually?
Math 125 Practice Final Exam pg.5
ANSWERS:
1.
 9 xy
z2
8.
22n  21
28n 2
14.
3 6 3
10
20. 2
2. 3 y
9.
3.
2y
x
2
x5
10.
15. 2
4.
6 y  20 x
16 y  3x
1  10 

 3 
26. length = 15 cm, width = 7 cm
30.d)
x x  12
30.a)
30.e)
x x  3
 f  g x   4 x 2  2 x  11
32.
34. f
36. 5
1
x   x  5
3

12.

 1

 38 
23. 
7. 1
15  3 2
23
13. 
18.  3  i
24. 59
19. 1
29.a) f 3  14
30.f) All positive Real Numbers
33. f
1
30.c) All Real Numbers
31. x 2  3 x  2
x   x  1
4
37.
y
5
y
x
x
-5
-5
-5
5 2  35
47
25. 2.3
30.b) All positive Real Numbers
g  f x   8x 2  38x  48
35. y  57
10n  26
15n
28. f  3  22
27. 127.3 feet
x x  3
6.
18  2 x
8  9x
17.  4  2 5
1  2i 

 5 
22. 
x2  2x
2x  4
5.
11.
16. empty set
21. 
29.b) f  10  25
6 xy 2
7z
5
-5
5
Math 125 Practice Final Exam pg.6
y
38. 5
39.
y
5
x
-5
-5
43. (1,7)
44.a) (7,0)
x  8x  3
17

52.  ,  
2

56.
-5
5
41. d  3 10
40. center (-2,3) radius = 3
48.
x
1
log  x   2
2
44.b) (-3,5)
57. 0
50.
 1

 17 
54. 
58. 38
59. 3.155
1
3
5
y
1
x3
3
42. d  3 13
46. 52 x  12 x  1
45. 136
49. 32 x  12 x  1
53.  9, 0, 2
m
-5
x  4 x 2  4 x  16
55.
9x2 y2
4
47.
51.
x  4x  8
2 A  hb1
2A
 b1
or
h
h
55. 5 x  2 y  18
60. 13.5 years
2x  3y  4