Math 0312 Final Review
Martin-Gay, 5e
1. Factor completely: 3x3  3x 2  36 x
a. Prime
b.  3x 2  9 x   x  4 
c. 3x  x  3 x  4 
d. 3x  x  3 x  4 
2. Factor completely: 15 y 2  26 y  8
a. Prime
b. 15 y  4 y  2
c.  3 y  45 y  2  d.  3 y  45 y  2 
3. Factor completely: 16a2  24a  9
a. Prime
b.  4a  3
2
c.  4a  3 4a  3
d.  4a  3
c. 2  x  2 
d. 2  x  2   x 2  2 x  4 
2
4. Factor: 2 x 3  16
a.
 x  2  x 2  2 x  4  b.
2x
2
 4   x  2
3
5. Solve: 25x2  20 x  4  0
a.
2
5
b.
5
2
c.
2 2
,
5 5
d. 
2
5
6. Solve: x 3  49 x
a. 0, 49
b. 0, 7
c. 7, 0, 7
d. 7, 7
b. 3, 2
c. 3, 6
d. 2,  3
7. Solve:  x  1 x  2  4
a. 2, 3
8. Solve: 6 x2  x  2
3 1
2 2
a.  ,
b.
1
,2
3
c.
2 1
,
3 2
d. 3,  2
9. Solve:  9 x  15x  2   0
a. 9,
5
2
1 2
9 5
b.  ,
c. 1, 2
d.
1
2
,
9
5
10. Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the
hypotenuse is 6 more than twice the shorter leg.
a. 9 m
b. 18 m
c. 10 m
d. 17 m
11. The function h(t )  2t 2  32t gives the height of a baseball hit straight up with an initial
velocity of 32 feet per second. What will the height of the baseball be after 2.5 seconds?
a. 75.5 feet
b. 67.5 feet
c. 75 feet
d. 675 feet


12. Find f    for f ( x)  5x2  4 x  1
 2
1
a.
1
4
b.
13. Find the domain: f ( x ) 
a. x 
9
4
7
4
c.
7
2
d.
x
.
9x  4
b. x 
4
9
c. x  0
z 2  8z
z 5
b.
z
2
z  12 z  32
c.
a.
7  x  2
2
b.
x
 x  2
2
 x  2
c.
b. x  4
a2
2  a  3
b.
a2
2  a  3
x
x2

x  4 7 x  14
2
1
x5
17. Perform the indicated operation and simplify if possible:
a.
c.
z
z5
2
a
 a  3
7x
d.
7x
c.
z 2  8z

z 2  12 z  32 z 2  8 z  15
d.
16. Perform the indicated operation and simplify if possible:
a. 7 x  4
z 2  7 z  12
1
z5
15. Perform the indicated operation and simplify if possible:
x
4
9
d. x  
14.Perform the indicated operation and simplify if possible:
a.
17
4
 x  2
2
4x  2
3x  2
 2
x  5x  4 x  5x  4
2
d.
1
x 1
3a
a 1

2a  6 a  3
d.
1
3
18. Perform the indicated operation and simplify if possible:
a.
77
2  m  10  m  10 
19. Solve: 2 
b.
7
2  m  10 
c.
70
7

m  100 2m  20
2
7
2  m  10 
d.
7  m  30 
2  m  10  m  10 
3
a

a 3 a 3
b. 3
a. 3
c. 9
d. 
20. A boat travels 6 kilometers upstream in the same amount of time it moves 18 kilometers
downstream. If the rate of the current is 6 kilometers per hour, find the rate of the boat in
still water.
a. 12 km/hr
b. 9 km/hr
c. 3 km/hr
d. 6 km/hr
21. Kathy can paint a house in 15 hours. With Jane’s help it takes only 6 hours. How long
would it take Jane by herself?
a. 4.5 hours
b. 9 hours
c. 15 hours
b. x  3 y
c.
d. 10 hours
x2  9 y 2
xy
22. Simplify:
1 3

y x
a.
1
x  3y
1
x  3y
d. x  3 y
23. Write the equation of the line through  5,  6 and 10,  21 .
1
3
a. f ( x)   x  3
1
3
b. f ( x)  x  3
c. f ( x)  3x  9
d. f ( x)  3x  9
c.  7,  4 
d.  7,  4
24. Solve: 32  4c  4  20
a.  4,7
b.  4,7 
2
25. Graph f ( x)   x  3
3
a.
b.
c.
d.
26. Solve: b  9  3  6
a. 
b. 0, 18
c. 0, 18
d. 0
b. 13,3
c. 8
d. 
b.  7, 11
c. 7, 14
d. 
b. 
c.  5,  1
d.  ,  5   1,  
27. Solve: x  5  12  20
a. 3,13
28. Solve: h  2  9
a.  7, 11
29. Solve: x  3  2
a.  ,  
30. Graph 3x  y  2
a.
b.
c.
d.
31. Given f ( x)  4 x  6 , find f (10) .
a. 8
b. 4
c. 2
d. 16
32. Simplify:
a.
3
125
8
5
2
33. Simplify:  27 
a. 
1
5 10
4
b. 5 3
c.
b. 3
c. 3
d. 2 5
3
1
3
d.
1
3
34. Find the midpoint of the line segment whose endpoints are  3, 7 and  9, 3 .
a.  6, 5
b. 12, 10
a. 4 xy 2 5
a. 4 x9 y 3 2
d.  5, 6
c. 4 xy 5
d. 4 x 2 5 y
c. 2 x3 y 3 4
d. 2 x9 y 3 4
80x 2 y
35. Simplify completely:
36. Simplify completely:
c.  6, 4 
b. 4 x 5 y
3
32x 27 y 3
b. 4 x13 y 3 2 xy
37. Use the distance formula to find the distance between the pair of points: 5,  5 and  7,  1 .
a. 2
b. 12 3
38. Rationalize the denominator:
a. 
3 2  12
14
a. 5
a. 6
d. 2 5
3
2 4
3 2  12
14
c.
3 2  12
14
d.
3 2  12
14
2x  1  x  8
39. Solve:
40. Solve:
b. 
c. 12
3
b. 13, 5
c. 6
d. 13
b. 0
c. 9
d. 3
2x  9  2  5
41. Simplify:
125
b. 25 5
a. 5 5
c. 5i 5
42. Perform the indicated operation and write in standard form:
a.
48 24
 i
5
5
d. 5i 5
3  3i
3i
b.
3 3
 i
2 16
c.
3
3
 i
32 16
d.
3 6
 i
5 5
b.
5  15
4
c.
10  15
2
d.
5  35
2
43. Solve: 2 x 2  10 x  5
a.
5  15
2
44. Solve: x 2  6 x  25  0
a. 3  4i
45. Solve:
 x  11
2
b. 3  8i
c. 3  4i
d. 3  8i
b. 16,  6
c. 11  5i
d. 11  5i
 25
a. 6, 16
46. What must be added to both sides of the equation x2  6 x  0 in order to solve by
completing the square?
a. 9
b. 3
c. 6
d. 5
b. 2401
c. 7
d. 7i,7i
c.  9,  
d.
c.  ,  4
d.  ,  4   3,  
47. Solve: x2  49  0
a. 7, 7
48. Solve:
x9
0
x3
a.  , 3
b.
 3, 9 
 , 3   9,  
49. Solve: x 2  7 x  12
a.  3,  
b.  4,  3
50. The height h in feet of a projectile after t seconds is given by the equation
h(t )  16t 2  96t . Find the maximum height of the ball.
a. 3 feet
b. 144 feet
c. 16 feet
d. 6 feet
Revised – November 2015
KEY
1. c
2. d
3. b
4. d
5. a
6. c
7. a
8. c
9. b
10. c
11. b
12. d
13. d
14. d
15. d
16. d
17. b
18. b
19. d
20. a
21. d
22. b
23. c
24. a
25. c
26. b
27. d
28. a
29. d
30. a
31. c
32. a
33. a
34. a
35. b
36. d
37. d
38. b
39. d
40. c
41. d
42. d
43. a
44. c
45. d
46. a
47. d
48. b
49. d
50. b