MATH 0990 Review for Final Exam
1. Solve: 7 (2 x 3) (7 x 5)
2. Solve:
2
7
x
2x
1
x
3( x
17
2
3. 72 is what percent of 240?
2
10)
(x
4)
4. Graph the line: 2 x
x-intercept _________
y-intercept _________
3y
6.
What are the x- and y- intercepts?
5. Graph the line: y
1
x
3 . What are the x- and y- intercepts? What is the slope?
2
x-intercept __________
6. Graph the line: a) y
y-intercept __________
3
slope __________
b) x = 4
7. Find the equation of the line that passes through point (4, 2) and has slope
1
4
.
8. Find the slope of the line that passes through the points (3, 5) and (-1, 1).
9. Given that f ( x )
10. Subtract 7 x 3 8 x 2
2x
4
5,
find a) f ( 1) and b) f (3) .
from 10 x 3
3x
9
.
11. Simplify: (3 x 6 )(2 x 2 y ) 3
12. Simplify: (2 x 6 y 6 )
2
13. Simplify:
3 y
2
1
y
2
2
3
3
14. Multiply: 2 y 5 (7 3 y
15. Multiply: (3 x 5 y )( 2 x
3
4y )
9 y)
16. Multiply: (3 x 5) 2
17. Divide: (4 x 4
3x
3
18. Divide: (8 x 3 10 x 2
2 x)
x
2
(3 x )
6)
(2 x
1)
19. Factor completely: x 4 81
20. Factor completely: 8 m 2 n 3
2
24 m n
21. Factor completely: 6 xy
21 x
22. Factor completely: 36 x 2
49
23. Factor completely: 36 x 2
49
24. Factor completely: 50 x 4
8y
8y
2
2
28
25. Factor completely: x 2
xy
30 y
2
26. Factor completely: 21m 2 13 m
2
27. Factor completely: 24 x 2
24
28. Solve: x 2
24
5x
20 x
29. Reduce to lowest terms:
2
30. Divide:
3p q
31. Multiply:
5r
32. Subtract:
5
9p q
5
p
p
4
2
2
2x
2
3x
4x
2
3
10 r
4p
5
p
4
7p
10
p
1
11 x
4
5x
13
2x
3
2x
3
25
5
2x
33. Add:
x
2
3
1
x
4
4a b
3
3a
4
2ab
34. Simplify:
b
2
4
2
2
1
x
4
x
x
35. Simplify: x
36. Solve:
1
4
z
z
2
3
4
2
z
37. Solve the system of equations:
38. Solve the system of equations:
4x
x
3y
y
5
3
2x
3y
13
5x
2y
6
39. Graph the solution to the system of inequalities:
x
2y
y
x
4
1
40. Simplify:
41. Simplify:
4
36 x y
10
128
25
42. Simplify: 3 27 x
43. Simplify: (4
4 48 x
5 )(3
2 3x
5)
44. Rationalize the denominator:
4
12
45. Solve:
2x
7
5
46. If 7 is subtracted from 5 times a number, the result is 27 less than 7 times the number. Find the number.
47. Doug’s copier can do a printing job in 7 hr. Scott’s copier can do the same job in 12 hr. How long would it
take to do the job using both copiers together?
48. A boat takes 3 hr to go 24 mi upstream (against the current). It can go 36 mi downstream (with the current)
in the same time. Find the speed of the current and the speed of the boat in still water.
49. Peanuts that sell for $1.20 per pound are to be mixed with cashews selling for $2.40 per pound to get 50
pounds of a mix that will sell for $1.92 per pound. How much of each type of nut should be used?
50. In his job at the post office, Joe works an 8 hour day. He sorts mail, sells stamps, and does supervisory
work. One day he sold stamps twice as long as he sorted mail, and he supervised 2 hr longer than he sorted
mail. How many hours did he spend at each task?