Math 0305 Review for Final Exam
Evaluate using order of operations.
1.
8 – │4 – 6 ∙ 4│ + (-8)2 ÷ 82
2.
-2 + 32 – (-8)
2–4+7
Evaluate the expression using the given values.
3.
__x2___ ; x = -1, y = -3, z = -5
2z + y
Solve.
4.
7y – 2(y – 7) = 11y – (7y +10)
Solve the equation for the indicated variable.
5.
x=w+y+z ;y
2
Solve the problem.
6.
The perimeter of a rectangular garden is to be 54 ft.
Find the length if the width is 10ft. (Use P = 2L + 2W)
Solve.
7.
4(2z – 5) = 7(z + 2)
Add.
8.
 5 1

3 12
6 12

7
x
9.
Solve for the missing number.
10.
A car travels 808 km in 12 days. At this rate, how far would it travel in 24 days?
11.
The sum of three consecutive even integers is 168. Find the integers.
12.
Paul left Springfield traveling north at an average speed of 60 miles per hour. Two hours later,
Tim left Springfield traveling south at an average speed of 63 miles per hour. How long will it take
after Paul left for them to be 489 mile apart?
13.
Bill invests in a plan that has an APR of 3%. He invests five times as much in a plan that has an APR
of 6%. If the total interest from the investments is $825 after one year, how much was invested in the
plan earning 3% interest?
11
) is a solution to the equation 8 x  5 y  19. Why or why not?
Determine whether the order pair (1,
5
Use the graph of the function f below to find f(1).
14.
15.
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16.
Find the y-intercept and the x-intercept for the equation y  4 x  5.
17.
Is the graph below a function? Explain why or why not.
18.
Subtract. (Simplify your answer)
(2x 3  5x 2  3)  (10x 2  3x  10)
19.
Multiply. (Simplify your answer)
(7x 4 y 2 )(8x3 y 4 )
20.
Multiply. (Simplify your answer)
( x  5)(2x 2  6x  3)
21.
Multiply. (Simplify your answer)
(2 x  5)( 3 x  4)
22.
Multiply. (Simplify your answer)
(5x  12)2
23.
Multiply. (Simplify your answer)
2x 3 y (3x 3  4xy 2  5y 3 )
24.
Divide. (Simplify your answer.)
18 x 7  12 x 3  24 x
3x
25.
Divide. (Simplify your answer.)
(5a3  18a2  8a  3)  (a  3)
26.
Simplify. (Write exponential notation with positive exponents.)
(4x 3 y 2 )4
Factor Completely.
27.
x 3  5 x 2  10 x  50
28.
x2 + 7x - 30
29.
x2 - 3xy - 10 y2
30.
4 x2 + 12x + 9
31.
20z2 - 7z - 6
32.
36x2 - 49
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33.
d3 + 64
34.
25x - 4 x
Solve.
35.
3
50n2 + 20n = 0
36.
x 2  2 x  48  0
37.
Find every value of the variable that makes the expression undefined.
38.
Simplify:
x5
2x  6
2 x 2  2 x  60
x 2  8 x  15
Perform the indicated operation.
39.
y 2  13 y  42 y 2  49

11y  22
5 y  10
41.
5
4

x6 x3
40.
5
3

a  2 a 1
43.
2y 1
3
4


2
y 4 y2 y2
Solve.
42.
x2 x3

x 1 x  6
3
3

a a3
5
1

a a3
44.
Simplify.
45.
A pool can be filled with one pipe in 8 hours, whereas a second pipe requires 20 hours to fill the
pool. How long will it take to fill the pool with both pipes turned on?
46.
A jet can fly 550 mph in calm air. Traveling with the wind, the plane can fly
2400 miles in the same amount of time it takes to fly 2000 miles against the wind.
Find the rate of the wind.
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687304668
MATH 0305 Review
**Answer Key**
1. -11
2. 3
1
3.
13
4. -24
5. y  2 x  w  z
6. 17 ft
7. 34
7
8.
4
9. -14
24. 6 x 6  4 x 2  8
25. 5a 2  3a  1
y8
26.
256 x12
27. ( x  5)( x 2  10)
28. ( x  10)( x  3)
29. ( x  5 y )( x  2 y )
30. (2 x  3)(2 x  3)
10. 1616 km
11. 54, 56, 58
33. (d  4)(d 2  4d  16)
34. x(5  2 x)(5  2 x)
2
35.
,0
5
36. -8, 6
37. 3
2( x  6)
38.
x3
5( y  6)
39.
11( y  7)
8a  1
40.
(a  2)(a  1)
x  39
41.
( x  6)( x  3)
3
42.
2
43. -5
3
44.
2a  5
5
45. 5 hr
7
46. 50 mph
31. (4 z  3)(5 z  2)
32. (6 x  7)(6 x  7)
12. 5 hr
13. $2500
14. yes, makes a True statement
15. 5
16. (0,5), (
5
, 0)
4
17. it is a function; each x-value has a unique y-value
18. 2 x3  15 x 2  3x  13
19. 56x 7 y 6
20. 2 x3  4 x 2  27 x  15
21. 6 x 2  23x  20
22. 25 x 2  120 x  144
23. 6 x6 y  8x 4 y3  10 x3 y 4
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Review for Final Exam