15. Find the greatest common factor of the following terms:
45, 50, 22
1
66y^{2}, 90x^{9}y, 15x^{8}y^{5}
3y
16. Factor the following polynomials:
28x^{5}  74x^{4} + 36x^{3}
28x^{3}(x  2)(x 
9
14
)
x^{2} + 12x + 35
(x + 7)(x + 5)
x^{7}  2x^{6}  143x^{5}
x^{5}(x  13)(x + 11)
17. For question 16, exercises b) and c), solve for x:
x =
7
and
5
x =
0
,
13
and
11
18. You have 8 CDs. How many different ways can you listen to them?
40320
19. Use the following data to construct a box and whiskers plot:
23, 19, 7, 15, 40, 35, 32, 20, 24
20. A bag contains 6 blue balls, 3 red balls, and 3 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
25.00%
A blue ball or red ball?
75.00%
Two red balls?
6.25%
A blue ball and a white ball?
12.50%
21. Solve and graph the following systems of linear equations:
x + y = 6 x  y = 5
A(5.5,0.5)
6x  5y = 15 2x + 9y = 4
B(2.42,0.09)
22. Write the following fractions in simplest form:
22x^{6}y^{7}z^{4}
44x^{7}y^{9}z^{2}
z^{2}
2xy^{2}
(x + 4)^{6}
(x + 4)^{5}
x + 4
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
88 = x^{2}  26x
x_{1} = 22, x_{2} = 4
24. Convert the following repeating decimal into a fraction:
x =
0.433
390
900
25. Solve the following equation:
32
x
= 4
x = 2
26. Rationalize the denominator of each fraction below:
10
10 +
35
20  2
35
13
27. Use a trigonometric ratio to find x:
x = 21.65 cm
28. The sum of two consecutive even integers is 50. What are the integers? (Hint: use 2x as the first even integer)
a=24, b=26
29. After you leave your house, you walk 9 blocks west and 12 blocks south. How far are you from your house?
I am
15
blocks from my house.
30. The sides of a square are increased by 5 ft. The area of the newly created square is 361ft^{2}. What was the original length of one side of the square?
13. Multiply the following polynomials and simplify:
(1x^{4} + 7x  4)(9x^{5} + 10x^{2})
9x^{9} + 73x^{6}  36x^{5} + 70x^{3}  40x^{2}
(10x^{4} + 8x  5)(1x^{4} + 4x)
10x^{8} + 48x^{5}  5x^{4} + 32x^{2}  20x
14. Divide:
4x^{2}  34x + 43 / x  8
(4x  2) with a remainder of 27
15. Find the greatest common factor of the following terms:
9, 90
9
63y^{4}, 55x^{2}y^{10}, 36x^{2}y^{7}
y^{4}
16. Factor the following polynomials:
15x^{4}  14x^{3} + 3x^{2}
15x^{2}(x 
3
5
)(x 
1
3
)
x^{2} + x  20
(x + 5)(x  4)
x^{5} + 12x^{4} + 20x^{3}
x^{3}(x + 2)(x + 10)
17. For question 16, exercises b) and c), solve for x:
x =
5
and
4
x =
0
,
2
and
10
18. You have 5 pants, 5 shirts, and 2 shoes. How many different ways can you dress?
50
19. Use the following data to construct a box and whiskers plot:
10, 30, 28, 36, 22, 33, 25
20. A bag contains 7 blue balls, 2 red balls, and 2 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
18.18%
A blue ball or red ball?
81.82%
Two red balls?
3.31%
A blue ball and a white ball?
11.57%
21. Solve and graph the following systems of linear equations:
x + y = 3 x  y = 18
A(10.5,7.5)
12x  13y = 13 6x + 2y = 2
B(0,1)
22. Write the following fractions in simplest form:
2x^{2}y^{8}
4xy^{5}
xy^{3}
2
(x + 10)^{6}
(x + 10)
(x + 10)^{5}
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
x^{2}  12x = 27
x_{1} = 9, x_{2} = 3
24. Convert the following repeating decimal into a fraction:
x =
0.36
33
90
25. Solve the following equation:

5
x
= 5
x = 1
26. Rationalize the denominator of each fraction below:
4
5
1 +
10

4
5
 20
2
9
27. Use a trigonometric ratio to find x:
x = 28.87 cm
28. The sum of two consecutive even integers is 22. What are the integers? (Hint: use 2x as the first even integer)
a=10, b=12
29. After you leave your house, you walk 8 blocks north and 15 blocks east. How far are you from your house?
I am
17
blocks from my house.
30. A rectangle has an area of 221m^{2}. Its width is 4 m less than its length. What are the dimensions of the rectangle?
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