15. Find the greatest common factor of the following terms:
390, 240, 405
15
468x^{6}y, 288y^{10}
36y
16. Factor the following polynomials:
24x^{3}  72x^{2} + 53x
24x(x 
18 +
6
12
)(x 
18 
6
12
)
x^{2} + 2x  24
(x + 6)(x  4)
x^{9}  13x^{8} + 22x^{7}
x^{7}(x  2)(x  11)
17. For question 16, exercises b) and c), solve for x:
x =
6
and
4
x =
0
,
2
and
11
18. You have 3 books to read. How many different ways can you read your books?
6
19. Use the following data to construct a box and whiskers plot:
27, 15, 4, 37, 1, 38, 39, 5, 19
20. A bag contains 3 blue balls, 6 red balls, and 4 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
30.77%
A blue ball or red ball?
69.23%
Two red balls?
21.30%
A blue ball and a white ball?
7.10%
21. Solve and graph the following systems of linear equations:
x + y = 2 x  y = 10
A(6,4)
6x  6y = 11 3x + 7y = 9
B(0.38,1.45)
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^{3}(x  8)
x^{6}  6x^{5}  16x^{4}
1
x(x + 2)
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
29x = x^{2} + 78
x_{1} = 26, x_{2} = 3
24. Convert the following repeating decimal into a fraction:
x =
0.486
486
999
25. Solve the following equation:
5
x
+ 3 = 20
x
 12
x = 1
26. Rationalize the denominator of each fraction below:
7
5
15 +
15
3
5

3
6
27. Use a trigonometric ratio to find x:
x = 24.25 cm
28. The sum of two consecutive odd integers is 28. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=13, b=15
29. After you leave your house, you walk 4 blocks west and 3 blocks south. How far are you from your house?
I am
5
blocks from my house.
30. A rectangle has a length 8 m greater than its width. The area of the rectangle is 48m^{2}. What are the length and width of the rectangle?
13. Multiply the following polynomials and simplify:
(2x^{5} + 8x^{2})7x^{3}
14x^{8} + 56x^{5}
(5x^{3}  10)(9x^{5} + 7x + 7)
45x^{8}  90x^{5} + 35x^{4} + 35x^{3}  70x  70
14. Divide:
5x^{2} + 26x  63 / 5x  9
x + 7
15. Find the greatest common factor of the following terms:
286, 180
2
48y^{6}, 162x^{3}y^{9}
6y^{6}
16. Factor the following polynomials:
30x^{4} + 17x^{3}  9x^{2}
30x^{2}(x 
1
3
)(x +
9
10
)
x^{2} + 6x + 5
(x + 1)(x + 5)
x^{4}  10x^{3} + 21x^{2}
x^{2}(x  3)(x  7)
17. For question 16, exercises b) and c), solve for x:
x =
1
and
5
x =
0
,
3
and
7
18. You are seating 8 people on 8 chairs. How many different ways can those people sit?
40320
19. Use the following data to construct a box and whiskers plot:
40, 31, 17, 15, 22, 38, 25, 16, 1, 20
20. A bag contains 4 blue balls, 6 red balls, and 7 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
41.18%
A blue ball or red ball?
58.82%
Two red balls?
11.03%
A blue ball and a white ball?
10.29%
21. Solve and graph the following systems of linear equations:
x + y = 2 x  y = 1
A(0.5,1.5)
4x  9y = 2 7x + 3y = 3
B(0.44,0.03)
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}(x + 8)
x^{3} + 13x^{2} + 40x
x^{3}
(x + 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} + 14 = 15x
x_{1} = 14, x_{2} = 1
24. Convert the following repeating decimal into a fraction:
x =
0.4
4
9
25. Solve the following equation:
13 +
4x + 5
= 10
x = 1
26. Rationalize the denominator of each fraction below:
15
7 
5
105 + 15
5
44
27. Use a trigonometric ratio to find x:
x = 24.75 cm
28. The sum of two consecutive odd integers is 60. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=29, b=31
29. After you leave your house, you walk 8 blocks east and 6 blocks south. How far are you from your house?
I am
10
blocks from my house.
30. A rectangle has a width that is 5 m less than its length. The area of the rectangle is 266m^{2}. What are the dimensions of the rectangle?
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