13. Multiply the following polynomials and simplify:
(4x^{4} + 3x)4x^{4}
16x^{8} + 12x^{5}
(8x^{4} + x^{2})(5x^{4} + 7)
40x^{8} + 5x^{6} + 56x^{4} + 7x^{2}
14. Divide:
6x^{3}  6x^{2}  20x + 20 / 2x  2
3x^{2}  10
15. Find the greatest common factor of the following terms:
100, 54
2
90x^{2}y^{8}, 12y^{5}
6y^{5}
16. Factor the following polynomials:
30x^{5}  56x^{4} + 24x^{3}
30x^{3}(x 
2
3
)(x 
6
5
)
x^{2}  5x  24
(x + 3)(x  8)
x^{5} + 7x^{4}  30x^{3}
x^{3}(x  3)(x + 10)
17. For question 16, exercises b) and c), solve for x:
x =
3
and
8
x =
0
,
3
and
10
18. You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate or vanilla. How many choices do you have?
8
19. Use the following data to construct a box and whiskers plot:
19, 23, 13, 29, 12, 10, 18, 40
20. A bag contains 5 blue balls, 4 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?
43.75%
A blue ball or red ball?
56.25%
Two red balls?
5.00%
A blue ball and a white ball?
14.58%
21. Solve and graph the following systems of linear equations:
x + y = 14 x  y = 17
A(1.5,15.5)
3x  9y = 4 3x + 9y = 9
B(0.83,0.72)
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 + 2)
(x^{2} + 4x + 4)
1
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.
x^{2} = 15x + 54
x_{1} = 6, x_{2} = 9
24. Convert the following repeating decimal into a fraction:
x =
0.767
767
999
25. Solve the following equation:
10
x
+ 17 = 1
x
 16
x = 9
26. Rationalize the denominator of each fraction below:
14
21
 7

21
+ 7
2
27. Use a trigonometric ratio to find x:
x = 18.38 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 12 blocks north and 16 blocks west. How far are you from your house?
I am
20
blocks from my house.
30. Each side of a square is decreased by 4 m. The area of the newly created square is 361m^{2}. What was the original length of one side of the square?
15. Find the greatest common factor of the following terms:
90, 30, 52
2
60x^{2}y^{3}, 48x^{4}y^{5}, 36y^{2}
12y^{2}
16. Factor the following polynomials:
60x^{3}  100x^{2} + 10x
60x(x 
5 +
19
6
)(x 
5 
19
6
)
x^{2}  x  2
(x  2)(x + 1)
x^{6}  12x^{5} + 36x^{4}
x^{4}(x  6)(x  6)
17. For question 16, exercises b) and c), solve for x:
x =
2
and
1
x =
0
,
6
and
6
18. You are seating 4 people on 4 chairs. How many different ways can those people sit?
24
19. Use the following data to construct a box and whiskers plot:
6, 21, 30, 3, 33, 37, 24, 7, 9
20. Suppose you toss a coin and spin a spinner numbered 1 through 6
What is the probability of getting heads and 1?
8.33%
What is the probability of getting tails and an odd number?
25%
What is the probability of getting heads and a multiple of 2?
25%
What is the probability of getting heads and a prime number?
25%
What is the probability of not heads and not 2?
41.67%
What is the probability of getting not tails and not a whole number?
0%
What is the probability of heads or tails and a whole number?
100%
What is the probability of getting heads?
50%
21. Solve and graph the following systems of linear equations:
x + y = 19 x  y = 4
A(11.5,7.5)
8x  6y = 4 6x + 4y = 6
B(0.29,1.06)
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  7)^{7}
(x  7)^{5}
(x  7)^{2}
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
4x + 4 = x^{2}
x_{1} = 2, x_{2} = 2
24. Convert the following repeating decimal into a fraction:
x =
0.319
288
900
25. Solve the following equation:
x  10
+ 6 = 20
x = 206
26. Rationalize the denominator of each fraction below:
25
3
 35

25
3
+ 875
1222
27. Use a trigonometric ratio to find x:
x = 21.21 cm
28. The sum of two consecutive even integers is 26. What are the integers? (Hint: use 2x as the first even integer)
a=12, b=14
29. After you leave your house, you walk 15 blocks east and 8 blocks north. How far are you from your house?
I am
17
blocks from my house.
30. Each side of a square is decreased by 3 ft. The area of the newly created square is 361ft^{2}. What was the original length of one side of the square?
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