13. Multiply the following polynomials and simplify:
(5x^{3}  6)(10x^{5}  3)
50x^{8}  60x^{5}  15x^{3} + 18
(4x^{5} + 9x^{3})(1x^{2} + 10x)
4x^{7} + 40x^{6} + 9x^{5} + 90x^{4}
14. Divide:
8x^{3} + 20x^{2}  14x  32 / 2x + 5
(4x^{2}  7) with a remainder of 3
15. Find the greatest common factor of the following terms:
72, 40
8
26y^{8}, 88x^{9}y^{3}
2y^{3}
16. Factor the following polynomials:
42x^{4}  70x^{3}  28x^{2}
42x^{2}(x +
1
3
)(x  2)
x^{2}  3x + 2
(x  2)(x  1)
x^{6}  12x^{5}  45x^{4}
x^{4}(x + 3)(x  15)
17. For question 16, exercises b) and c), solve for x:
x =
2
and
1
x =
0
,
3
and
15
18. You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate, vanilla, strawberry or peach. How many choices do you have?
16
19. Use the following data to construct a box and whiskers plot:
33, 38, 12, 11, 7, 15, 28
20. Suppose you toss a coin and spin a spinner numbered 1 through 17
What is the probability of getting heads and 5?
2.94%
What is the probability of getting heads and an odd number?
23.53%
What is the probability of getting heads and a multiple of 7?
5.88%
What is the probability of getting tails and a prime number?
20.59%
What is the probability of not heads and not 5?
47.06%
What is the probability of getting not heads 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 = 5 x  y = 4
A(0.5,4.5)
8x  9y = 20 5x + 9y = 5
B(1.15,1.2)
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^{5}  12x^{4} + 35x^{3}
x^{2}(x  7)
x(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.
56 = x^{2}  10x
x_{1} = 4, x_{2} = 14
24. Convert the following repeating decimal into a fraction:
x =
9.30
921
99
25. Solve the following equation:
1 +
2x  5
= 10
x = 63
26. Rationalize the denominator of each fraction below:
6
15
21
21
2
35
49
27. Use a trigonometric ratio to find x:
x = 22.52 cm
28. The sum of two consecutive odd integers is 24. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=11, b=13
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. The sides of a square are increased by 2 ft. The area of the newly created square is 361ft^{2}. What was the original length of one side of the square?
15. Find the greatest common factor of the following terms:
90, 60, 10
10
84x^{4}y^{9}, 24x^{7}y^{4}, 65x^{9}y^{2}
x^{4}y^{2}
16. Factor the following polynomials:
8x^{5} + 32x^{4} + 26x^{3}
8x^{3}(x 
4 +
3
2
)(x 
4 
3
2
)
x^{2} + 11x + 30
(x + 6)(x + 5)
x^{6} + 4x^{5}  21x^{4}
x^{4}(x + 7)(x  3)
17. For question 16, exercises b) and c), solve for x:
x =
6
and
5
x =
0
,
7
and
3
18. You can purchase your ice cream in a cup or a cone. Orders can be one, two, or three scoops. Flavors can be chocolate, vanilla, strawberry or peach. How many choices do you have?
24
19. Use the following data to construct a box and whiskers plot:
12, 30, 13, 3, 15, 31, 20
20. Suppose you toss a coin and spin a spinner numbered 1 through 14
What is the probability of getting tails and 10?
3.57%
What is the probability of getting tails and an even number?
25%
What is the probability of getting tails and a multiple of 3?
14.29%
What is the probability of getting heads and a prime number?
21.43%
What is the probability of not heads and not 14?
46.43%
What is the probability of getting not heads 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 = 17 x  y = 8
A(4.5,12.5)
x  7y = 13 3x + 10y = 13
B(7.13,0.84)
22. Write the following fractions in simplest form:
30x^{8}y^{6}
15x^{9}y^{2}
2y^{4}
x
(x^{2}  10x + 25)
(x  5)
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} = 21x + 90
x_{1} = 15, x_{2} = 6
24. Convert the following repeating decimal into a fraction:
x =
0.339
336
990
25. Solve the following equation:
9 
x  9
= 18
x = 738
26. Rationalize the denominator of each fraction below:
10
14
+ 9

10
14
 90
67
27. Use a trigonometric ratio to find x:
x = 24.04 cm
28. The sum of two consecutive odd integers is 16. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=7, b=9
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. The length of a rectangle is 9 less than 3 times the width. What are the dimensions of the rectangle if the area is 390ft^{2}?
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