13. Multiply the following polynomials and simplify:
(10x4 + 4x + 5)-9
-90x4 - 36x - 45
(2x - 6)(6x5 + 4x4)
12x6 - 28x5 - 24x4
14. Divide:
15x2 - 2x - 1 / 3x - 1
5x + 1
15. Find the greatest common factor of the following terms:
75, 30, 96
3
50y3, 30y7, 36x8y6
2y3
16. Factor the following polynomials:
12x5 - 56x4 + 59x3
12x3(x -
14 +
19
6
)(x -
14 -
19
6
)
x2 - 14x + 40
(x - 10)(x - 4)
x9 - 27x8 + 182x7
x7(x - 14)(x - 13)
17. For question 16, exercises b) and c), solve for x:
x =
10
and
4
x =
0
,
14
and
13
18. You can purchase your ice cream in a cup or a cone. Orders can be one, two, three, or four scoops. Flavors can be chocolate or vanilla. How many choices do you have?
16
19. Use the following data to construct a box and whiskers plot:
33, 11, 31, 28, 4, 36, 24
20. Suppose you toss a coin and spin a spinner numbered 1 through 8
What is the probability of getting heads and 8?
6.25%
What is the probability of getting heads and an odd number?
25%
What is the probability of getting tails and a multiple of 4?
12.5%
What is the probability of getting heads and a prime number?
25%
What is the probability of not tails and not 6?
43.75%
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 = 7 x - y = 6
A(6.5,0.5)
2x - 6y = 16 6x + 12y = 18
B(5,-1)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
(x + 2)4
(x + 2)2
(x + 2)2
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
-7x - 78 = -x2
x1 = 13, x2 = -6
24. Convert the following repeating decimal into a fraction:
x =
0.79
720
900
25. Solve the following equation:
-12
x
+ 6 = 7
x
- 13
x = 1
26. Rationalize the denominator of each fraction below:
21
14 +
14
42 - 3
14
26
27. Use a trigonometric ratio to find x:
x = 41.01 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 south. How far are you from your house?
I am
17
blocks from my house.
30. A rectangle has a width that is 2 ft less than its length. The area of the rectangle is 3ft2. What are the dimensions of the rectangle?
15. Find the greatest common factor of the following terms:
63, 90
9
48x5, 60x4y5
12x4
16. Factor the following polynomials:
45x5 - 54x4 - 72x3
45x3(x +
4
5
)(x - 2)
x2 - x - 72
(x + 8)(x - 9)
x5 + 8x4 - 84x3
x3(x + 14)(x - 6)
17. For question 16, exercises b) and c), solve for x:
x =
-8
and
9
x =
0
,
-14
and
6
18. You are seating 3 people on 3 chairs. How many different ways can those people sit?
6
19. Use the following data to construct a box and whiskers plot:
19, 10, 22, 39, 35, 17, 23, 12
20. Suppose you toss a coin and spin a spinner numbered 1 through 15
What is the probability of getting tails and 15?
3.33%
What is the probability of getting tails and an odd number?
23.33%
What is the probability of getting tails and a multiple of 3?
16.67%
What is the probability of getting heads and a prime number?
20%
What is the probability of not tails and not 14?
46.67%
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 - 6y = -16 7x + 10y = 13
B(-1.58,2.4)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
(x + 4)4
(x + 4)
(x + 4)3
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
-11x = x2 + 18
x1 = -2, x2 = -9
24. Convert the following repeating decimal into a fraction:
x =
0.3953
3950
9990
25. Solve the following equation:
-20 +
x + 6
= 20
x = 1594
26. Rationalize the denominator of each fraction below:
10
15
21
20
5
3
21
27. Use a trigonometric ratio to find x:
x = 40.00 cm
28. The sum of two consecutive even integers is 54. What are the integers? (Hint: use 2x as the first even integer)
a=26, b=28
29. After you leave your house, you walk 6 blocks south and 8 blocks east. How far are you from your house?
I am
10
blocks from my house.
30. Each side of a square is decreased by 7 ft. The area of the newly created square is 361ft2. What was the original length of one side of the square?
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