13. Multiply the following polynomials and simplify:
(1x5 + 7x2)(7x3 + 3x2 + 5)
7x8 + 3x7 + 54x5 + 21x4 + 35x2
(5x4 + 4x2)(10x5 + 3x2 + x)
50x9 + 40x7 + 15x6 + 5x5 + 12x4 + 4x3
14. Divide:
3x2 - 24x - 27 / 3x + 3
x - 9
15. Find the greatest common factor of the following terms:
63, 35, 33
1
66x7y10, 24xy3, 70y
2y
16. Factor the following polynomials:
33x3 - 95x2 - 12x
33x(x - 3)(x +
4
33
)
x2 + 14x + 45
(x + 9)(x + 5)
x8 - 23x7 + 126x6
x6(x - 14)(x - 9)
17. For question 16, exercises b) and c), solve for x:
x =
-9
and
-5
x =
0
,
14
and
9
18. You have 5 books to read. How many different ways can you read your books?
120
19. Use the following data to construct a box and whiskers plot:
28, 10, 35, 9, 15, 27, 5, 39, 13, 24
20. A bag contains 5 blue balls, 2 red balls, and 2 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
22.22%
A blue ball or red ball?
77.78%
Two red balls?
2.78%
A blue ball and a white ball?
13.89%
21. Solve and graph the following systems of linear equations:
x + y = -3 x - y = 17
A(7,-10)
11x - 6y = -18 13x + y = 3
B(0,3)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
x5(x - 8)
x6 - 15x5 + 56x4
x
(x - 7)
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
x = x2 - 2
x1 = -1, x2 = 2
24. Convert the following repeating decimal into a fraction:
x =
0.9
9
9
25. Solve the following equation:
-
12
x
= -15
x =
144
225
26. Rationalize the denominator of each fraction below:
2
15 +
15
15 -
15
105
27. Use a trigonometric ratio to find x:
x = 35.36 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 12 blocks east and 5 blocks south. How far are you from your house?
I am
13
blocks from my house.
30. The length of a rectangle is 6 less than 6 times the width. What are the dimensions of the rectangle if the area is 180m2?
13. Multiply the following polynomials and simplify:
(1x4 + 4x2 + 8x)(3x5 + 9x4 + 3)
3x9 + 9x8 + 12x7 + 60x6 + 72x5 + 3x4 + 12x2 + 24x
(8x5 + 3x + 3)(1x4 + 6x3 + 4x2)
8x9 + 48x8 + 32x7 + 3x5 + 21x4 + 30x3 + 12x2
14. Divide:
6x2 - 20x + 6 / 2x - 6
3x - 1
15. Find the greatest common factor of the following terms:
90, 12, 36
6
25x3y5, 54x4y3
x3y3
16. Factor the following polynomials:
54x3 - 66x2 + 18x
54x(x -
11 +
13
18
)(x -
11 -
13
18
)
x2 + 0x - 1
(x - 1)(x + 1)
x7 + 17x6 + 30x5
x5(x + 15)(x + 2)
17. For question 16, exercises b) and c), solve for x:
x =
1
and
-1
x =
0
,
-15
and
-2
18. You have 6 CDs. How many different ways can you listen to them?
720
19. Use the following data to construct a box and whiskers plot:
34, 16, 2, 19, 35, 11, 30
20. A bag contains 4 blue balls, 5 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?
14.79%
A blue ball and a white ball?
9.47%
21. Solve and graph the following systems of linear equations:
x + y = 11 x - y = -14
A(-1.5,12.5)
6x - 2y = -9 7x + 9y = 2
B(-1.13,1.1)
22. Write the following fractions in simplest form:
25x6y6
50x2y10
x4
2y4
(x - 4)
(x2 - 8x + 16)
1
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.
34x = x2 + 33
x1 = 1, x2 = 33
24. Convert the following repeating decimal into a fraction:
x =
0.483
479
990
25. Solve the following equation:
2 +
x + 6
= 7
x = 19
26. Rationalize the denominator of each fraction below:
6
21
4
2
3
42
4
27. Use a trigonometric ratio to find x:
x = 22.00 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 12 blocks east and 9 blocks south. How far are you from your house?
I am
15
blocks from my house.
30. A rectangle has an area of 322m2. Its width is 9 m less than its length. What are the dimensions of the rectangle?
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