15. Find the greatest common factor of the following terms:
200, 270
10
378x3y7, 432x6y10
54x3y7
16. Factor the following polynomials:
30x4 - 30x3 + 6x2
30x2(x -
5 +
5
10
)(x -
5 -
5
10
)
x2 - 10x + 21
(x - 7)(x - 3)
x8 - 6x7 + 5x6
x6(x - 5)(x - 1)
17. For question 16, exercises b) and c), solve for x:
x =
7
and
3
x =
0
,
5
and
1
18. You have 4 pants, 4 shirts, and 2 shoes. How many different ways can you dress?
32
19. Use the following data to construct a box and whiskers plot:
23, 20, 30, 33, 19, 29, 17, 14, 27
20. A bag contains 6 blue balls, 4 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?
16.67%
A blue ball or red ball?
83.33%
Two red balls?
9.09%
A blue ball and a white ball?
9.09%
21. Solve and graph the following systems of linear equations:
x + y = 9 x - y = -6
A(1.5,7.5)
4x - 4y = 16 2x + 8y = 4
B(3.6,-0.4)
22. Write the following fractions in simplest form:
19xy6
38x8y
y5
2x7
(x - 7)
(x2 - 14x + 49)
1
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.
-x2 = -11x - 26
x1 = 13, x2 = -2
24. Convert the following repeating decimal into a fraction:
x =
0.170
1690
9900
25. Solve the following equation:
17
x
+ 16 = 18
x
- 9
x = 625
26. Rationalize the denominator of each fraction below:
2
6
21 +
21
7
6
-
14
70
27. Use a trigonometric ratio to find x:
x = 15.00 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 5 blocks east and 12 blocks south. How far are you from your house?
I am
13
blocks from my house.
30. Each side of a square is lengthened by 2 ft. This makes the area of the square 49ft2. What is the original length of a side of the square?
13. Multiply the following polynomials and simplify:
(7x3 + 6)5x5
35x8 + 30x5
(6x4 + 3x)(5x5 + x3 + 2x2)
30x9 + 6x7 + 27x6 + 3x4 + 6x3
14. Divide:
10x3 - 12x2 - 25x + 33 / 5x - 6
(2x2 - 5) with a remainder of 3
15. Find the greatest common factor of the following terms:
396, 300
12
99x5y9, 120x4y9
3x4y9
16. Factor the following polynomials:
6x3 - 75x2 - 39x
6x(x +
1
2
)(x - 13)
x2 + 3x - 70
(x + 10)(x - 7)
x4 + 7x3 + 12x2
x2(x + 4)(x + 3)
17. For question 16, exercises b) and c), solve for x:
x =
-10
and
7
x =
0
,
-4
and
-3
18. You have 8 CDs. How many different ways can you listen to them?
40320
19. Use the following data to construct a box and whiskers plot:
28, 40, 13, 22, 17, 31, 33, 29, 25, 37
20. A bag contains 7 blue balls, 7 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?
12.50%
A blue ball or red ball?
87.50%
Two red balls?
17.50%
A blue ball and a white ball?
5.83%
21. Solve and graph the following systems of linear equations:
x + y = -6 x - y = 5
A(-0.5,-5.5)
10x - 8y = -19 3x + 5y = 15
B(0.34,2.8)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
(x - 6)
(x2 - 12x + 36)
1
x - 6
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
-x2 = -5x - 6
x1 = -1, x2 = 6
24. Convert the following repeating decimal into a fraction:
x =
0.6
6
9
25. Solve the following equation:
7
x
- 17 = 10
x
- 20
x = 1
26. Rationalize the denominator of each fraction below:
1
14
+ 35
-
14
- 35
1211
27. Use a trigonometric ratio to find x:
x = 26.87 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 north and 6 blocks east. How far are you from your house?
I am
10
blocks from my house.
30. The sides of a square are increased by 4 ft. The area of the newly created square is 289ft2. What was the original length of one side of the square?
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