15. Find the greatest common factor of the following terms:
90, 60, 66
6
39x7y2, 78x2y10
39x2y2
16. Factor the following polynomials:
68x5 + 51x4 - 17x3
68x3(x -
1
4
)(x + 1)
x2 + 0x - 36
(x + 6)(x - 6)
x7 + 13x6 + 36x5
x5(x + 9)(x + 4)
17. For question 16, exercises b) and c), solve for x:
x =
-6
and
6
x =
0
,
-9
and
-4
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:
35, 21, 1, 10, 6, 30, 16, 40, 15, 19
20. A bag contains 3 blue balls, 2 red balls, and 5 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
50.00%
A blue ball or red ball?
50.00%
Two red balls?
2.22%
A blue ball and a white ball?
16.67%
21. Solve and graph the following systems of linear equations:
x + y = -8 x - y = 5
A(-1.5,-6.5)
7x - 3y = -11 4x + 9y = 1
B(-1.28,0.68)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
x8 + 1x7 - 72x6
x4(x - 8)
x2(x + 9)
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
x2 + 84 = 20x
x1 = 14, x2 = 6
24. Convert the following repeating decimal into a fraction:
x =
0.5
5
9
25. Solve the following equation:
10
x
- 9 = 9
x
+ 13
x = 484
26. Rationalize the denominator of each fraction below:
15
9
9
21
5
21
21
27. Use a trigonometric ratio to find x:
x = 27.71 cm
28. The sum of two consecutive odd integers is 52. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=25, b=27
29. After you leave your house, you walk 8 blocks west and 6 blocks south. How far are you from your house?
I am
10
blocks from my house.
30. Each side of a square is lengthened by 3 m. This makes the area of the square 100m2. What is the original length of a side of the square?
15. Find the greatest common factor of the following terms:
70, 44, 90
2
72x4y9, 90x10y3, 42x10y7
6x4y3
16. Factor the following polynomials:
2x5 - 18x4 + 31x3
2x3(x -
9 +
19
2
)(x -
9 -
19
2
)
x2 - 2x + 1
(x - 1)(x - 1)
x5 - 20x4 + 84x3
x3(x - 14)(x - 6)
17. For question 16, exercises b) and c), solve for x:
x =
1
and
1
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:
36, 11, 32, 29, 22, 18, 21
20. A bag contains 3 blue balls, 4 red balls, and 3 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
30.00%
A blue ball or red ball?
70.00%
Two red balls?
16.00%
A blue ball and a white ball?
9.00%
21. Solve and graph the following systems of linear equations:
x + y = 5 x - y = -16
A(-5.5,10.5)
10x - 7y = 10 8x + 10y = 13
B(1.22,0.32)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
(x2 + 18x + 81)
(x + 9)
x + 9
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
70 = x2 - 9x
x1 = 14, x2 = -5
24. Convert the following repeating decimal into a fraction:
x =
0.69
69
99
25. Solve the following equation:
6
x
= 12
x =
36
144
26. Rationalize the denominator of each fraction below:
35
15 -
21
525 + 35
21
204
27. Use a trigonometric ratio to find x:
x = 19.92 cm
28. The sum of two consecutive odd integers is 36. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=17, b=19
29. After you leave your house, you walk 8 blocks south and 15 blocks west. How far are you from your house?
I am
17
blocks from my house.
30. The sides of a square are increased by 5 m. The area of the newly created square is 324m2. What was the original length of one side of the square?
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