13. Multiply the following polynomials and simplify:
(9x3 + x + 4)(5x4 + 2x3 + 4x2)
45x7 + 18x6 + 41x5 + 22x4 + 12x3 + 16x2
(4x5 + 6x2 + 9)(10x4 + 6x2)
40x9 + 24x7 + 60x6 + 126x4 + 54x2
14. Divide:
6x2 - 24x + 18 / 3x - 9
2x - 2
15. Find the greatest common factor of the following terms:
176, 300, 390
2
364x10, 324x5y7
4x5
16. Factor the following polynomials:
2x3 + 43x2 - 22x
2x(x + 22)(x -
1
2
)
x2 - 15x + 50
(x - 5)(x - 10)
x5 + x4 - 20x3
x3(x + 5)(x - 4)
17. For question 16, exercises b) and c), solve for x:
x =
5
and
10
x =
0
,
-5
and
4
18. You are seating 6 people on 6 chairs. How many different ways can those people sit?
720
19. Use the following data to construct a box and whiskers plot:
35, 26, 33, 15, 8, 23, 30, 21, 11
20. A bag contains 7 blue balls, 4 red balls, and 5 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
31.25%
A blue ball or red ball?
68.75%
Two red balls?
6.25%
A blue ball and a white ball?
13.67%
21. Solve and graph the following systems of linear equations:
x + y = 3 x - y = 6
A(4.5,-1.5)
8x - 10y = 19 x + 9y = 12
B(3.55,0.94)
22. Write the following fractions in simplest form:
10xy5
40x8y2
y3
4x7
(x - 4)
(x - 4)7
1
(x - 4)6
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
8x - 9 = -x2
x1 = -9, x2 = 1
24. Convert the following repeating decimal into a fraction:
x =
0.338
305
900
25. Solve the following equation:
18
x
= 3
x = 2
26. Rationalize the denominator of each fraction below:
5
3
9 +
21
3
3
-
7
4
27. Use a trigonometric ratio to find x:
x = 20.51 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 8 blocks south and 15 blocks east. How far are you from your house?
I am
17
blocks from my house.
30. The sides of a square are increased by 6 m. The area of the newly created square is 256m2. What was the original length of one side of the square?
13. Multiply the following polynomials and simplify:
7x5(8x + 5)
56x6 + 35x5
(1x5 + x2)(7x3 + 7x + 8)
7x8 + 7x6 + 15x5 + 7x3 + 8x2
14. Divide:
12x2 + 29x + 15 / 4x + 3
3x + 5
15. Find the greatest common factor of the following terms:
189, 273
21
300x10y2, 234x5y10
6x5y2
16. Factor the following polynomials:
48x5 + 69x4 + 24x3
48x3(x -
-23 +
17
32
)(x -
-23 -
17
32
)
x2 + 20x + 100
(x + 10)(x + 10)
x5 + 3x4 - 10x3
x3(x + 5)(x - 2)
17. For question 16, exercises b) and c), solve for x:
x =
-10
and
-10
x =
0
,
-5
and
2
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, peach or kiwi. How many choices do you have?
20
19. Use the following data to construct a box and whiskers plot:
15, 22, 31, 7, 24, 30, 37, 18, 6
20. A bag contains 5 blue balls, 4 red balls, and 3 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
25.00%
A blue ball or red ball?
75.00%
Two red balls?
9.09%
A blue ball and a white ball?
11.36%
21. Solve and graph the following systems of linear equations:
x + y = 17 x - y = -4
A(6.5,10.5)
3x - 8y = -12 3x + 13y = -12
B(-4,0)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
(x + 9)
(x2 + 18x + 81)
1
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.
-78 = x2 + 41x
x1 = -2, x2 = -39
24. Convert the following repeating decimal into a fraction:
x =
9.4
85
9
25. Solve the following equation:
19 -
x - 5
= 2
x = 294
26. Rationalize the denominator of each fraction below:
6
10
- 5
-
2
10
+ 10
5
27. Use a trigonometric ratio to find x:
x = 12.12 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 16 blocks north and 12 blocks east. How far are you from your house?
I am
20
blocks from my house.
30. The sides of a square are increased by 8 ft. The area of the newly created square is 169ft2. What was the original length of one side of the square?
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