13. Multiply the following polynomials and simplify:

(10x^{4} + 4x + 5)-9

-90x^{4} - 36x - 45

(2x - 6)(6x^{5} + 4x^{4})

12x^{6} - 28x^{5} - 24x^{4}

14. Divide:

15x^{2} - 2x - 1 / 3x - 1

5x + 1

15. Find the greatest common factor of the following terms:

75, 30, 96

3

50y^{3}, 30y^{7}, 36x^{8}y^{6}

2y^{3}

16. Factor the following polynomials:

12x^{5} - 56x^{4} + 59x^{3}

12x^{3}(x -

14 +

19

6

)(x -

14 -

19

6

)

x^{2} - 14x + 40

(x - 10)(x - 4)

x^{9} - 27x^{8} + 182x^{7}

x^{7}(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:

22x^{6}y^{7}z^{4}

44x^{7}y^{9}z^{2}

z^{2}

2xy^{2}

(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 = -x^{2}

x_{1} = 13, x_{2} = -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 3ft^{2}. What are the dimensions of the rectangle?

15. Find the greatest common factor of the following terms:

63, 90

9

48x^{5}, 60x^{4}y^{5}

12x^{4}

16. Factor the following polynomials:

45x^{5} - 54x^{4} - 72x^{3}

45x^{3}(x +

4

5

)(x - 2)

x^{2} - x - 72

(x + 8)(x - 9)

x^{5} + 8x^{4} - 84x^{3}

x^{3}(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:

22x^{6}y^{7}z^{4}

44x^{7}y^{9}z^{2}

z^{2}

2xy^{2}

(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 = x^{2} + 18

x_{1} = -2, x_{2} = -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 361ft^{2}. What was the original length of one side of the square?

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