# MAT 117 week 9 Final Exam

September 17, 2015

**MAT 117 week 9 Final Exam in $18 only **

MAT-117-week-9-Final-Exam-Guide

1. Determine whether the expression is a polynomial. If it is, state how many terms and variables the polynomial contain. Then state its degree.

-8x + 1/6x

2. Determine whether the expression is a polynomial. If it is , state how many terms and variables the polynomial contain. Then state its degree.

2x^{-3}y^{2}

3. Add the polynomials.

(5ab^{4 }+ a^{4}b^{4}) + (3a^{4}b^{4} – 5ab)

4. Multiply and simplify the expression.

(2- z)z

5. Multiply

(6xy)(x+y)

6. Multiply and simplify the expression.

(5w – 1) (6w – 3)

7. Find the product.

(3b +6) (3b-6)

8. Multiply.

(x^{4} +y^{4})(x^{4 }–y^{4})

9. Divide and check.

(x^{7}+x^{2})/x

10. Identify the greatest common factor. Then factor the expression.

3x^{7} + 6x^{6} – 9x^{5} + 6x^{4}

11. Completely factor the polynomial.

3x^{3} + 15x^{2} + 3x +15

12. Factor the trinomial completely.

x^{2} + 33x + 37

13. Factor the trinomial completely.

x^{2} – 6x + 5

14. Factor the trinomial.

x^{2} – x- 2

15. Factor the trinomial completely.

Y^{3} – 14y^{2} + 48y

16. Factor the trinomial.

25r^{2} + 5r – 42

17. Factor the trinomial by grouping.

2x^{3} – 7x^{2} – 15

18. Factor .

X^{3} – 8

19. Solve the equation.

(x-8) (4x + 9) = 0

20. Solve and check.

25x^{2} – 8x = 0

21. Solve and check.

2x^{2} + 3x = 5

22. Multiply and simplify to lowest terms.

x^{2}/(x^{2} + 10) *(x+4)/x

23. Divide and simplify to lowest terms.

(3x^{2}-6x)/(6x-5)÷(x-2)/(6x-5)

24. Simplify to lowest terms.

16a^{2}/(4a+9b) – 81b^{2}/(4a+9b)

25. Find the least common multiple (LCM).

x^{2} – 9x , x^{2} + 9x

26. Simplify the expression. Write your answer in lowest terms and leave it in factored form.

3y/y(2y-1) + 4/(2y – 1)

27. Solve and check your answer.

3/(1-x) = 4/(1+ x)

28. Four inches of heavy, wet snow are equivalent to two inches of rain. Estimate the water content in 14 inches of heavy, wet snow.

29. Write the domain and range of the function in interval notation.

f(x) = √(x- 3)

30. Find the domain of the rational function.

F(y) = (y+3)/(y^{2} – 3y)

31. Simplify the expression. Assume that all variables are real numbers.

^{3}√125(x-9)^{3}

32.a) Write the expression 27^{-2/3} in radical notation.

b) Evaluate the radical expression.

33. Simplify by factoring.

√ 54

34. Find the maximum y-value on the graph of y = f(x)

f(x) = -x^{2} + 4x + 3

35. For y = x^{2} – 1 do the following.

a) Sketch a graph of the equation.

b) Identify the vertex.

c) Compare the graph of y = f(x) to the graph of y = x^{2}.

36. To solve by completing square, what value should you add to each side of the equation?

x^{2} + 12x = -4

37. Use the quadratic formula to find any x-intercepts on the graph of the equation.

Y = x^{2} + 4x -11

38. A table for y = 9x^{2} – 9 is given below. Solve each equation or inequality.

a) 9x^{2} – 9 = 0

b) 9x^{2} – 9 < 0

c) 9x^{2} – 9 > 0

x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |

y | 72 | 27 | 0 | -9 | 0 | 27 | 72 |

39.Use the horizontal line test to determine whether the graph represents a one-to-one function.

40. Find f^{-1}(x). f(x) = ^{3}√(x-6)

41. Simplify the expression, if possible.

log 1

42. Find the approximate the logarithm to four decimal places.

log 2.95

43. Graph y = f(x). Compare the graph to the graph of y = log x.

f(x) log (x ) – 5

44. Determine if the given sequence is an arithmetic sequence. If it is, find the common difference, d.

n | 1 | 2 | 3 | 4 |

f(n) | -5 | 3 | 11 | 19 |

45. Find the general term a_{n} for the geometric sequence.

a_{1} = -2 and a_{2} = 10

46. A theater has 40 seats in the first row, 44 seats in the second row, 48 seats in the third row, and so on.

a) Can the number of seats in each row be modeled by an arithmetic or geometric sequence?

b) Write the general term for sequence a_{n} that given the number of seats in row n.

c) How many seats are there in row 20?

47. Write the terms of the series and find there sum.

4

∑ (k + 9)^{2}

K = 1

48. A company offers a staring yearly salary of $ 36000 with raises of $ 3500 per year. Find the total salary over a ten-years period.

49. Solve C/L = m for L.

50. Solve N = cs/(c +s) for s.

51. Determine whether f(x) represents a polynomial function. If possible, identify the degree the degree and type of polynomial Function.

F(x) = 8x^{2} + 6 -2x^{3}

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