Honors Algebra II Final Exam Review - Typepad · Honors Algebra II Final Exam Review 8. Factor completely: 2xx2 9. Factor completely: 6xx2 10. Factor completely: 8x4 11. Factor completely:

Honors Algebra II Final Exam Review Name________________________________

1. Find the quotient: 3 25 7 2 2x x x x

2. Find the quotient: 3 22 17 23 42 2 7x x x x

3. Find the difference: 2 29 3 7 4 8 9x x x x

4. Multiply: 3 8 4 2 5 7x x x

5. Simplify:

52 3

14

x y

xy

6. Simplify: 6 3

5 3 5 62 4x y x y

7. Solve: 5 33 15 18x x x

Honors Algebra II Final Exam Review

8. Factor completely: 26 12x x

9. Factor completely: 220 7 6x x

10. Factor completely: 43 48x

11. Factor completely: 26 5 3 3x x

12. Factor completely: 2 2 26 4 3 2x x xy y

13. Find all the factors, zeros, and x-intercepts: 3 26 4 24f x x x x

14. Find all the factors, zeros, and x-intercepts: 4 3 22 5 12 4f x x x x x

15. Find all the factors, zeros, and x-intercepts: 4 3 25 4 20f x x x x x


16. Find the value of k so the remainder is 7: 3 2 9 2x kx x

17. Find the value of k so the remainder is 1: 2 3 3x x x k

18. Given the graph:

Degree: Even / Odd

Leading Coefficient: Positive / Negative

How many relative maxima?

How many relative minima?

Least possible degree of the polynomial?

Real zeros:

Known factors from real zeros:

Domain:

Range:

19. Write a polynomial function of least degree with a leading coefficient of 1 given the

following zeros: 4, 7 5

20. Write a polynomial function of least degree with a leading coefficient of 1 given the

following zeros: 0 (double root), 3 2i


21. Given the functions below, perform the indicated operations:

28 9 2 1f x x g x x h x x

(a) g h x (b) g f x (c) 3f g (d) 2f g h

22. Simplify: 12 9

32

343

27

x y

z

23. Simplify:

1 1

3 3

3 2

3x x

x

24. Simplify: 249 56 16x x

25. Solve: 2 1 5x x

26. Solve: 2

31 16

2 43 3

x

27. Solve: 25 5x x


28. Find the inverse of the following:

(a) 2

16 6 9f x x (b) 32 6

9

xg x

29. Verify algebraically that the following functions are inverses of each other:

3 9f x x and 1

33

g x x

30. Use 9log 7 0.8856 and 9log 4 0.6309 to evaluate the following:

(a) 9

7log

4 (b) 9log 28 (c) 9log 324 (d) 9

112log

36

31. Evaluate: 7log 57

x

32. Evaluate: 97log 7

33. Evaluate: 3lnln4ee


34. Evaluate:

1

3

1ln

e

35. Expand:

3

2

2ln

x y

w z

36. Condense: 1 1

log2 log 2log log2 2

w y z

37. Solve: 27 7log 6 log 4x x x

38. Solve: 216 16

1log 9 5 log 1

2x x

39. Solve: 3 35 4x x

40. Solve: 9 9 9

1 1log log 64 log 81

3 4x

Honors Algebra II Final Exam Review 41. Graph 2log 3y x

Domain: _______________ Range: _______________

x-intercepts: _______________ y-intercepts: _______________

Asymptotes: _______________ End Behavior: _______________

42. Growth or Decay?

(a) 112

4xf x (b) 32 27

x

g x

43. Write an exponential function whose graph passes through the points:

1

3, 243 0,3

44. Given the function 1

1

3

x

f x

, write the equation for g x given each of the

following transformations:

(a) Vertically stretch by a factor of 4, shifted down 3 units, and reflected over the y-axis.

(b) Horizontally compress by a factor of 1

5 and reflected over the x-axis.

(c) Horizontally stretched by a factor of 8 and shifted down 3 units.


45. Graph 1

32

2

x

y

Domain: _______________ Range: _______________



46. Graph 3

13

2

x

y

Domain: _______________ Range: _______________



47. In 2002, 1219 carnivorous gerbils were observed in the United States. For the next 11

years, about 12% more carnivorous gerbils were observed each year. Use the formula

1n

A P r .

(a) Write an exponential function showing the growth of the population of carnivorous

gerbils.


(b) In 2008, about how many carnivorous gerbils were observed in the US?

(c) In what year were 1712 carnivorous gerbils observed?

48. Simplify: 2

3 6

2 43 1

2 2

x x

x x

49. Simplify: 2 2

1 6

4 4 4

x

x x x

50. Simplify: 2

2

6 1

24 3

x

x xx x

x x

51. Graph: 2

2

5 11 2

7 10

x xf x

x x

_______________ hole(s) _______________ x-intercept(s) _______________ VA _______________ HA/SA _______________ y-intercept


52. Graph: 9

7f x

x

_______________ hole(s) _______________ x-intercept(s) _______________ VA _______________ HA/SA _______________ y-intercept

53. Graph: 2 3

2

2

13

x xf x

x

_______________ hole(s) _______________ x-intercept(s) _______________ VA _______________ HA/SA _______________ y-intercept 54. Perform the partial-fraction decomposition:

(a) 2

2

25

xy

x

(b)

3 2

2

2 2

5 6

x x xy

x x


55. 7

1

2n

n

56.

1

1

13

7

n

n

57. Find the sum of the first 15 terms of the geometric sequence with 1 4a and 2

4

5a .

58. Find the 28th term of the arithmetic sequence if 9 57a and 13 73a .

59. Find the 17th term of the geometric sequence if 5 64a and 8 91a .

60. Write the formula for the apparent nth term of the sequence: 5 7 9 11

, , , ,...2 6 24 120

61. Simplify:

3 !

6 !

n

n


62. Evaluate the following:

(a) 3 5 6i i (b) 3 2 2 5i i (c) 4

3

i

i

63. Given

2

2

19, 0

3

3 , 0

x xf x

x x

(a) Find 0f

(b) Is f x continuous?

64. What is an even function? An odd function?

65. Are the following functions even, odd, or neither?

(a) 6 4 23 7f x x x x

(b) 3

3 3 4 323 5

3g x x x x x x x

(c) 3 15 1

2h x x x


66. What does it mean for a function to be one-to-one?

67. Is f x below a one-to-one function? Why or why not?

68. You are given $5000 for a high school graduation gift. You decide to put the money into

a savings account.

(a) What amount do you have after 4 years if your account pays 6.5% interest compounded

quarterly?

(b) What amount do you have after ten years if your account pays 5.9% interest

compounded continuously?

(c) How long will it take to triple your money if the account pays 6.2% interest

compounded monthly?

69. What is the domain of 9 5y x ?

70. If 2i is a root of 3 23 4 12f x x x x , what are the other roots?

x 0 1 2 3 4

f(x) 0 1 1 5 3

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Honors Algebra II Final Exam Review - Typepad · Honors Algebra II Final Exam Review 8. Factor completely: 2xx2 9. Factor completely: 6xx2 10. Factor completely: 8x4 11. Factor completely: