Algebra II - Semester 2 Review Name ____________________________________

Part 1 (_____ problems complete): Stamp Date____________

Overall Due Date: ______________

Notes: No graphing calculator allowed on Final Exam. One single-sided, 8.5x11 sheet of notes allowed.

Chapter 9:

Analyze and graph each function. Show algebraically how you found each of the following: domain, x intercepts, y intercept, holes, vertical asymptotes, and horizontal/oblique asymptotes. Also, split the domain into intervals (use the x values when the numerator or denominator equal zero to define the intervals), and test a point within each interval to determine whether the function is positive or negative.

1. 2.

Interval table: Interval table:

3. The variable z varies jointly with x and y. Use the given values to write an equation relating x, y, and z. Then find z when x = 5 and y = -6.

x = 6, y = 8, z = -6

4. The variable z varies inversely with y. Use the given values to write an equation relating y and z. Find z when y = 2.y = -2, z = 2

Simplify each expression.

5. x2−2x−3x+1

÷ x2+ x−12x2 6.

x+36

1+ x3

7. x2

3+ x

x+18.

x2−918 x

∗3 x2

x2+5 x+6∗x3+2 x

x+1

Solve the equation using any method. Remember to check for extraneous solutions.

9. x

x−1=2 x+10

x+11 10. 3x+2x+1

=2−2 x+3x+1

Chapter 7:

11. Given and

a. Findf (g (2 )) b. Find

c. Find f (g ( x )) d. Find g(g ( x ))

Find the inverse of each function:

12. 13.

Simplify. All exponents should be positive. Rationalize if needed.

14. (−64 )23 15. 5

13∗5

43

16. 9−32 17.

(4 x )2

(4 x )12

18. 6√6 x6 y7 z10 19. 3√4 a6+a 3√108 a3

Solve each radical equation. Check for extraneous solutions.

20. √4 x=x−8 21. (4 x+15 )12−3 (x )

12=0

Graph each function and state the domain and range.

22. y= 3√x−7 23. y=−2 ( x )12 +4

Domain: ________________ Domain: ________________

Range: _________________ Range: _________________

Chapter 8:

24. Given: and . Find each of the following:

a. b.

c. g (−2 )=¿

d.

Evaluate without a calculator.

25. 26. 3log3 2 x−1−e ln x2+4

Expand or contract each logarithm.

27. 28.

Solve each equation. Round any decimals to the nearest hundredth.

29. 30.

31. 32.

33. 34.

35. A child’s grandparents wish to purchase a bond to be used for her college education. The bond pays 4% interest compounded semiannually.

a. If the bond matures in 18 years, how much should they pay now so that the bond will be worth $85,000 at maturity?

b. The grandparents find another bond that pays interest compounded continuously. If the grandparents invest $25,000 now, how much will the bond be worth in 18 years?

Sketch a graph of each function. State the domain and range. Each function needs to have the critical intercept as well as any asymptotes. You do not need to plot any other points.

36. y=2x+3+5 37. y=−3(34 )

x

−2

Domain: ________________ Domain: ________________

Range: _________________ Range: _________________

38. y= log1/2(x−3) 39. y=ln ( x )+5

Domain: ________________ Domain: ________________

Range: _________________ Range: _________________

Chapter 13: Trigonometry Part I

40. Convert each angle to radians or degrees.

a. 135o b. 2π3 c. −15o d.

−3 π2

Determine a co-terminal angle inside the unit circle in the equivalent type of measure (radians or degrees). Then write the quadrant for the angle and find the reference angle. (5 points each)

41. -930o 42. 7 π3

Co-terminal angle: _______________ Co-terminal angle: _______________

Quadrant: _____________ Quadrant: _____________

Reference angle: ____________ Reference angle: ___________

43. Find the exact value of each expression (do not use a calculator):

a. sec (−5 π4 ) b. tan ( 270o ) c. csc (−210o ) d.

Find the exact value of each of the 6 trig functions:

44. , π2<θ<π

45. , is in the third quadrant

Complete each special right triangle below.

46. 47.

Sketch each scalene triangle. Then use the Law of Cosines and/or the Law of Sines to solve the triangle. Remember to check for the case of two triangles!

48. A=75o , a=10 , c=5 49. a=9 , b=3 , c=11

Find the area of a triangle with the following dimensions. You may want to sketch the triangle first. Remember both area formulas to avoid rounding inaccuracies and extra work.

50. a=20 , b=21, c=37 51. B=110o , a=11 ,c=24

Chapter 14: Trigonometry Part II

Graph one period of each function. Show the 5 key points of one complete cycle and label the midline, minimum, and maximum.

52. + 3

53.

54. y=tan( 12

θ)

55. y=3 csc( π3

θ)

Write two equivalent equations using two trigonometric functions for the graphs below.

56. 57.

Chapter 14: Trigonometry Part III

Find the exact value of each expression in the allowable range for the inverse function.

58. 59. 60.

61. 62. 63.

Prove each identity. Do not manipulate both sides and clearly show all steps.

64. 65.

66. 67.

68. 69.

Find the exact value of each expression (no decimal answer). Remember to simplify and rationalize your answer.

70. cos ( 11π12 ) 71. 72. sin (−22.5o)

Given: ; AND ;

Find the exact value of:

73. 74.

75. tan (2 β) 76.

77. 78.

78.

Find the general solution to each equation and the solution(s) on the interval .

79. 80.

81. 82.

83. cos x csc2 x+3 cos x=7 cos x 84. tan2 x=sin x sec x