1. (Ch 7) Show different ways to simplify the complex fraction:

Method I: Method II:

2. (Ch 7) Simplify:

3. (Ch 7) Solve:

4. (Ch 7 & 12) Which graph(s) will have a vertical asymptote and what will be the equation of the asymptote(s)?

A. ( )

B. f(x) = x

2 + y

2 = 9 C. ( )

D. ( )

5. (Ch 7) A river has a current of 4 km/hr. find the speed of Lynn’s boat in still water if it goes 40 km

downstream in the same time that it takes to go 24 km upstream.

Algebra 2 w/ Trig

Review for Final Exam

Chapters 7, 10, 11, 12, 13, 17, 18 & 19, 20.4

NAME _____________________________

Review Problem Due Dates: Mon 5/5: Problems 1-9 Due on Tues 5/6: Problems 10-26 Due on Wed 5/7: Problems 27-37 Due on Thurs 5/8: Problems 38-42 Due on Fri 5/9: Problems 43-55 Due on Mon 5/12: Problems 56-60 Due on Tues 5/13: Problems 61-89 Due on Wed 5/14: Work day – Class meets in the Eannelli Lab Due on Thurs 5/15: Problems 90-99 Due on Fri 5/16: Problem100 Class meets in the Eannelli Lab Turn in your list to Ms. H (10 pts)

Exam Format: True/False

Multiple Choice

Show your work problems

Graphs

Extra Credit

Small calculator only - Ms. H will provide them.

6. (Ch 10) Given f(x) = 2x2 – 8x + 1, use any method of your choice to fill in the blanks below and then graph the

function.

A. Opens (circle one): Up Down Left Right B. Shape near vertex (circle one): Basic Wider Narrow

C. Vertex: (________ , _______)

D. Equation of Axis: _____________

E. Domain: ____________________

F. Range: ______________________

7. Given x = -0.5(y + 3)2 + 2, use any method of your choice to fill in the blanks below and then graph the function.

A. Opens (circle one): Up Down Left Right B. Shape near vertex (circle one): Basic Wider Narrow

C. Vertex: (________ , _______)

D. Equation of Axis: _____________

E. Domain: ____________________

F. Range: ______________________

8. What is the most efficient way you can explain to a friend that there are no x-intercepts for f(x) = x2 + x + 10? Are there other ways to recognize this as well?

9. A projectile is fired straight upward from ground level so that its distance (in feet) above the ground t seconds after

firing is given by s(t) = – 16t2 + 400 t.

a. What is the height after 5 seconds? b. What is the maximum height achieved? c. When does the projectile hit the ground? (Ch 11) Multiple Choice.

10. Which expression is equivalent to loga b = c?

A. ab = c B. b

c = a C. a

c = b D. b

a = c E. none of these

11. Simplify: log2 8 = ?

A. 0 B. 1 C. 2 D. 3 E. none of these

12. What is the base in log 100?

A. 0 B. 1 C. 10 D. 100 E. e

13. What is the base in ln 100?

A. 0 B. 1 C. 10 D. 100 E. e

14. Which of these values is closest to e?

A. 2 B. 3 C. 2.8 D. 2.7 E. 3.14

15. Simplify: ln e?

A. – 1 B. 0 C. 1 D. 2 E. 3

16. What is the common log of 0.001?

A. – 3 B. –2 C. 1 D. 2 E. 3

17.

=

A. – 3 B. –2 C. 1 D. 2 E. 3

18. log 27

=

A.

B.

C.

D.

E.

19. √ =

A. 6 B. 4 C. 8 D. 3 E.

20. Solve:

A. 4 B.

C.

D.

E.

21. For any value of x that is greater than zero,

A. – 1 B.

C. 0 D. 1 E. x

22. Solve: 1 – 2x

= 16 x – 3

A. 2 B. 0 C.

D.

E.

23. log

=

A. 10 log x B. log 10 + log x C. (log 10)(log x)

D. log x E. 1 – log x

24. log 3 2

x =

A. log 3 2 – log 3 x B. x log 3 2 C. 2x

D. log 2 2 + log 3 x E. x log 3 4

25. ln √ A. ½ B. ½ ln (2 – e) C. ½ (ln 2 – 1)

D. ½ ln 2 – ln e E. ½ – ln e-1/2

26. Graph each:

A. y = ex B. y = e

x – 2 + 1 C. y = 10

x D. y = 10

– x

E. y = ln x F. y = –ln (x + 5) G. y = log2x H. y = – log2(x – 1)

27. (Ch 12) Use synthetic division to find f(2) given f(x) = 3x3 – 12x

2 + x – 10.

28. (Ch 12) f(x) = 6x3 + 17x

2 – 63x + 0

A. List the possible Rational Zeros of f(x): ________________________________________________________

B. Describe the End Behavior of f(x): as x , y ________ and as x , y ________

C. What is the maximum number of zeros f(x) could have?______________

D. What is the maximum number of turning points the graph of f(x) could have?___________

E. Given that -5 is a zero of f(x), use synthetic division to find all the zeros:__________________

F. Write f(x) in factored form:______________________________________________________

29. (Ch 12) Show your work to find all the zeros of f(x) = x3 + x

2 + 6x – 8

30. (Ch 12) A. If 2 and 3 + 2i are zeros of some f(x), what else must be a zero?__________________

B. Multiply the factors to find a possible polynomial expression for f(x) above. _____________________________

31. (Ch 13) Circle the type of conic section for each and fill in the blanks where applicable.

A. (x – 2)2

+ (y – 3)2

= 49 Circle Ellipse Hyperbola Parabola Center:_____________ Radius: ___________

B. ( )

( )

Circle Ellipse Hyperbola Parabola Center:_____________

Distance from center to major vertices:______ Distance from center to minor vertices:______ Distance from center to foci:______

C. ( )

( )

Circle Ellipse Hyperbola Parabola Center:_____________

Distance from center to vertices:______ Distance from center to foci:______ Is transverse axis vertical or horizontal?___________

D. y = -8(x – 1)2

+ 3Circle Ellipse Hyperbola Parabola Vertex:______ Opens: Up Down Left Right Distance from vertex to focus:______ Equation of axis:___________ Equation of Directrix:___________

E. 2x 2 + 3y 2 – 4x + y = 49 Circle Ellipse Hyperbola Parabola

F. 2x 2 – 3y 2 – 4x + y = 49 Circle Ellipse Hyperbola Parabola

G. 2x 2– 4x + y = 49 Circle Ellipse Hyperbola Parabola

H. 3x 2

+ 3y 2

– 4x + y = 49 Circle Ellipse Hyperbola Parabola

32. (Ch 13) Give the equation of a parabola which has its focus at (2, 0) and directrix x = – 2. Graph and fill in the

other information below. Equation of parabola: Vertex: Equation of Axis: Focus: (2, 0) Equation of Directrix:

33. (Ch 13) A. Write the equation of a circle with center at the origin and radius of 1:_________________________ B. In trig, what name do we give to this circle? ______________________

34. (Ch 13) Graph (x – 3)2 + (y + 2)

2 = 25.

Center: Radius:

35. (Ch 13) ( )

( )

Graph the conic section labeling key pts and fill in the other information below.

Center: Intercepts: Foci: Length of Major Axis: Length of Minor Axis:

36. (Ch 13) ( )

Graph the conic section labeling key pts and fill in the other information below.

Center: Intercepts: Foci: Equation of Transverse Axis:

37. (Ch 13) Convert 4x2+ 4y

2 + 8x – 16y – 20 = 0 to standard/graph form. Then graph the conic section labeling

key pts. 38. (Ch 17) Graph each basic trig function labeling key pts and equations of asymptotes: A. y = sin x and y = csc x B. y = cos x and y = sec x C. y = tan x D. y = cot x

*For these inverse trig functions, be sure to restrict the domain and range to the accepted 1-1 sections!

E. y = sin -1

x F. y = arc cos x G. y = tan -1

x

39. (Ch 17) Fill in the blanks below and graph (labeling key pts): y = 1 –

cos 2x

Amplitude: Period: Phase Start: Phase End:

40. (Ch 17) Fill in the blanks below and graph (labeling key pts): y = 2 sin (

)

Amplitude: Period: Phase Start: Phase End:

41. (Ch 17) Fill in the blanks below and graph (labeling key pts): y = csc (

)

Period: Phase Start: Phase End: 42. (Ch 18) Write the definitions of the six trig rations in the unit circle (when hypotenuse = 1) and using SOHCAHTOA

(when hypotenuse ≠ 1).

sin cos tan cot csc sec

In Unit Circle

When hyp ≠ 1

43. (Ch 18) Write 3 different Pythagorean Identities so that all six trig ratios appear somewhere in your answers. A. B. C. 44. (Ch 18) Use a Pythagorean Identity to complete each equation below.

A. 1 – sin2x = B. csc2x = C. tan2x + 1 = 45. (Ch 18) Complete the Cofunction Identities:

A. sin (

) = B. sec (

) = C. csc ( ) =

D. Given sin 17o = a, what conclusion can you reach using a Cofunction Identity?______________________ 46. (Ch 18) Complete the Negative Angle Identities: A. sin ( ) = B. cos ( ) = C. tan ( ) = D. csc ( ) = E. sec ( ) = F. cot ( ) =

G. Given sin 17o = a, what conclusion can you reach using a negative angle identity?______________________

H. Given cos 147o = b, what conclusion can you reach using a negative angle identity?_____________________

47. (Ch 18) Use trig identities (on each side without crossing over) to verify the identity:

A. ( )

B.

Sum and Difference Identities (Section 18.3 - 18.4)

( ) ( )

( )

( ) ( )

( ) 48. (Ch 18) Which expression is equivalent to sin(50o) cos(12o) – cos(12o) sin(50o) 48. _________

A. sin(50o) B. sin(62o) C. sin(38o) D. cos(38o) E. tan(62o)

49. (Ch 18) Use a Sum Identity to find the value of cos (75o) Hint: 75o = 45o + 30o 49. __________________

50. (Ch 18) Given cos s =

and sin t =

and angles s & t are in quadrant IV. 50. sin s = ____________________

Place your answer in the blank for each value.

cos t = ______________________

sin (s – t) = ___________________

51. (Ch 18) Use your Trig Identity Handout or p834 of your textbook to name the type of identity used below: sin 38o = 2sin19ocos19o

52. (Ch 19) Simplify each. Be sure you are using the proper restrictions for each inverse trig function.

A. ( √

) B. cos

-1 ( ) = C. tan-1

( ) =

D. arc cos ( ) = E. arc tan ( √ ) = F. ( √

)

D. arc sin (

) = E. arc tan (

√ ) = F. (

)

53. An angle , in standard position, terminates at the point ( 7, 24). Find cot . 54. Given sin = ¼ and tan < 0. cos = _________ tan = _______ ends in quadrant ______ 55. (Ch 18 & 19) Solve each trig equation.

A. Find all x in [0, 2 ]: B. Find ALL solutions (using n form):

C. Find all x in [0, 2 ]: D. Find ALL solutions (using n form):

(Common Functions & Transformations – all chapters mixed)

56. Given the graph of f(x) shown:

A. Graph f(–x) + 2

B. Graph – f(x + 2)

57. Sketch a graph for each. Label key pts or axis tick marks and equations of asymptotes.

A. f(x) = 3 B. g(x) = x C. f(x)= |x| D. g(x) = –|x–1|

E. f(x) = √ F. g(x) =2 – √ G. f(x)= √

H. g(x) = x3

58. (Ch 12.4) Graph each rational function. Label all key pts and give equations of asymptotes.

A. f(x) =

B. f(x) =

C. f(x) =

1

1

-1 -1 3 -3

3

-3

f(x)

59. Graph each piece-wise defined function.

A. ( ) {

B. ( ) {

√

60. Give the Domain of 59A:_____________________ Range of 59A:______________________________ (Mixed Practice) True or False.

61. The logarithm of 32 in base 2 is 5. 62. Division is commutative. 63. Addition is commutative. 64. (0, 1) is a point on the graph of y = cos x. 65. The amplitude of y = 3 cos 2x is 2. 66. The period of y = 3 cos 2x is π.

67. The graph of y = cot x has asymptotes at x =

and x =

.

68. The range of y = cos x is * +.

66. y = 2– x

and y = (½)x have the same graph.

67. The graphs of y = e– x

and y = ex are reflections across the y-axis.

68. The graphs of y = – e x and y = e

x are reflections across the x-axis.

69. If a > 1 and ax = a

y, then x = y.

70. (0, 1) is a point on the graph of y = ex.

71. y = 0 is an asymptote of the graph of y = ex.

72. The graph of 4x2 – 4y

2 + x – 6y + 10 = 0 is a circle.

73. The graph of 4x2+ x – 6y + 10 = 0 is a parabola.

74. The length of the major axis of ( )

( )

is 10.

75. The equation of the axis of x = (y + 1)2 – 3 is y = – 1

76. log 5x2 is equivalent to (log 5 + 2log x).

77. For f(x) = 7x5 – 6x

3 + 2x – 1, as x , y .

78. For f(x) = 7x5 – 6x

3 + 2x – 1, as x , y .

79. For f(x) = –

, as x , y .

80. For f(x) = –

, the domain is * +.

81. f(x) = –

has a horizontal asymptote at y = 2.

82. f(x) = –

has a vertical asymptote at x = 5.

83. f(x) = –

has a y-intercept of

.

84. f(x) = –

has an x-intercept of

.

85. sin2x – 1 = cos

2x.

86. Which is the equation of the graph shown?

A.

B. √

C. √

D. √

E. none of these

87. Which is the graph of f(x) = (

)

?

88. In which of these graphs is y quadratic while x is linear? A. B. C. D. E. none of these 89. Find the balance if $12,000 is invested for 18 years at 4% annual interest. . . (You need not memorize these formulas)

A. compounded monthly:

B. compounded continuously:

90. Expand: (x + 2)5

91. Expand: (x + 3)3

(0, 3)

(– 5, 0) (5, 0)

𝐴 𝑃 ( 𝑟

𝑛)𝑛𝑡

𝐴 𝑃𝑒𝑟𝑡

92. Factor: f(x) = 8x3 – 27

93. Find all the complex zeros of f(x) = 8x3 – 27

94. (Ch 20.4) Use the figure to find: a + b, a – b, – a. Use (x, y) notation. 95. Given vectors a = – i + 2j, b = i – j. Find: 2a, 2a + 3b, b – 3a

96. Sketch the resultant for vectors u and w with angle between them. |u| = 8, |w| = 12, = 30o 97. Find the magnitude and direction angle for vector u: <–7, 24> 98. Write the vector in <–7, 24> form.

99. Given forces of 283 and 125 newtons, forming an angle 132o, find the magnitude of the resultant force.

Due Date: Friday, 5/16 Name__________________________________ ____/10 You will tear off this page and turn it in to be scored. 100. Find and watch 8 review videos that help you review topics that are difficult for you. Be sure the URL addresses

are complete, so Ms. H can view your videos.

URL Topic(s) Covered What did you learn or re-learn?

1.

2.

3.

4.

5.

6.

7.

8.