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|PRECALCULUS: MIDTERM Review NAME ____________________ |

|2011-2012 DATE __________ PER ______ |

PART I: Multiple Choice: Choose the letter of the BEST answer. Write answers on the answer sheet. Do/show all necessary work on this paper. This section would be similar to a NO CALCULATOR section on your midterm.

Let f(x) = 3x + 5 and g(x) = x2 ( 6.

1) Find f(4). a) 12 b) 17 c) 10 d) 60

2) Find g(-3). a) -15 b) 15 c) 0 d) 3

3) Find (f + g)(x).

a) x2 + 3x + 1 b) x2 + 3x – 11 c) x2 + 3x ( 1 d) x2 + 3x + 11

4) Find [pic].

a) 3x2 ( 13 b) 9x2 + 30x + 19 c) 3x2 ( 18 d) 3x ( 1

5) Find [pic]. a) [pic] b) 3x ( 5 c) [pic] d) [pic]

#6(8 Choose the letter of the graph that represents each of the following.

6) y = 3x2 - 4 a) b)

c) d)

7) f(x) = x3 + 1 a) b)

c) d)

8) y = (x + 2( a) b)

c) d)

9) Which graph is the reflection of this figure about the y-axis?

a) b)

c) d)

10) Give the equation of the line passing through (2,-3) with a slope of [pic].

a) y – 3 = [pic](x – 2) b) y – 2 = [pic](x + 3) c) 5x – 4y = 22 d) 5x – 4y = (13

11) The graph of f(x) = x2 - 9 has which symmetry?

a) x-axis b) y-axis

c) origin d) no symmetry

12) What is a point with origin symmetry with (-5,3)?

a) (0,0) b) (-5,-3) c) (5,3) d) (5,-3)

13) The range of g(x) = 5 + [pic] is which of the following?

a) (0, () b) (5, () c) [0, () d) [5, ()

14) What are the domain restrictions for g(x) = [pic]

a) x ( -6, 1 b) x ( 6, -1

c) x ( -4, 1 d) x ( 4, -1

15) What is the inverse for the relation {(0,-2), (4,-1), (-7,2)}?

a) {(0, 2), (-4,1), (7,-2)} b) {(0,2), (4,1), (7,2)}

c) {(0,-2), (-4,-1), (-7,-2)} d) {(-2,0), (-1,4), (2,-7)}

16) Which equation is NOT a function?

a) y = [pic] b) y = [pic] c) y2 = [pic] d) xy = 12

17) A rotation of (920( lies in which quadrant?

a) I b) II c) III d) IV

18) Which angle is NOT coterminal with 70(?

a) (360( b) 430( c) (290( d) 790(

19) Find the reference angle for [pic] radians.

a) [pic] b) [pic] c)[pic] d) [pic]

20) Convert [pic] to degrees.

a) 900( b) 600( c) 300( d) 108(

21) Convert 120( to radians.

a) [pic] b) [pic] c)[pic] d) 4.1888

22) Which expression is NOT equal to sin (?

a) cos [pic] b) [pic] c) 1 – cos2 ( d) tan ( cos (

23) In which quadrant is sec ( < 0 and tan ( > 0?

a) I b) II c) III d) IV

24) The amplitude of the graph of y = (2cos 3x is what value?

a) 2 b) (2 c) 3 d) (3

25) What is the phase shift of the graph of y = 4sin(2x + ()?

a) ( left b) ( right c) 2( right d) [pic] left

26) What is the period of the graph of y = 4tan x?

a) ( b) 4 c) [pic] d) 2

27) Which one of the following does NOT have a period of 2(?

a) sec x b) csc x c) cot x d) sin x

28) Determine two values of ( if 0 ( ( < 2( and cos ( = [pic].

a) [pic], [pic] b) [pic], [pic] c) [pic], [pic] d) none of these

29) If sin ( is odd, then which of the following is TRUE?

a) sin((() = sin ( b) sin(-() = (sin (

c) sin ( = sin ( d) sin ( = sin (

30) Which of the following is an identity for tan (?

a) [pic] b) [pic] c) [pic] d) [pic]

PART II: Free Response. Complete the following. Do/show all necessary work

on this paper Write answers on the answer sheet. Write all interval answers in

interval notation form.

31) Use this diagram to find ( B.

32) Find side a to the nearest whole number.

NOTE: sin 27( ( 0.4540; cos 27( ( 0.8910; tan 27( ( 0.5095

33) ( is an angle in standard position whose terminal side contains ((1,(3).

Identify the EXACT value of csc (.

34) Find the EXACT value of cos (, if ( is in quadrant III and sin ( = [pic] .

35) Determine the EXACT value of sec ( if [pic] ( ( ( ( and sin ( = [pic].

36) Find the EXACT value of sin ( for an angle ( in standard position which passes through the point (8, (15).

37) Where are the asymptotes for the graph of the tangent function located?

38) Solve tan 200o cot (-346o)

Find the domain of each function.

39) f(x) = [pic] 40) g(x) = [pic]

Find the range of each function.

41) f(x) = [pic] 42) g(x) = [pic]

Use the graph of the function shown below to answer the questions.

43) Determine the zeroes of f(x)..

44) State all intervals over which f(x) is decreasing.

45) Determine f(2).

#46 - #60 Completely label Quadrant I of the unit circle.

(see answer sheet)

Graph and label each of the following on the answer sheet.

61) f(x) = 2x - 3, x ( 0 62) y = 4cos (3x - ()

[pic] , x ( 0

63) y = 3sin (2x + () + 1 64) y = sec [pic]

65) y = csc [pic] 66) y = tan (4x + ()

PART III: Use a graphing calculator.

Use f(x) = x2 + 2x - 8 to identify each of the following.

67) axis of symmetry 68) vertex

60) x-intercepts 70) y-intercept

Solve each equation for x.

71) [pic] 72) [pic]

Solve #73 - 75 using triangle.ABC and #76 use triangle DEF. Round answers to the nearest tenth.

73) c =? 74) ( B = ? 75) ( A =?

76) Let (D = 36(, d = 8, e = 5. f ( _________

77) Use your calculator set in degree mode evaluate [pic].

78) Write the equation of the line that passes through the points [pic].

79) Using the function [pic] simplify the quotient. [pic].

80) Write the equation of the line that is perpendicular to the line [pic] and passes through

the point [pic].

81) The angle of elevation from a ship on the ocean to the top of a cliff 50 feet high is 21(. How far is the ship from the base of the cliff? (Round the answer to the nearest foot.)

82) A street light is positioned 9 feet above the street level. It illuminates a walk all the way to the curb which is 25 feet away. Find the angle of depression from the light to the curb. (Round the answer to the nearest tenth of a degree.)

83) Find the real zeros of y = 8x3 – 125.

84) Give the slope of the line through points [pic] and [pic].

Classify the following statements as TRUE or FALSE. Explain why you chose FALSE either in words or show what the right answer should have been!

85) The number 2.17849987 rounded to three decimal place accuracy is 2.179.

86) ( is a quadrantal angle measure.

87) y = x3 is a function.

88) f-1(x) is the notation for the reciprocal of f(x).

89) A function is a relation in which each element in the domain is mapped to exactly

one element in the range.

90) A one-to-one function passes both the vertical and horizontal line tests.

91) Another name for the root, or zero, of a function is the “y-intercept”.

92) The secant is the reciprocal for the sine.

93) The six trigonometric functions must have their domains restricted in order to

have inverse functions.

94) The Pythagorean Theorem can be used to find the third side in any triangle given

two other sides.

95) An angle of elevation is measured from a horizontal reference line.

PRECALCULUS: MIDTERM EXAM NAME ____________________

PART I: ANSWER SHEET DATE __________ PER _____

1. _______

2. _______

3. _______

4. _______

5. _______

6. _______

7. _______

8. _______

9. _______

10. _______

11. _______

12. _______

13. _______

14. _______

15. _______

16. _______

17. _______

18. _______

19. _______

20. _______

21. _______

22. _______

23. _______

24. _______

25. _______

26. _______

27. _______

28. _______

29. _______

30. _______

PART II: ANSWER SHEET

31. ________________

32. __________________

33. _________________

34. _________________

35. _________________

36. ________________

37. ________________

38. ________________

39. ________________

40. ________________

41. ________________

42. ________________

43. ________________

44. ________________

45. ________________

PRECALCULUS: MIDTERM EXAM NAME ____________________

PART II: ANSWER SHEET (cont) DATE __________ PER _____

#46 - 60 DEGREES POINT RADIANS

y

61) 62)

63) 64)

65) 66)

PRECALCULUS: MIDTERM EXAM NAME ____________________

PART III: ANSWER SHEET DATE __________ PER _____

USE a GRAPHING CALCULATOR.

67. __________

68. __________

69. __________

70. __________

71. __________

72. __________

73. __________

74. __________

75. __________

76. ___________

77. ___________

78. ___________

79. ___________

80. ___________

81. ___________

82. ___________

83. ___________

84. ___________

#85 - 95 TRUE or FALSE. Explain why you chose FALSE.

85) __________

86) __________

87) __________

88) __________

89) __________

90) __________

91) __________

92) __________

93) __________

94) __________

95) __________

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16

56

A

B

C

F

E

D

86

56

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( , )

( , ) [pic] ) [pic]

b

( , )

x

y

x

y

x

y

x

y

x

y

x

y

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13

C

B

A

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