Are You suprised
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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. _______
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PART II: ANSWER SHEET
31. ________________
32. __________________
33. _________________
34. _________________
35. _________________
36. ________________
37. ________________
38. ________________
39. ________________
40. ________________
41. ________________
42. ________________
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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. ___________
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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) __________
-----------------------
16
56
A
B
C
F
E
D
86
56
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( , )
a
( , )
( , ) [pic] ) [pic]
b
( , )
x
y
x
y
x
y
x
y
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y
x
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C
B
A
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