PRECALCULUS: MIDTERM Review
2011-2012
NAME ____________________
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 f  g .
a) 3x2  13
b) 9x2 + 30x + 19
c) 3x2  18
d) 3x  1
5) Find f
1
.
a)
x5
3
b) 3x  5
c)
x5
3
d)
1
3x  5
#68 Choose the letter of the graph that represents each of the following.
6) y = 3x2 - 4
7) f(x) = x3 + 1
8) y = x + 2
a)
b)
c)
d)
a)
b)
c)
d)
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
a) y – 3 =
5
(x – 2)
4
b) y – 2 =
5
(x + 3)
4
c) 5x – 4y = 22
11) The graph of f(x) = x2 - 9 has which symmetry?
a) x-axis
c) origin
b) y-axis
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 +
a) (0, )
b) (5, )
x  7 is which of the following?
c) [0, )
d) [5, )
5
.
4
d) 5x – 4y = 13
x 2  5x  6
x 2  3x  4
14) What are the domain restrictions for g(x) =
a) x  -6, 1
c) x  -4, 1
b) x  6, -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 =
1
x3
b) y = 16  x
c) y2 =
16
x
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
c) 290
b) 430
5
radians.
6
2
5
b)
c)
3
6
d) 790
19) Find the reference angle for
a)

3
d)

6
20) Convert
5
to degrees.
3
a) 900
b) 600
c) 300
21) Convert 120 to radians.
a)
2
3
b)
4
3
c)
5
6
d) 4.1888
22) Which expression is NOT equal to sin ?


a) cos    
2

b)
1
csc 
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)
left
2
d) 108
26) What is the period of the graph of y = 4tan x?

a)  b) 4
c)
d) 2
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
2
.
2
28) Determine two values of  if 0   < 2 and cos  =
a)
 3
,
4 4
b)
 5
,
4 4
c)
 7
,
4 4
d) none of these
29) If sin  is odd, then which of the following is TRUE?
a) sin() = sin 
c) sin  = sin 
b) sin(-) = sin 
d) sin  = sin 
30) Which of the following is an identity for tan ?
1
cos 
cot 
sin 
a)
b)
c)
d)
cos 
sin 
1
cos 
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.
B
31) Use this diagram to find  B.
13
A
a
27
C
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  =
35) Determine the EXACT value of sec  if
5
.
13
3

    and sin  =
.
2
2
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) =
7 x
40) g(x) =
1
x2
Find the range of each function.
41) f(x) =
7 x
42) g(x) =
1
x2
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
x , x0
62) y = 4cos (3x - )
63) y = 3sin (2x + ) + 1

1
64) y = sec  x  
2
2
1 
65) y = csc  x 
3 
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) 4 x 3  9 x 2  2 x  0
72) 4 x3  25 x
Solve #73 - 75 using triangle.ABC and #76 use triangle DEF. Round answers to the nearest tenth.
B
73) c =?
74)  B = ?
76) Let D = 36, d = 8, e = 5.
75)  A =?
f  _________
E
5
6
C
A
1
6
D
77) Use your calculator set in degree mode evaluate csc95 .
78) Write the equation of the line that passes through the points  2,5 and  4,7 .
79) Using the function f x   x 2  3 simplify the quotient.
f  x  2   f 2 
.
x
8
6
F
5
6
80) Write the equation of the line that is perpendicular to the line 3x  6 y  11 and passes through
the point  3,2 .
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.
3  

  
84) Give the slope of the line through points  sin ,   and  cos ,  .
2 2
2 


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
PART I: ANSWER SHEET
NAME ____________________
DATE __________ PER _____
1. _______
11. _______
21. _______
2. _______
12. _______
22. _______
3. _______
13. _______
23. _______
4. _______
14. _______
24. _______
5. _______
15. _______
25. _______
6. _______
16. _______
26. _______
7. _______
17. _______
27. _______
8. _______
18. _______
9. _______
19. _______
10. _______
20. _______
28. _______
29. _______
30. _______
PART II: ANSWER SHEET
31. ________________
37.________________
43.________________
32.__________________
38.________________
44.________________
33._________________
39.________________
45.________________
34._________________
40.________________
35._________________
41.________________
36.________________
42.________________
PRECALCULUS: MIDTERM EXAM
PART II: ANSWER SHEET (cont)
#46 - 60
NAME ____________________
DATE __________ PER _____
DEGREES
(
y
(
POINT
,
RADIANS
)
,
)
(
,
(
)
,
)
(
x
y
61)
(
,
,
)
)
)
y
x
62)
x
y
y
x
63)
x
64)
y
y
x
65)
x
66)
PRECALCULUS: MIDTERM EXAM
PART III: ANSWER SHEET
NAME ____________________
DATE __________ PER _____
USE a GRAPHING CALCULATOR.
67. __________
76. ___________
68. __________
77. ___________
69. __________
78. ___________
70. __________
79. ___________
71. __________
80. ___________
72. __________
81. ___________
73. __________
82. ___________
74. __________
83. ___________
75. __________
84. ___________
#85 - 95 TRUE or FALSE. Explain why you chose FALSE.
85)
__________
86)
__________
87)
__________
88)
__________
89)
__________
90)
__________
91)
__________
92)
__________
93)
__________
94)
__________
95)
__________