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Pre-Calculus Practice Final Spring 2010
Use a graph of the sine function to find the value of  for which sin   1.
1.
A.     2k
B.  
A.   0  k
3.
D.  
3
 k
2
D.     k
C.   0  2k
B. 178.76°
C. 1.06°
D. 312.10°
Find the arc length of a central angle of 110° in a circle of radius 7 cm.
A.
77
cm
36
B.
18
cm
77
C. 110 cm
D.
77
cm
18
Find the area of a sector with a central angle of 225° and a radius of 6 cm.
A. 331.7 cm 2
B. 110.4 cm 2
C. 29.4 cm 2
D. 70.7 cm 2


Find the amplitude, period, and phase shift of f ( x)  4 cos     6.
2

A. amplitude = -6
B. amplitude = 6
Period = 4 
Phase shift = 
Period = 
Phase shift = 2 
3
2
C. amplitude = 6
Period =
D. amplitude = 4

Phase shift =
3
2
Write an equation of the sine function with amplitude 35.7 and period
A. y  35.7 sin 8 x
8.
C.     k
Change 3.12 radians to degree measure. Round to the nearest hundredth.
4.
7.
2
 2k
B.     2k
A. 199.40°
6.

Use a graph of the cosine function to find the value of  for which cos  = -1.
2.
5.
Name________________
B. y  2 sin 8 x
1
1
C. y   sin( x)
2
8
Period = 4 
Phase shift = -2 

.
4
D. y  35.7 sin 4 x
What basic trigonometric identity would you use to verify that tan x cos x = sin x?
A. sin 2 x  cos 2 x  1
B.
sin x
 tan x
cos x
C.
1
 csc x
sin x
D.
cos x
 cot x
sin x
9.
What basic trigonometric identity would you use to verify that
A. cos x =
10.
1
tan x
C. sin 2 x + cos 2 x = 1
B. sin 2 x + cos 2 x = 1
C. csc x =
D. 1 + cot 2 x = csc 2 x
sin x  1
 1  csc x ?
sin x
1
sin x
D. 1 + cot 2 x = csc 2 x
Write an equation of the sine function with the given amplitude, phase shift, and vertical shift .
C
3

amplitude = 50, period =
, phase shift = , vertical shift = -25.
4
2
8
4
4 
8
A. y  50sin(    )  25
B. y  50sin   
  25
3
3
3 
3
8
4
4 
8
D. y  50sin(    )  25

25
C. y= 50sin   

3
3
3
3

12.
sin x
B.
 tan x
cos x
What basic trigonometric identity would you use to verify that
A. cot x =
11.
1
sec x
sin 2 x  cos 2 x
 sec x ?
cos x

1
and sec < 0, find cos and tan  .
3
2
1
1
1
A. cos   and tan  
B. cos    and tan  
3
3
3
2
2
1
2
2
C. cos    and tan   
D. cos   and tan  
3
2
3
1
Given sin  
13.
Find csc x if cos x tan x =
A. csc x = 5
14.
2
.
5
B. csc x = 
Find tan x if cos x tan x sec x =
A. 7
15.
B.
5
2
C. csc =
5
D. csc x =
5
.
7
5
7
C.
7
5
D.
5
D.
2 6
4
Find the exact value of sin 255°.
A.
6 2
4
B.
 2 6
4
C.
2 6
4
5
2
If  and  are angles in Quadrant I, cos  
16.
A.
17.
56
65
B.
16
65
4
5
and sin   , find cos(   ).
5
13
C.
63
65
D.
33
65
Which sum or difference identity would you use to verify that cos(90   )  sin  ?
A. cos(   )  cos  cos   sin  sin 
B. cos(   )  cos  cos   sin  sin 
C. cos(   )  cos  cos   sin  sin 
D. cos(   )  cos  cos   sin  sin 
If sin  
18.
A.
5
and θ terminates in the first quadrant, find the exact value of sin 2θ.
13
120
169
B.
If csc   
19.
A.
20.
10
13
25
169
C.
D.
10
26
5
and θ terminates in the third quadrant, find the exact value of tan 2θ.
3
24
25
B.
7
25
24
7
C.
D.

7
25
Use a half angle identity to find the exact value of cos 165°.
2 3
2
A.
2 3
4
B.
C.
2 3

2
D.
0.966
Solve 2 cos x  1  0 for 0  x  2 .
21.
A.

6
and
5
6
B.
C.

2
and
3
3

3
and
5
3
D.
Solve 4cosx – 2 = 0 for 0° ≤ x ≤ 90°.
22.
A. 30°
23.
Solve
A.
B. 60°
2 cos 2 x  cos x  1  0
0 and120
C. 60
C.
120°
for principal values of x.
B. 30
D.
0 and 60
D.
150°
7
11
and
6
6
24.
Write the standard form of the equation of the line for which the length of the normal is 6 and
makes an angle of 120° with the positive x-axis.
A.
x  3 y  12  0
B.
C.
3 x  y  12  0
D.
25.
x  3 y  12  0
3 x  y  12  0
Write the equation 3x +4y -7 = 0 in normal form.
A.
3
4
7
x y 0
5
5
5
B.  x 
3
5
D.
C.  x 
26.
3
5
4
7
y 0
5
5
4
7
y 0
5
5
3
4
7
x y 0
5
5
5
Find the distance between (-4,3) and the line with equation 2x-5y=-7
A.
27.
B. 0
14 29
29

C.
16 29
29
16 29
29
D.
Find the slope of the line passing through (5, 2) and (-2, 3).
A.
28.

B.
1
7
-1
D.
1
9
C.
5
Write the equation of the circle with the center at (4, -3) and a radius of 3.
A.
(x + 3)2 + (y – 4)2 = 9
C. (x - 3)2 + (y + 4)2 = 3
B. (x - 4)2 + (y + 3)2 = 9
D. (x - 4)2 + (y - 3)2 = 3
Write the equation of the circle 6 x 2  12 x  6 y 2  36 y  36 in standard form.
29.
A.
C.
( x  3) 2   y  1  16
2
 x  1   y  3
2
2
 16
B.
D.
 x  2
2
2
 x  1
3
 y  3

2
4
2
 y  3

2
1
2
1
Sketch the graph of (x + 3)2 + (y -2)2 = 4.
30.
y
y
A.
B.
4
4
2
2
-4
-4
x
-2
x
-2
-2
-2
-4
-4
y
C.
y
D.
4
4
2
-4
2
x
-2
-4
x
-2
-2
-2
-4
-4
x2
31. Which of the following is the graph of 9 + y 2 = 1?
A.
y
B.
y
x
C.
y
x
D.
x
y
x
32.
A.
x2 y 2
Graph

1
25 16
y
B.
y
x
C.
x
D.
y
y
x
x
Fix graph c. Graph y2 = 4x + 12
33.
A.
y
B.
y
x
x
C.
y
D.
x
y
x
Fix question Write the equation of the parabola y = 4x2 – 8x – 9 in standard form.
34.
A.
 y  9  4( x 1)2
C.
1
 y  9   ( x  1)2
4
D. 4  y  9   ( x  1)
2

Simplify each expression 2x 3 y 4
35
8x 6
y12
A.
  32 
Evaluate  64 


36
A.
-8
B.

1
 y  9   ( x  1)2
4
B.

2
y 12
8x 6
C.
y12
8x6
D.
y8
4 x6
C.
8
D.
-4
1
3
B. 4
Solve the equation 4  4  2 3 x2
37.
A.
38.
8.6
B. 8.6, -8.6
C.
8
D.
-8, 8
A corporate jet originally cost 15,000,000. If it depreciates by 4% per year compounded yearly.
What will its value be after 10 years?
A.
39.
$8,981,054.09
B. $24,433,419.40
C. $9,972,.489.54
D.
$8,079,226.71
In the first week of it release, the latest best selling books sold 400,000. The publishers use the
formula P = P0e -0.4t to predict future sales t weeks after the release. Use this equation to predict
the sales to the nearest 100 after 4 weeks.
A.
40.
20,400
B. 80,758
C.
12,266,300
D.
0
If the Chang family deposits 1,300 in a savings account at 6.5% interest, compounded continuously,
how much will be in the account after 20 years?
A.
$4,770.09
B. $1,387.30
C.
$27,746.13
D.
$10,165.00
41.
Evaluate: log 4
A.
1
64
3
C.
-6
D.
-3
C.
5
D.
125
B. -0.1249
C.
-0.0706
D.
1.8751
B. 26.454
C.
0.515
D.
1.186
B. 5208.333
C.
625
D.
1397.542
B. 1.093
C.
5404.704
D.
2.518
B. 2.497
C.
5.841
D.
5.366
B. 1.267
C.
0.980
D.
-0.054
B.
1
6
Evaluate: log 4 x  3
42.
A.
43.
64
B.
3
5
3
Evaluate: log 0.85
A.
44.
0.01249
Find antilog 1.4225
A.
1885.385
3
4
Solve: x  125
45.
A.
976562.5
Solve: log 2 2.13  x
46.
A.
47.
3.632
Find ln 344.
A.
5.366
Solve e3x = 7.1
48.
A.
49.
0.653
Find the amount of time required to triple an amount at 15% if the interest is compounded
continuously.
A.
18.31 years
B. 12.21 years
C.
3.91 years
D.
7.324 years