Pre-Calculus Honors
Final Exam Review
Chapter 4
Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
1. A tower that is 125 feet tall casts a shadow of 172 feet. Find the angle of elevation of the sun to the nearest
degree.
a. 40 
b. 37 
c. 36 
d. 41
e. 48
3
2. If arctan     then
5
3
3
3
3
a. cot   
b. tan  
c. sin  
d. tan   
e. sin   3
5
5
5
5
3. The horizontal translation of the function f ( x)  2  4 cos4x  5 is
a. exactly two units to the right
b. exactly five units to the left

c. exactly 1.25 units to the right
d. exactly
units to the left
2
e. exactly five units to the right
4. A student looks out a second-story school window and sees the top of the school flagpole at an angle of
elevation of 22o. The student is 18 ft. above the ground and 50 ft. from the flagpole. Find the height of the
flagpole.
a. 21.8
b. 23.5
c. 38.2
d. 48.6
e. 58.2
5. cos( ) is equivalent to which of the following?
a.  cos 
b. cos 
c. sin 
d.  sin 
e.  cos( )
6. Which of the following is an even function?
a. sin 
b. tan 
c. csc
d. cos(  1)
e. sec
7. An airplane flying at 490 mph has a bearing of N 27E . After flying for two hours how far north and how
far east has the plane traveled?
a. 444.9 mi. N,
873.2 mi. E
8. If sin( x) 
a.
5
7
b. 873.2 mi. N,
444.9 mi. E
c. 436.6 mi. N,
222.5 mi. E
d. 222.5 mi. N
436.6 mi. E
e. 237.1 mi. N,
452.8 mi. E
5
then sin( x ) equals:
7
b. 45.58
c. -45.88
d. 
5
7
e.  74
2
then sec( x) equals:
3
2
3
2
3
a. 
b. 
c.
d. 13
e.
3
2
3
2
10. A 50 meter line is used to tether a helium filled balloon. Because of a breeze, the line makes an angle of
71 with the ground. What is the height of the balloon?
9. If cos( x) 
a. 16.3 m
b. 47.3 m
c. 145.2 m
d. 39.7 m
e. 24.8 m
11. Determine the exact value of csc  given (7 , -10) on the terminal side of the angle in standard position.
51
149
51
10
7
a. 
b. 
c. 
d. 
e.
7
10
10
149
51
12. Determine the exact value of sin  given (-4 , -10) on the terminal side of the angle in standard position.
a. 
116
10
116
4
c. 
b.  5 29
29
5
d. 
e. 
5 29
29
13. Determine the exact value of cos given (-2 , 3) on the terminal side of the angle in standard position.
a. 
2 5
5
b. 
2 13
13
c. 
3 5
5
d. 
3 13
13
e.  2 5
14. State the reference angle for   211 .
a. 149
b. 571
c. 59
d. 49
e. 31
c.  45
d.  75
e. 75
c. 22
d. 68
e.  22
c. III
d. IV
c. III
d. IV
c. III
d. IV
c. III
d. IV
15. State the reference angle for   315 .
a. 45
b. 135
16. State the reference angle for   292 .
a. 112
b.  68
17. Determine the quadrant for  
a. I
b. II
18. Determine the quadrant for  
a. I

10
7
.
4
b. II
19. Determine the quadrant for   
a. I
.
2
.
3
b. II
20. Determine the quadrant for   910 .
a. I
b. II
21. Determine the quadrant for   550 .
a. I
b. II
c. III
22. Find the complement and supplement for  
a.

2
,
b. none , 
c.


d. IV
3
2
6 3
,
d. 
5 7
,
3
3
3
in terms of degrees. Round if necessary.
2
a. 90
b. 180
c. 240
d. 300
7
24. Express the angle 
in terms of degrees. Round if necessary.
6
a.  420
b.  315
c.  330
d.  210
e.
2 5
,
3
3
23. Express the angle
e. 270
e.  300
25. Express the angle
a. 480
8
in terms of degrees. Round if necessary.
3
b. 310
c. 60
d. 120
e. 150
26. Express the angle -1.7 in terms of degrees. Round if necessary.
a.  306
b.  97.4
c.  0.03
d. 102
e.  138.3
d. 900
e. 7.86
27. Find the arc length given r  5 and   180 .
a. 10
b. 15.71
28. Find the arc length given r  4 and  
a. 4
b. 45
29. Find the arc length given r  7 and  
a. 13.19
b. 15.43
c. 36

4
.
c. 180
d. 3.14
e. 5.18
3
.
5
c. 756
d. 151.61
e. 4.24
30. An airplane flying at 520 mph has a bearing of S 58W . After flying for 1.5 hours, how far south and how
far west has the plane traveled?
a. 661.5 mi. S,
413.3 mi. W
b. 275.6 mi. S,
c. 441.0 mi. S,
d. 413.3 mi. S
e. 388.5 mi. S,
441.0 mi. W
275.6 mi. W
661.5 mi. W 511.9 mi. W
31. At a point 150 feet from the base of a building, the angle of elevation to the top of the building is 35 , and
the angle of elevation to the top of the flag pole that sits atop the building is 40 .
Find the height of the flag pole.
a. 105.0 feet
b. 86.0 feet
d. 16.4 feet
e. 20.8 feet
32. Given y  5 sin 2x     10 state the period.
2
a. 2
b. 5
c.

33. Given y  5 sin 2x     10 state the vertical shift.
d. 2
e. 
a. 10
d. 2
e. 
d. 2
e. 
d. 3
e. 6
b. 5
c. 125.9 feet
c. -5
34. Given y  5 sin 2x     10 state the amplitude.
a. -5
b. 10
 x
35. Given y  tan   state the period.
3

a.
b. 2
3
36. Given y  3 tan( 2 x) state the period.
a. 2
b. 
c. 5
c.
2
3
c. 3
d.

2
e. 4


37. Given y  3 cos x     6 state the period.
4


a. 4
b. 8
c.
4


38. Given y  3 cos x     6 state the phase shift.
4

a. 
b. 4
c.  


39. Given y  3 cos x     6 state the vertical shift.
4

a. 6
b. -3
c. -6

40. Simplify sec arcsin

4
a.
b.
5
3
.
5
5
3
5

41. Simplify cot arccos  .
13 

5
12
a.
b.
12
13

 3 
42. Simplify sin  arctan    
 7 

7 58
 3 58
a.
b.
58
58
d.
1
8
d. 
e. 8
1
4
d. 3
e. -4
e. 
c.
3
5
d.
4
3
e.
5
4
c.
13
12
d.
12
5
e.
5
13
c.
 3 10
20
d.
7 10
20
e. 
40
3
Pre-Calculus Honors
Final Exam Review
Chapter 5
Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
1. The graph represented by the equation y  3 sin( 4 )  5 has a maximum value of:
a. 2
b. 3
2. The expression
a.
1
sin 
c. 5
e. -3
d. cot 
e. cos
sec 
is equivalent to:
tan  cot 
b.
1
cos 
c. sin 
3. If  is measured in radians and cos  
a. 
d. 8
3
5
b. 
4
5
3
, then we know that cos(  2 ) is:
5
3
4
c.
d.
5
5
 5 
4. Determine g   given that g ( x)  sin( 4 x) .
 16 
1
1
1
a.
b. 
c.
2
2
2
1
2
d. 
e. 1
e.
3
2
5. Find the exact value of the cos 75  .
a.
6 2
4
6. Given sin A 
a.
10
10
b.
 6 2
4
6 2
4
c.
d.
3
A
, A in quadrant II, find cos .
5
2
3
3 10
b.
c.
10
10
d.
 6 2
4
e. not possible
e. 
3
3
10
7. Solve: cos 2 A  cos A, 0 , 360
a. 0  ,90 , ,180 
b. 0  ,120 , ,240 
c. 90 , ,270 
d. 0  ,180,
e. 22.5 ,112.5, ,202.5 ,292.5
8. 2 sin a cos a is equivalent to which of the following?
a. cos 2a
b. sin 2a
d. sin
c. tan 2a
9. Solve: tan x sin 2 x  2 tan x, 0,2 
a. 0, 
b. 0,  ,2
c. 0,
 3
4
,
d.
4
a
2
 3
4
,
4
e. cos
e. 0,

4
a
2
, ,
cos  cot  csc 
?
csc 
2
10. Which of the following equals
a. cos 2 
b. csc 2 


c. 1  sin 2  1  cot 2 

d. cot 2 
e. none of these
5
4
Pre-Calculus Honors
Final Exam Review
Chapter 6
Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
1. Two homes are located on opposite sides of a small hill at points P and Q. To measure the distance between
them, a surveyor walks the distance of 50 feet from house P to point R, uses a transit to measure PRQ ,
which is found to be 80  , and then walks to house Q, a distance of 60 feet. How far apart are the houses?
a. 71.12 ft
b. 72.11 ft
c. 81.12 ft
d. 82.11 ft
e. 83.21 ft
2. In a triangle, suppose we know that b = 3 feet, c = 2 feet, and angle A = 140. According to the Law of
Cosines, the length of side a is approximately
a. 3.9 ft
b. 4.2 ft
c. 3.6ft
d. 17.6 ft
e. 4.7 ft
3. In triangle ABC , c = 2, B = 45o and a = 6. Find the area of triangle ABC.
a. 3.6
b. 4.8
c. 7.5
d. 4.2
e. 10.1
c. 8.4
d. 10.7
e. 12.6
c. 17.9
d. 23.5
e. 35.3
4. Find the value of x.
a. 3.4
b. 7.4
5. Find the value of x.
a. 16.3
b. 16.8
6. Given P (4,8) and Q(12,7) , find the component form of the vector 
 .
PQ
a.  16,1
b.  8,1
c. 8,1
d.  8,1
e. 16,1
d. 8,5
e.  15,2
7. Let u   7,1 and v  8,3 . Find v  u .
a. 10,7
b. 15,2
c. 1,4
8. Find the angle between the vectors 6,3 and  5,3 to the nearest tenth of a degree.
a. 77.8°
b. 175.6°
c. 87.8°
d. 185.6°
e. 126.5 
9. Given P (3,5) and Q(8,7) , find the component form of the vector 
.
PQ
a.  11,2
b.  8,1
d.  11,2
c. 11,2
e. 8,1
10. Given P(12,4) and Q(4,6) , find the magnitude of the vector 
.
PQ
a. 2 17
b. 2 65
c.
258
d.  2 17
e. 260
d. 2,8
e.  8,2
11. Let u  8,5 and v   10,3 . Find v  u .
a.  18,2
b. 18,2
c.  2,2
12. Let u  3,5 and v  4,8 . Find u  v .
b.  2 17
a. 52
c. 2 7
d. 28
e. -28
d. 5 2 ,5 2
e.
13. Let u  5,5 and find the unit vector in the direction of u.
1
a.
,
1
5 2 5 2
b.  5,5
1
c.
2
,
1
2
1
2
,
1
2
14. Find the angle between the vectors 4,3 and 3,5 to the nearest tenth of a degree.
a. 157.8°
b. -157.8°
c. 22.2°
e. 112.2 
d. -22.2°
15. Which of the following would be the corresponding rectangular equation by eliminating the parameter given
1
x  and y  2t  3 .
t
1
2
1
1
a. y 
b. x 
c. y   3
d. y  2 x  3
e. x 
2x  3
x
2y  3
2y  3
5
16. Convert the polar equation  
into a rectangular equation.
3
3
x
a. x 2  y 2   3
b. y   3 x
c. x 2  y 2  3
d. y  
e. y  x  3
3
17. Convert the polar equation r  10 into a rectangular equation.
a. x 2  10 x  100
b. x 2  y 2  10
c. x 2  y 2  10 y  100
d. y  10 x
e. x 2  y 2  100
18. Convert the polar equation r  7 into a rectangular equation.
a. x 2  y 2  49
b. x 2  7 y  7
c. x 2  y 2  7
d. 7 y 2  x
e. y  7x 2
d. 0 ,  2
e. 2 , 180
19. Convert 2,   to rectangular coordinates.
a. 2 , 0
b.  2 , 0
c. 0 , 2
2 

20. Convert   4,
 to rectangular coordinates.
3 


a. 2 ,  2 3

b. 4 , 120

c.  2 , 2 3


d.  2 3 , 2


e. 2 3 , 2



21. Convert   3,   to rectangular coordinates.
3

 3 3 3
 3 3 3
3 3
3
  ,




,

a.   ,
b.
c.

 2

 2

2
2
2
2








22. Convert  2,   to rectangular coordinates.
4

2, 2
a. 2 , 2
b.  2 , 2
c.






 3 3
3
, 
d.  
2
2

e. 3 , 60
d. 2 , 45
e. 

2, 2

23. Convert the rectangular coordinate 3,  2 to polar coordinates.
a.

5 ,  0.588

b.

5 , 3.730

c.
 13 , 0.588
e.
 13 ,  0.588
d.  3 ,  0.896
e.

 3 
d.  8 ,

4 

5 

e.   2 2 ,

4 

d. r  5 csc
e. r  5
d. r  10 csc
e. r  10
d.
 13 , 3.730
24. Convert the rectangular coordinate  4, 5 to polar coordinates.
a. 3 ,  2.246
b.

41 ,  0.896

c. 3 , 2.246
41 , 2.246

25. Convert the rectangular coordinate 2, 2 to polar coordinates.
 
a.  8 , 
 4


b.  2 2 ,  
4



c.   2 2 , 
4

26. Convert the rectangular equation y  5 to a polar equation.
a. r  5 sec
b. r  5 sin 
c. r  5 cos
27. Convert the rectangular equation x  10 to a polar equation.
a. r  10 sec
b. r  10 sin 
c. r  10 cos
28. Convert the rectangular equation x 2  y 2  8 y  0 to a polar equation.
a. r  8 cos
b. r  8 sin 
c. r  8 sin 
d. r  8 cos 
e. r  8 sec
Pre-Calculus Honors
Midterm Review
Chapter 7 Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
 2 x  y  5
1. Solve the system  2
2
 x  y  25
A. ( 0 , -5)
B. (4 , 3)
C. (0 , -5) and (4 , 3)
D. (3 , 4)
E. (3 , 4) and (0 , 5)
2. A small business has an initial investment of $5000. The unit cost of the product is $21.60 and the selling
price is $34.10. How many units must be sold to break even?
A. 90
B. 200
C. 147
D. 400
E. 231
3. The solution to a system of equations represents:
A.
B.
C.
D.
E.
The zeros of each graph.
The minimum or maximum of each graph.
Where the graphs intersect.
The y-intercepts of the graphs.
Where the graphs have slopes of zero.
4. Two planes start from the same airport and fly in opposite directions. The second plane starts one half of an
hour after the first plane, but its speed is 80kilometers per hour faster. Find the airspeed of each plane if two
hours after the first plane departs the planes are 3200 kilometers apart.
A.
B.
C.
D.
E.
800 km/hr, 880 km/hr
450 km/hr, 530 km/hr
200 km/hr, 280 km/hr
960 km/hr, 1040 km/hr
880 km/hr, 960 km/hr
5. How many liters of an 80% acid solution must be added to 10 liters of a 20% acid solution to get a 30% acid
solution?
A. 1
B. 2
C. 3
D. 4.5
E. 8
C. no solution
D. (1, -1, 3)
E. (2, 1, 5)
 x  2 y  3z  9
6. Solve the system  x  3 y  4
2 x  5 y  5 z  17

A. (-1 , 3, 0)
B. (1 , -1, 2)
7. Write the partial fraction decomposition for
A.
1
2

x 3 x 2
B.
1 .8
.8

x3 x2
C.
x7
x2  x  6
.
2
1

x 3 x  2
D.
5
1

x 3 x  2
E.
2
1

x 3 x 2
8. A total of $1520 a year is received in interest from three investments. The interest rates for the three
investments are 5%, 7% and 8%. The 5% investment is half of the 7% investment and the 7% investment
is $1500 less than the 8% investment. Find the amount in each investment.
A.
B.
C.
D.
E.
$3000 5%, $6000 at 7%, $7500 at 8%
$11,200 at 5%, $5600 at 7%, $4100 at 8%
$800 at 5%, $16000 at 7%, $17500 at 8%
$4000 at 5%, $8000 at 7%, $9500 at 8%
$10000 at 5%, $5000 at 7%, $6500 at 8%
9. Write the form of the partial fraction decomposition
A.
D.
A
x2

B
( x  1) 3
A
B
C


x x  1 x( x  1)
6x 2  1
x 2 ( x  1) 3
B.
A B
C
D
E




x x 2 ( x  1) ( x  1) 2 ( x  1) 3
E.
A
B
C


x  1 ( x  1) 2 ( x  1) 3
10. The first step in writing the partial fraction decomposition of
A. factoring the numerator
B. writing it as
A
B

x4 x2
C. graphing to find all rational zeros
D. graphing to find all asymptotes
E. doing long division
. Do not solve for the constants.
C.
A
B

x x 1
2 x 3  4 x 2  15 x  5
x 2  2x  8
.
Pre-Calculus Honors
Final Exam Review
Chapter 10
Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
x
1. lim
x 1 1
x 0
a. 0
b. -1
d. 2
e. does not exist
1
2
d. 3
e. does not exist
b. 3
c. 0
d. 
b. 0
c.
1
4
d.
1
2
e. does not exist
1
4
c.
1
2
d.
1
16
e. does not exist
x 1
x  2x  3
2. lim
2
x 1
a.
c. 1
1
3
b.
1
4
c.
7
x3
3. lim
x 3
a. 7
7
3
e. does not exist
1
1

4. lim x  2 4
x2
x2
a.
1
16
5. lim
x  4
x
2
x2
x4
a. 0
b.
x 3  27
6. lim
x  3
x3
a. 27
b. 9
c. -9
b. 0
c.
d. 0
e. does not exist
1
8
e. does not exist
d. -2
e. does not exist
4  18  x
x2
7. lim
x2
a. -2
1
2
d.
x  1 , x  2
8. lim f ( x)  
x 2
2 x  3 , x  2
a. 2
9.
b. 1
sin 3 x

x
lim
x
a.
c. 3
3

6
b.

6
c.
6

d.
9

e. does not exist
10. lim
x 5
5 x
x 2  25
1
5
a. 
11. lim 
x 16
a.
b. -5
c. 
1
8
c. 4
1
10
d.
1
5
e. does not exist
4 x
x  16
1
4
b. -
d. 
1
4
e. does not exist
12. Find the slope of the tangent line to f ( x)  3x  1 at (2 , 5).
a. 6
b. 14
c. 2
d. 5
e. 3
d. 5
e. -1
13. Find the slope of the tangent line to f ( x)  2 x  5 at (2 , 1).
a. 2
b. -2
c. 1
14. Find the slope of the tangent line to f ( x)  5 x 2  3x at (-1 , 8).
a. -13
b. -8
c. -10
d. -7
e. 8
d. 3
e. –2
d. 2x  7
e. -5
d. 12 x  2
e. 6x  5
15. Find the slope of the tangent line to f ( x)  3x 2  5 x at (2 , 2).
a. -5
b. 7
c. 2
16. Find the derivative of f ( x)  x 2  5 x  7 .
a. x 2  5
b.  5x  7
c. 2x  5
17. Find the derivative of f ( x)  6 x 2  2 x  5 .
a. 12x  5
b.  2x
c. 6x  2
18. Find the derivative of f ( x)  3x 4  10 x 2  9 .
a. 12 x 3  10 x
b. 12 x 3  20 x  9
c. 12 x 3  9
d. 4 x 3  2 x
e. 12 x 3  20 x
19. Find the derivative of f ( x)  5 x 3  12 x 2  3x .
a. 15 x 2  24 x  3
b. 15 x 2  24 x
c. 3 x 2  2 x  3
d. 5 x 2  12 x  3
e. 15 x 2  3
d. 5xh  3xh  2h
e. 5xh  3h
20. Find the difference quotient for f ( x)  5 x 2  3x  2 .
a. 10x  3
b. 10x  5h  3
c. 10 x  3h
21. Find the difference quotient for f ( x)  2 x 2  4 x  7 .
a. 4x  4
b. 4x  2h  4
c. 2x  4h
d. 4x  6h  7
b. 0
c. 1
d.
b. 0
c. 1
d. 5
b. 0
c. 1
d. 
a. does not exist
3
26. lim 8 
x
x 
b. 0
c. -4
d. 5
e. 1
a. does not exist
b. 0
c. 11
d. 8
e. 3
b. 0
c. -5
d. -4
e. 5
1
5
d. 1
e. 5
1
3
d. 1
e. 3
d. 
e. does not exist
8x  4
22. lim
10 x 2  3
x
a. does not exist
23.
a. does not exist
a. does not exist
5
lim
n  
1
3n 2

5n
n2
the limit of the sequence an 
n2
5n 3  1
b. 0
29. Find the limit of the sequence an 
a. does not exist
a. 1
lim
x  5
e. -5
x2
a. does not exist
30.
5
2
4
a. does not exist
Find
5
2
2x 2  1
x 
28.
e.
 5x 3  2
24. lim
27.
e. 8
2x 2  4
x  
x 
4
5
5x 2  1
lim
25. lim
e. 2x  h
b. 0
c.
n2
3n  2
c.
x5
x5
b. -1
c. 0