Download HONORS ALGEBRA 2

PRECALCULUS FINAL EXAM REVIEW
****
This packet is intended to be used as supplemental review and practice of problems that reflect the topics
which will be covered on the final exam. It should NOT be used as your only review.
Chapter 3 Exponential and Logarithmic functions
1
2. f  x    
2
Graph the exponential function. 1. f  x   3  1
x
1
 log 49 7
2
Write each equation in exponential form
3.
Write each equation in logarithmic form.
5. 63  216
Evaluate each expression, without a calculator.
11. log17 17
12 log3 38
13. ln e5
7. log 4 64
14. ln
1
e2
4. 3  log 4 x
6. b 4  625
8. log5
1
25
9. log3  9 
15. log3  log8 8 
Graph each logarithmic function. 18. f  x   log 2  x  2 
Find the domain of the logarithmic function.
x
16. ln e6 x
10. log16 4
17. eln
19. f  x   1  log 2 x
21. f  x   ln  x  1
20. f  x   log8  x  5
2
 xy 2 
x
23. log 2 
24. ln 3

e
 64 
1
25. ln x  2ln  x  1
26.
27. 3log 2  x  1
log z
5
Expand each expression as much as possible. 22. log 6 36x3
Write each expression as a single logarithm.
28
Solve:
1
1
log a  x  3  log a  x  3
2
3
29. 24 x 2  64
31. log 4  3x  5  3
30. 9 x  2  27 x
32. ln  x  4   ln  x  1  ln x
33. log 4  2 x  1  log 4  x  3  log 4  x  5
34. Using compound interest formulas, find the missing values.
a)
b)
c)
d)
Principle
$1500
?
$5000
$1000
Interest Rate
10%
8%
5%
?
Compounded
monthly
quarterly
continuously
semiannually
Time
12 yrs
10 yrs
?
4 yes
35. Using exponential the decay model, find missing values:
a)
b)
c)
Initial Amount
300 mg
22 mg
?
5
Half-Life
140 days
1600 yrs
30 yrs
Time
?
4000 yrs
80 yr
Amount .
200 mg
?
1.6 g
Amount
?
$20,000
$10,000
$1435.77
Chapter 4 Trigonometric Functions
9
b)   105 .
10
2. A bicycle wheel with a radius of 13 inches makes 2.1 revolutions pr second. What is the speed of the bicycle?
1. In which quadrant is the terminal side of a)   
3. A point on the rim of a wheel has a linear speed of 14 cm/s. If the radius of the wheel is 20 cm, what is the
angular speed of the wheel in radians per second?
4. The needle of the scale in a bulk food section of a supermarket is 28 cm long. Find the distance the tip of the
needle travels if it rotates 174.
5. Find the coordinates of the point of intersection of a 150 and the unit circle.
6. Evaluate: a) cos
9
4
 3 
b) tan   
 4 
 7 
c) csc  

 6 
4
, find sin  t  2  .
19
8. Find the exact values of the sine and cosine functions for the angle  shown in the figure
7. If sin t 
1

3
tan 
9. Use the fundamental identities to simplify:
sin 
15
, find csc
17
b) if csc  26 find cot 
0. If  is an acute angle, find the indicated trigonometric function: a) if sin  
11. A 12-foot ladder makes an angle of 50 with the ground as it leans against a house. How far up the house does
the ladder reach?
12. The cable supporting a ski lift rises 3 feet for each 8 feet of horizontal length. The top of the cable is fastened
675 feet above the cable’s lowest point. Find the lengths b and c, and find the measure of angle 
c
675

b
13. To find the height of a pole, a surveyor moves 100 feet away from the base of the pole and then, from an eyelevel height of 6.5 feet, measures the angle of elevation to the top of the pole to be 40 . Find the height of the
pole to the nearest foot.
14. Find the quadrant the terminal side of  lies if tan   0 and cos  0
12
15. Given: tan   
and sin   0 , find cos  .
35
16. The point  9, 40  lies on the terminal side of an angle in standard position. Determine the exact value of sin 
17. Find the reference angle: a)   3.5
b)  
5
3
c)   159
18. Find the exact value of cos150
19. Find the five key points for the graph of y  2sin x on the interval  0, 2 
20. Find the amplitude and period: a) y  2.5cos
x
2
21. Find a cosine function that has an amplitude of
3 x
2
7x
f) y  cot
4
22. Graph: a)
y  sin
23. Evaluate: a) arctan 1
b) y  1.5cos
2x
3
1
and a period of 8
2

x
3x
2x

b) y  3cos  2.5 c) y  4sin  x   d) y  tan
e) y   tan
2
2
2
3


5x
5x
 3x 3 
g) y   cot
h) y  2sec  
 i) y  1.5csc
8 
4
3
 2

2
 1 4 
b) cot  arctan
 c) csc  cos

x 
5


24. An airplane is flying east at a constant altitude of 28,000 meters. When first seen to the east of an observer, the
angle of elevation to the airplane is 71.5 . After 73 seconds, the angle of elevation is 51.6 . Find the speed of
the airplane.
25. At a distance 56 feet from the base of a flagpole, the angle of elevation to the top of a flag that is 3.1 feet tall is
25.6 . The angle of elevation to the bottom of the flag is 22.9 . The pole extends 1 foot above the flag. Find
the height of the pole.
26. An energy company uses one wellhead to drill several exploratory wells at different angles. They strike oil when
they have drilled 2879 feet along an angle of depression of 44 . Find the depth of the oil deposit.
27. A hiker travels 3.9 miles per hour at a heading of S 21 E from a ranger station. After 3.5 hours, how far south and
how far east is the hiker from the ranger station?
28. A ship leaves port at 20 miles per hour, with a heading of S 44 W. There is a warning buoy 5 miles directly north
of port. What is the bearing of the warning buoy as seen from the ship after 5.5 hours?
Chapter 6 Additional Topics in Trigonometry
C
1. Find c
92
40
A
c
35
2. Find c if A  31, a  11, and b  13
B
3. Solve the triangle: B  32, C  25, and a  18
4. Find the area of the triangle: a) A  39, a  13.3, and b  13.3
b) B  6511', a  5 and c  2
5. A pole 85 feet tall is situated at the bottom of a hill that slopes up at an angle of 17.8 . A guy wire from
the top of the pole to the hillside forms an angle of 24 with the top of the pole. Find the distance from
the base of the pole to the guy wire’s point of attachment.
6. A loading dock ramp that is 18 feet ling rises at an angel of 17.8 from the horizon. Due to new design
specifications, a longer ramp is to be used, so that the angle is reduced to 8 . How much farther out from the
dock will that put the foot of the ramp?
7. Two Coast Guard stations located 75 miles apart on a north-south line each receive a radio signal from a ship at
sea. From the northernmost station, the ship’s bearing is S 65 E. From the other station, the ship’s bearing is
N 20 E. How far is the ship from the northernmost station?
8. Find the third side of the triangle.
9
51
9
72. Use the law of cosines to solve triangle ABC given: a  11, b  16, c  15
10. Use the law of cosines to solve triangle ABC given: A  42, b  3, c  9
11. Two ships leave a port at the same time. When ship A is
200 miles due west of the port, ship B is 185 miles from
the port and 250 miles from ship , in the direction shown
at the right What is ship B’s bearing?
Ship B
Ship A
Port
12. A plane travels 170 miles at a heading of N 41 W. It then changes direction and travels 165 miles at a
heading of N 70 W. How far is the plane from its original position?
13. Find the area of the triangle: a) equilateral triangle with perimeter of 29.4 b) a  23.5, b  23.5, and c  26.4
Chapter 5 Analytic Trigonometry
1. Find an expression that completes the fundamental trig identity: a) tan   x   ____
b) cos   x   ____


c) cot      ____
2


2
2
2
2. Factor the expression and use identities to simplify cos x sin x  cos x
1
4
1  cos
sin 
b)

 2csc
sin 
1  cos
3. Find the remaining trig functions given csc x  17 and tan x  
4. Verify the identity: a)
sin 2 x
1  sec x

1  cos x
sec x
5. Find solutions for each equation in the interval  0,2  : a) 3cot 2 x  9  0
c) 10cos x  5 2  0
d) tan 2 x  sec x  1
e) tan 2  
3
6
2
0
2
7. Find the exact value of sine, cosine, and tangent of the angle
8. Find the exact value of cos345 .
3
7

12
5 
3
 A   ; and   B 
8 2
2
9. Find cos  A  B  given sin A  ; cos B   ;
x
2
x
2
f) 3sec2  4sec  4  0
g) 4cos3x  2 3  0
6. Find all solutions: sin 2 x 
b) 9tan x  8 3  17tan x
1
3
;   x
11
2
6
3
11. Find the exact values of sin 2 and cos 2 given sin    , and
   2
11
2

27
12. Find the exact value of tan given sin  
and  is in quadrant I
2
45
10. Find the exact value of sin 2x given sin x  
13. Find the exact value of sin

2
given tan  
48
3
and    
55
2