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Algebra II
Name:_________________
Hr:_____
Semester 2 Final Exam REVIEW 2014
CHAPTER 12 – Trigonometry
Evaluate the six trig functions of the angle  .
1.
sin
9


=
csc

=
cos

=
sec

=
tan

=
cot

=
12
Find the value of x for the triangle. Round your answers to the nearest hundredth.
2.
3.
4.
35°
4
9
3
63°
23°
x
x
Find the EXACT value of x and y for the triangle. HINT: These are SPECIAL TRIANGLES.
5.
6.
x
60°
y
3
3
45°
x
y
x = _________ , y =__________
Find the value of angle
7.
θ
5

x = _________ , y =__________
for the triangle. Round answers to the nearest hundredth.
8.
17
11
θ
12
PAGE 1
x
9. You are standing on an observation deck 550 feet from the base of Mt. Rushmore. You look up at the top of
Mount Rushmore at an angle of 39°. How high is the top of the monument? Round your answer to the
nearest hundredth.
10. A flagpole casts a shadow 10 feet long. Viewed from the end of the shadow, the top of the flagpole makes
a 63° angle with the ground. Sketch a diagram that represents this situation. What is the height of the
flagpole? Round your answer to the nearest hundredth.
Draw the following angles in standard position.
11. 150

12. 480

13. -45

Convert the following angles to radians. (Use: ___________)
14. 80

15. 120

16. -135
Convert the following angles to degrees. (Use: ___________)
7

17.
18.
6
4
Find one positive and one negative angle that are coterminal with the angle given.
3


20. 50
21. -200
22.
4
PAGE 2
19. 
2
3
23. 

3

Use the given point on the terminal side of an angle in standard position to evaluate sine, cosine, and tangent.
24. (7, 24)
25. (-3, 4)
sin

=
sin

=
cos

=
cos

=
tan

=
tan

=
Sketch the angle. Then find its reference angle.
26.
150°
27.
240°
28.
3
4
Evaluate the function without using a calculator. HINT: Find the reference angle and then use SPECIAL
TRIANGLES to evaluate.
11
29. sin 120°
30. cos 210°
31. tan
6
To solve triangles, we learned how to use two different laws:
 LAW OF SINES:
o

Use when you have ___ ___ ___ or ___ ___ ___
LAW OF COSINES:
o
Use when you have ___ ___ ___ or ___ ___ ___
PAGE 3
32.
If A = 40°, C = 75°, c = 20, find the length of side b.
33.
If A = 52°, a = 32, b = 42, find the measure of angle B.
34.
If B = 70°, b = 85, c = 88, find the measure of angle C.

35. If C = 115 , a = 4, b = 6, find the length of side c.
36. If a = 16, b = 14, c = 18, find the measure of the largest angle.
37. Two airplanes leave an airport at the same time, and the angle between their flight paths is 40º. An hour
later, one plane has traveled 300 miles while the other has traveled 200 miles. How far apart are the planes
at this time? Round your answer to the nearest hundredth.
38. Two forest rangers, 12 miles from each other on a straight service road, both site an illegal bonfire off the
road. Using their radios to communicate, they discover the fire is between them. The first ranger’s line of
sight to the fire makes an angle of 38° with the road and the second ranger’s line of sight to the fire makes a
63° angle with the road. How far is the fire from each ranger? Round your answer to the nearest hundredth.
PAGE 4
CHAPTER 12 ANSWERS
3
3
4
5
1. sin:
cos:
tan:
csc:
5
5
3
4
sec:
3 2
3 2
, y
2
2
4. x = 6.61
5. x 
9.
10. 19.63 feet
14.
445.38 feet
4
9
15.
2
3
21. 160°, -560°
25. sin =
30. 
16. 
3
4
22. 495°, -225°
4
3
4
cos = 
tan = 
5
5
3
3
2
5
4
cot:
3
4
31. 
34. C = 77° OR 103°
3
3
35. c = 8.5
2.
x = 21.20
3. x = 2.29
6. x  3 3 , y  6
11.
7.
 = 27.04°
12.
17. 315°
18. 30°
23. 300°, -420°
26. 30°
32. b = 18.8
36. C = 73°

= 54.78°
13.
19. -120°
24. sin =
27. 60°
8.
20. 410°, -310°
24
7
24
cos =
tan =
25
25
7
28. 45°
29.
3
2
33. No Solution
37. 195.13 miles
38. 10.89 miles and 7.53 miles
 Statistics and Probability
Find the mean, median, and range of the data set. Round answers to the nearest tenth.
1. 3, 3, 4, 5, 5, 7, 8, 10, 11
2. 95, 76, 88, 82, 73, 65, 76, 76, 84, 90
Mean:_________________
Mean:_________________
Median:_______________
Median:_______________
Range:________________
Range:________________
Find the median, upper quartile, lower quartile, maximum/upper extreme, and minimum/lower extreme. Then
construct a box-and-whisker plot of the data.
3. 25, 56, 43, 44, 35, 31, 73, 66, 62, 29, 37
Median:_______
Upper Quartile: _______
Lower Quartile: _______
Maximum: _______
Minimum: _______
PAGE 5
4. 17, 38, 22, 15, 13, 24, 18, 10, 20, 13, 17, 12
Median:_______
Upper Quartile: _______
Lower Quartile: _______
Maximum: _______
Minimum: _______
Given the probability of a certain event, state the odds of that event
5.
3
5
6.
1
4
7.
Given the odds of a certain event, state the probability of that event
8. 5:16
9. 4:21
10
27
10. 12:7
Given the spinner below, state the probability of each outcome.
11. Landing on red:_________________
12. Landing on orange or purple:_______________
13. Does not land on green:________________
14. Does not land on purple or orange:________________
15. Does not land on purple or orange or red or green:____________
A jar contains 3 white, 1 red, 6 green and 5 blue marbles. If one marble is drawn at random, state the
probability of each outcome.
16. A white marble
17. A red marble
18. A black marble
19. Not a white marble
20. Not a blue marble
21. A red or green marble
PAGE 6
Given a standard deck of 52 cards, if one card is drawn at random, state the probability and odds of each
situation.
22. A black card
23. A ten
24. A red jack
25. Not a black card
26. Not a four
27. Not a black jack
28.
A men’s department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs
of pants. How many different suits consisting of a jacket, shirt, tie, and pants are possible?
29.
Subway offers 5 different types of bread, 10 different types of meat, 3 different types of cheese, 9 different
vegetable toppings, and 7 different condiments. If you can pick only one type of bread, one meat, one
cheese, one veggie, and one condiment, then how many different subs can you order?
30.
A license plate will consist of three letters followed by two digits. How many different license plates are
possible?
31. A license plate will consist of 2 letters and 4 digits and no letters or digits can be repeated. How many
license plates are possible?
Evaluate each permutation or combination.
32. 4 P3
33. 8 P4
34.
6
C4
35.
14
C10
36.
A photographer lines up the 13 players of a basketball team in a single line to take a team picture. How
many different ways can the photographer arrange the team for the picture?
37.
A teacher must choose 4 students from the 20 students in your chemistry class to represent your school in
an Academic Challenge. How many different combinations of 4 students can the teacher choose?
PAGE 7
38.
Nine students enter a race. Awards are given for first place through third place. In how many ways can
the students finish first through third?
39.
A teacher is holding tryouts for the school play. There are 15 students trying out for 7 parts. Each student
can play each part. In how many ways can the teacher select the students?
40.
A pizza parlor offers ten different toppings. How many different 5-topping pizzas can be created using the
10 toppings? (Assume no topping is used more than once.)
STATISTICS AND PROBABILITY ANSWERS
1.
Mean: 6.2; Median: 5; ; Range: 8
3.
Median: 43, UQ: 62, LQ: 31, Max: 73, Min: 25
5. 3:2
6. 1:3
2
5
13.
4
5
14.
3
5
19.
4
5
20.
2
3
21.
7
15
1
Odds: 1:25
26
25. Prob:
Mean: 80.5; Median: 79; Range: 30
4.
5
8.
21
1
15.
5
7. 10:17
12.
24. Prob:
2.
Median: 17, UQ: 21, LQ: 13, Max: 38, Min: 10
12
4
1
9.
10.
11.
19
25
5
1
0
1
16.
17.
18.
15
15
5
1
1
Odds: 1:1
23. Prob:
Odds: 1:12
13
2
12
25
26. Prob:
Odds: 12:1
27. Prob:
Odds: 25:1
13
26
22. Prob:
1
Odds: 1:1
2
28. 576
29. 9,450
30. 1,757,600
31. 3,276,000
32. 24
33. 1,680
34. 15
35. 1,001
36. 6,227,020,800
37. 4,845
38. 504
39. 6,435
40. 252
PAGE 8
CHAPTER 9 – Rational Functions
Graph each of the following functions and fill in the missing information.
1.
y
2
x3
x
y
x
y
Vertical Asymptote:
Horizontal Asymptote:
Domain:
Range:
x-intercept:
y-intercept:
2.
y
1
1
x2
Vertical Asymptote:
Horizontal Asymptote:
Domain:
Range:
x-intercept:
y-intercept:
Simplify each expression.
3.
6x  3
4x 2  1
4
6.
4.
4 y 2 27

9 x 16 xy2
7.
2 x  4 x x  3x  2

x2  4
3x  6
2
32 x y 8 xy

3 xy2 21 y 4
x 2  2 x  15
x 2  x  30
9.
x 2  11x  24
x 2  3 x  18
2
10.
5.
2
2
3
 2
3x 2 x
n4
8. n 2  6n  9
n  2n  8
3 n
2
11.
PAGE 9
x 2  3x
x2  x  2

x 2  3x  2 x 2  4 x  3
4
5
 3
2
6x
3x
12.
x
3

x4 x2
13.
3x
2

x4 x5
14.
x
3x
 2
x 1 x 1
15.
3x
4x
 2
x2 x 4
16.
3
2

x  8 x  15 x  5
17.
x
2x  2
 2
3x  15 x  4 x  5
2
Solve the following equations.
18.
x
2x

2x  1 x  2
19.
20.
7 3
 3
2 x
21. 8 
PAGE 10
15 4 7
 
x 5 x
2
2x

x 1 x 1
22.
2
3
 2
x 1 x
24.
x
1
5

 2
x 1 x 1 x 1
23.
5
1 5
 
x2 x x
CHAPTER 9 ANSWERS
1.
3.
8.
13.
VA: x = -3
HA: y = 0
D: ARN except -3
R: ARN except 0
x-int: None
y-int: (0, 2/3)
3
3
4.
2x  1
4x 2
1
n  3n  2
3x 2  13 x  8
x  4x  5
9.
14.
x  3
 x  8
x x  4 
x  1x  1
2. VA: x = -2
HA: y = -1
D: ARN except -2
R: ARN except - 1
x-int: (-1, 0)
y-int: (0, -1/2)
7.
6x
x  2x  1
2x  5
3x 3
12.
x 2  x  12
x  4x  2
2 x  3
x  5x  3
17.
x6
3x  5
5.
x
x 1
6. 28x 2 y
10.
4x  9
11.
16.
15.
6x 2
x3x  10 
x  2x  2
18. x = 0
19. x = -10
20. x = -6
23. x = 8
24. x = 3, 2
25. x =
3
2
PAGE 11
21. No Solution
22. x = ½, 3
 Chapter 11 – Sequences and Series
Write the first five terms of the sequence.
1. a n  n  1
2. an  3n  5
3.
an  n 2  6
Determine whether the following sequences are arithmetic, geometric, or neither. Then find the next term.
4. 1, 4, 7, 10, 13,…
5. 1, -2, 3, -4, 5, …
6. 2, 4, 8, 16, 32
Write a rule for the nth term of the arithmetic sequence. Then find a 8.
7. 7, 10, 13, 16, …
8. 3, 1, -1, -3, -5,…
9.
d = 2, a5 = 1
10. d = -5, a10 = -60
Find the sum of the first 10 terms of the arithmetic series.
11. -1 + 2 + 5 + 8 + 11 +…
12. 4 + 3 + 2 + 1 + 0 + …
13. 3 + 6 + 9 + 12 + 15 +…
Write a rule for the nth term of the geometric sequence. Then find a6.
14. 4, 8, 16, 32,…
15. 5000, 500, 50, 5,…
16. r = 3, a1 = 4
17. r = 2, a1 = 1
Find the sum of the first 10 terms of the geometric series.
18. 2 + 4 + 8 + 16 + 32 +…
19. 1 + 3 + 9 + 27 + …
PAGE 12
20. ½ + 1 + 2 + 4 + …
CHAPTER 11 ANSWERS
1.
2, 3, 4, 5, 6, 7
2.
-2, 1, 4, 7, 10, 13
3.
7, 10, 15, 22, 31, 42
4.
Arithmetic, 16
5.
Neither, -6
6.
Geometric, 64
7.
an = 3n + 4; a8 = 28
8.
an = -2n + 5; a8 = -11
9.
an = 2n - 9; a8 = 7
10. an = -5n – 10; a8 = -50
14. an = 4(2)n-1; a6 = 128
17. an = 1(2)n-1; a6 = 32
11. 125
12. -5
1
1
 
15. an = 5000   n-1; a6 = 0.05 =
20
 10 
13. 165
18. 2046
20. 511.5
19. 29,524
16. an = 4(3)n-1; a6 = 972
 Chapter 13 – Conic Sections
Identify the center and radius of the circle. Then graph the circle.
1.
x 2   y 2  25
2.
x 2  y 2  10
3.
x  32   y  12
9
Center:______________
Center:______________
Center:______________
Radius:______________
Radius:______________
Radius:______________
Write the equation of a circle that satisfies the given information.
4. Center (0, 0) r = 4
5. Center (-5, 7) r =
2 3
PAGE 13
6. Center (0, 0); point on circle (2, -6)
Graph the ellipse. Identify the vertices, co-vertices, and foci.
7.
x2 y2

1
25 4
8.
x2 y2

1
9 36
9.
9 x 2  16 y 2  144
Vertices:_______________
Vertices:______________
Vertices:_______________
Co-Vertices:___________
Co-Vertices:___________
Co-Vertices:___________
Foci:__________
Foci:__________
Foci:__________
Write an equation for the ellipse with center at (0, 0) that satisfies the given information.
10. Vertex (0, -4) Co-vertex (3, 0)
11. Vertex (5, 0) Focus (4, 0)
Identify the focus and directrix for the parabola and graph the equation.
12.
y 2  12 x
13.
x2  8y
Focus:_______________
Focus:_______________
Directrix:_____________
Directrix:_____________
PAGE 14
14.
x 2  4 y
15.
y 2  16 x
Focus:_______________
Focus:_______________
Directrix:_____________
Directrix:_____________
Write the standard form of the equation of the parabola with vertex at (0, 0) and the given focus or directrix.
16. Directrix: x = -3
17. Directrix: y = 4
18. Focus: (0, 5)
19. Focus: ( 
1
, 0)
2
Graph the hyperbola. Identify the vertices, foci, and asymptotes.
20.
x2 y2

1
25 4
21.
y2 x2

1
16 9
22.
y 2  16 x 2  16
Vertices:_____________________
Vertices:_____________________
Vertices:_____________________
Foci:_________________________
Foci:_________________________
Foci:_________________________
Asymptotes:__________________
Asymptotes:__________________
Asymptotes:__________________
PAGE 15
Write an equation of the hyperbola centered at (0, 0) with the given foci and vertices.
23. Foci: (0, -4) (0, 4)
Vertices: (0, -2) (0, 2)
24. Foci: (-6, 0) (6, 0)
Vertices: (-3, 0) (3, 0)
CHAPTER 13 ANSWERS
1. C(0, 0); r = 5
5.
x  52   y  7 2  12
8. V (0,
11.
x2 y2

1
25 9
y 2  2 x
21. V (0,
23.
6.
12. F(3, 0) dir. x = -3
16.
x2 y2

1
9 27
 3); F(  7 , 0)
13. F(0, 2); y = -2
y 2  12 x
20. V (  5, 0); F( 
24.
7. V (  5, 0); CV(0,
9. V (  4, 0); CV(0,
4
 4); F(0,  5); Asymp. y   x
3
y2 x2

1
4 12
3. C(3, -1); r = 3
10
x 2  y 2  40
 6); CV(  3, 0); F(0,  27 )
15. F(-4, 0); x = 4
19.
2. C(0, 0); r =
17.
x 2  16 y
4.
x 2  y 2  16
 2); F(  21 , 0)
10.
x2 y2

1
9 16
14. F(0, -1); y = 1
18.
x 2  20 y
2
29 , 0); Asymp. y   x
5
22. V(0,
 4); F(0,  17 ); Asymp. y  4 x
CHECK ONLINE KEY FOR GRAPHS!!!
PAGE 16