3 3

3 θ

17 x

49˚

Algebra II: Chapter 13 Semester II Exam Review Name _______________________________________

Evaluate the six trigonometric functions of the angle . Answers must be reduced fractions and cannot be decimals.

1.

Cos = Sin = Csc =

Tan = Sec = Cot =

Find one positive angle and one negative angle that are coterminal with the given angle.

2. 109

Answer: _____________

3.

Find one positive angle and one negative angle that are coterminal with 310°. Answer: _____________

A. 100°, – 670° B. – 120°, 400° C. 50°, – 670° D. – 50°, 670°

Convert the degree measure to radians or the radian measure to degrees.

4. 18 Answer: _____________

5. 12

7

Answer: _____________

Find the value of x. Round your answers to the nearest hundredth.

6.

Equation for x:

x = _______

Solve ABC using the diagram and the given measurements. Round your answers to the nearest hundredth.

7. A = 35°, a = 12

Equation for B:

B = _______

Equation for b:

b = _______

Equation for c:

c = _______

8.

A string is tied from the tip of a flagpole to a stake in the ground. The string is 16-feet long. A student is standing at the

stake and measures the angle of elevation to the top of the pole at 42°. How tall is the pole?

A. 12 ft B. 5.6 ft C. 10.7 ft D. 14.4 ft

Use the given point on the terminal side of an angle in standard position to evaluate the trig. functions of . Answers should be reduced fractions and cannot be decimals.

9. ( 7, 5)

Cos =

Sec =

Sin =

10.

Find the value of the Cot if the terminal side of the angle in standard position contains the point 8,15 .

A.

8

15 B.

8

17 C.

8

15 D.

17

15

Find the exact value of each function. Answers should be reduced fractions and cannot be decimals.

11. 4

3sin

12. csc 330°

13.

Answer: _____________ Answer: _____________ Answer: _____________

Use the given information to find the value of the trigonometric function. Answers should be reduced fractions and cannot be decimals.

14. Find Cos , if Tan = 18090;3

4

Cos = _____________

15. Find Sin , if Cos = 360270;7

6

Sin = _____________

3 5

tan

Multiple Choice: Circle the answer to each question.

16.

Point P (0.8, 0.6) is located on a unit circle. Find sin , cos

A. sin = 0.6,

cos = 0.8

B. sin = 0.14,

cos = 0.6

C. sin = 0.8,

cos = 0.6

D. sin = -0.8,

cos = 0.2

17.

Given the angle on the unit circle, find sin , cos .

A. sin =

2

1 ,

cos = 2

1

B. sin = 2

1

cos = 2

1

C. sin = 2

3 ,

cos = 2

1

D. sin = 2

1

cos = 2

3

Determine whether you would use the Law of Sines or the Law of Cosines for each problem. Circle your method. Once you start using one method, you must use that method through the whole problem. Formulas will not be provided on the exam. You will need to write them on your notecard. Round answers to the nearest tenth.

Law of Sines :c

C

b

B

a

A sinsinsin Law of Cosines:

)2/()(cos

cos2

2221

22

bccbaA

Acbcba

18. 12,83,43 bCA

LOS LOC

a = ______ B = ______ c = ______

19. 17,20,75 caB

LOS LOC

b = ______ A = ______ C = ______

20. 50,77,26 cBA

LOS LOC

C = ______ a = ______ b = ______

21. 14,11,19 cba

LOS LOC

A = ______ B = ______ C = ______

Algebra II: Chapter 14 Semester II Exam Review

Directions: Identify the following values and describe the shifts (up, down, left, right).

1. xy2

1sin4

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

2. xy2

sin4

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

3. 42cos xy

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

4. 42

cos

xy

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

5. 52

cos3

xy

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

6. 126sin8 xy

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

7. 944cos xy

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

Algebra II CP: Chapter 10 Semester II Exam Review

For the given configuration, determine how many different license plates are possible if (a) digits and letters can be repeated, and (b) digits and letters cannot be repeated.

1. 2 letters followed by 3 digits

2. 1 digit, followed by 1 letter, followed by 2 digits, followed by 1 letter

a.

a.

b.

b.

Determine whether each situation involves a permutation of combination. Then find the number of possibilities.

3. the winner, runner-up, third, and fourth place finishers in a competition with 14 competitors

4. a 6 person committee being chosen from a group of 15 people

Combination or Permutation Answer: _______________ Combination or Permutation Answer: _______________

5. grabbing 3 sweaters from a stack of 10

6. labeling your 11 friends as Best friend and Second Best friend

Combination or Permutation Answer: _______________ Combination or Permutation Answer: _______________

A card is randomly drawn from a deck of 52 cards. Find the probability or odds of the given event.

7. P(a red Jack is chosen)

8. P(a black 9 is chosen)

ANSWER: _________________ ANSWER: _________________

Algebra II CP: Chapter 8 Semester II Exam Review Find the vertical and horizontal asymptotes, as well as the x-intercepts/zeros of the graph of the function. If the graph does not have one of the above, simply write “none” or cross it out. Round all decimals to the nearest tenth.

1. 36

1522

2

x

xxy

2. 2

122

2

x

xxy 3.

7

122

x

xy

VA: x = ____________

HA: y = ____________

X-intercept(s): , ,

VA: x = ____________

HA: y = ____________

X-intercept(s): , ,

VA: x = ____________

HA: y = ____________

X-intercept(s): , ,

4. 12

1811

x

xy

5. 25

952

2

x

xy 6.

2

20152

x

xy

VA: x = ____________

HA: y = ____________

X-intercept(s): , ,

VA: x = ____________

HA: y = ____________

X-intercept(s): , ,

VA: x = ____________

HA: y = ____________

X-intercept(s): , ,

Determine each of the following values, then graph the function. Round all decimals to the nearest tenth. Vertical Asymptote:

x = ____________

Horizontal Asymptote:

y = ____________

7. 62

4

x

xxf

X-intercepts/Zeros:

, ,

Domain : ___________________________ Range : ____________________________

Vertical Asymptote:

x = ____________

Horizontal Asymptote:

y = ____________

8. 52

34

x

xxf

X-intercepts/Zeros:

, ,

Domain : ___________________________ Range : ____________________________

Vertical Asymptote:

x = ____________

Horizontal Asymptote:

y = ____________

9. 4

252

2

x

xy

X-intercepts/Zeros:

, ,

Domain : ___________________________ Range : ____________________________ 10.

Find the quotient: 4

3

2

92

2

x

x

x

x

A. 2

3

x

x

B. 2x

C. 23 xx D.

842

279323

23

xxx

xxx

11.

Find the product: 123

62

65

452

2

x

x

xx

xx

A. 3

4

x

x B.

23

12

x

x C.

23

41

xx

xx D.

3

2

Find the product. Find the quotient.

12. 34

54

25

32

2

2

2

cc

cc

c

cc

13. 5

2

4

2

7

274

14

1816

p

pp

p

pp

Simplify.

14.

25

2

5

32

xx

15.

2

1

42

3

x

x

x

x

16.

xx 24

5

18

72

17.

xyx 14

3

6

132

Solve the following equations. Check for extraneous solutions.

18.

54

9

1

3

xx

19. 24

6

2

2

xx

20.

6

121

6

1

x

x

xx

x

21. 33

149

3

2

x

x

x

x

22.

xx

3

5

81

23. 4

1

3

4

3

9

x

x

x

Algebra II CP: Chapter 12 Semester II Exam Review

NOTE: The following formulas will NOT be provided on the exam.

dnaan 11

2

1 nn

aanS

1

1

n

nraa

r

raS

n

n1

11

r

aS

1

1

daa nn 1 1 nn ara

Tell whether the sequence is arithmetic, geometric, or neither.

1. ,...7

48,

7

12,

7

3,

28

3

2. ...3

1,0,3,6,9

3. ,...82,47,12,23

Given the following arithmetic sequences, find the next three terms.

4. ...,6,10,14,18

_________________

5. ...,25.4,5,75.5,5.6

_________________

Write a rule for the nth term of the arithmetic sequence. Then find the indicated term.

6. ,...9,2,5,12

7. ,...2

5,

8

15,

4

5,

8

5

Rule: _____________________________

16a = ________

Rule: _____________________________

20a = ________

8. 11,9913 da

9. 9,166 da

Rule: _____________________________

16a = ________

Rule: _____________________________

20a = ________

Write a rule for the nth term of the arithmetic sequence.

10. 101,29 2011 aa

Rule: _____________________________

11. 135,31 146 aa

Rule: _____________________________

Find the n

S of the arithmetic series.

12.

8

1

52x

x

13.

30

1

205n

n

14.

5

1

9n

n

Write a rule for the nth term of the geometric sequence. Then find the indicated term.

15. ...,16

27,

8

9,

4

3,

2

1

16. ,...25

7,

5

7,7,35

Rule: _____________________________

13a = ________

Rule: _____________________________

10a = ________

17. 2,968

ra

Rule: _____________________________ 15

a = ________

Find the sum of the geometric series.

18.

5

1

1

2

117

n

n

19.

10

1

125

i

i

20.

18

1

1

4

13

n

n

Find the sum of the infinite geometric series, if it exists. If not, explain why.

21.

1

1

3

2

3

2

x

x

22.

1

1

4

13

x

x

23.

1

1

2

36

k

k

24. ...

16

27

8

9

4

3

2

1

Write the first three terms of the sequence.

25. naa

a

nn3

4

1

0

_________ 321 aaa

26. naa

a

nn52

11

1

0

_________ 321 aaa

Algebra II CP: Chapter 9 Semester II Exam Review

Determine the vertex, the p value, the direction of opening, the focus, and the equation for the directrix. Graph the vertex, the focus, the directrix, as well as two additional points to complete the graph. Any non-integer values should be written as reduced fractions. No decimals!!

1. yx 102

1 2

2. xy 34

1 2

3. 68)1( 2 yx

Vertex , Vertex , Vertex ,

p = __________ p = __________ p = __________

Opens __________ Opens __________ Opens __________

Focus ,

Focus , Focus ,

Directrix __________

Directrix __________ Directrix __________

4. On the exam, how will you know that the question is asking about a parabola? What vocabulary/equations could you

look for to help you?

Determine the vertex, the p value, the direction of opening, the focus, and the equation for the directrix. Graph the vertex, the focus, the directrix, as well as two additional points to complete the graph. Any non-integer values should be written as reduced fractions. No decimals!!

5. 54)4( 2 yx

Vertex , p = __________

Opens __________ Focus ,

Directrix __________

Write the standard form of the equation of the parabola with the given directrix and vertex.

6. Vertex = 0,0 ; Directrix 2x

7. Vertex = 0,0 ; Directrix 10x

Standard Form: _________________________ Standard Form: _________________________

8. Vertex = 0,0 ; Directrix4

3x

Standard Form: _______________________________

9. The focus is always located ______________________ _______________________________________________. The directrix is always located _______________________ _______________________________________________.

Determine the center and radius of the circle. Answers cannot be decimals.

10. 22 120 yx

11. 223275 xy

12. 22248 yx

Center , Center , Center ,

r = __________

r = __________

r = __________

Write the standard form of the equation of the circle with the given radius and given center.

13. 32r , Center = 5,0

14. 25r , Center = 6,1

15. 52r , Center = 0,8

Equation: ____________________________ Equation: ____________________________ Equation: ____________________________

16. On the exam, how will you know that the question is asking about a circle? What

vocabulary/equations could you look for to help you?

17. On the exam, how will you know that the question is asking about an ellipse? What

vocabulary/equations could you look for to help you?

18. On the exam, how will you know that the question is asking about a hyperbola? What

vocabulary/equations could you look for to help you?

Determine the center, the vertices, the co-vertices, and the foci. Graph the center, vertices, a line along the major axis, co-vertices, a line along the minor axis, and foci. Use the major and minor axis lines to help you sketch the ellipse. All non-integer values should be reduced radicals.

19. 1616 22 yx

20. 4001251622 yx

21. 1449516 22 yx

Center ,

Vertices , ,

Center ,

Vertices , ,

Center ,

Vertices , ,

Co-vertices , ,

Co-vertices , ,

Co-vertices , ,

Foci , ,

Foci , ,

Foci , ,

Determine the center, the vertices, the co-vertices, and the foci. Graph the center, vertices, a line along the major axis, co-vertices, a line along the minor axis, and foci. Use the major and minor axis lines to help you sketch the ellipse. All non-integer values should be reduced radicals.

22. 4414492922 yx

23. 64316422 yx

24. 364536 22 yx

Center ,

Vertices , ,

Center ,

Vertices , ,

Center ,

Vertices , ,

Co-vertices , ,

Co-vertices , ,

Co-vertices , ,

Foci , ,

Foci , ,

Foci , ,

Determine the center, the vertices of the transverse axis, the conjugate axis points, and the foci. All non-integer values should be reduced radicals.

25. 1169

22

xy

26. 11336

22

yx

27. 11764

22

xy

Center ,

Vertices , ,

Center ,

Vertices , ,

Center ,

Vertices , ,

Conjugate

axis points: , ,

Conjugate

axis points: , ,

Conjugate

axis points: , ,

Foci , ,

Foci , ,

Foci , ,