Algebra II CP Semester II Review Packet...

21
3 3 3 θ 17 x 49˚ Algebra II: Chapter 13 Semester II Exam Review Name _______________________________________ Evaluate the six trigonometric functions of the angle θ θ θ. Answers must be reduced fractions and cannot be decimals. 1. Cos θ = Sin θ = Csc θ = Tan θ = Sec θ = Cot θ = 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 7π - 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

Transcript of Algebra II CP Semester II Review Packet...

Page 1: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

3 3

3 θ

17 x

49˚

Algebra II: Chapter 13 Semester II Exam Review Name _______________________________________

Evaluate the six trigonometric functions of the ang le θθθθ. Answers must be reduced fractions and cannot be dec imals.

1.

Cos θ = Sin θ = Csc θ =

Tan θ = Sec θ = Cot θ =

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

7π−

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. Roun d 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

Page 2: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

Use the given point on the terminal side of an angl e θθθθ in standard position to evaluate the trig. function s of θθθθ. Answers should be reduced fractions and cannot be d ecimals. 9. ( 7, −5)

Cos θ =

Sec θ =

Sin θ =

10.

Find the value of the Cot θ if the terminal side of the angle θ 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

π−

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 θ , if Tan θ = °<<°− 18090;3

4 θ

Cos θθθθ = _____________

15. Find Sin θ , if Cos θ = °<<° 360270;7

6 θ

Sin θθθθ = _____________

3 5 π

tan

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Multiple Choice: Circle the answer to each question .

16.

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

A. sin = 0.6, cos = 0.8

B. sin cos

17.

Given the angle

A. sin =

2

1− ,

cos = 2

1−

B. sin

cos

Determine whether you would use the Law of Sines or the Law of Cosines for each prOnce you start using one method, you must use that method through the whole problem. Formulas will provided on the exam. You will need to write them on your notecard. Round answers to th e nearest tenth.

Law of Sines :c

C

b

B

a

A sinsinsin ==

18. 12,83,43 =°=°= bCA

LOS LOC

a = ______ B = ______ c = ______

19. 17,20,75 ==°= caB

LOS LOC

b = ______ A = ______ C = ______

Multiple Choice: Circle the answer to each question .

) is located on a unit circle. Find sin , cos

= 0.14, = 0.6

C. sin = 0.8, cos = 0.6

on the unit circle, find sin , cos .

= 2

1

= 2

1−

C. sin = 2

3− ,

cos = 2

1−

Determine whether you would use the Law of Sines or the Law of Cosines for each pr oblem. Circle your metOnce you start using one method, you must use that method through the whole problem. Formulas will

to write them on your notecard. Round answers to th e nearest tenth.

Law of Cosines: ( ) ( ) ( )( )(( ) ( ) ( )( )( ) ( ) ( )( )babac

cacab

cbcba

2

2

2

222

222

222

−+=

−+=

−+=

= ______

= ______

D. sin = -0.8, cos = 0.2

D. sin = 2

1−

cos = 2

3−

oblem. Circle your met hod. Once you start using one method, you must use that method through the whole problem. Formulas will not be

to write them on your notecard. Round answers to th e nearest tenth.

)( ))( ))( )C

B

A

cos

cos

cos

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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 foll owing values and describe the shifts (up, down, lef t, right).

1. xy2

1sin4=

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

2. xy2

sin4π−=

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

3. 42cos −= xy π Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

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4. 42

cos −

= xyπ

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

5. 52

cos3 +

−= πxy

Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

6. ( ) 126sin8 −+−= πxy Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

7. ( ) 944cos +−= xy π Amplitude = _______

h = _______ Shift = ______________________

b = _______

Period = ________________

k = _______ Shift = ______________________

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Algebra II CP: Chapter 10 Semester II Exam Review Name ____________________________________ For the given configuration, determine how man y different license plates are possible if (a) digi ts and letters can be repeated, and (b) digits and letters cannot be r epeated.

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 permuta tion of combination. Then find the number of possi bilities.

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: _______________

Disjoint Events:

Formula:

Overlapping Events:

Formula:

Independent Events:

Formula:

Dependent Events:

Formula:

Circle whether the events are disjoint, overlapping , independent, or dependent. Then, find the probabi lity.

7. You are selecting a single card from a standard deck of 52 cards. Find the probability that you select a 7 or a Queen.

8. You are selecting a single card from a standard deck of 52 cards. Find the probability that you select a face card or a Heart.

DISJOINT OR OVERLAPPING ANSWER: ________ _________ DEPENDENT OR INDEPENDENT

DISJOINT OR OVERLAPPING ANSWER: _________________ DEPENDENT OR INDEPENDENT

Page 7: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

9. A single die is rolled. Find the probability that a 2 or a 6 is rolled.

10. A single die is rolled. Find the probability that an even number or a number whose name contains 4-letters is rolled.

DISJOINT OR OVERLAPPING ANSWER: ________ _________ DEPENDENT OR INDEPENDENT

DISJOINT OR OVERLAPPING ANSWER: ________ _________ DEPENDENT OR INDEPENDENT

11. If three coins are tossed one right after the other, what is the probability that the first is heads, the second is tails, and the third is tails?

12. You draw three cards one at a time from a standard deck of 52 cards. Find the probability that you select a Club, then a Diamond, and then another Club with replacement.

DISJOINT OR OVERLAPPING ANSWER: ________ _________ DEPENDENT OR INDEPENDENT

DISJOINT OR OVERLAPPING ANSWER: ________ _________ DEPENDENT OR INDEPENDENT

13. You draw three cards one at a time from a standard deck of 52 cards. Find the probability that you select a Club, then a Diamond, and then another Club without replacement.

14. The owner of a bakery offers Dean a cookie from a jar containing 14 chocolate chip cookies, 11 sugar cookies and 5 oatmeal cookies. Dean selects one cookie, puts it back in, and then randomly selects another. What is the probability that the first selection was a sugar cookie and the second was another sugar cookie?

DISJOINT OR OVERLAPPING ANSWER: ________ _________ DEPENDENT OR INDEPENDENT

DISJOINT OR OVERLAPPING ANSWER: ________ _________ DEPENDENT OR INDEPENDENT

15. A bowl contains 10 purple jelly beans, 7 green jelly beans, and 5 black jelly beans. Three beans are drawn one at a time. After each bean is drawn, the color is recorded and then it is eaten. What is the probability of drawing a green, followed by a black, followed by another black?

16. A bowl contains 10 purple jelly beans, 7 green jelly beans, and 5 black jelly beans. Three beans are drawn one at a time. After each bean is drawn, the color is recorded and then it is returned to the bowl. What is the probability of drawing a purple, followed by a black, followed by another purple?

DISJOINT OR OVERLAPPING ANSWER: ________ _________ DEPENDENT OR INDEPENDENT

DISJOINT OR OVERLAPPING ANSWER: ________ _________ DEPENDENT OR INDEPENDENT

Page 8: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

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

17. P(a red Jack is chosen)

18. P(a black 9 is chosen)

ANSWER: _________________ ANSWER: _________________

19. Odds in favor of choosing an Ace

20. Odds against choosing a 2 21. Odds against choosing a Queen

ANSWER: _________________ ANSWER: _________________ ANSWER: _________________

Page 9: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

Algebra II CP: Chapter 8 Semester II Exam Review Find the vertical and horizontal asymptotes, as wel l as the xdoes not have one of the above, simply write “none” or cross it out

1. 36

1522

2

−−+=

x

xxy

2.

VA: x = ____________

HA: y = ____________

X-intercept(s): ( ), ( ),

VA:

HA:

X

4. 12

1811

++=

x

xy

5.

VA: x = ____________

HA: y = ____________

X-intercept(s): ( ), ( ),

VA:

HA:

X

Determine each of the following values, then graph the function. Round all decimals to the nearest ten th. Vertical Asymptote: x = ____________

X-intercepts/Zeros:

( ), ( ),

Domain : ___________________________ Range : ____________________________

Name ________________________________________Find the vertical and horizontal asymptotes, as wel l as the x -intercepts/zeros of the graph of the function. If t he graph does not have one of the above, simply write “none” or cross it out . Round all decimals to the nearest tenth.

2. 2

122

2

−+−=

x

xxy 3.

2=x

y

VA: x = ____________

HA: y = ____________

X-intercept(s): ( ), ( ),

VA: x

HA: y

X-intercept(s):

5. 25

952

2

−+=

x

xy 6.

−=y

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 ten th. Horizontal Asymptote: y = ____________

7. ( ) =xf

Additional Points:

x y

____________________________________ intercepts/zeros of the graph of the function. If t he graph

. Round all decimals to the nearest tenth.

7

122 +

+x

x

x = ____________

y = ____________

intercept(s): ( ), ( ),

2

20152 +

−−x

x

x = ____________

y = ____________

intercept(s): ( ), ( ),

Determine each of the following values, then graph the function. Round all decimals to the nearest ten th.

62

4

−=

x

x

Page 10: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

Vertical Asymptote: x = ____________

X-intercepts/Zeros:

( ), ( ),

Domain : ___________________________ Range : ____________________________

Vertical Asymptote: x = ____________

X-intercepts/Zeros:

( ), ( ),

Domain : ___________________________ Range : ____________________________

10.

Find the quotient: 4

3

2

92

2

−+÷

+−

x

x

x

x

A.

2

3

+−

x

x

B. −x

Horizontal Asymptote: y = ____________

8. ( ) =xf

Additional Points:

x y

Horizontal Asymptote: y = ____________

9. =x

xy

Additional Points:

x y

2− C. ( )( )23 −− xx

52

34

−−=

x

x

4

252

2

−−

x

D. 842

279323

23

−−+−−+

xxx

xxx

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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

Page 12: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

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

Page 13: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

Algebra II CP: Chapter 12 Semester II Exam Review Name ____________________________________ NOTE: The following formulas will NOT be provided o n the exam.

( )dnaan 11 −+=

+=

21 n

n

aanS

1

1

−= n

n raa

−−=

r

raS

n

n 1

11

r

aS

−=

11

daa nn += −1 1−⋅= nn ara

Tell whether th e 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 = ________

Page 14: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

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 nS of the arithmetic series.

12. ( )∑=

+8

1

52x

x

13. ( )∑ +−=

30

1205

nn

14. ∑=

5

1

9n

n

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

15. ...,16

27,

8

9,

4

3,

2

1

16. ,...25

7,

5

7,7,35

−−

Rule: _____________________________

13a = ________

Rule: _____________________________

10a = ________

Page 15: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

17. 2,968 −=−= ra

Rule: _____________________________ 15a = ________

Find the sum of the geometric series.

18. ∑

=

−5

1

1

2

117

n

n

19. ( )∑=

−10

1

125i

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

nn 3

4

1

0

−=−=

_________ 321 === aaa

26. naa

a

nn 52

11

1

0

+=−=

_________ 321 === aaa

Page 16: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

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 tw o additional points to complete the graph. Any nonshould be written as reduced f ractions. No decimals!!

1. yx 102

1 2 −=

2.

Vertex ( ), Vertex

p = __________ p =

Opens __________ Opens __________

Focus ( ),

Focus

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?

x y

Name ____________________________________

value, the direction of opening, the focus, and the equation for the directrix. Graph the vertex, the focus, the directrix, as well as tw o additional points to complete the graph. Any non

ractions. No decimals!!

xy 34

1 2 =

3. )1( 2 =−x

Vertex ( ), Vertex (= __________ p = __________

Opens __________ Opens __________

Focus ( ), Focus ( ,

Directrix __________ Directrix __________

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

x y

x

Name ____________________________________ value, the direction of opening, the focus, and the equation for the directrix. Graph

the vertex, the focus, the directrix, as well as tw o additional points to complete the graph. Any non -integer values

( )68 −−= y

),

__________

Opens __________

),

__________

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

y

Page 17: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

Determine the vertex, the p value, the direction of opening, the focus, and the equationthe vertex, the focus, the directrix, as well as tw o additional points to complete the graph. Any nonshould 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 2−=x

Standard Form: _________________________

8. Vertex = ( )0,0 ; Directrix4

3−=x

Standard Form: _______________________________

Determine the center and radius of the circle. Answ ers cannot be decimals.

10. ( )22 120 +−= yx

11.

Center ( ), Center

r = __________

r =

value, the direction of opening, the focus, and the equation for the directrix. Graph the vertex, the focus, the directrix, as well as tw o additional points to complete the graph. Any nonshould be written as reduced fractions. No decimals !!

x y

__________

),

he equation of the parabola with the given directrix and vertex.

7. Vertex = ( )0,0 ; Directrix 10=x

________ Standard Form: ________________

Standard Form: _______________________________

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

Determine the center and radius of the circle. Answ ers cannot be decimals.

. ( ) ( )22 3275 −−=− xy

12. ( )28x +

Center ( ), Center (

= __________

r = __________

for the directrix. Graph the vertex, the focus, the directrix, as well as tw o additional points to complete the graph. Any non -integer values

10

_____________________

The focus is always located ______________________

_______________________________________________.

The directrix is always located _______________________

_______________________________________________.

224 y−=

),

__________

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

13. 32=r , Center = ( )5,0

14. 25=r , Center = ( )6,1−

15. 52=r , 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?

Page 19: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

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

19. 1616 22 =+ yx

20.

Center ( ),

Vertices ( ), ( ),

Center

Vertices

Co-vertices ( ), ( ),

Co

Foci ( ), ( ),

Foci

Determine the center, the vertices, the co -vertices, and the foci. Graph the cent er, vertices, a line along the major vertices, a line along the minor axis, and foci. Us e the major and minor axis lines to help you sketch the

integer values should be reduced radicals.

. ( ) 40012516 22 =−+ yx

21. ( )516 −x

Center ( ),

Vertices ( ), ( ),

Center (

Vertices (

Co-vertices ( ), ( ),

Co-vertices (

Foci ( ), ( ),

Foci ( ,

er, vertices, a line along the major vertices, a line along the minor axis, and foci. Us e the major and minor axis lines to help you sketch the

) 1449 22 =+ y

),

), ( ),

( ), ( ),

) ( ),

Page 20: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

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

22. ( ) ( ) 44144929 22 =++− yx

23.

Center ( ),

Vertices ( ), ( ),

Center

Vertices

Co-vertices ( ), ( ),

Co

Foci ( ), ( ),

Foci

the vertices, the co -vertices, and the foci. Graph the center, vertices, a line along the major vertices, a line along the minor axis, and foci. Us e the major and minor axis lines to help you sketch the

integer values should be reduced radicals.

. ( ) 643164 22 =−+ yx

24. ( 536 +x

Center ( ),

Vertices ( ), ( ),

Center (

Vertices (

Co-vertices ( ), ( ),

Co-vertices (

Foci ( ), ( ),

Foci ( ,

vertices, and the foci. Graph the center, vertices, a line along the major vertices, a line along the minor axis, and foci. Us e the major and minor axis lines to help you sketch the

) 3645 22 =+ y

),

), ( ),

( ), ( ),

) ( ),

Page 21: Algebra II CP Semester II Review Packet 10-11mi01000971.schoolwires.net/cms/lib05/MI01000971/Centricity/Domain/2361... · Multiple Choice: Circle the answer to each question. 16.

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 ( ), ( ),