Post on 13-Mar-2020
3 3
3 θ
17 x
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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
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
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
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 = ______________________
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 = ______________________
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
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
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: _________________
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
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
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 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 = ________
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 = ________
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
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
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−=
),
__________
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?
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
),
), ( ),
( ), ( ),
) ( ),
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
),
), ( ),
( ), ( ),
) ( ),
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 ( ), ( ),