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ALGEBRA II CP
FINAL EXAM REVIEW PACKET
NAME:______________________
TEACHER:__________________
Algebra II CP: Chapter 7.4-7.6 Semester II Exam Review Name:__________________________________________
Convert each of the following.
1. 932 to logarithmic form
2. 127 e to logarithmic form
3. x10ln3
1 to exponential form
4. xx 20ln to exponential form
Use the Change of Base Theorem to evaluate the following expressions.
5. 37log 4
6. 17log3
Use the rules of logs to condense the expression.
7. 5loglog 33 xx
8. 8loglog 3
2
3 x 9. y5log2 10. 2log52log4 33
Solve each logarithmic equation.
11.
2
1log 4 x
12. 2124log6 x
13. 13ln x
14. 32loglog22
xx
15. 36loglog 33 xx
Solve each exponential equation. Round all decimals to two decimal places.
16. 82 3 z
17. 11
93
nn
18.
25
6
5
15
x
x
19. 5352 x
20. 1514 2 xe
Use the formulas to solve the following story problems. You will need to have these on your notecard for the exam.
rtPeA tray 1
nt
n
rPA
1
21. A computer system depreciates at a rate of 15% per year. If the computer system originally cost $4000, how long would it take for it to be worth half its value?
22. A car depreciates in value 17% per year. After approximately how long will a $30,000 car be worth half its original value?
23. Suppose you deposit $1,000 in an account paying 6.5% annual interest compounded continuously. What is the balance after 6 years?
24. You deposit $10,000 in an account paying 6.5% annual interest compounded continuously. What is the balance after 6 years?
Find the inverse of the function.
25. )1(log5 xy
26. 3ln xy
3
3 θ
17 x
49˚
Algebra II CP: Chapter 13 Semester II Exam Review
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:
Cbabac
Bcacab
Acbcba
cos2
cos2
cos2
222
222
222
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 8.4-8.6 Semester II Exam Review Name______________________________________
1.
Simplify: 9
24112
2
x
xx
2.
Simplify: 5163
1022
2
xx
xx
3.
Simplify: 54
3
14
6
cdab
bda
4.
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
5.
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.
6. 34
54
25
32
2
2
2
cc
cc
c
cc
7. 5
2
4
2
7
274
14
1816
p
pp
p
pp
Simplify.
8.
25
2
5
32
xx
9. 2
1
42
3
x
x
x
x
10. xx 24
5
18
72
11. xyx 14
3
6
132
Solve the following equations. Check for extraneous solutions.
12.
54
9
1
3
xx
13.
24
6
2
2
xx
14.
6
121
6
1
x
x
xx
x
15. 33
149
3
2
x
x
x
x
16.
xx
3
5
81
17. 4
1
3
4
3
9
x
x
x
Algebra II CP: Chapter 10 Semester II Exam Review Name ____________________________________
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: _______________
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 probability.
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. Find 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: Chapter 11 Semester Review Name _____________________________________________
Find the margin of error for a survey that has the given sample size. Round your answer to the nearest tenth of a percent.
1. 935
1. _________
2. 7103
2. _________
A recent survey of 5000 people showed that 78% returned a purchase during the month of December. Find the margin of error for the survey.
3.
MOE: _________
Calculate the following values for each data set. Round decimals to the nearest tenth. 4.
−7.2 3.9 2.6 −9.1
3.9 −7.2 2.5 −7.2
5.
16 8 29 30
38 46 34 35
Mean: _________ Median: _________ Range: _________ Mean: _________ Median: _________ Range: _________
Mode: _________
Standard Deviation: _________
Mode: _________
Standard Deviation: _________
Use the given situations to label the deviations and mean of the provided bell curve. Then answer the questions. You must provide the work/numbers you used to arrive at your answer.
An Algebra II teacher calculates the mean of the latest test scores to be 72 points with a standard deviation of 8.5 points.
6. What percentage of the scores were at least 80.5 points? Answer:__________
7. What percentage of scores were more than 89 points? Answer:__________
8. What percentage of the scores were more than 55 points? Answer:__________
9. What percentage of the scores were between 63.5 and 97.5 points? Answer:__________
For a randomly selected x-value from the distribution, find the following probabilities. You must provide the work/numbers you used to arrive at your answer.
10. 3 xxP
Answer:__________
11. 1 xxP
Answer:__________
Algebra II CP: Chapter 12.1-12.3 Semester II Exam Review Name ____________________________________
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
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 = ________
Find the n
S of the arithmetic series.
10.
8
1
52x
x
11.
30
1
205n
n
12.
5
1
9n
n
Write a rule for the nth term of the geometric sequence. Then find the indicated term.
13. ...,16
27,
8
9,
4
3,
2
1
14. ,...25
7,
5
7,7,35
Rule: _____________________________
13a = ________
Rule: _____________________________
10a = ________
15. 2,968
ra
Rule: _____________________________ 15
a = ________
Find the sum of the geometric series.
16.
5
1
1
2
117
n
n
17.
10
1
125
i
i
18.
18
1
1
4
13
n
n
