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Algebra II Name_________________________________________ Final Exam Review Chapter 7 REVIEW:

EXPONENT RULES

MADD MAPP DIS Flip

Simplify the expression using the properties of exponents. Assume all variables are positive.

1. 43

41

88

2. 31

2x 3. 3

1

3

1

xx

4. 32

3x 5.

5

2

5

3

9

9 6. 31

x

7. 2

3

36

8. 3

138x

9.

7

1

7

3

2

2

RADICAL FORM «----------» RATIONAL EXPONENTS

Write using rational exponents . . . Write in radical form . . .

49 3

32

15

Write the expression using rational exponents. Write the expression in radical form.

10. 45 3 11. 23 7 12. 53

5 13. 114

16

Evaluate each expression. (CALCULATOR)

14. 32

8 15. 41

81 16. 5 243 17. 3 8

Write each radical expression in SIMPLEST FORM. Assume all variables are positive. (Remember to make your ladder OR factor tree and look for groups based on the index.)

18. 3 5108x index = _____

19. 3 34250 yx index = _____

20. 4 9464 ba index = _____ 21. 5 65160 yx index = _____

Solve each equation. Remember to write both answers when the radical has an EVEN INDEX!

22. 6254 x 23. 1084 3 x

24. 2743

x 25. 813

x

Solve the equation. Make sure to check your answer for any extraneous solutions.

26. xx 1012 27. 33 10510 xx

28. 823

x 29. 6431

x

Perform the operations given 22xxf , 23 xxg , 52 xxh , and 36xxj .

30. xgxh 31. xhxg 31. xgxh

Find each composition. 23 xxg and 52 xxf

32. xfg

33. xgf

Find the inverse of each function.

34. 15)( xxf 35. 153 xxf

Graph the PARENT graph for both the square root function and the cube root function.

36. xy

x h y a k

0 ,

1 ,

2 ,

3 ,

37. 3 xy

x h y a k

-1 ,

0 ,

1 ,

2 ,

Graph the square root and cube root equations and then describe the transformation from the parent graph.

38. 23 xy

a = _______

SHRINK STRETCH FLIP

h = _______

RIGHT LEFT

k = _______

UP DOWN

x h y a k

0 ,

1 ,

2 ,

3 ,

39. 123 xy

a = _______

SHRINK STRETCH FLIP

h = _______

RIGHT LEFT

k = _______

UP DOWN

x h y a k

-1 ,

0 ,

1 ,

2 ,

38. xy2

1

a = _______

SHRINK STRETCH FLIP

h = _______

RIGHT LEFT

k = _______

UP DOWN

x h y a k

0 ,

1 ,

2 ,

3 ,

39. 32 xy

a = _______

SHRINK STRETCH FLIP

h = _______

RIGHT LEFT

k = _______

UP DOWN

x h y a k

-1 ,

0 ,

1 ,

2 ,


Determine the base (b) and then circle whether the function represents exponential growth or exponential decay.

1.

x

y

4

1

b = _______ growth decay

2. 228 xy


3. 52

5

x

y


Determine the a, b, h, k, as well as the equation for the Horizontal Asymptote, and if it represents growth or decay. Describe any shifts on the line provided. Then, fill out the table and graph the function. Round all decimals to two decimal places.

4. xy 21

a = _______

b = _______

Growth OR Decay

h = _______

______________________

k = _______

______________________

HA = _______________

x h y k

1

,

0

,

1

,

2

,

5.

x

y

3

11

a = _______

b = _______

Growth OR Decay

h = _______

______________________

k = _______

______________________

HA = _______________

x h y k

1

,

0

,

1

,

2

,

6. 223 1 xy

a = _______

b = _______

Growth OR Decay

h = _______

______________________

k = _______

______________________

HA = _______________

x h y k

1

,

0

,

1

,

2

,

7. 12

14

2

x

y

a = _______

b = _______

Growth OR Decay

h = _______

______________________

k = _______

______________________

HA = _______________

x h y k

1

,

0

,

1

,

2

,

8. The graph of which function is shown?

Solve the following exponential equations. Check for any extraneous solutions. Round to 2 decimal places.

#9 and #10 THE BASES ARE THE SAME!

9. 314 88 x 10.

4622 xx


#11—14 THE BASES ARE NOT THE SAME!

11. 13525 xx 12. 366 75 m

13. 65525 xx

14. 34864 x

KNOW YOUR FORMULAS FOR THE FINAL EXAM. Below each formula write what each one is used for. Make sure to write them on your note sheet!

tray 1 tray 1

nt

n

rPA

1

rtPeA

15. You buy a new stereo system for $640. The value of the system decreases by 7% each year. What will the value of the stereo system be in 3 years?

16. You deposit $2200 into an account that pays 3% interest compounded quarterly. How much will be in your account after 15 years?

17. You deposit $3000 in an account that pays 5% annual interest compounded continuously. What is the balance in the account after 2 years?

18. In 1990, the population of a town was 2200. If the population increased by about 3% each year, about how many people will live in the town after 5 years?

LOG FORM «----------» EXPONENTIAL FORM

Write using exponential form . . . Write using logarithmic form . . .

932

Rewrite in logarithmic form. Convert to exponential form.

19. 1624

20. 115 0

21. 3

14log 64

22. 236

1log6

Condense the expression.

23. 3log12log 77 24. 3log212log 77

25. x33 log45log 26. 7loglog3 22 y

Expand the expression.

27. 3

5 3log y 28.

4log 3

x

29. 5log xy 30.

7log

3

2

x

Evaluate each expression. (Set each expression equal to x and rewrite in exponential form to help!)

31. 169log13

32. 64log2

1 33. 1000log

34. 1log 3


#35 and #36 WHEN YOU CAN’T REWRITE WITH THE SAME BASE!

35. 604 x 36. 1507 x

Solve the following logarithmic equations. Check for any extraneous solutions. Round any decimals to the 100th.

#37 and #38 WHEN THE BASES ARE THE SAME WITH LOGS on BOTH SIDES!

37. 94log119log 22 xx 38. 34log72log 33 xx

Solve the following logarithmic equations. Check for any extraneous solutions. Round any decimals to the 100th.

#39 and #40 WHEN THERE IS ONLY A LOG ON ONE SIDE!

39. 246log8 x 40. 232log 7 x

Algebra II Name_________________________________________ Final Exam Review Chapter 12: REVIEW

SOH CAH TOA & CSC SEC COT

Evaluate the six trigonometric functions of the angle θ shown in the triangle. (Answer should be simplified ratios!) 1.

2.

Find the value of x for each missing side. Round your answer to two decimal places. (SOH CAH TOA) 3.

x = _____

4.

x = _____

5.

x = _____

Hypotenuse = _________

Cos = Sec =

Sin = Csc =

Tan = Cot =

9

x

23°

x

4 35°

3 x 63°

Hypotenuse = _________

Cos = Sec =

Sin = Csc =

Tan = Cot =

8 17

Find the value of angle for the triangle. Round angles to the nearest degree. (SOH CAH TOA) 6.

=_____

7.

=_____

8.

=_____

REVIEW: Fill in the patterns below and then use them to find the values of x and y.

9.

x = _____ y =_____

10.

x = _____ y =_____

11.

x = _____ y =_____

Solve the following word problems by drawing a picture.

12. You lean a 20 foot ladder against a wall. The base of the ladder is 4 feet from the wall. What is the angle of elevation to the top of the ladder.

13. A flagpole casts a shadow 10 feet long. The angle of depression from the top of the flagpole is 63. Sketch a diagram that represents this situation. What is the height of the flagpole? Round your answer to the nearest hundredth.

45°

y x

5

60°

3

x

y 60°

y

x

8

5

θ

11

θ

12

17

θ

13

20

45°

45°

60°

30°

Find one positive and one negative angle that is COTERMINAL with the given angle.

Angle + ___________

Angle − ___________

14. 50° 15. 200°

Use a calculator to evaluate the following.

16.

2

1cos 1

17. 1tan 1

18.

2

3sin 1

Determine if the given trig function in the specified quadrant is positive or negative.

19. tangent in quadrant II 20. sine in quadrant IV 21. Cosine in quadrant IV

Use the given point on the terminal side of an angle θ in standard position. Find the exact value of sine, cosine, and tangent.

22. (8, 15)

Cos = Sin = Tan =

23. (3, 4) Cos = Sin = Tan =

Convert to radians.

Multiply by:

Convert to degrees.

Multiply by:

24. 128 25. 210 26.

5

9

27. 3

2

Draw an angle with the given measure in standard position. Determine which quadrant the terminal side lies and find the reference angle.

28. 225

Quadrant = ____ Reference Angle=______

29. 240

Quadrant = ____ Reference Angle=______

Find the following exact values. Do you remember how to determine if the function is positive or negative depending on the quadrant?

30. sin 150 31. cos 315°

Use a calculator to evaluate each quadrantal angle.

32. sin 90 33. sec −180°

34. tan 180

Use the Law of Sines to find the specified value. 35.

x =________

36.

C =_______

Use the Law of Cosines to find the specified value. 37.

A =_______

38. x =_______

Sine Graphs:

Sine graph always starts at:

xbay sin

Cosine Graphs:

Cosine graph always starts at:

xbay cos

How to find the amplitude: How to find the period:

x

x

180°

360°

90°

270°

Directions: Identify a, b, and the length of one period. Then complete the table, and sketch the graph.

39. xy sin a = _______

b = _______

Length of period = ________________

x y Ordered Pairs

,

,

,

,

,

40. xy cos a = _______

b = _______


x y Ordered Pairs

,

,

,

,

,

41. xy 2cos4 a = _______

b = _______


x y Ordered Pairs

,

,

,

,

,

42. xy 4sin3

1 a = _______

b = _______


x y Ordered Pairs

,

,

,

,

,

43. xy5

2sin a = _______

b = _______


x y Ordered Pairs

,

,

,

,

,

44. xy4

1cos2 a = _______

b = _______


x y Ordered Pairs

,

,

,

,

,

Choose the best answer for each multiple choice question.

45. What is the amplitude of the graph? A. 30 B. 1 C. 2 D. 120

46. Which of the following is the equation for the trig graph shown? A. xy 2sin5

B. xy2

1sin10

C. xy 2cos5

D. xy2

1cos10

Match the graph with its equation by writing the appropriate letter next to the equation.

47. xy 2sin3 ________

48. xy2

1sin3 ________

49. xy 2cos3

________

Algebra II Name_________________________________________ Final Exam Review Statistics REVIEW:

Mean Median Mode Range

For #12, find the mean, median, mode, and range, for each data set. DON’T FORGET TO PUT THE NUMBERS IN ORDER FIRST!

1. The number mice born in nine different litters: 5, 7, 6, 3, 8, 6, 4, 5, 4

Mean _______ Median _______ Mode(s) ________ Range _______

2. A student’s quiz scores for the first semester of an algebra class:

18, 20, 14, 15, 20, 17, 16

Mean _______ Median _______ Mode(s) ________ Range _______

For #310, use each box-whisker plot to answer the following questions.

3. Find each: LQ: _______ Range:_______ Median: ______ UQ: _______ IQR: ________

4. What percent of the data is greater than 1331? 5. What percent of the data is between 1067 and 1331? 6. What percent of the data is less than 1331?

7. Find each: LQ: _______ Range:_______ Median: ______ UQ: _______ IQR: ________

8. What percent of the data is less than 17? 9. What percent of the data is between 10 and 22? 10. What percent of the data is greater than 22?

Algebra II Name_________________________________________ Final Exam Review Probability REVIEW:

Counting Principle Permutations Combinations Probability Odds

For #1−4, find the number of possibilities. (COUNTING PRINCIPLE) 1. Graham has 5 shirts, 3 ties, and 4 pairs of pants. If he wears a shirt, a tie, and a pair of pants, in how many different outfits can he appear?

2. How many four digit numbers can be formed from the digits 4, 5, 6, 7, 8, 9 if the digits MAY NOT REPEAT?

3. How many license plates can be formed using a letter followed by five digits (the digits MAY REPEAT)?

4. How many license plates can be formed using three letters followed by two digits and repetition is NOT

ALLOWED?

Use your calculator to evaluate #14. Make sure you know how to find these keys on your calculator for the exam!

5. 38 C 6. 410 P 7. 411C

8. 215 P

For #914, circle whether each is a Permutation or Combination and then determine the number of possibilities. Make sure to SHOW THE NUMBERS YOU USE!

9. An employee at a pet store needs to catch 5 tetras in an aquarium containing 27 tetras. In how many groupings can the employee capture 5 tetras? Permutation Combination

10. Fifty-two athletes are competing in a bicycle race. In how many orders can three of the bicyclists finish in first, second, and third? Permutation Combination

11. How many different all-star teams of 9 members can be formed from a group of 14 talented players? Permutation Combination

12. You are required to read 5 books from a list of 12 great American authors. How many groups can be selected? Permutation Combination

13. At Hollywood Video, 14 DVDs are on sale. How many different ways could you choose 3 of them to buy? Permutation Combination

14. Sixteen people are competing in a pie baking contest. In how many ways can first, second, third, and fourth place be awarded? Permutation Combination

Given the spinner below, state the probability of each outcome for #1518 if landing on each number is equally likely. Simplify ALL fractions.

15. Landing on an EVEN number 16. Landing on 1, 4, OR 7

17. Not landing on a 1, 4, or 7 18. Does not land on a number that is divisible by 3

For #1924 if a card is drawn at random from a standard deck of 52 cards, find each probability or odds. Simplify ALL fractions.

19. P(a red Jack is chosen) 20. P(a black 9 is chosen) 21. P(a black card is chosen)

22. Odds in favor of choosing an Ace

23. Odds against choosing a 2 24. Odds against choosing a Queen

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.

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

26. 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


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

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



29. 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?

30. 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.



31. 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.

32. 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?



33. 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?

34. 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?




Find the specified term of a sequence given the rule.

EXAMPLE: If you are looking for the Tenth term, you PLUG IN _________.

1. Find the tenth term of the sequence: 32 nan

10a =

2. Find the seventh term of the sequence: 54 nan

7a =

ARITHMETIC GEOMETRIC

Arithmetic is when you: Geometric is when you:

d:

r:

To find the value of d:

To find the value of r:

Determine if the sequence is arithmetic (d) or geometric (r) and write the next three terms in the sequence.

3. ...,24,19,14,9,4

ARITHMETIC GEOMETRIC _______, _______, _______

d = ______ r = ______

4. ...,108,36,12,4


d = ______ r = ______

5. ...,256

1,

64

1,

16

1,

4

1


d = ______ r = ______

6. ,...3

7,

3

6,

3

5,

3

4


d = ______ r = ______

The following formulas will NOT be given on the EXAM so make sure you write them on your note sheet. Below each formula, write what each is used for.

dnaan 11

2

1 n

n

aanS

1

1

n

n raa

r

raaS

n

n

1

11

Given the arithmetic sequence, find the next 3 terms.

7. ...,20,14,8,2,4

d = ______ _______, _______, _______

8. ...37,33,29,25

d = ______ _______, _______, _______

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

9. ...,2,1,4,7,10

__________,1

da

Rule: _____________________________

10. ...2

1,

4

1,0,

4

1

__________,1

da

Rule: _____________________________

11. 2,106

da

__________,1

da

Rule: _____________________________

12. 5,335

da

__________,1

da

Rule: _____________________________

dnaan 11

2

1 n

n

aanS

1

1

n

n raa

r

raaS

n

n

1

11

Find the sum of the first 10 terms of the arithmetic series.

13. ...1013161922

______

______

______

_____

___

1

a

n

d

a

_____n

S

14. ...3.39.25.21.27.1

______

______

______

_____

___

1

a

n

d

a

_____n

S

Find the specified term of each geometric sequence.

15. Find the fifth term if 261 ra

5a =

16. Find the seventh term if 381 ra

7a =

Write a rule for the nth term of each geometric sequence.

17. ...,144,72,36,18,9

__________,1 ra

Rule: _____________________________

18. ...,3,9,27,81

__________,1

da

Rule: _____________________________

Find the sum of the first 7 terms of the geometric series.

19. ...241263

______

______

_____1

n

r

a

_____n

S

20. ...125002500500100

______

______

_____1

n

r

a

_____n

S

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