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Review Final Exam - Algebra 2 (Chapters 5, 6, 7, 8, 10)

Simplify the expression.

1

2

____ 3 What is the simplified form of ?

A. C.

B. D.

____ 4 What is the simplified form of ?

F. H.

G. I.

____ 5 What is the simplified form of ?

A. C.

B. D.

____ 6 What is the simplified form of ?

F. H.

G. I.

7

____ 8 Use synthetic substitution to evaluate when = 3.

F. H.

G. I.

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Find the sum or difference.

9

10

Find the product.

11

Factor the polynomial completely.

12

13

Divide using polynomial long division.

14

Divide using synthetic division.

15

List the possible rational zeros of the function using the rational zeros theorem.

____ 16

F. H.

G. I.

Find all zeros of the polynomial function.

17

____ 18 Use the graph to approximate the real zeros of the function.

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F.

2 4 6 8 10246810 x

4

8

12

16

20

4

8

12

16

20

y

H.

2 4 6 8 10246810 x

4

8

12

16

20

4

8

12

16

20

y

G.

2 4 6 8 10246810 x

4

8

12

16

20

4

8

12

16

20

y

I.

2 4 6 8 10246810 x

4

8

12

16

20

4

8

12

16

20

y

____ 21 Write the expression using rational exponent notation.

A. C.

B. D.

____ 22 Write the expression using rational exponent notation.

F. H.

G. I.

Evaluate:

23

24

Write the expression in simplest form.

____ 25 What is the simplest form of the expression ? Assume all variables are positive.

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A. C.

B. D.

____ 26 What is the simplest form of the expression ? Assume all variables are positive.

F. H.

G. I.

Simplify the expression.

27

28 Let and . Find .

____ 29 Let and . Find .

A. C.

B. D.

30 Find an equation for the inverse of the relation

31 Graph the function f(x) = .

32 Find the domain and range of the function .

33 Graph the function .

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1010 x

10

10

y

Solve the equation. Check for extraneous solutions.

34

35

Graph:

36

37 The amount of money, A, accrued at the end of nyears when a certain amount, P, is invested at a compound

annual rate, r, is given by . If a person invests $250 in an account that pays 10% interest

compounded annually, find the balance after 15 years.

38 The projected worth (in millions of dollars) of a large company is modeled by the equation

The variable xrepresents the number of years since 1997. What is the projected annual percent of growth,and what should the company be worth be in 2007?

____ 39 Graph the function:

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A. C.

B. D.

Simplify:

____ 40

F. 5 H. 5 G. 1

5

I. 1

5

41 Use the formula If $5500 is deposited in an account at the bank and earns 9% annual interest,compounded continuously, what is the amount in the account, rounded to the nearest dollar, after 6 years?

42 Evaluate without using a calculator.

____ 43 Express as a single logarithm:

A. C.

B. D.

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44 Solve. = 0.3

Solve the equation. Check for extraneous solutions.

45

____ 46 It takes a train 8 hours to travel from Capital City to Johnson City when it travels at a speed of 65 mi/h.How long would it take the train to go the same distance when it travels 40 mi/h?

F. 13 h H. 13

8 h

G. 11 h I. 8

13 h

47 Decide whether the data show inverse variation. If so, find the missing value.

Identify the vertical asymptote(s) of the graph of the function.

48

Simplify the rational expression, if possible.

49

Multiply the expressions. Simplify the result.

50

51

Divide the expressions. Simplify the result.

52

( )

53

____ 54 Graph the rational function . Identify any asymptotes and other discontinuities.

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F. vertical asymptotes: ,

horizontal asymptote:

2 4 6 8 10 1224681012 x

2

4

6

8

10

12

2

4

6

8

10

12

y

H. vertical asymptotes: ,

horizontal asymptote:

2 4 6 8 10 1224681012 x

2

4

6

8

10

12

2

4

6

8

10

12

y

G. vertical asymptotes: ,

horizontal asymptote:

2 4 6 8 10 1224681012 x

2

4

6

8

10

12

2

4

6

8

10

12

y

I. vertical asymptotes: ,

horizontal asymptote:

2 4 6 8 10 1224681012 x

2

4

6

8

10

12

2

4

6

8

10

12

y

Perform the indicated operation(s) and simplify.

____ 55

A. B. C. D.

____ 56 +

F. G. H. I.

Solve the equation. Check for extraneous solutions.

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____ 57

A. 7 B. 8 C. 10 D. 9

58

59 Find the first four terms of the sequence .

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

60 12,5, 2, 9, . . .

61 Find the common difference of the arithmetic sequence.

____ 62 Identify the sequence as arithmetic, geometric, or neither.81, 108, 144, 192, . . .

If possible, find the common ratio or difference.

F. geometric with r=3

4 H. geometric with r=

4

3.

G. arithmetic with d=4

3. I. It is neither arithmetic nor geometric.

63 Find the first 4 terms of the geometric sequence for which and

64 Find the sum of the infinite geometric series .

65 Find the number of distinguishable permutations of the letters LUCKY.

66 Expand .

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Review Final Exam - Algebra 2 (Chapters 5, 6, 7, 8, 10)

Answer Section

1

2

3 A

4 F

5 C

6 I

7

8 I

9

10

11

12

13

14

15

16 F

17

18 I

19 D20 G

21 A

22 I

23 27

24

25 A

26 G

27

28 46

29 A

30

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31

32

33

1010 x

10

10

y

34 22

35 7

36

37 $104438 4%; $378.94 million

39 C

40 G

41 $9438

42 4

43 A

44 15.050

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45

46 F

47 not an inverse variation

48 x= 3,x= 5

49

50

51

52

53

54 H

55 A

56 I

57 B

58

59 6,8,6, 0

60

61

62 H

63 9,45,225,1125

64

65 5! = 120

66