ALGEBRA 2 FINAL EXAM REVIEW - Quia

[Pages:17]Name: ______________________ Class: _________________ Date: _________

ID: A

ALGEBRA 2 FINAL EXAM REVIEW

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. Classify ?6x5 + 4x3 + 3x2 + 11 by degree. a. quintic b. cubic

c. quartic d. quadratic

____ 2. Classify 8x4 + 7x3 + 5x2 + 8 by number of terms.

a. trinomial

c. polynomial of 5 terms

b. binomial

d. polynomial of 4 terms

Consider the leading term of each polynomial function. What is the end behavior of the graph?

____

3. 5x8 ! 2x7 ! 8x6 + 1 a. The leading term is 5x 8 . Since n is even and a is positive, the end behavior is down and up. b. The leading term is 5x 8 . Since n is even and a is positive, the end behavior is up and down. c. The leading term is 5x 8 . Since n is even and a is positive, the end behavior is up and up. d. The leading term is 5x 8 . Since n is even and a is positive, the end behavior is down and down.

____

4. !3x 5 + 9x 4 + 5x 3 + 3 a. The leading term is !3x 5 . Since n is odd and a is negative, the end behavior is up and up. b. The leading term is !3x 5 . Since n is odd and a is negative, the end behavior is down and down. c. The leading term is !3x 5 . Since n is odd and a is negative, the end behavior is up and down. d. The leading term is !3x 5 . Since n is odd and a is negative, the end behavior is down and up.

Write the polynomial in factored form.

____ 5. x3 + 9x2 + 18x a. 6x(x + 1)(x + 3) b. 3x(x + 6)(x + 1)

c. x(x + 6)(x ? 3) d. x(x + 3)(x + 6)

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Name: ______________________

What are the zeros of the function? Graph the function.

____ 6. y = x(x ! 2)(x + 5) a. 2, ?5

c. 0, 2, ?5

ID: A

b. 0, ?2, 5

d. 2, ?5, ?2

____ 7. Divide 4x 3 + 2x 2 + 3x + 4 by x + 4. a. 4x2 ! 14x + 59 b. 4x 2 + 18x ! 53, R 240

Divide using synthetic division.

____ 8. Divide !6x 3 + 18x 2 ! 7x ! 10 by (x ! 2).

a. !6x 2 + 6x + 5 b. 6x 2 ! 6x ! 5

c. 4x2 ! 14x + 59, R ?232 d. 4x 2 + 18x ! 53

c. !6x 2 + 30x ! 19, R ?20 d. 6x 2 ! 30x + 19, R 20

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Name: ______________________

ID: A

____

9. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation

x3 ! 6x2 + 4x + 9 = 0. Do not find the actual roots.

a. ?9, ?1, 1, 9

c. ?9, ?3, ?1, 1, 3, 9

b. 1, 3, 9

d. no roots

Use Pascal's Triangle to expand the binomial.

____ 10. (d ! 2)6

a. d 6 + 12d 5 + 60d 4 + 160d 3 + 240d 2 + 192d + + 64 b. d 6 ! 6d 5 + 15d 4 ! 20d 3 + 15d 2 ! 6d + 1 c. d 6 ! 12d 5 + 60d 4 ! 160d 3 + 240d 2 ! 192d + 64 d. d 6 + 6d 5 + 15d 4 + 20d 3 + 15d 2 + 6d + 1

____ 11. Find all the real square roots of 0.0004. a. 0.00632 and ?0.00632 b. 0.06325 and ?0.06325

c. 0.0002 and ?0.0002 d. 0.02 and ?0.02

Find the real-number root.

____ 12. 3 ! 125 343

a. 25 49

b. ! 125 343

c. ! 125 1029

d. ! 5 7

Multiply and simplify if possible.

4

4

____ 13. 11 " 3

a. 3

b. 11

____ 14. 7x ?????? x ! 7 7 ^?~~~~ a. x 7 ! 49 x b. 7x ! 49x

4

c. 11 3

4

d. 33

c. x 7 ! x 49 d. ! 42x

What is the simplest form of the expression?

3

____ 15. 108a16b9

3

a. 3a 5 b 3 4a

3

b. 4a 5 b 3 3a

3

c. 3a 5 b a d. none of these

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Name: ______________________

What is the simplest form of the product?

____ 16. 50x7 y7 " 6xy4 a. 2x4 y6 75y b. 10x 4 y 5 3y

c. 5x4 y6 12 d. 30x 4 y 5 y

What is the simplest form of the quotient?

3

____ 17. 162 3 2 3 a. 3 3

3

b. 162

3

c. 3 3

d. 3 3

What is the simplest form of the radical expression?

____ 18. 3 2a ! 6 2a a. !6 2a b. 9 2a

c. !3 2a d. not possible to simplify

What is the simplest form of the expression?

____ 19. 20 + 45 ! 5 a. 4 5 b. 6 5

c. 13 5 d. 5 5

What is the product of the radical expression?

____ 20. ??????7 ! 2 ^?~~~~ ??????8 + 2 ^?~~~~ a. 54 + 56 2 b. 54 ! 2

c. 13 + 15 2 d. 58 + 56 2

____ 21. ??????5 ! 2 ^?~~~~ ??????5 + 2 ^?~~~~ a. 23 b. 20

c. 27 d. 18

ID: A

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Name: ______________________

How can you write the expression with rationalized denominator?

____ 22.

3! 6

3+ 6

a. !1 ! 2 18 3

b. !3 ! 2 18 9

____ 23.

3

2+ 3

3

6

3

3

a. 2 6 + 9 18

6

3

3

b. 2 36 + 3 2

6

c. !3 + 2 2 d. 9 ! 2 18

3

3

c. 2 6 + 9 4

6

3

3

d. 2 36 + 3 4

6

Simplify.

1

1

____ 24. 3 3 " 9 3

a. 9

3

b. 3

c. 3

1

____ 25. 16 2

a. 16 2 b. 4

c. 16 2 d. 16

3

____ 26. Write the exponential expression 3x 8 in radical form.

8

a. 3 x3

8

b. 3x 3

3

c. 3 x8

d. 3

3

d. 3 8 8 x 3

What is the solution of the equation?

____ 27. 2x + 8 ! 6 = !4

a. 4

b. ?2

3

____ 28. (x + 6) 5 = 8 a. 14

b. 2

c. 12 c. 26

d. ?3 d. 38

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ID: A

Name: ______________________

____ 29. Let f(x) = 4x ! 5 and g(x) = 6x ! 3. Find f(x) ! g(x).

a. 10x ? 8

b. 10x ? 2

c. ?2x ? 8

____ 30. Let f(x) = 3x + 2 and g(x) = 7x + 6. Find f " g and its domain.

a. 6x2 + 4x + 42; all real numbers except x = ! 2 3

b. 6x 2 + 4x + 42; all real numbers c. 21x 2 + 32x + 12; all real numbers d. 21x 2 + 32x + 12; all real numbers except x = ! 6

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f ____ 31. Let f(x) = x 2 ! 16 and g(x) = x + 4. Find and its domain.

g

a. x + 4; all real numbers except x # 4 b. x + 4; all real numbers except x # !4 c. x ! 4; all real numbers except x # 4 d. x ! 4; all real numbers except x # !4

____ 32. Let f(x) = x + 2 and g(x) = x 2 . Find ???g ? f^?~ (!5) .

a. 9

b. ?3

c. 49

d. ?2x ? 2 d. ?10

What is the inverse of the given relation?

____ 33. y = 7x2 ! 3.

a. y = ? x + 3 7

b. x =

y+3 7

____ 34. y = 3x + 9 a. y = 1 x + 3 3

b. y = 3x ! 3

c. y2 = x ! 3 7

d. y = ? x ! 3 7

c. y = 3x + 3 d. y = 1 x ! 3

3

ID: A

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Name: ______________________

Graph the exponential function.

____ 35. y = 4x

a.

c.

b.

d.

ID: A

____ 36. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will

you have in the account after 4 years?

a. $800.26

b. $6,701.28

c. $10,138.07

d. $1,923.23

____ 37. How much money invested at 5% compounded continuously for 3 years will yield $820?

a. $952.70

b. $818.84

c. $780.01

d. $705.78

Write the equation in logarithmic form.

____ 38. 25 = 32 a. log 32 = 5 " 2

b. log2 32 = 5

c. log 32 = 5 d. log5 32 = 2

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Name: ______________________

Evaluate the logarithm.

____

39.

log5

1 625

a. ?3

____ 40. log3 243 a. 5

____ 41. log 0.01 a. ?10

b. 5 b. ?5 b. ?2

c. ?4 c. 4 c. 2

d. 4 d. 3 d. 10

Write the expression as a single logarithm.

____

42.

3

log b

q

+

6

log b

v

a. log (q 3 v 6 ) b

b.

log b

?????? q v

3

+

6

^?~~~~

____ 43. log3 4 ! log3 2 a. log3 2

b. log3 2

c.

(3

+

6)

log b

??? q

+

v ^?~

d.

log b

??????

q

3

+

v 6 ^?~~~~

c. log 2

d. log 2

Expand the logarithmic expression.

____

44.

log3

d 12

a. log3 d ! log3 12

b. !d log 3 12

c. log3 d log3 12

d. log3 12 ! log 3 d

____ 45. log3 11 p 3 a. log3 11 " 3 log3 p b. log 3 11 ! 3 log 3 p

c. log3 11 + 3 log3 p d. 11 log 3 p 3

____ 46. Use the Change of Base Formula to evaluate log7 28.

a. 1.712

c. 1.712

b. 3.332

d. 1.447

ID: A

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