ALGEBRA 2 FINAL EXAM REVIEW
[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)
1
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
2
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
3
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
4
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
5
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
7
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
6
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
7
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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