Name___________________________________ Pd___ Accelerated Math III Final Exam Review

MULTIPLE CHOICE. Choose the one alternative thatbest completes the statement or answers the question.

Solve the inequality. Use algebra to solve thecorresponding equation.

1) x2 - 5x - 6 < 0A) (-1, 6)B) (- , -1) (6, )C) (- , -1)D) (6, )

Answer: A

2) x2 + 2x - 35 0A) [-7, 5]B) [5, )C) (- , -7]D) (- , -7] [5, )

Answer: D

3) x2 + 2 0A) No solution B) (- , 2)C) (- , ) D) (2, )

Answer: C

4) 4x2 + 5x 6

A) -34

, 2

B) ( , -2] 34

,

C) ( , -34

[2,

D) -2, 34

Answer: B

Solve the problem.5) A coin is tossed upward from a balcony 290 ft

high with an initial velocity of 32 ft/sec.During what interval of time will the coin be ata height of at least 50 ft? (h = -16t2 + vot + ho.)

A) 0 t 1 B) 0 t 5C) 4 t 5 D) 5 t 10

Answer: B

6) If a rocket is propelled upward from groundlevel, its height in meters after t seconds isgiven by h = -9.8t2 + 107.8t. During whatinterval of time will the rocket be higher than294 m?

A) 5 < t < 6 B) 0 < t < 5C) 10 < t < 11 D) 6 < t < 10

Answer: A

Write out the first five terms of the sequence.7) an = n2 - n

A) 2, 6, 12, 20, 30 B) 1, 4, 9, 16, 25C) 0, 2, 6, 12, 20 D) 0, 3, 8, 15, 24

Answer: C

Find the first six terms of the sequence.8) a1 = 4, a2 = 5; for n 3, an = an-1 + an-2

A) 4, 5, 20, 100, 2000, 200,000B) 4, 5, 8, 12, 16, 20C) 4, 5, 9, 14, 23, 37D) 4, 5, 9, 10, 14, 14

Answer: C

Determine whether the sequence converges or diverges. Ifit converges, give the limit.

9) 72, 18, 92

, 98

, ...

A) Converges; - 6120B) Converges; 0C) Converges; 96D) Diverges

Answer: B

10) 1462

, 1154

, 3154

, 9154

, ...

A) Converges; 0

B) Converges; 3231

C) Diverges

D) Converges; 1308

Answer: C

1

Find an explicit rule for the nth term of the arithmeticsequence.

11) -21, -26, -31, -36, ...A) an = -21 × (-5)(n-1)B) an = -21 + (-5)(n-1)C) an = -21 - (-5)(n+1)D) an = -21 + (-5)(n+1)

Answer: B

12) a11 = 39, a13 = 127A) an = -401 + 44(n - 2)B) an = -401 + 44(n - 1)C) an = -401 - 44(n + 1)D) an = -401 + 44(n + 1)

Answer: B

Find an explicit rule for the nth term of the sequence.13) 9, 45, 225, 1125, ...

A) an = 9 · 5n-1 B) an = 9 · 5n

C) an = 5 · 9n-1 D) an = 9 · 5n+1

Answer: A

14) The second and fifth terms of a geometricsequence are 6 and 48, respectively.

A) an = 3 · 2n-2 B) an = 3 · 2n+1

C) an = 3 · 2n-1 D) an = 3 · 2n+3

Answer: C

Find a recursive rule for the nth term of the sequence.15) 3, 5, 7, 9, ...

A) an= an-1 + 4 B) an= an-1 - 2C) an= an-1 + 3 D) an= an-1 + 2

Answer: D

16) 4, -20, 100, -500, ...A) an= an-1 · -5 B) an= an-1 · -9C) an= an-1 · -4 D) an= an-1 · -10

Answer: A

Write the series using summation notation.17) 4 - 20 + 100 - 500 + ...

A)n = 0

4(-5)n+1 B)n = 0

4(-5)n

C)n = 0

4 · 5n D)n = 0

4 · 5n+1

Answer: B

18) -9 - 1 + 7 + 15 + ... + 111

A)15

n = 0-72 · n

B)n = 0

(-9 + n · 8)

C)15

n = 0(-9 + n · 8)

D)n = 0

-72n

Answer: C

Find the sum of the arithmetic sequence.19) -2, 1, 4, 7 , 10, 13, 16

A) 56 B) 49C) -14 D) 19

Answer: B

20) 40, 42, 44, 46, ..., 62A) 504 B) 64C) 612 D) 480

Answer: C

Find the sum of the geometric sequence.

21) 3, 32

, 34

, 38

, 316

A) 93 B) 34

C) 0 D) 9316

Answer: D

2

SHORT ANSWER. Write the word or phrase that bestcompletes each statement or answers the question.

22) Find the sum of the geometric sequence whose

5th term is 316

and whose 9th, and last, term is

3256

Answer:1533256

MULTIPLE CHOICE. Choose the one alternative thatbest completes the statement or answers the question.

Find the sum of the first n terms of the sequence.23) 4, -8, 16, ... ; n = 11

A) - 1365 B) 16380C) - 5460 D) 2732

Answer: D

24) 1, 12, 23, 34, ... ; n = 11

A) 616 B) 12212

C) 13532 D) 738

Answer: A

Determine whether the infinite geometric seriesconverges. If the series converges, determine the limit.

25) 7 + 21 + 63 + 189 + ...A) Converges; 847 B) Converges; 91C) Diverges D) Converges; 280

Answer: C

26) 36 - 12 + 4 -43

+ ...

A) Converges; 720 B) Converges; 27C) Diverges D) Converges; 54

Answer: B

27) 60 - 20 +203

-209

+ ...

A) DivergesB) Converges; 90C) Converges; 1200D) Converges; 45

Answer: D

Write the repeating decimal number as a fraction.28) 0.42424242 . . .

A) 23 B) 4442

9999

C) 1433 D) 1

25

Answer: C

29) 0.28282828 . . .

A) 150 B) 10

9

C) 2899 D) 2228

9999

Answer: C

Solve.30) An auditorium has 20 rows with 10 seats in the

first row, 12 in the second row, 14 in the thirdrow, and so forth. How many seats are in theauditorium?

A) 390 B) 400C) 580 D) 620

Answer: C

31) A collection of dimes is arranged in atriangular array with 14 coins in the base row,13 in the next, 12 in the next, and so forth with1 dime in the last row. Find the value of thecollection.

A) $5.25 B) $10.50C) $1.05 D) $21.00

Answer: B

32) A sequence of yearly payments of $6000 isinvested at an interest rate of 5%,compounded annually. What is the totalamount of the annuity after 8 years?

A) $56,794.65 B) $57,294.65C) $56,294.65 D) $58,294.65

Answer: B

3

State an explicit rule for the nth term of therecursively-defined sequence.

33) an= an-1 + 8; a1 = 4A) an = 8 + 4(n-1) B) an = 4 + 8(n)C) an = 4 + 8(n-1) D) an = 8 + 4(n)

Answer: C

34) an = 10 · an-1; a1 = 4

A) an = 10 · 4n-1 B) an = 10 · 4n

C) an = 4 · 10n-1 D) an = 4 · 10n

Answer: C

Find the sum.35) 7 + 11 + 15 + 19 + ... + 607

A) 91,657 B) 46,357C) 45,750 D) 46,968

Answer: B

36)n

k=1(k2 + 26)

A) n(n+1)(2n+1) + 6n6

B) n(n+1)(2n+1) + 1566

C) n(n+1)(2n+1) + 156n6

D) n(n+1)(2n+1)6

Answer: C

37)n

k=1(k2 + 6k + 11)

A) n(n+1)(2n+1)6

+ 11n

B) n(n+1)(2n+1)6

+6n(n+1)

2

C) 6n(n+1)2

+ 11n

D) n(n+1)(2n+1)6

+6n(n+1)

2+ 11n

Answer: D

Rewrite the expression as a sum or difference or multipleof logarithms.

38) log56

19s2r

A) 16

log5 19 - 2 log5 s - log5 r

B) 6 log5 19 - 2 log5 s - log5 6C) log5 19 - log5 s - log5 r

D) 16

log5 19 - 2 log5 s - 2 log5 r

Answer: A

39) log3x4 y6

4A) 4 log3 x - 6 log3 y - log3 4B) 4 log3 x + 6 log3 y - log3 4C) (4 log3 x)(6 log3 y) - log3 4D) 4 log3 x + 6 log3 y + log3 4

Answer: B

Use the product, quotient, and power rules of logarithmsto rewrite the expression as a single logarithm. Assumethat all variables represent positive real numbers.

40) 2log x + 5log yA) log(2x + 5y) B) log(10xy)C) log(x2 + y5) D) log (x2y5)

Answer: D

41) 4 log4 (4x + 8) + 3 log4 (2x + 7)

A) log4(4x + 8)4

(2x + 7)3

B) 12 log4 (4x + 8)(2x + 7)

C) log4 (4x + 8)4(2x + 7)3

D) log4 ((4x + 8)4 + (2x + 7)3)

Answer: C

Use the change of base rule to find the logarithm to fourdecimal places.

42) log 7 20.19A) 1.5444 B) 2.8843C) 0.6475 D) 1.3051

Answer: A

4

43) log2 0.54A) -0.8890 B) 0.8890C) -1.7779 D) -1.1249

Answer: A

Write the expression using only the indicated logarithms.44) log5 x using natural logarithms

A) ln x · ln 5 B) ln x + ln 5

C) ln 5ln x D) ln x

ln 5

Answer: D

Find the exact solution to the equation.45) log5(x - 4) = - 1

A) x =9 B) x = 1C) x = -3.8 D) x = 4.2

Answer: D

46) 3 ln (x - 9) = 1A) x = e3 + 9 B) x = e1/3 - 9C) x = e1/3 + 9 D) x = 3e + 9

Answer: C

47) 320 14

x/5= 5

A) x = 3 B) x =35

C) x = 15 D) x = 16

Answer: C

Use a calculator to find an approximate solution to theequation.

48) 4(4x - 2) = 20A) 1.040 B) 0.902C) 1.750 D) 0.040

Answer: A

49) 0.276e0.08x = 0.000276A) -86.346941 B) -37.5C) 86.346941 D) No solution

Answer: A

50) 2ln (x + 2.8) = 3.2A) 1.221 B) -2.598C) 2.153 D) No solution

Answer: C

Find the domain of the function.51) f(x) = ln (-9 - x)

A) (- , 9) B) (9, )C) (-9, ) D) (- , -9)

Answer: D

52) f(x) = log8 (36 - x2)A) (- , -6) (6, )B) (-36, 36)C) (-6, 6)D) [-6, 6]

Answer: C

53) f(x) = log10 (x2 - 13x + 42)A) (- , -6) B) (- , 6) (7, )C) (7, ) D) (-6, 7)

Answer: B

Solve the equation.54) log 5 x = log 3 + log (x + 2 )

A) 54 B) 3

4

C) 3 D) -3

Answer: C

55) log ( 4 + x) - log (x - 2 ) = log 3

A) 12 B)

C) 5 D) - 5

Answer: C

56) log4(2x + 5) - log4(x - 2) = 1

A) 2.408 B) 6.5C) 3.125 D) No solution

Answer: B

57) 8001 + 99e-0.3t

= 200

A) 11.655 B) 9.003C) 6.098 D) 13.174

Answer: A

5

58) 23t - 3 = 5t + 11

A) t = -79 B) t =

72

C) t =143 D) t =

79

Answer: D

59) 14

(16x - 20) =15

(25x - 20)

A) x =19 B) x = -1

C) x = -9 D) x = 1

Answer: B

60) 4x - 72

+3x - 3

2= -

75

A) x = -6435 B) x =

635

C) x =3635 D) x =

9370

Answer: C

State the domain of the rational function.

61) f(x) =x - 2

x2 + 9xA) (- , -9) (-9, )B) (- , -9) (-9, 0) (0, )C) (- , 2) (2, )D) (- , 9) (9, )

Answer: B

62) f(x) =x - 1x2 + 3

A) (- , )B) (- , -3) (-3, )C) (- , - 1) (- 1, 1) (1, )D) (- , 3) (3, )

Answer: A

Use limits to describe the behavior of the rationalfunction near the indicated asymptote.

63) f(x) =3

x - 4Describe the behavior of the function near itsvertical asymptote.

A) limx -4-

f(x) = - , limx -4+

f(x) =

B) limx 4-

f(x) = , limx 4+

f(x) = -

C) limx 4-

f(x) = - , limx 4+

f(x) =

D) limx -4-

f(x) = , limx -4+

f(x) =

Answer: C

64) f(x) =x + 1

x2 - 2xDescribe the behavior of the function near itsvertical asymptotes.

A) limx 0-

f(x) = 0, limx 0+

f(x) = - ,

limx -2-

f(x) = - , limx -2+

f(x) =

B) limx 0-

f(x) = , limx 0+

f(x) = - ,

limx -2-

f(x) = , limx -2+

f(x) = -

C) limx 0-

f(x) = - , limx 0+

f(x) = ,

limx 2-

f(x) = - , limx 2+

f(x) =

D) limx 0-

f(x) = , limx 0+

f(x) = - ,

limx 2-

f(x) = - , limx 2+

f(x) =

Answer: D

6

65) f(x) =x + 1

x2 - 2xDescribe the behavior of the function near itshorizontal asymptote (the end behavior).

A) limx -

f(x) = - , limx

f(x) =

B) limx 0-

f(x) = , limx 0+

f(x) =

C) limx -

f(x) = 0, limx

f(x) = 0

D) limx -

f(x) = -1, limx

f(x) = 1

Answer: C

Evaluate the limit based on the graph of f shown.66)

limx -1-

f x

A) B) 1 C) 0 D)Answer: D

For the given function, find all asymptotes of the typeindicated (if there are any)

67) f(x) =x + 9

x2 + 5x + 2, horizontal

A) y = x B) y = 0C) None D) y = 9

Answer: B

68) f(x) =x2 + 2x - 3

x - 5, slant

A) None B) y = x - 3C) y = x + 7 D) x = y + 7

Answer: C

69) f(x) =8x2 - 2x - 23x2 - 7x + 6

, horizontal

A) y = 8/3 B) NoneC) y = 0 D) y = 2/7

Answer: A

7