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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