AFM Review for Final ExamName ______
Multiple Choice
Identify the choice that best completes the statement or answers the question.
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1.Solve the equation .
a. /b. / 4, 5
c. /
d. /
2.Simplify .
a. /b. /
c. /
d. /
3.A bookstore offers a collection of books. A student can select from one of 6 algebra books,
one of 4 geometry books, and one of 3 calculus books. How many different possibilities are available for that collection?
a. / 48b. / 30
c. / 36
d. / 72
4.Find the value of .
a. / 15b. / 2
c. / 24
d. / 360
5. How many ways can the top 5 teams be arranged in a league containing 21 teams?
a. / 15,504b. / 143,640
c. / 2,441,880
d. / 1,860,480
6.In a race between 21 people, how many ways can the top 6 finishers be arranged?
a. / 39,070,080b. / 54,264
c. / 27,907,200
d. / 2,441,880
7.Find C(9, 5).
a. / 45b. / 126
c. / 15,120
d. / 84
8.Find the standard deviation for the given data.
a. /b. /
c. /
d. /
9.Find the variance and standard deviation for the given set of data to the nearest tenth.
{5.1, 14.5, 22.7, 34.3, 22, 41.8, 18.3, 46, 15, 61.8}
a. / variance = 16.5, standard deviation = 273b. / variance = 303.4, standard deviation = 17.4
c. / variance = 273, standard deviation = 16.5
d. / variance = 273, standard deviation = 136.5
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10.Find the range of the data shown on the box-and-whisker plot below.
a. / 46 / c. / 61b. / 49 / d. / 31
11.Find the upper quartile of the data shown on the box-and-whisker plot below.
a. / 42 / c. / 56b. / 73 / d. / 31
12.Find the lower quartile of the data shown on the box-and-whisker plot below.
a. / 38 / c. / 27b. / 16 / d. / 21
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13.Describe the set of numbers using interval notation.
x > 12 or 8
a. /b. /
c. /
d. /
14.Determine the domain of the function
a. /b. /
c. /
d. /
15.Find f(2) for f(x) = .
a. / f(2) = 24b. / f(2) = 48
c. / f(2) = –12
d. / f(2) = 0
Without graphing, describe the end behavior of the graph of the function.
16.
a. / As xf (x) As xf (x)
b. / As xf (x)
As xf (x)
c. / As xf (x)
As xf (x)
d. / As xf (x)
As xf (x)
17.
a. / As xh(x) As xh(x)
b. / As xh(x)
As xh(x)
c. / As xh(x)
As xh(x)
d. / As xh(x)
As xh(x)
Which statement best describes a method that can be used to sketch the graph.
18.y = |x| + 1
a. / Translate the graph of y = |x| one unit right.b. / Translate the graph of y = |x| one unit left.
c. / Translate the graph of y = |x| one unit up.
d. / Translate the graph of y = |x| one unit down.
Estimate and classify the critical points for the graph of each function.
19.
a. / (0.5, 7), minimum; (2, 1), point of inflection; (3.5, -5), maximumb. / (0.5, 7), maximum; (2, 1), point of inflection; (3.5, -5), minimum
c. / (0.5, 7), maximum; (3.5, -5), minimum
d. / no critical points
20.
a. / (-1, 0), maximum; (1, -4), minimum; (3, 0), maximumb. / (1, -4), point of inflection
c. / (1, -4), minimum
d. / (0, -3), point of inflection; (1, -4), minimum
21.
a. / (-4, -4.5), minimum; (0, 4), maximum; (4, -4.5), minimumb. / (-4, -4.5), minimum; (0, 4), point of inflection; (4, -4.5), minimum
c. / (-4, -4.5), minimum; (-2, 0), point of inflection; (0, 4), maximum; (2, 0), point of inflection; (4, -4.5), minimum
d. / no critical points
22. Use a power function to model the data and estimate y for x = 10.
x / y1 / 9
2 / 144
3 / 729
4 / 2,304
5 / 5,625
6 / 11,664
7 / 21,609
8 / 36,864
a. / 59,049
b. / 131,769
c. / 90,000
d. / 52,119
23.Solve.
a. / 7b. / –6
c. / –3, 4
d. / no real number solution
24.Solve.
a. /b. /
c. /
d. /
25.State the number of possible real zeros and turning points of f(x) = Then determine all of the real zeros by factoring.
a. / 4 real zeros and 3 turning points;–5, and 5
b. / 4 real zeros and 3 turning points;
–5, and –5
c. / 4 real zeros and 3 turning points;
5, and 5
d. / 4 real zeros and 3 turning points;
5, and –5
26.Determine the zeros for and the end behavior of f(x) = .
a. / 0, 4, –5 (multiplicity of 4)As x, f(x) -
As x, f(x)
b. / 0, –4, 5 (multiplicity of 4)
As x, f(x) -
As x, f(x)
c. / 0, 4, –5 (multiplicity of 4)
As x, f(x) -
As x, f(x)+
d. / 0, –4, 5 (multiplicity of 4)
As x, f(x) -
As x, f(x)+
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27.Use a graphing calculator to write a polynomial function to model the data.
a. /b. /
c. /
d. /
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28.Use the remainder theorem to find which of the following is not a factor of .
a. /b. /
c. /
d. /
29.Solve.
a. /b. /
c. /
d. /
Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f.
30.f(x) = ex;g(x) =
a. / g(x) is the graph of f(x) translated 3 unit(s) to the , 3 unit(s) , and vertically by a factor of .b. / g(x) is the graph of f(x) translated 3 unit(s) to the , 3 unit(s) , and vertically by a factor of .
c. / g(x) is the graph of f(x) translated 3 unit(s) to the , 3 unit(s) , and vertically by a factor of .
d. / g(x) is the graph of f(x) translated 3 unit(s) to the , 3 unit(s) , and vertically by a factor of .
31.The world’s population is expected to grow at a rate of 1.3% per year until at least the year 2020. In 1994 the total population of the world was about 5,642,000,000 people. Use the formula to predict the world’s population , n years after 1994, with equal to the population in 1994 and i equal to the expected growth rate. What is the world’s predicted population in the year 2020, rounded to the nearest million?
a. / 12,632,000,000b. / 7,911,000,000
c. / 7,549,000,000
d. / 7,317,000,000
32.If the Laffite family deposits $8500 in a savings account at 6.75% interest, compounded continuously, how much will be in the account after 25 years?
a. / $227,338.93b. / $45,950.57
c. / $38,094.36
d. / $38,720.02
33.Evaluate the expression .
a. /b. /
c. /
d. / 3
Evaluate each expression.
34.
a. / 3b. / 5
c. / 2
d. / 4
35.log 94
a. / 9.4b. / 1.97
c. / 0.51
d. / 3.95
Use the graph of f to describe the transformation that results in the graph of g.
36.f(x) = log x; g(x) =
a. / The graph of g(x) is the graph of f(x) compressed horizontally by a factor of 2.b. / The graph of g(x) is the graph of f(x) compressed horizontally by a factor of 2.
c. / The graph of g(x) is the graph of f(x) expanded horizontally by a factor of 2.
d. / The graph of g(x) is the graph of f(x) compressed horizontally by a factor of 2.
Express each logarithm in terms of ln 3 and ln 5.
37.ln
a. /b. /
c. /
d. /
38.Solve for x correct to four decimal places.
a. / –0.4030b. / –0.4351
c. / 0.7559
d. / –0.7559
Solve each equation.
39.
a. /b. /
c. /
d. /
40.
a. /b. / infinite solutions
c. /
d. /
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41.Radioactive Iodine-129 decays over time into stable Xenon-129. The percent of I-129 remaining in several mineral samples can be used to calculate the radioactive half-life of I-129, based on the ages of the mineral samples determined by other “dating” techniques. The following table shows data on the percent of I-129 remaining in minerals of different ages.
Age (billions of years) / 2.0 / 3.5 / 4.2 / 4.3Percent of original I-129 / 74 / 59 / 53 / 52
a. Find the regression equation for the percent of I-129 remaining as a function of time x.
b. Write the regression equation in terms of base e.
c. Use the equation from part b to estimate the half-life of Iodine-129.
a. / a.b.
c. x = 3.2 billion years / c. / a.
b.
c. x = 4.4 billion years
b. / a.
b.
c. x = 3.3 billion years / d. / a.
b.
c. x = 4.5 billion years
42.The following table contains the account balance at year’s end for an account which has had zero deposits and zero withdrawals over a period of seven years.
Year / 1992 / 1993 / 1994 / 1995Balance / $3489.44 / $3749.95 / $4029.90 / $4330.75
Year / 1996 / 1997 / 1998 / 1999
Balance / $4654.07 / $5001.52 / $5374.91 / $5776.17
a. Find a function that models the amount as a function of x years since 1992.
b. Write the equation from part a in terms of base e.
c. Find the interest on the account, assuming it was compounded continuously.
a. / a.b.
c. 7.4% / c. / a.
b.
c. 7.2%
b. / a.
b.
c. 4.55% / d. / a.
b.
c. 7.4%
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43.Find an exponential function to model the data.
x / y1 / 7
2 / 16
3 / 30
4 / 61
5 / 124
6 / 271
7 / 522
a. / f(x) = 116.4 - 42.8 ln x
b. / f(x) = 2.04(3.56)x
c. / f(x) = 3.56(2.04)x
d. / f(x) = -42.8 + 116.4 ln x
44.Find the linear regression equation for the data according to the given model.
x / y1 / 50
2 / 140
3 / 260
4 / 400
5 / 560
6 / 750
7 / 925
8 / 1130
a. / 49.79x1.50
b. / 5.48x0.32
c. / 156.13x - 175.71
d. / 1.5x + 3.91
45.As automobiles age, the average miles traveled per gallon decreases. Determine the regression equation that best models the data.
Age (years) / MPG1 / 35
3 / 34
5 / 33
7 / 31
9 / 28
11 / 26
13 / 23
15 / 18
a. / power
b. / logarithmic
c. / quadratic
d. / exponential
46.If , find .
a. /b. /
c. /
d. /
47.Write ° ´ ´´ as a decimal to the nearest thousandth.
a. / °b. / °
c. / °
d. / °
48.Change 3.94 radians to degree measure. Round to the nearest tenth.
a. /b. /
c. /
d. /
49.Write in degrees.
a. /b. /
c. /
d. /
50.Write in degrees
a. /b. /
c. /
d. /
51.Find one positive and one negative angle coterminal with an angle of 126°.
a. / 486°, –234°b. / 526°, –54°
c. / 486°, –36
d. / 216°, –36°
52.For a circle of radius 2 feet, find the arc length s subtended by a central angle of
a. / feetb. / feet
c. / feet
d. / feet
53.Jack’s bicycle tires have a diameter of 22 inches. If he rides at 6 miles per hour, what is the angular velocity of the wheels in revolutions per minute (rpm)?
a. / 4.17 rpmb. / 15.28 rpm
c. / 288 rpm
d. / 91.67 rpm
54.Find the least positive angle measurement that is coterminal with °.
a. / °b. / °
c. / °
d. / °
55.Suppose is an angle in the standard position whose terminal side is in Quadrant III and . Find the exact values of the five remaining trigonometric functions of .
a. / , , ,, and
b. / –, –, –,
, and
c. / , , ,
, and
d. / , –, –,
, and
56.Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (10, 24) lies on its terminal side.
a. / sin = , cos = , tan =csc = , sec = , cot =
b. / sin = , cos = , tan =
csc = , sec = , cot =
c. / sin = , cos = , tan =
csc = , sec = , cot =
d. / sin = , cos = , tan =
csc = , sec = , cot =
57.Find the exact value of .
a. /b. /
c. /
d. /
58.Find the exact value of .
a. / 1b. /
c. /
d. / 0
59.Find the reference angle for 288
a. / 89b. / 59
c. / 72
d. / 108
60.Find the exact value of sin.
a. /b. /
c. / undefined
d. /
61.Use the unit circle to find the value of .
a. /b. /
c. /
d. / undefined
62.
a. /b. / 2
c. /
d. /
63.Write an equation of the sine function with the given amplitude, period, phase shift, and vertical shift.
amplitude: 4, period = , phase shift = – , vertical shift = –1
a. /b. /
c. /
d. /
64. Find the amplitude of . Then graph the function.
a. / amplitude:b. / amplitude:
c. / amplitude: does not exist
d. / amplitude:
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65. The normal monthly temperatures (F) for Omaha, Nebraska, are recorded below.
Month / Jan / Feb / Mar / Apr / May / Jun / Jul / Aug / Sep / Oct / Nov / Dect / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12
Temp. / 21 / 27 / 39 / 52 / 62 / 72 / 77 / 74 / 65 / 53 / 39 / 25
a. Write a sinusoidal function that models Omaha’s monthly temperature variation.
b. Use the model to estimate the normal temperature during the month of April.
a. / a.b. / c. / a.
b.
b. / a.
b. / d. / a.
b.
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66.Given a triangle with a = , A = °, and B = °, what is the length of c? Round to the nearest tenth.
a. /b. /
c. /
d. /
67.Find all solutions for the triangle with . If no solutions exist, write none. Round to the nearest tenth.
a. /b. /
c. / none
d. /
68.Solve .
, ,
a. / , ,b. / , ,
c. / , ,
d. / , ,
69.Determine whether has no solution or onesolution. Then solve the triangle.
, ,
a. / one solution; ; ;b. / one solution; ; ;
c. / no solution
d. / one solution; ; ;
70.Determine whether should be solved by using the Law of Sines or the Law of Cosines. Then solve the triangle.
a = 19, b = 20, C = 63°
a. / Law of Sines; , ,b. / Law of Cosines; , ,
c. / Law of Sines; , ,
d. / Law of Cosines; , ,
71.Find .
a. /b. /
c. /
d. /
72.Write an arithmetic sequence that has three arithmetic means between 155 and 215.
a. / 155, 170, 185, 200, 215b. / 155, 200, 185, 170, 215
c. / 155, 165, 175, 185, 215
d. / 155, 175, 195, 205, 215
73.Form a sequence that has two arithmetic means between –18 and 9.
a. / –18, –60, –102, –144b. / –18, –36, –72, –144
c. / –18, –17, 8, 9
d. / –18, –81, –144
Find the next four terms of each arithmetic sequence.
74.–36, –53, –70,
a. / 1190, –20230, 343910, –5846470b. / –78.5, –87, –95.5, –104
c. / –104, –138, –172, –206
d. / –87, –104, –121, –138
75.Find Sn if , ,and .
a. / –1870b. / –3300
c. / 2310
d. / –1650
76.Find the sum of the given arithmetic series.
a. / 1,446,309b. / 1,439,100
c. / 1,372,410
d. / 1,440,855
77.Find the sum of the first 50 terms of the sequence 8, 10, 12, 14, 16, ...
a. / 2850b. / 2852
c. / 2851
d. / 2849
78.Find the geometric means in the following sequence.
a. / –144, –576, –2,304, –9,231b. / 36, 144, 576, 2,304
c. / –720, –1,080, –1,440, –1,800
d. / –36, –144, –576, –2,304
79.Find a1 if , , and .
a. / 2,385.58b. / 3,056.70
c. / 5,325.87
d. / 16,258.27
80.Find the next term of the geometric sequence.
7, –35, 175, –875...
a. / –700b. / 4,275
c. / 4,498
d. / 4,375
Find the specified nth term of each geometric sequence.
81.a2 = 2, r = –3, n = 9
a. / –4374b. / 13122
c. / 1458
d. / –2187
82.Frank has a sheet of paper which is thick. If the sheet is folded in half, the total thickness will be A second fold will produce a total thickness of What will be the thickness of the sheet if Frank folds it 8 times?
a. / 0.41 in.b. / 14.001 in.
c. / 0.205 in.
d. / 128 in.
83.Form a sequence that has two geometric means between –6 and –162.
a. /b. /
c. / –6, –18, –54, –162
d. / , 54,
84.Find the sum of the first 8 terms of the series.
a. / –681b. / –680
c. / –682
d. / –679
85.Find the sum of the first five terms of a geometric series with .
a. / 435.4b. / 51.4
c. / 311.08
d. / 874.94
86.Find the sum of an infinite geometric series in which .
a. / –9.71b. / –9.7
c. / –10.31
d. / –43.33
87.Use the Binomial Theorem to expand .
a. /b. /
c. /
d. /
Find the coefficient of the indicated term in each expansion.
88.
a. / 60b. / 20000
c. / 2000
d. / 120000
1
89.Use the Binomial Theorem to expand .
a. /b. /
c. /
d. /
1
90. In how many different orders can you line up 8 cards on a table?
a. / 8b. / 1
c. / 1,680
d. / 40,320
91.In how many ways can 12 basketball players be listed in a program?
a. / 665,280b. / 1
c. / 479,001,600
d. / 12
92.There are 10 students participating in a spelling bee. In how many ways can the students who go first and second in the bee be chosen?
a. / 1 wayb. / 90 ways
c. / 3,628,800 ways
d. / 45 ways
93.Lynn and Dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of tossing heads using Lynn and Dawn’s results?
a. /b. /
c. /
d. /
94.What is the theoretical probability of being dealt exactly three 4's in a 5-card hand from a standard 52-card deck?
a. /b. /
c. /
d. /
95.If a dart hits the target at random, what is the probability that it will land in the shaded region?
a. /b. /
c. /
d. /
96.The probability that a city bus is ready for service when needed is 85%. The probability that a city bus is ready for service and has a working radio is 67%. Find the probability that a bus chosen at random has a working radio given that it is ready for service. Round to the nearest tenth of a percent.
a. / 18.0%b. / 12.7%
c. / 82.8%
d. / 78.8%
97.A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth.
a. / 0.241b. / 0.345
c. / 0.252
d. / 0.034
98.The numbers of cookies in a shipment of bags are normally distributed, with a mean of 64 and a standard deviation of 4. What percent of bags of cookies will contain between 60 and 68 cookies?
a. / 50%b. / 13.5%
c. / 68%
d. / 34%
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