AFM Final Exam Review #1

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1 AFM Final Exam Review # Name. A home security company offers a security system that uses the numbers 0 through 6, inclusive, for a -digit security code. How many different security codes are possible if no digit may be repeated? a) 5 b) 0 c) 0 d) 0. Using a standard deck of playing cards, find the probability of randomly selecting a queen, replacing it in the deck, and then selecting a heart. a) b) c) d) Josie has classical, jazz, and folk CD in her car. If she pulls CDs from her CD case without looking, what is the probability that both CDs are jazz? a) b) c) d) 5 5. A bag contains yellow, blue, and white marbles. What is the probability that a marble selected at random will not be blue? 5 a) b) c) d) Find the number of distinguishable permutations using the letters from the word ROBMURRO. a),0 b) 60 c) 0,0 d) A committee composed of men and women is to be selected from a group of 0 men and 6 women. How many different committees can be formed? a),07,800 b) 80 c),7,00 d) How many ways can 5 digits on a license plate be arranged if the first digit cannot be 0? (digits can repeat) a) 90,000 b) 00,000 c) 0,0 d) Two cards are chosen from a deck of 5 cards. What is the probability that the first card is a heart and the second card is a black face card? 9. From a standard deck of 5 cards, a card is dealt. What is the probability that a red card or an ace is drawn? 0. Joe gets $ if a coin shows up heads and $ if it shows up tails. What is his expected value? a) $.00 b) $.5 c) $. d) $.50. For the data set {, -5, 7,, 8,,, -, -6}, find the 5-number summary. a) minimum = -6, median =, maximum =, range = 7, mean =. b) minimum = -6, maximum =, mean =., median =, mode = none c) minimum = -6, lower quartile = -, median =, upper quartile = 7.5, maximum = d) lower quartile = -, upper quartile = 7.5, mean =., minimum = -6, maximum =

2 . Use the frequency table to find the mean, median, and mode. Aptitude Score 5 Frequency 5 a) mean = b) mean = c) mean =. d) mean =. median = median = median = median = mode = none mode = mode = mode =. Find the range and the interquartile range of the set of values: 7,,, 9,, 7, 6,, 5,,, 5 a) range: 7, interquartile range: 6 b) range: 6, interquartile range: 6 c) range: 6, interquartile range: 0 d) range: 6, interquartile range:. The lengths of a certain species of fish were found to be normally distributed. The mean length is 99 cm with a standard deviation of cm. In a school of 80 of these fish, about how many would be longer than 7 cm? a) 65 fish b) 6 fish c) 68 fish d) fish 5. Which method would produce the least biased sample of a school population of 000 students? a) One student from each letter of the alphabet b) all the members of faculty are selected. (by last name) are selected. c) all the student body officers are selected. d) all the members of the archery club are selected. 6. Identify the outlier of the set of values: 55, 57, 0, 7, 9, 8, 7 a) 7 b) 7 c) 8 d) none of the above 7. Suppose a lumber mill can turn out up to 900 units of product each week. The mill must produce at least 00 units of lumber and 00 units of plywood. Write the constraints as a system of inequalities where x = the number of units of lumber and y = the number of units of plywood. a) x 00, y 00, and x + y 900 b) x 00, y 00, and x + y 900 c) x 00, y 00, and x + y 900 d) x 00, y 00, and x + y Find the maximum value of f(x, y) = x + y - for the system of inequalities: y -x + y x - x 0 y 0 a) alternate optimal solutions b) c) infeasible d) unbounded 9. A feasible region has vertices at (, 6), (-, ), (, -), and (, ). At which point is the maximum value of the function f(x, y) = x + y? a) f(,6) b) f(-, ) c) f(, -) d) f(, )

3 0. A small fish market sells only tuna and salmon. Tuna costs the fish market $0.75 per pound to buy and $.5 per pound to clean and package. Salmon costs the fish market $.00 per pound to buy and $.75 per pound to clean and package. The fish market makes $.50 per pound profit for each tuna it sells and $.80 per pound profit for each salmon it sells. The fish market owner can spend only $59.00 per day to buy fish and $97. per day to clean and package the fish. What are the coordinates of the vertices of the feasible region, and what are the vales of t and s that maximize the objective function? a) (0, 0), (0, 5), (78, 0), (6, 8); t = 6 and s = 8. b) (0, 0), (5, 0), (0, 78), (8, 6); t = 8 and s = 6. c) (0, 0), (0, 5), (78, 0), (8, 6); t = 8 and s = 6. d) (0, 0), (0, 5), (78, 0), (6, 8); t = 0 and s = 5.. Solve the system of inequalities by graphing. x + y x - y < y 0 A. B. C. D.. Which graph represents the following system: y x +, and y x +? A. B. C. D.

4 . Use the formula, h6t v0t, to answer the questions below if a bullet is shot straight upward with an initial speed of 800 ft/sec. a) When does the bullet fall back to ground level? b) When does it reach a height of 600 feet? c) How high is the highest point the bullet reaches?. Write an exponential function to model this situation: a population of 00 animals increases at an annual rate of %. a) f(x) = 00(0.) x b) f(x) = 00(.87) x c) f(x) = 00(0.087) x d) f(x) = 00(.) x 5. In 98, the average number of TV stations that were received in the US households was 7 channels. In 990, there were 7 channels. a) Assuming the data is a linear model; find the line of best fit. b) Explain the slope and y-intercept in practical terms. c) Predict the average number of TV stations that a household will receive in Among all rectangles that have a perimeter of 0 feet, find the dimensions of the one with the largest area. 7. Which type of function (linear, quadratic, cubic, quartic, or exponential) best represents the data in the table? Wind speed (km/h) Mosquito Bites Find the domain of the function: f ( x) x a) (0,) (, ], c) [0,) (, ) 9. The graph b) y x x 9 is increasing between what interval/s? d), a),7.9.9, b),.7.7, c).7,.7 d).9, Evaluate the piecewise function at f(0), f(), and f(). 6 if x f( x) x if x a) f(0) = - b) f(0) = 6 c) f(0) = 0 d) f(0) = 6 f() = 6 f() = 7 f() = 6 f() = 7 f() = f() = f() = cannot determine f() = 7. Graph the previous piecewise function and state the domain and range.. A silk-screen shop charges an initial fee of $0 to create the silk screen and $8.50 per shirt for the first 5 shirts. If you decide to purchase more than 5 shirts, the price goes down to $7.75 per shirt (after the first 5 shirts are purchased). Write a function that gives the cost, C, for an order of x shirts. How much does it cost to purchase 0 shirts? 0 shirts?. Change from logarithmic form to exponential form: log 7 9 a) 9 7 b) 9 7 c) 9 7 d) 7 9

5 . Convert from exponential form to logarithmic form: 6 a) log b) log 6 c) log 6 d) log 6 5. Solve 6x = 96. a) 0.67 b) 0.76 c).6 d) Evaluate the following: ( problems here!) log 5 a) log6 6 = b) ln = c) log0 = d) = 7. Solve the logarithmic equations, accurate to decimal places. ( problems here!) a) log ( ) x x b) log (x ) c) e 9 8. The graph ylog ( x) has an asymptote of. a) y = b) y = c) x = d) x = 9. Find the balance of a $500 investment after 8 years earning 7.9% interest compounded continuously. a) $50.0 b) $5.0 c) $6. d) $ What interest rate is required for an investment with continuously compounded interest to double in 5 years? a).7% b) 6.9% c).86% d).86. Determine the amount of money in a money market account providing an annual rate of 7% compounded daily if George invested $500 and left it in the account for 0 years. a) $97.88 b) $95.5 c) $97.7 d) $50.0. The half-life of radium-6 is 590 years. a) If a sample has a mass of 50 mg, find the mass that remains after 000 years. b) After how many years will only 50 mg remain?. The number of bacteria in a culture is modeled by the function, n(t) = 500e 0.5t. How many bacteria are in the culture after hours?. If P = 7, R = 90, and r =, find p. a). b) 5.6 c) 9.8 d) The angle of elevation of a ladder leaning against a wall is 55. The ladder is 0 feet long. How high up the wall does it reach? a) About 5.0 ft b) about 7. ft c) about.57 ft d) about.8 ft 6. In ABC, find c if A = 6, B = 0, and b =.7. a) about 0. b) about 9.7 c) about 5. d) about.8 7. Determine the number of possible solutions for ABC, given A = 0, a = 7, and b = 9. a) two b) one c) three d) none 8. Determine the number of possible solutions for ABC, given a = 7, b =, and A = 5. a) two b) one c) three d) none 9. In ABC, given a =, b = 9 and c = 9, find B. a) about b) about 6 c) about 6 d) about 5

6 50. Two motorists start at the same point and travel in straight courses. The courses diverge by 95. If one is traveling at 50mph and the other is traveling at 60mph, how far apart will they be after hours? 5. A geologist measured a angle of elevation to the top of a volcano crater. After moving 0.5 km farther away, the angle of elevation was 8. Find the height of the volcano crater. 5. For a circle of radius 6 feet, find the arc length s cut off by a central angle of 8. a) about.78 ft b) about 5.65 ft c) about.88 ft d) about 08 ft 5. Find the measure of the reference angle of -00. a) 0 b) 0 c) 60 d) A sector has an area of.5 square meters. The radius of the circle is meters. Find the radian measure of the central angle to the nearest tenth. a) 7. radians b).6 radians c).8 radians d).6 radians 55. Evaluate tan. a) - b) c) - d) 56. Find an angle between 0 and 60 that is coterminal to -00. a) 00 b) 0 c) 60 d) Find the terminal point of t = a), b),.. 6 c), d), 58. Given that sin t > 0 and cos t < 0, find the quadrant in which the terminal point determined by t lies. a) I b) II c) III d) IV 59. Convert to radians: 05 a) 7 b) 7 c) 7 6 d) State the amplitude and period for the function y = - sin θ. a) -; b) -, c), d), 6. What is the next term in the geometric sequence 6, -,, a) 8,? b) 0 c) 6 d) 8 6. If the first term in an arithmetic series is, the last term is 6, and the sum is 90, what are the first terms? a), 0, 7 b),, c), 6, 70 d), 9, 5

7 6. Find the 9th term in the arithmetic sequence -9, -,, 6,.... a) 6 b) c) 6 d) 6. Evaluate the infinite geometric series a) 9/0 b) c).09 d) 9/9 65. In a certain arithmetic sequence, a = -8, d = 7, and a n = 7. Find n. a) 6 b) 7 c) 6 d) The sequence will never equal Find the sum of the first 5 terms in the series a) 7 b) 78 c) 75 d) Find the fifth term of a geometric sequence whose first term is 6 and whose common ratio is. a) 5/7 b) 8/9 c) 08/8 d) / 68. Find the next three terms in the sequence 65, 50, 00, 0,. a) 5,.5, 5.5 b) 5, 5, c) 0, 5, 0 d) 6, 6.,.56 FORMULAS: Law of Cosines: a b c bccosa Law of Sines: sin A sin B sin C a b c Arc Length (in radians): s r Area of a sector (in radians): A r Compounded n times per year: r A P( ) n nt Compounded continuously: A Pe rt Exponential Growth: nt () ne 0 rt Half-Life: mt () me rt 0, r ln half - life **Will be given Sequences & Series Formulas and Law of Cosines/Law of Sines