2. A stock dropped 36% in value. By what percentage must the stock increase to regain its value? 2 is four times as far from 3. 7 d.

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1 March, 010

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3 1. The tallest man-made structure in the world is the Burj Khalifa in Dubai, UAE. Its elevator is very fast taking less than a minute to reach the observation deck on the 1 th floor which is 10 feet high. If the elevator travels 6.1 mph, how long is the elevator ride from the bottom floor to the observation deck? a..9 sec b. 1. sec c. 8. sec d.. sec e. 1.8 sec. A stock dropped 6% in value. By what percentage must the stock increase to regain its value? a. 6% b..% c..% d. % e. 6.%. What rational number between 1 and is four times as far from as it is from 1? a. b. c. 1 d. 1 8 e. 9. Line L has equation x + y = 1. Line M is parallel to line L and has the same y-intercept as x 9y = 1. Which of the following points lies on line M? a. (,) b. (,) c. ( 1, ) d. (,) e. (, ). Mark is selling buttons for $1. at a craft fair. He paid $ for the booth space and $0 for supplies. If he sells 1 buttons, what will his profit be? a. $1. b. $161. c. $6. d. $19. e. $ For how many integers x is the value of 1 x + 1 an integer? a. 6 b. 9 c. 1 d. 1 e. 18 1

4 . On January 8, 010, the temperature was. degrees Fahrenheit at :00 AM. For the next 8 hours, the temperature fell at a constant rate of 0.8 degrees each hour. On January 1, 010, the temperature was. degrees Fahrenheit at :00 AM. For the next 8 hours, the temperature rose at a constant rate of. degrees each hour. At what time was the temperature exactly the same for the two days? a. 9:00 AM b. 9:6 AM c. 10: AM d. 8: AM e. 9: AM 8. If f ( x) = x, then which of the following is true? a. f ( f ( x)) = x 1x + 9 b. f ( f ( x)) = x 9 c. f ( f ( x)) = x 6 d. f ( f ( x)) = x 6x 9 e. f ( f ( x)) = x + 1x Let A be the smallest positive integer divisible by 10, 1, 1, 16, and 18. What is the sum of the digits of A? a. 6 b. 9 c. 1 d. 1 e. 10. The Jones family decided to build a mountain retreat home. They downloaded plans for an A-frame home that was advertised as feet wide at the base and with a roof pitch (slope) of 1. ft/ft. How tall would the home be? a. feet b. 1 feet c. 1. feet d. 0 feet e. 16. feet 11. The unique solution to the equation ax + b = 10 is x =, and the unique solution to the equation bx a = 8 is x =. Find a + b. a. 6 b. c. 6 d. 8 e. 1. Let P ( x) = x x + x. Find the largest prime factor of ( ) P( ) P. a. 1 b. 1 c. d. 19 e. 1

5 1. Jamal scored points in his last basketball game and his average went from 1 points per game to 1 points per game. How many points does he need to score in the next game to increase his average to 16 points per game? a. b. 6 c. 8 d. 0 e. 1. In a relay race, Amy runs the first lap in seconds. Betty runs the second lap at of Amy s speed. 10 Cathy runs the third lap at of Betty s speed. Sue runs the last lap at of Cathy s speed. What was 9 their total time, to the nearest second? a. sec b. sec c. 6 sec d. sec e. 8 sec 1. A box contains apples and pears. An equal number of apples and pears are rotten. One-third of all the apples are rotten. Three-fifths of all the pears are rotten. What fraction of the total number of pieces of fruit in the box is rotten? a. b. c. 1 1 d. 1 e. 16. Which of the following rates is the fastest? a. 0 miles per hour b. 10 yards per minute c. feet per second d. 0.8 miles per minute e. yards per second 1. A student drives from one town to another and averages 6 mph. On the return trip he averages miles per hour and it takes minutes longer. How far apart are the two towns? a. 180 miles b. 18 miles c. 190 miles d. 19 miles e. 00 miles

6 18. Which of the following represent the total number of quarts in x gallons, y quarts, and z pints? x a. + y + z b. z x + y + c. z x x + y + d. + y + z e. z x + y Determine the number of factors when x x with integer coefficients. 9 is completely factored into monomials and polynomials a. b. c. 6 d. 8 e The number of non-business Chapter 11 bankruptcies, B, can be modeled by the function B () t = 1.8 t t 8.8 t + 99., where t is the years since 1998 and 0 t 6. How is the number of non-business Chapter 11 bankruptcies changing between 1998 and 000? a. Bankruptcies are increasing at an increasing rate. b. Bankruptcies are increasing at a decreasing rate. c. Bankruptcies are decreasing at a constant rate. d. Bankruptcies are decreasing at an increasing rate. e. Bankruptcies are decreasing at a decreasing rate. 1. Let p be a prime number and k an integer such that x + kx + p = 0 has two positive integer solutions. What is the value of k + p? a. 1 b. 1 c. 0 d. e.. How many pairs of positive integers ( b) a + b a, with a + b 100 satisfy the equation = 1 1 a + b 1 a. 0 b. 1 c. d. e.

7 . An automobile tire manages to get two punctures at the same time. The first puncture by itself will cause a flat in nine minutes and the second puncture by itself will cause a flat in six minutes. Assuming air leaks out at a constant rate, how long before the tire is flat from both punctures? a..6 minutes b. minutes c.. minutes d.. minutes e. 1 minutes. In the 1960s every playground in the country had a metal slide that was 10 feet tall and very steep. In the late 190s federal regulations put an end to tall, steep metal slides. The new regulations require that the length of a slide be more than or equal to twice its height. Assuming the end of the slide is on the ground, what is the tallest a slide can be to the nearest hundredth of a foot if the horizontal distance from the end of the slide to the base of the ladder is 6. feet?? a.. ft b..8 ft c.. ft d.. ft e.. ft. Recall the following Roman Numeral values: VII = : IX = 9; XXV = ; XLVI = 6; XCII = 9; and MDCLXI = Compute XXIX + CCXXXV + DCCCXLII + MMCLIV. a. MMMCCLX b. MMMDLVII c. MMMCLIX d. MMMCCLIX e. MMMCCXL

8 SHORT ANSWER Place the answer in the appropriate space. 66. Write as a fraction in lowest terms. x 6. If = y and = 18, what is the value of xy? 68. Assuming all machines work at the same speed, if machines can do jobs in days, how long will it take one machine to finish one job? 69. Compute the smallest value of n for which the mean and median of the set {1, 1, 6, 8, 1, n} are equal. 0. Harry chooses a three-digit number in which no two digits are the same. He then reverses the order of the digits and subtracts the smaller number from the larger. The units digit of the difference is ; what is the entire difference? 6

9 1. a. e. d. e. b 6. c. a 8. b 9. b 10. e 11. a 1. d 1. c 1. d 1. e 16. c 1. d 18. c 19. b 0. e 1. b. d. a. c. a

10 1hour 600 sec 1mile 10 feet 1. * * *. 9 sec. 6.1 miles 1hour 80 feet 1. Let x be the original value of the stock and let y be the percentage needed to regain its value. This gives 1 + y 0.6x = x y = 0. or 6.%. ( )( ) 6. Let x be the number. Then 1 8 x = x x =. 1. Line M has equation = x y. The only point lying on this line is (, ).. 1 ( 1.) 0 = $ x + 1 Hence there are 1 integer values of x. is an integer if and only if x + 1 is a divisor of 1. The divisors of 1 are { 1, ±, ±, ±, ± 6, ± 1} ±.. Let x be the number of hours since :00 AM. Then. 0.8x =. +.x x = hours. So the temperature was the same at 9:00 AM both days. 8. f ( f ( x) ) = ( x ) = x 9 9. The smallest positive integer divisible by 10, 1, 1, 16, and 18 is * ** = 00. The sum of the digits of 00 is The top of an A-frame house is in the middle of the house. So the run is 11 feet making the rise rise 1. = rise = 1.( 11) = 16. feet a + b = 10 and b a = 8. Solving for a and b gives 1 a = and b =. Hence 6 a + b =. 1. ( ) P( ) = 8 P. The largest prime factor of 8 is Let x be the number of games Jamal played before his average increased to 1. Then 1x + = 1 x =. Now let y be the number of points he needs in game. Then x + 1 6( 1) + y = 16 y = 8 points. 8

11 = sec. If Cathy runs at of Betty s 10 = sec. If Sue runs at of Cathy s speed, then her time was 9 1. If Betty runs at of Amy s speed, then her time was ( ) 100 speed then her time was ( 100) ( 80) = sec. Thus the total relay time was seconds. x 1. Let x be the number of rotten apples. Then the number of apples is x and the number of pears is. Hence the ratio of rotten fruit to the total number of fruit is x x + x =. 16. Changing all the rates to feet per second gives 0 mph. fps, 10 yd/min =. fps, 0.8 m/min =.8 fps, and yd/ sec = fps. This means the fastest rate is fps. 1. Let x be the time to drive at 6 mph. Then 6 = ( x + 0.) x = miles apart. x hours. Thus the towns are There are quarts in a gallon and pints in a quart. That means there are x = x( x 1)( x + 1)( x + 1)( x + 1) x so there are factors. z x + y + quarts. 0. Between 1998 and 000 the number of bankruptcies is decreasing and the drop between 1998 and 1999 is greater than the drop between 1999 and 000. That means that bankruptcies are decreasing at a decreasing rate. 1. If p is a prime number and x + kx + p = 0 has two positive integer solutions then ( x p)( x 1) = x + ( p 1) x + kx + p = x + p k = p 1. Thus k + p = ab a + a + b b b a = = =. Setting up a table of values gives the following integer solutions 1 a + b 1 1+ ab b + b a a 1,1 ;, ; 1, ; 68, ; 8,. Hence there are. {( ) ( ) ( ) ( ) ( )} Let x be the time required with both punctures. Then + = x = = x minutes.. Let x be the height of the slide, then ( ) x = 6. x = 60 or MMMCCLX. x feet. 9

12 = y x y xy 18 = and ( ) = = Hence xy =. 68. Five machines would take one day to do one job. So each machine is doing one fifth of the job in a day. Hence one machine would take days to do one job. 69. There are three possibilities. Either n 1, 1 < n < 6 ; or n 6. For the smallest value of n, assume 19 + n n 1. Then the median is.. This gives. = n = Let the hundreds digit be x and the tens digit be y and the ones digit be z. Then ( 100x + 10y + z) ( 100z + 10y x) = 99x 99z. This means the difference is divisible by 99. Looking at a table of values shows that the three digit multiples of 99 all have a tens digit of 9 with the sum of the hundreds digit and units digit being 9. Hence the difference is