1995 AJHSME Problems - AoPSWiki

Search Wiki Go SearchPage ToolsPage Discussion View source HistoryPersonal toolsLog inNavigationMain pageCommunity portal Recent changes Random page HelpToolboxWhat links here Related changes Special pages Printable version Permanent linkArt of Problem Solving1992 AJHSME ProblemsFrom AoPSWikiContents1 Problem 12 Problem 23 Problem 34 Problem 45 Problem 56 Problem 67 Problem 78 Problem 89 Problem 910 Problem 1011 Problem 1112 Problem 1213 Problem 1314 Problem 1415 Problem 1516 Problem 1617 Problem 1718 Problem 1819 Problem 1920 Problem2021 Problem2122 Problem 2223 Problem 2324 Problem 2425 Problem2526 See alsoProblem 1SolutionProblem 2Which of the following is not equal to ?SolutionProblem 3What is the largest difference that can be form ed by subtracting two num bers chosen from the set?SolutionProblem 4During the softball season, Judy had hits. Am ong her hits were hom e run, triple and doubles. The rest of her hits were single. What percent of her hits were single?SolutionProblem 5A circle of diam eter is rem oved from a rectangle, as shown. Which whole num ber is closest to thearea of the shaded region?SolutionProblem 6Suppose that m eans . For exam ple, is . Then the sumisSolutionProblem 7The digit-sum of is . How m any 3-digit whole num bers, whose digit-sum is , are even?SolutionProblem 8A store owner bought pencils at $0.10 each. If he sells them for $0.25 each, how m any of them m ust he sell to m ake a profit of exactly $100.00?SolutionProblem 9The population of a sm all town is . The graph indicates the num ber of fem ales and m ales in the town,but the vertical scale-values are om itted. How m any m ales live in the town?SolutionProblem 10An isosceles right triangle with legs of length is partitioned into congruent triangles as shown. Theshaded area isSolutionProblem 11The bar graph shows the results of a survey on color preferences. What percent preferred blue?SolutionProblem 12The five tires of a car (four road tires and a full-sized spare) were rotated so that each tire was used the sam e num ber of m iles during the first m iles the car traveled. For how m any m iles was each tire used?SolutionProblem 13Five test scores have a m ean (average score) of , a m edian (m iddle score) of and a m ode (m ost frequent score) of . The sum of the two lowest test scores isSolutionProblem 14When four gallons are added to a tank that is one-third full, the tank is then one-half full. The capacity of the tank in gallons isSolutionProblem 15What is the letter in this sequence?SolutionProblem 16Which cylinder has twice the volum e of the cylinder shown above?SolutionProblem 17The sides of a triangle have lengths , , and , where is a whole num ber. What is the sm allestpossible value of ?SolutionProblem 18On a trip, a car traveled m iles in an hour and a half, then was stopped in traffic for m inutes, then traveled m iles during the next hours. What was the car's average speed in m iles per hour for the -hour trip?SolutionProblem 19The distance between the and exits on an interstate highway is m iles. If any two exits are atleast m iles apart, then what is the largest num ber of m iles there can be between two consecutive exitsthat are between the and exits?SolutionProblem 20Which pattern of identical squares could NOT be folded along the lines shown to form a cube?SolutionProblem 21Northside's Drum and Bugle Corps raised m oney for a trip. The drum m ers and bugle players kept separate sales records. According to the double bar graph, in what m onth did one group's sales exceed the other's by the greatest percent?SolutionProblem 22Eight square tiles are arranged as shown so their outside edges form a polygon with a perim eter ofunits. Two additional tiles of the sam e size are added to the figure so that at least one side of each tile is shared with a side of one of the squares in the original figure. Which of the following could be the perim eter of the new figure?SolutionProblem 23If two dice are tossed, the probability that the product of the num bers showing on the tops of the dice is greater than isSolutionProblem 24Four circles of radius are arranged as shown. Their centers are the vertices of a square. The area of the shaded region is closest toSolutionProblem 25One half of the water is poured out of a full container. Then one third of the rem ainder is poured out. Continue the process: one fourth of the rem ainder for the third pouring, one fifth of the rem ainder for thefourth pouring, etc. After how m any pourings does exactly one tenth of the original water rem ain?SolutionSee also1992 AJHSME (Problems • Resources)Preceded by 1991 AJHSMEFollowed by 1993 AJHSME1 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20• 21 • 22 • 23 • 24 • 25AJHSMEAJHSME Problem s and SolutionsMathem atics com petition resourcesRetrieved from "http://www.artofproblem /Wiki/index.php/1992_AJHSME_Problem s"This page was last m odified on 16 January 2010, at 18:39. This page has been accessed 7,413 tim es. Privacy policy About AoPSWiki Disclaim ers。

美国管理学会学报最佳论文（1995-2014）1.Huselid M A.The Impact of Human Resource Management Practices on Turnover, Productivity,and Corporate Financial Performance[J]. Social Science Electronic Publishing,1995, 38(3):635-672.ler D,Shamsie J. The Resource-Based View of the Firm in Two Environments: TheHollywood Film Studios From 1936 to 1965[J]. Academy of Management Journal,1996, 39(3):519-543.3.Tsui A S,Pearce J L, Porter L W, et al. Alternative approaches to theemployee–organization relationship: Does investment in employees pay off?[J].Academy of Management Journal, 1997, 40(5):1089-1121.4.Barkema H G,Vermeulen F. International Expansion through Start up or Acquisition: ALearning Perspective[J]. Academy of Management Journal, 1998, 41(1):7-26.5.Ferrier W J,Grimm C M. The Role of Competitive Action in Market Share Erosion and IndustryDethronement: A Study of Industry Leaders and Challengers[J]. Academy ofManagement Journal, 1999, 42(4):372-388.6.Zahra S A,Ireland R D, Hitt M A. International expansion by new venture firms: Internationaldiversity, mode of market entry, technological learning, and performance.[J].Academy of Management Journal, 2000, 43(5):925-950.7.Seibert S E,Liden R C. A SOCIAL CAPITAL THEORY OF CAREER SUCCESS[J]. Academy of ManagementJournal, 2001, 44(2):219-237.8.Sherer P D,Lee K. Institutional Change in Large Law Firms: A Resource Dependency andInstitutional Perspective[J]. Academy of Management Journal, 2002,45(1):102-119.9.Elsbach K D,Kramer R M. Assessing Creativity in Hollywood Pitch Meetings: Evidence for aDual-process Model of Creativity[J]. Academy of Management Journal, 2003,46(3):283-30110.Agarwal R,Echambadi R, Franco A M, et al. KNOWLEDGE TRANSFER THROUGH INHERITANCE:SPIN-OUT GENERATION, DEVELOPMENT, AND SURVIVAL[J]. Academy of Management Journal,2004, 47(4):págs. 501-522.11.Gilbert C G.Unbundling the Structure of Inertia: Resource versus Routine Rigidity[J].Academy of Management Journal, 2005, 48(5):págs. 741-763.12.Ferlie E,Fitzgerald L, Wood M, et al. THE NONSPREAD OF INNOVATIONS: THE MEDIATING ROLEOF PROFESSIONALS[J]. Academy of Management Journal, 2005, 48(1):págs. 117-134.13.Greenwood R,Suddaby R. Institutional Entrepreneurship in Mature Fields: The Big FiveAccounting Firms[J]. Academy of Management Journal, 2006, 49(1):27-48.14.Plowman D A,Travis D V. Radical Change Accidentally: The Emergence and Amplification ofSmall Change[J]. Academy of Management Journal, 2007, 50(3):515-543.15.Barnett M L,King A A. Good Fences Make Good Neighbors: A Longitudinal Analysis of anIndustry Self-Regulatory Institution[J]. Academy of Management Journal, 2008,51(6):1150-1170.16.Graebner M E.Caveat venditor: Trust asymmetries in acquisitions of entrepreneurialfirms.[J]. Academy of Management Journal, 2009, 52(3):435-472.17.Hekman D R,Aquino K, Owens B P, et al. AN EXAMINATION OF WHETHER AND HOW RACIAL AND GENDERBIASES INFLUENCE CUSTOMER SATISFACTION[J]. Academy of Management Journal, 2010,53(2):238-264.18.Detert J R,Edmondson .A C. IMPLICIT VOICE THEORIES: TAKEN-FOR-GRANTED RULES OFSELF-CENSORSHIP AT WORK[J]. Academy of Management Journal, 2011, 54(3):461-488.19.Smets M,Morris T I M, Greenwood R. From practice to field: A multilevel model ofpractice-driven institutional change[J]. Academy of Management Journal, 2012,55(4): 877-904.20.Chua R Y J.The Costs Of Ambient Cultural Disharmony: Indirect Intercultural Conflicts InSocial Environment Undermine Creativity[J]. Academy of Management Journal,2013, 56(6):1545-1577.21.ElkeSchüssler, Charles-Clemens Rüling, Bettina B. F. Wittneben. On Melting Summits:The Limitations of Field‐configuring Events as Catalysts of Change inTransnational Climate Policy[J]. Academy of Management Journal, 2014,57(2014):140-171。

Copyright © 2016 Art of Problem Solving Mindy made three purchases for dollars, dollars, and dollars. What was her total, tothe nearest dollar?The three prices round to , , and , which has a sum of2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byFirstQuestion Followed by Problem 21 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_1&oldid=55964"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingOn the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesn'tanswer the last 5. What is his score?As the AMC 8 only rewards 1 point for each correct answer, everything is irrelevant except the number Billy answered correctly, .2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 1Followed by Problem 31 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_2&oldid=55965"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingElisa swims laps in the pool. When she first started, she completed 10 laps in 25 minutes. Now, she canfinish 12 laps in 24 minutes. By how many minutes has she improved her lap time?When Elisa started, she finished a lap in minutes. Now, she finishes a lap is minutes.The difference is .2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 2Followed by Problem 41 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_3&oldid=55966"SolutionSee AlsoCopyright © 2016 Art of Problem Solving Initially, a spinner points west. Chenille moves it clockwise revolutions and then counterclockwiserevolutions. In what direction does the spinner point after the two moves?If the spinner goes clockwise revolutions and then counterclockwise revolutions, it ultimately goes counterclockwise which brings the spinner pointing.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 3Followed by Problem 51 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_4&oldid=55967"SolutionSee AlsoPoints and are midpoints of the sides of the larger square. If the larger square has area 60, what is the area of the smaller square?Drawing segments and , the number of triangles outside square is the same as the number of triangles inside the square. Thus areas must be equal so the area of is half the area of thelarger square which is .If the side length of the larger square is , the side length of the smaller square is . Therefore the area of the smaller square is , half of the larger square's area, .Thus, the area of the smaller square in the picture is .Copyright © 2016 Art of Problem Solving The letter T is formed by placing twoinch rectangles next to each other, as shown. What is theperimeter of the T, in inches?If the two rectangles were seperate, the perimeter would be . It easy to see that their connection erases 2 from each of the rectangles, so the final perimeter is .2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 5Followed by Problem 71 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'s American Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_6&oldid=55969"SolutionSee AlsoCopyright © 2016 Art of Problem Solving Circle has a radius of . Circle has a circumference of . Circle has an area of . List thecircles in order from smallest to largest ing the formulas of circles, and , we find that circle has a radius of and circle has a radius of . Thus, the order from smallest to largest radius is.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 6Followed by Problem 81 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21• 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'s American Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_7&oldid=55970"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingThe table shows some of the results of a survey by radiostation KAMC. What percentage of the males surveyedlisten to the station?Filling out the chart, it becomes Thus, the percentage of males surveyed that listen to the station is .2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 7Followed by Problem 91 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_8&oldid=55971"SolutionSee AlsoCopyright © 2016 Art of Problem Solving What is the product of?By telescoping, it's easy to see the sum becomes .2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 8Followed by Problem 101 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_9&oldid=55972"SolutionSee AlsoJorge's teacher asks him to plot all the ordered pairs of positive integers for which is the width and is the length of a rectangle with area 12. What should his graph look like?Copyright © 2016 Art of Problem SolvingThe length of the rectangle will relate invertly to the width, specifically using the theorem . Theonly graph that could represent a inverted relationship is . (The rest are linear graphs thatrepresent direct relationships)2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded by Problem 9Followed by Problem 111 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_10&oldid=55973"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingHow many two-digit numbers have digits whose sum is a perfect square?There is integer whose digits sum to : .There are integers whose digits sum to : .There are integers whose digits sum to : .There are integers whose digits sum to :.Two digits cannot sum toor any greater square since the greatest sum of digits of a two-digit number is.Thus, the answer is.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded by Problem 10Followed by Problem 121 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_11&oldid=80944"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingAntonette gets on a 10-problem test, on a 20-problem test and on a 30-problem test. Ifthe three tests are combined into one 60-problem test, which percent is closest to her overall score?Adding them up gets. The overall percentage correct would be.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded by Problem 11Followed by Problem 131 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_12&oldid=55975"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingCassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike. He bikes at a uniform rate of 16 miles per hour. They both bike on the same 62-mile route between Escanaba and Marquette. At what time inthe morning do they meet?If Cassie leavesan hour earlier then Brian, when Brian starts, the distance between them will be. Every hour, they will getmiles closer., so 2 hours from 9:00AM is when they meet, which is.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded by Problem 12Followed by Problem 141 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_13&oldid=55976"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingProblems 14, 15 and 16 involve Mrs. Reed's English assignment.A Novel AssignmentThe students in Mrs. Reed's English class are reading the same -page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in seconds and Chandra reads a page inseconds.If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?The information is the same for Problems 14,15, and 16. Therefore, we shall only use the information we need. All we need for this problem is that there's 760 pages, Bob reads a page in 45 seconds and Chandrareads a page in 30 seconds. A lot of people will find how long it takes Bob to read the book, how long it takes Chandra to read the book, and then find the seconds. However, if we just set up the expression, we can find an easier way.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded by Problem 13Followed by Problem 151 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_14&oldid=55977"SolutionSee AlsoLet be the number of pages that Chandra reads.Distribute theAdd to both sidesDivide both sides by to make it easier to solveDivide both sides bySolution 2Bob and Chandra read at a rate of seconds per page, respectively. Simplifying that gets us Bob reads pages for every pages that Chandra reads. Therefore Chandra should read of the book. =$\boxed{\textbf{(C)} 456}See AlsoCopyright © 2016 Art of Problem SolvingProblems 14, 15 and 16 involve Mrs. Reed's English assignment.A Novel AssignmentThe students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds.Before Chandra and Bob start reading, Alice says she would like to team read with them. If they divide the book into three sections so that each reads for the same length of time, how many seconds will each have toread?The amount of pages Bob, Chandra, and Alice would read is in the ratio 4:6:9. Therefore, Bob, Chandra, and Alice read 160, 240, and 360 pages respectively. They would also be reading in the same amount of time because the ratio of pages read was based on the time it takes each of them to read a page. Therefore, the amount of seconds each person reads is.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded by Problem 15Followed by Problem 171 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_16&oldid=55979"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingJeff rotates spinners ,andand adds the resulting numbers. What is the probability that his sum isan odd number?In order for Jeff to have an odd number sum, the numbers must either be Odd + Odd + Odd or Even + Even +Odd. We easily notice that we cannot obtain Odd + Odd + Odd because spinner contains only even numbers.Therefore we must work with Even + Even + Odd and spinner will give us one of our even numbers. We also see that spinner only contains odd, so spinner must give us our odd nmber. We still need one evennumber from spinner . There is only 1 even number: . Since spinning the required numbers are automatic onthe other spinners, we only have to find the probability of spinning a in spinner , which clearly is2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded by Problem 16Followed by Problem 181 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24• 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_17&oldid=55980"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingA cube with 3-inch edges is made using 27 cubes with 1-inch edges. Nineteen of the smaller cubes are white and eight are black. If the eight black cubes are placed at the corners of the larger cube, what fraction of the surface area of the larger cube is white?The surface area of the cube is . Each of the eight black cubes has 3 faces on the outside,making black faces. Therefore there are white faces. To find the probability,we evaluate.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded by Problem 17Followed by Problem 191 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 •25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_18&oldid=55981"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingTriangleis an isosceles triangle with . Pointis the midpoint of bothand, and is 11 units long. Triangleis congruent to triangle . What is the length of?Since triangleis congruent to triangleand ,. Since,. Because pointis the midpoint of,.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded by Problem 18Followed by Problem 201 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19• 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_19&oldid=55982"SolutionSee AlsoA singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how manygames did Monica win?Since there are 6 players, a total ofgames are played. So far,games finished (one person won from each game), so Monica needs to win.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 19Followed byProblem 211 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 •20• 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'sAmerican Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_20&oldid=81054"SolutionSee AlsoCopyright © 2016 Art of Problem SolvingCopyright © 2016 Art of Problem Solving An aquarium has a rectangular base that measures cm by cm and has a height ofcm. The aquarium is filled with water to a depth of cm. A rock with volume is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?The water level will rise cm for every . Since is of , the waterwill rise 2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 20Followed by Problem 221 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22• 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'s American Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_21&oldid=55984"SolutionSee AlsoThree different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process toobtain a number in the top cell. What is the difference between the largest and smallest numbers possible inthe top cell?If the lower cells contain and , then the second row will contain and , and the top cell will contain . To obtain the smallest sum, place in the center cell and and in the outer ones. The top number will be . For the largest sum, place in the center cell and and in the outer ones. This top number will be . The difference is .2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 21Followed by Problem 231 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 •22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'s American Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_22&oldid=55985"SolutionSee AlsoThe counting numbers that leave a remainder of 4 when divided by 6 are The counting numbers that leave a remainder of 3 when divided by 5 are So 28 isthe smallest possible number of coins that meets both conditions. Because , there areIf there were two more coins in the box, the number of coins would be divisible by both 6 and 5. The smallest number that is divisible by 6 and 5 is , so the smallest possible number of coins in the box isand the remainder when divided by 7 is .The problems on this page are copyrighted by the Mathematical Association of America ()'s American Mathematics Competitions ().Copyright © 2016 Art of Problem Solving In the multiplication problem below , , , and are different digits. What is?, so . Therefore, and , so.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 23Followed by Problem 251 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 •24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'s American Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_24&oldid=68712"SolutionSee AlsoCopyright © 2016 Art of Problem Solving Barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides areprime numbers. What is the average of the hidden prime numbers?Notice that 44 and 38 are both even, while 59 is odd. If any odd prime is added to 59, an even number will be obtained. However, the only way to obtain this even number would be to add another even number to 44, and a different one to 38. Since there is only one even prime (2), the middle card's hidden number cannot be anodd prime, and so must be even. Therefore, the middle card's hidden number must be 2, so the constant sum is . Thus, the first card's hidden number is , and the last card's hidden number is .Since the sum of the hidden primes is, the average of the primes is.2006 AMC 8 (Problems • Answer Key • Resources(/Forum/resources.php?c=182&cid=42&year=2006))Preceded byProblem 24Followed by Last Problem1 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 •19 • 20 • 21 • 22 • 23 • 24 • 25All AJHSME/AMC 8 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'s American Mathematics Competitions ().Retrieved from "/wiki/index.php?title=2006_AMC_8_Problems/Problem_25&oldid=55988"SolutionSee Also。

Guidance for Industry Immediate Release Solid Oral Dosage FormsScale-Up and Postapproval Changes: Chemistry, Manufacturing, and Controls, In Vitro Dissolution Testing, and In Vivo Bioequivalence DocumentationCenter for Drug Evaluation and Research (CDER)November 1995CMC 5TABLE OF CONTENTSI.PURPOSE OF GUIDANCE (1)II.DEFINITION OF TERMS (3)PONENTS AND COMPOSITION (6)IV.SITE CHANGES (13)V.CHANGES IN BATCH SIZE (SCALE-UP/SCALE-DOWN) (16)VI.MANUFACTURING (18)VII.IN VITRO DISSOLUTION (23)VIII.IN VIVO BIOEQUIVALENCE STUDIES (23)IX.REFERENCES (25)APPENDIX A: NARROW THERAPEUTIC RANGE DRUGS . . . . . . . . . . . . . . . A-1This guidance has been prepared by the Immediate Release Scale-up and Post 1Approval Change (SUPAC) Expert Working Group of the Chemistry Manufacturing Controls Coordinating Committee (CMC CC) of the Center for Drug Evaluation and Research at the Food and Drug Administration. This guidance is an informal communication under 21 CFR 10.90(b)(9) that reflects the best judgment of CDER employees at this time. It does not create or confer any rights, privileges or benefits for or on any person, nor does it operate to bind or obligate FDA in any way. For additional copies of this guidance contact the Consumer Affairs Branch (formerly the Executive Secretariat Staff), HFD-8, Center for Drug Evaluation and Research, 7500 Standish Place, Rockville, MD 20855 (Phone: 301-594-1012). An electronic version of this guidance is also available via Internet by connecting to the CDER file transfer protocol (FTP) server ().GUIDANCE FOR INDUSTRY 1IMMEDIATE RELEASE SOLID ORAL DOSAGE FORMSSCALE-UP AND POSTAPPROVAL CHANGES:CHEMISTRY, MANUFACTURING, AND CONTROLS,IN VITRO DISSOLUTION TESTING,AND IN VIVO BIOEQUIVALENCE DOCUMENTATION I.PURPOSE OF GUIDANCEThis guidance provides recommendations to sponsors of new drug applications (NDA's), abbreviated new drug applications (ANDA's), and abbreviatedantibiotic applications (AADA's) who intend, during the postapproval period, to change: 1) the components or composition; 2) the site of manufacture; 3) the scale-up/scale-down of manufacture; and/or 4) the manufacturing (process and equipment) of an immediate release oral formulation.This guidance is the result of: 1) a workshop on the scale-up of immediate release drug products conducted by the American Association ofPharmaceutical Scientists in conjunction with the United States Pharmacopoeial Convention and the Food and Drug Administration (FDA); 2) researchconducted by the University of Maryland at Baltimore on the chemistry,manufacturing and controls of immediate release drug products under the FDA/University of Maryland Manufacturing Research Contract; 3) the drug categorization research conducted at the University of Michigan and theUniversity of Uppsala on the permeability of drug substances; and 4) the Scale-See Workshop Report: Scale-up of Immediate Release Oral Solid Dosage Forms,2Pharmaceutical Research , 10 (2): 313-316, Skelly et al; and Federal Register. Vol. 59,No. 183, Thursday, September 22, 1994, pages 48754-59.2Up and Post Approval Changes (SUPAC) Task Force which was established by the Center for Drug Evaluation and Research (CDER) Chemistry, Manufacturing and Controls Coordinating Committee to develop guidance on scale-up andother postapproval changes.The guidance defines: 1) levels of change; 2) recommended chemistry,manufacturing, and controls tests for each level of change; 3) in vitro dissolution tests and/or in vivo bioequivalence tests for each level of change; and 4)documentation that should support the change. For those changes filed in a “changes being effected supplement” [21 CFR 314.70(c)], the FDA may, after a review of the supplemental information, decide that the changes are notapprovable. This guidance thus sets forth application information that should be provided to CDER to assure continuing product quality and performancecharacteristics of an immediate release solid oral dose formulation for specified postapproval changes. This guidance does not comment on or otherwise affect compliance/inspection documentation that has been defined by CDER’s Office of Compliance or FDA’s Office of Regulatory Affairs. This guidance does not affect any postapproval changes other than the ones specified. For changes not addressed in this guidance, or for multiple changes submitted at one time or over a short period of time, or where the number of batches needed for stability testing is not specified, sponsors should contact the appropriate CDER review division or consult other CDER guidances/guidelines to obtain information about tests and application documentation.21 CFR 314.70(a) provides that applicants may make changes to an approved application in accordance with a guideline, notice, or regulation published in the FEDERAL REGISTER that provides for a less burdensome notification of the change (for example, by notification at the time a supplement is submitted or in the next annual report). This guidance permits less burdensome notice ofcertain postapproval changes within the meaning of § 314.70(a).For postapproval changes for immediate release dosage forms that affectcomponents and composition, scale-up, site change, and manufacturingprocess or equipment changes, this guidance supersedes the recommendations in section 4.G of the Office of Generic Drugs Policy and Procedure Guide 22-90(September 11, 1990). For all other dosage forms and changes, this guidance does not affect the recommendations in Guide 22-90.II.DEFINITION OF TERMS 2A.BatchA specific quantity of a drug or other material produced according to asingle manufacturing order during the same cycle of manufacture andintended to have uniform character and quality, within specified limits [21 CFR 210.3(b)(2)].B.Contiguous CampusContinuous or unbroken site or a set of buildings in adjacent city blocks.C.Dissolution TestingCase A:Dissolution of Q = 85% in 15 minutes in 900 milliliters (mL)of 0.1N hydrochloride (HCl), using the United StatesPharmacopeia (USP) <711> Apparatus 1 at 100 revolutionsper minute (rpm) or Apparatus 2 at 50 rpm.Case B:Multi-point dissolution profile in the application/compendialmedium at 15, 30, 45, 60, and 120 minutes or until anasymptote is reached for the proposed and currentlyaccepted formulation.Case C:Multi-point dissolution profiles performed in water, 0.1N HCl,and USP buffer media at pH 4.5, 6.5, and 7.5 (five separateprofiles) for the proposed and currently acceptedformulations. Adequate sampling should be performed at15, 30, 45, 60, and 120 minutes until either 90% of drugfrom the drug product is dissolved or an asymptote isreached. A surfactant may be used with appropriatejustification.3D.Drug ProductA drug product is a finished dosage form (e.g., tablet, capsule, orsolution) that contains a drug substance, generally, but not necessarily, in association with one or more other ingredients [21 CFR 314.3(b)]. A solid oral dosage form includes tablets, chewable tablets, capsules, and softgelatin capsules.E.Drug SubstanceAn active ingredient that is intended to furnish pharmacological activity or other direct effect in the diagnosis, cure, mitigation, treatment, orprevention of a disease, or to affect the structure of any function of thehuman body, but does not include intermediates used in the synthesis of such ingredient [21 CFR 314.3(b)].F.EquipmentAutomated or non-automated, mechanical or non-mechanical equipment used to produce the drug product, including equipment used to packagethe drug product.G.FormulationA listing of the ingredients and composition of the dosage form.H.JustificationReports containing scientific data and expert professional judgment tosubstantiate decisions.I.New Drug SubstanceAny substance that, when used in the manufacture, processing, orpacking of a drug, causes that drug to be a new drug, but does notinclude intermediates used in the synthesis of such substance [21 CFR310.3(g)].J.Operating PrincipleRules or concepts governing the operation of the system.4K.Pilot ScaleThe manufacture of either drug substance or drug product by a procedure fully representative of and simulating that used for full manufacturingscale.For solid oral dosage forms this is generally taken to be, at a minimum,one-tenth that of full production, or 100,000 tablets or capsules,whichever is larger (see the FEDERAL REGISTER of Thursday,September 22, 1994, 59 FR 48754-59).L.ProcessA series of operations and/or actions used to produce a desired result. M.RangesThe extent to which or the limits between which acceptable variationexists.N.SameAgreeing in kind, amount; unchanged in character or condition.O.Scale-upThe process of increasing the batch size.P.Scale-downThe process of decreasing the batch size.Q.SimilarHaving a general likeness.R.Significant body of informationA significant body of information on the stability of the drug product islikely to exist after five years of commercial experience for new molecular entities, or three years of commercial experience for new dosage forms.5S.ValidationEstablishing through documented evidence a high degree of assurancethat a specific process will consistently produce a product that meets itspredetermined specifications and quality attributes. A validatedmanufacturing process is one that has been proven to do what it purportsor is represented to do. The proof of validation is obtained throughcollection and evaluation of data, preferably beginning from the processdevelopment phase and continuing through the production phase.Validation necessarily includes process qualification (the qualification ofmaterials, equipment, systems, buildings, and personnel), but it alsoincludes the control of the entire processes for repeated batches or runs.PONENTS AND COMPOSITIONThis section of the guidance focuses on changes in excipients in the drugproduct. Changes in the amount of drug substance are not addressed by thisguidance. Changes in components or composition that have the effect ofadding a new excipient or deleting an excipient are defined at Level 3 (definedbelow), except as described below.A.Level 1 Changes1.Definition of LevelLevel 1 changes are those that are unlikely to have any detectableimpact on formulation quality and performance.Examples:a.Deletion or partial deletion of an ingredient intended to affectthe color or flavor of the drug product; or change in theingredient of the printing ink to another approved ingredient.b.Changes in excipients, expressed as percentage (w/w) oftotal formulation, less than or equal to the following percentranges:6EXCIPIENT PERCENT EXCIPIENT(w/w) OUT OF TOTALTARGET DOSAGEFORM WEIGHT Filler±5DisintegrantStarch±3Other±1Binder±0.5LubricantCalcium (Ca) orMagnesium (Mg) Stearate±0.25Other±1GlidantTalc±1Other±0.1Film Coat±1These percentages are based on the assumption that the drug substance in the product is formulated to 100% of label/potency. The total additive effect of all excipient changes should not be more than 5%. (Example: In a product consisting of active ingredient A, lactose, microcrystalline cellulose and magnesium stearate, the lactose and microcrystalline cellulose should not vary by more than an absolute total of 5% (e.g. lactose increases 2.5% and microcrystalline cellulose decreases by 2.5%) relative to the target dosage form weight if it is to stay within the Level 1 range).7The components (active and excipients) in the formulation shouldhave numerical targets which represent the nominal composition ofthe drug product on which any future changes in the compositionof the product are to be based. Allowable changes in thecomposition should be based on the approved target compositionand not on previous Level 1 changes in the composition.2.Test Documentationa.Chemistry DocumentationApplication/compendial release requirements and stabilitytesting.Stability testing: one batch on long-term stability datareported in annual report.b.Dissolution DocumentationNone beyond application/compendial requirements.c.In Vivo Bioequivalence DocumentationNone.3.Filing DocumentationAnnual report (all information including long-term stability data).B.Level 2 Changes1. Definition of LevelLevel 2 changes are those that could have a significant impact onformulation quality and performance. Tests and filingdocumentation for a Level 2 change vary depending on threefactors: therapeutic range, solubility, and permeability.Therapeutic range is defined as either narrow or non-narrow. A listof narrow therapeutic range drugs is provided in Appendix A. Drugsolubility and drug permeability are defined as either low or high.Solubility is calculated based on the minimum concentration ofdrug, milligram/milliliter (mg/mL), in the largest dosage strength,determined in the physiological pH range (pH 1 to 8) and8otemperature (37 + 0.5C). High solubility drugs are those with a dose/solubility volume of less than or equal to 250 mL. (Example:oCompound A has as its lowest solubility at 37 + 0.5C, 1.0 mg/mL at pH 7, and is available in 100 mg, 200 mg and 400 mg strengths. This drug would be considered a low solubility drug as itsdose/solubility volume is greater than 250 mL (400 mg/1.0mg/mL=400 mL). Permeability (P, centimeter per second) isedefined as the effective human jejunal wall permeability of a drug and includes an apparent resistance to mass transport to the intestinal membrane. High permeability drugs are generally those with an extent of absorption greater than 90% in the absence of documented instability in the gastrointestinal tract, or those whose permeability attributes have been determined experimentally).Examples:a. Change in the technical grade of an excipient. (Example:Avicel PH102 vs. Avicel PH200.)b.Changes in excipients, expressed as percent (w/w) of totalformulation, greater than those listed above for a Level 1change but less than or equal to the following percentranges (which represent a two fold increase over Level 1changes):EXCIPIENT PERCENT EXCIPIENT (w/w)OUT OF TOTAL TARGETDOSAGE FORM WEIGHTFiller±10DisintegrantStarch±6Other±29Binder±1LubricantCa or Mg Stearate±0.5Other±2GlidantTalc±2Other±0.2Film Coat±2These percentages are based on the assumption that the drugsubstance in the drug product is formulated to 100% oflabel/potency. The total additive effect of all excipient changesshould not change by more than 10%.The components (active and excipients) in the formulation shouldhave numerical targets that represent the nominal composition ofthe product on which any future changes in the composition of the product are to be based. Allowable changes in the compositionshould be based on the approved target composition and not onthe composition based on previous Level 1 or Level 2 changes.2.Test Documentationa.Chemistry DocumentationApplication/compendial release requirements and batchrecords.Stability testing: 1 batch with 3 months accelerated stabilitydata in supplement and 1 batch on long-term stability.b.Dissolution DocumentationCase A:High Permeability, High Solubility Drugs10Dissolution of 85% in 15 minutes in 900 mL of0.1N HCl. If a drug product fails to meet thiscriterion, the applicant should perform thetests described for Case B or C (below).Case B: Low Permeability, High Solubility DrugsMulti-point dissolution profile should beperformed in the application/compendialmedium at 15, 30, 45, 60 and 120 minutes oruntil an asymptote is reached. The dissolutionprofile of the proposed and currently usedproduct formulations should be similar.Case C:High Permeability, Low Solubility DrugsMulti-point dissolution profiles should beperformed in water, 0.1 N HCl, and USP buffermedia at pH 4.5, 6.5, and 7.5 (five separateprofiles) for the proposed and currentlyaccepted formulations. Adequate samplingshould be performed at 15, 30, 45, 60, and120 minutes until either 90% of drug from thedrug product is dissolved or an asymptote isreached. A surfactant may be used, but onlywith appropriate justification. The dissolutionprofile of the proposed and currently usedproduct formulations should be similar.c.In Vivo Bioequivalence DocumentationNone: if the situation does not meet the description inCase A, Case B or Case C, refer to Level 3 changes.3.Filing DocumentationPrior approval supplement (all information including acceleratedstability data); annual report (long-term stability data).11C.Level 3 Changes1.Definition of LevelLevel 3 changes are those that are likely to have a significantimpact on formulation quality and performance. Tests and filingdocumentation vary depending on the following three factors:therapeutic range, solubility, and permeability.Examples:a.Any qualitative and quantitative excipient changes to anarrow therapeutic drug beyond the ranges noted in SectionIII.A.1.b.b.All other drugs not meeting the dissolution criteria underSection III.B.2.b.c.Changes in the excipient ranges of low solubility, lowpermeability drugs beyond those listed in Section III.A.1.b.d.Changes in the excipient ranges of all drugs beyond thoselisted in Section III.B.1.b.2.Test Documentationa.Chemistry DocumentationApplication/compendial release requirements and batchrecords.Significant body of information available:One batch with three months acceleratedstability data reported in supplement; onebatch on long-term stability data reported inannual report.Significant body of information not available:Up to three batches with three monthsaccelerated stability data reported in12supplement; one batch on long-term stabilitydata reported in annual report.b.Dissolution DocumentationCase B dissolution profile as described in Section III.B.2.b.c.In Vivo Bioequivalence DocumentationFull bioequivalence study. The bioequivalence study may bewaived with an acceptable in vivo/in vitro correlation hasbeen verified.3.Filing DocumentationPrior approval supplement (all information including acceleratedstability data); annual report (long-term stability data).IV.SITE CHANGESSite changes consist of changes in location of the site of manufacture for bothcompany-owned and contract manufacturing facilities and do not include anyscale-up changes, changes in manufacturing (including process and/orequipment), or changes in components or composition. Scale-up is addressed in Section V of this guidance. New manufacturing locations should have asatisfactory current Good Manufacturing Practice (CGMP) inspection.A.Level 1 Changes1.Definition of LevelLevel 1 changes consist of site changes within a single facilitywhere the same equipment, standard operating procedures(SOP's), environmental conditions (e.g., temperature and humidity)and controls, and personnel common to both manufacturing sitesare used, and where no changes are made13to the manufacturing batch records, except for administrativeinformation and the location of the facility. Common is defined asemployees already working on the campus who have suitableexperience with the manufacturing process.2.Test Documentationa.Chemistry DocumentationNone beyond application/compendial release requirements.b.Dissolution DocumentationNone beyond application/compendial release requirements.c.In Vivo Bioequivalence DocumentationNone.3.Filing DocumentationAnnual report.B.Level 2 Changes1.Definition of LevelLevel 2 changes consist of site changes within a contiguouscampus, or between facilities in adjacent city blocks, where thesame equipment, SOP's, environmental conditions (e.g.,temperature and humidity) and controls, and personnel common toboth manufacturing sites are used, and where no changes aremade to the manufacturing batch records, except for administrativeinformation and the location of the facility.2.Test Documentationa.Chemistry DocumentationLocation of new site and updated batch records. Nonebeyond application/compendial release requirements.14One batch on long-term stability data reported in annualreport.b.Dissolution DocumentationNone beyond application/compendial release requirements.c.In Vivo Bioequivalence DocumentationNone.3.Filing DocumentationChanges being effected supplement; annual report (long-term stability test data).C.Level 3 Changes1.Definition of LevelLevel 3 changes consist of a change in manufacturing site to adifferent campus. A different campus is defined as one that is noton the same original contiguous site or where the facilities are notin adjacent city blocks. To qualify as a Level 3 change, the sameequipment, SOP's, environmental conditions, and controls shouldbe used in the manufacturing process at the new site, and nochanges may be made to the manufacturing batch records exceptfor administrative information, location and language translation,where needed.2.Test Documentationa.Chemistry DocumentationLocation of new site and updated batch records.Application/compendial release requirements.15Stability:Significant body of data available:One batch with three months acceleratedstability data reported in supplement; onebatch on long-term stability data reported inannual report.Significant body of data not available:Up to three batches with three monthsaccelerated stability data reported insupplement; up to three batches on long- termstability data reported in annual report.b.Dissolution DocumentationCase B:Multi-point dissolution profile should beperformed in the application/compendialmedium at 15, 30, 45, 60 and 120 minutes oruntil an asymptote is reached. The dissolutionprofile of the drug product at the current andproposed site should be similar.c.In Vivo Bioequivalence DocumentationNone.3.Filing DocumentationChanges being effected supplement; annual report (long-termstability data).V.CHANGES IN BATCH SIZE (SCALE-UP/SCALE-DOWN)Postapproval changes in the size of a batch from the pivotal/pilot scale biobatch material to larger or smaller production batches call for submission of additional information in the application. Scale-down below 100,000 dosage units is notcovered by this guidance. All scale-up changes should be properly validatedand, where needed, inspected by appropriate agency personnel.A.Level 1 Changes161.Definition of LevelChange in batch size, up to and including a factor of 10 times thesize of the pilot/biobatch, where: 1) the equipment used to producethe test batch(es) is of the same design and operating principles;2) the batch(es) is (are) manufactured in full compliance withCGMP's; and 3) the same standard operating procedures (SOP's)and controls, as well as the same formulation and manufacturingprocedures, are used on the test batch(es) and on the full-scaleproduction batch(es).2.Test Documentationa.Chemistry DocumentationApplication/compendial release requirements. Notificationof change and submission of updated batch records inannual report.One batch on long-term stability reported in annual report.b.Dissolution DocumentationNone beyond application/compendial release requirements.c.In Vivo BioequivalenceNone.3.Filing DocumentationAnnual report (long-term stability data).B.Level 2 Changes1.Definition of LevelChanges in batch size beyond a factor of ten times the size of thepilot/biobatch, where: 1) the equipment used to produce the testbatch(es) is of the same design and operating principles; 2) thebatch(es) is (are) manufactured in full compliance with CGMP'S;and 3) the same SOP's and controls as well as the same17formulation and manufacturing procedures are used on the testbatch(es) and on the full-scale production batch(es).2.Test Documentationa.Chemistry DocumentationApplication/compendial release requirements. Notificationof change and submission of updated batch records.Stability testing: One batch with three months acceleratedstability data and one batch on long-term stability.b.Dissolution DocumentationCase B testing.c.In Vivo BioequivalenceNone.3.Filing DocumentationChanges being effected supplement; annual report (long-termstability data).VI.MANUFACTURINGManufacturing changes may affect both equipment used in the manufacturingprocess and the process itself.A. Equipment1.Level 1 Changesa.Definition of ChangeThis category consists of: 1) change from non-automatedor non-mechanical equipment to automated or mechanicalequipment to move ingredients; and 2) change to alternativeequipment of the same design and operating principles ofthe same or of a different capacity.18b.Test Documentationi.Chemistry DocumentationApplication/compendial release requirements.Notification of change and submission of updatedbatch records.Stability testing: One batch on long-term stability.ii.Dissolution DocumentationNone beyond application/compendial releaserequirements.iii.In Vivo Bioequivalence DocumentationNone.c.Filing DocumentationAnnual report (long-term stability data).2.Level 2 Changesa.Definition of LevelChange in equipment to a different design and differentoperating principles.b.Test Documentationi.Chemistry DocumentationApplication/compendial release requirements.Notification of change and submission of updatedbatch records.19Stability testing:Significant body of data available:One batch with three monthsaccelerated stability data reported insupplement; one batch on long-termstability data reported in annual report.Significant body of data not available:Up to three batches with three monthsaccelerated stability data reported insupplement; up to three batches onlong-term stability data reported inannual report.ii.Dissolution DocumentationCase C dissolution profile.iii.In Vivo Bioequivalence DocumentationNone.c.Filing DocumentationPrior approval supplement with justification for change;annual report (long-term stability data).B. Process1.Level 1 Changesa.Definition of LevelThis category includes process changes including changessuch as mixing times and operating speeds withinapplication/validation ranges.b.Test Documentation20i.Chemistry DocumentationNone beyond application/compendial releaserequirements.ii.Dissolution DocumentationNone beyond application/compendial releaserequirements.iii.In Vivo Bioequivalence DocumentationNone.c.Filing DocumentationAnnual report.2.Level 2 Changesa.Definition of LevelThis category includes process changes including changessuch as mixing times and operating speeds outside ofapplication/validation ranges.b.Test Documentationi.Chemistry DocumentationApplication/compendial release requirements.Notification of change and submission of updatedbatch records.Stability testing: One batch on long-term stability.ii.Dissolution DocumentationCase B dissolution profile.iii.In Vivo Bioequivalence DocumentationNone.21。

Search Wiki Go SearchPage ToolsPage Discussion View source HistoryPersonal toolsLog inNavigationMain pageCommunity portal Recent changes Random page HelpToolboxWhat links here Related changes Special pages Printable version Permanent linkArt of Problem Solving1993 AJHSME ProblemsFrom AoPSWikiContents1 Problem 12 Problem 23 Problem 34 Problem 45 Problem 56 Problem 67 Problem 78 Problem 89 Problem 910 Problem 1011 Problem 1112 Problem 1213 Problem 1314 Problem 1415 Problem 1516 Problem 1617 Problem 1718 Problem 1819 Problem 1920 Problem 2021 Problem 2122 Problem 2223 Problem 2324 Problem 2425 Problem2526 See alsoProblem 1Which pair of numbers does NOT have a product equal to?SolutionProblem 2When the fraction is expressed in sim plest form , then the sum of the num erator and the denom inator willbeSolutionProblem 3Which of the following num bers has the largest prim e factor?SolutionProblem 4SolutionProblem 5Which one of the following bar graphs could represent the data from the circle graph?SolutionProblem 6A can of soup can feed adults or children. If there are cans of soup and children are fed, then howm any adults would the rem aining soup feed?SolutionProblem 7SolutionProblem 8To control her blood pressure, Jill's grandm other takes one half of a pill every other day. If one supply ofm edicine contains pills, then the supply of m edicine would last approxim atelySolutionProblem 9Consider the operation defined by the following table:For exam ple, . ThenSolutionProblem 10This line graph represents the price of a trading card during the first m onths of .The greatest m onthly drop in price occurred duringSolutionProblem 11Consider this histogram of the scores for students taking a test:The m edian is in the interval labeledSolutionProblem 12If each of the three operation signs, , , , is used exactly ONCE in one of the blanks in the expressionthen the value of the result could equalSolutionProblem 13The word "HELP" in block letters is painted in black with strokes unit wide on a by rectangular white sign with dim ensions as shown. The area of the white portion of the sign, in square units, isSolutionProblem 14The nine squares in the table shown are to be filled so that every row and every colum n contains each of the num bers . ThenSolutionProblem 15The arithm etic m ean (average) of four num bers is . If the largest of these num bers is , then the m ean of the rem aining three num bers isSolutionProblem 16SolutionProblem 17Square corners, units on a side, are rem oved from a unit by unit rectangular sheet of cardboard.The sides are then folded to form an open box. The surface area, in square units, of the interior of the box isSolutionProblem 18The rectangle shown has length , width , and and are m idpoints of and ,respectively. The area of quadrilateral isSolutionProblem 19SolutionProblem 20When is expressed as a single whole num ber, the sum of the digits isSolutionProblem 21If the length of a rectangle is increased by and its width is increased by , then the area isincreased bySolutionProblem 22Pat Peano has plenty of 0's, 1's, 3's, 4's, 5's, 6's, 7's, 8's and 9's, but he has only twenty-two 2's. How far can he num ber the pages of his scrapbook with these digits?SolutionProblem 23Five runners, , , , , , have a race, and beats , beats , beats , and finishes afterand before . Who could NOT have finished third in the race?SolutionProblem 24What num ber is directly above in this array of num bers?SolutionProblem 25A checkerboard consists of one-inch squares. A square card, inches on a side, is placed on the board so that it covers part or all of the area of each of squares. The m axim um possible value of isSolutionSee also1993 AJHSME (Problems • Resources)Preceded by 1992 AJHSMEFollowed by 1994 AJHSME1 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20• 21 • 22 • 23 • 24 • 25AJHSMEAJHSME Problem s and SolutionsMathem atics com petition resourcesRetrieved from "http://www.artofproblem /Wiki/index.php/1993_AJHSME_Problem s"This page was last m odified on 12 Novem ber 2012, at 16:50. This page has been accessed 6,428 tim es. Privacy policy About AoPSWiki Disclaim ers。

1995年美国大学生数学建模竞赛题目Problem A: Helix ConstructionA small biotechnological company must design, prove, program and test a mathematical algorithm to locate "in real time" all the intersections of a helix and a plane in general positions in space. Design, justify, program and test a method to compute all the intersections of a plane and a helix, both in general positions (at any locations and with any orientations) in space. A segment of the helix may represent, for example, a helicoidal suspension spring or a piece of tubing in a chemical or medical apparatus. Theoretical justification of the proposed algorithm is necessary to verify the solution from several points of view, for instance, through mathematical proofs of parts of the algorithm, and through tests of the final program with known examples. Such documentation and tests will be required by government agencies for medical use.Problem B: Faculty CompensationAluacha Balaclava College, and undergraduate facility, has just hired a new Provost whose first priorityis the institution of a fair and reasonable faculty-compensation plan. She has hired your consulting team to design a compensation system that reflects the following circumstances and principles: [Three paragraphs of details omitted] Design a new pay system, first withoutcost-of-living increases. Incorporate cost-of-living increases, and then finally, design a transistion process for current faculty that will move all salaries towards your system without reducing anyone's salary. The Provost requires a detailed compensation system plan for implementation, as well as a brief, clear, executive summary outlining the model, its assumptions, strengths, weaknesses and expected results, which she can present to the Board and faculty. [A detailed table of current salaries is omitted.]。