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 \n(A)2 (B)5 (C)10 (D)15 (E)20  \n# 2007 AMC 10A,Problem \\#1—2007 AMC 12 A,Problem \\#1—“Find the total cost for Susan and Pam”\n\nSolution  \nAnswer(C):  Susan pays(4)(0.75)(20)=60 dollars.Pam pays  \n(5)(0.70)(20)=70 dollars,so she pays 70-60=10 more dollars thanSusan.  \nDifficulty:Easy  \nNCTM Standard:Number and Operations Standard:understand numbers,ways of representingnumbers,relationships among numbers,and number systems.Mathworld.com Classification:Number Theory>Arithmetic>Fractions>Percent  \n1  \n_1__ -_______  \n_---------------__  \ntb07-01,hb07-01  \nlsabella's house has 3 bedrooms.Each bedroom is 12feet long,10 feet wide,and 8 feet high.Isabella mustpaint the walls of all the bedrooms.Doorways andwindows,which willnot be painted,occupy 60 squarefeet in each bedroom.How many square feet of wallsmust be painted?  \n(A)678  (B)768 (C)786  (D)867 (E)876  \n2007 AMC 10 B,Problem \\#1—2007 AMC 12 B,Problem \\#1—  \n\"Paint only the walls,that means no ceilings andfloors.\"  \nSolution  \nAnswer(E):The perimeter of each bedroom is2(12+10)=4 feet,sothe surface to be painted in each bedroom has an area of 4·8-60=292square feet.Since there are 3 bedrooms,Isabella must paint 3·292=876square feet.  \nDifficulty:Mediuu-cisy  \nNCTM Standard:Gicornctry Stanclard:ualy zo chauracteristics and projportics of tuc-and thucc-dimcnsicnal gcotnctrie shapcs ard devcfop mathicnaticad argumcnts about gcomctric relatiouships.Mathworld.con Classification:Goonctrs >SolieGiconctryPolyhcdra>C'ubes  \nAMC10/AMC12 Practice Problems  \ntb07-02  \nDefine the operation ★by a*b=(a+b)b.What is(3*5)-(5*3)?  \n(A)-16 (B)-8  (C)0 (D)8 (E)16  \n2P0ug AM3.50or a,roblem\\#²  \nSolution  \nAnswer(E):Since 3*5=(3+5)5=8·5=40 and 5*3=(5+3)3=8·3=24,we have  \n3*5-5*3=40-24=16.  \nDifficulty:Medium-easy  \nNCTM Standard:Number and Operatlions Standard:Understand meanings of operations andhow they relate to one another.  \nMathworld.com Classification:Algebra>Algebraic Operations>General Algebraic Operations>Binary Operation  \n-----------------  \n_-----_--------___  \nAMC10/AMC12 Practice Problems  \nta07-03,ha07-02  \nAn aquarium has a rectangular base that measures100 cm by 40 cm and has a height of 50 cm.It isfilled with water to a height of 40 cm.A brick with arectangular base that measures 40 cm by 20 cm anda height of 10 cm is placed in the aquarium.By howmany centimeters does the water rise?  \n(A)0.5 (B)1 (C)1.5  (D)2 (E)2.5  \n2007 AMC 10 A,Problem \\#3—2007 AMC 12 A,Problem \\#2—  \n“The additional volume of water occupied in theaquarium is equal to the volume of the brick.”  \n## Solution\n\nAnswer(D):  The brick has a volume of 40·20·10=8000 cubiccentimeters.Suppose that after the brick is placed in the tank,the waterlevel rises by h centimeters.Then the additional volume occupied in theaquarium is 100·40·h=4000h cubic centimeters.Since this must be thesame as the volume of the brick,we have  \n8000=4000h and h=2 centimeters  \nDifficulty:Medium  \nNCTM Standard:Geometry Standard:analyze characteristics and properties of two-and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.Mathworld.com Classification:Geometry >Solid Geometry >Volume  \nha07-04  \nKate rode her bicycle for 30 minutes at a speed of 16mph,then walked for 90 minutes at a speed of 4mph.What was her overall average speed in miles per hour?  \n(A)7 (B)9 (C)10 (D)12 (E)14  \n# 2007 AMC 12 A,Problem \\#4—\n\n\"Find the total distance Kate travels in 30+90=120minutes =2 hours”  \nSolution  \nAnswer(A):Kate rode for 30 minutes =1/2 hour at 16mph,so sherode 8 miles.She walked for 90 minutes=3/2 hours at 4 mph,so shewalked 6 miles.Therefore she covered a total of 14 miles in 2 hours,soher average speed was 7 mph.  \nDifficulty:Medium-easy  \nNCTM Standard:Problem Solving ","cbCaidyt4ww3jLkS","https://ap.wps.com/l/cbCaidyt4ww3jLkS","pdf",874338,"English","# AMC 10/AMC 12 Practice Problems\n## Solutions and Answer Choices","[{\"question\":\"How do the problems typically define what to solve for?\",\"answer\":\"Each problem states a real-world or number-based scenario (such as ticket costs or water rise) and asks for a specific quantity, usually with multiple-choice options.\"},{\"question\":\"What solution methods appear most often in the practice set?\",\"answer\":\"Percent discount and proportional reasoning are used frequently, along with equation setup for algebraic relationships between variables.\"},{\"question\":\"What types of geometry calculations are included?\",\"answer\":\"Geometry tasks include computing areas for wall painting and using volume displacement to determine how much a water level rises after placing a brick.\"}]","AMC 10/AMC 12 Practice Problems - Arithmetic and Geometry Word Problems | PDF",1790707494,126]