AMC 8 Practice Questions Example

1 1 AMC 8 Practice (A)1212(B)20(C)25(D)3313(E)37122011 AMC8, problem #7 Findthe shadedportionof eachsquare separately. SolutionAnswer (C):Theupperleftandthelower rightsquaresare eachone-fourthshaded, leftsquaresmakeup thetotalshadedareaisonefullsquare,whichi s25% :MediumSMP-CCSS:2,7 CCSS- , original problem and choices from the 2011 AMC 8 contestProblem number HintSolution from official solutionsDifficulty, Percent correctEasy 100 80%Med Easy 80 60%Medium 60 40%Med Hard 40 20%Hard 20 0%Standards for Math PracticeCommon Core State Standard2 AMC 8 Practice Questions (A)1(B)2(C)3(D)4(E)52013 AMC8, problem #1 Whatis the smallestmultipleof6thatis at least24?

2 SolutionAnswer (A):Thesmallestmultipleof6thatis atleast23is24,so :EasySMP-CCSS:1. Make senseof problemsandpersevere in solvingthem;7. Look for andmake use withmulti-digitnumbers and findcommonfactorsand 8 Practice Questions Continued13-02 Asignatthefishmarketsays, 50%off,todayonly:half-poundpackagesforju st$3perpackage. Whatistheregularpriceforafullpoundoffish ,indollars?(A)6(B)9(C)10(D)12(E)152013 AMC8, problem #2 How muchdoes a half-poundpackage cost at the regularprice? SolutionAnswer (D):Ahalf-poundpackagecosts$3atthesalepr ice,soitwouldcost$ $ :MediumEasySMP-CCSS:1.

3 Make senseof problemsand persevere in solvingthem;4. Model Analyzeproportionalrelationshipsand use themto solve real-worldand 8 Practice Questions Continued13-03 Whatis thevalueof4 ( 1+2 3+4 5+6 7+ +1000)?(A) 10(B)0(C)1(D)500(E)20002013 AMC8, problem #3 Findthe suminsidethe parentheses. SolutionAnswer (E):Insidetheparenthesesare500pairsof numbers,eachwithasumof1. Thereforetheexpressionequals4 500= :MediumSMP-CCSS:1. Make senseof problemsandpersevere in solvingthem;7. Look for andmake use propertiesof operationsto generateequivalent 8 Practice Questions (A)18(B)14(C)38(D)12(E)342013 AMC8, problem #8 Listthe number of possibleequallylikely outcomes.

4 SolutionAnswer (C):Listthe8possibleequallylikelyoutcome s:HHH,HHT,HTH,HTT,THH,THT,TTH, ,HHT,THHhaveatleast2consecutiveheads,sot heprobabilityofat :MediumHardSMP-CCSS:1. Make senseof problemsand persevere in solvingthem;4. Model Investigatechanceprocessesand develop,use,and 8 Practice Questions Continued13-10 Whatis theratiooftheleastcommonmultipleof180and 594tothegreatestcommonfactorof180and594? (A)110(B)165(C)330(D)625(E)6602013 AMC8, problem #10 Findthe primefactorizationof180and594. SolutionAnswer (C):Becausetheprimefactorizationsof180an d594are22 32 5and2 33 11, respectively, theleastcommonmultipleof180and594is22 33 5 11, andtheirgreatestcommonfactoris2 32.

5 Theratiooftheirleastcommonmultipletothei rgreatestcommonfactoris22 33 5 112 32=2 3 5 11= :MediumHardSMP-CCSS:1. Make senseof problemsand persevere in withmulti-digitnumbers and findcommonfactorsand 8 Practice Questions Continued13-15If3p+34=90,2r+44=76, and53+6s= 1421,whatistheproductofp,r, ands?(A)27(B)40(C)50(D)70(E)902013 AMC8, problem #15 Findthe valueforp,randsfromthe equationsgiven. SolutionAnswer (B):Fromthefirstequation,3p+81=90,so3p=9 , andp= ,2r=32,sor= ,6s+ 125=1421,so6s= 1296, ands=4. Theproductofp,r,andsis2 5 4= :MediumSMP-CCSS:1. Make senseof problemsand persevere in withradicalsand 8 Practice Questions Continued13-20A1 (A) 2(B)2 3(C) (D)4 3(E)5 32013 AMC8, problem #20 UsethePythagoreanTheoremto findtheradiusof thesemicircle.

6 SolutionAnswer (C): 2111 BythePythagoreanTheorem,theradiusofthese micircleis 2,so itsareais ( 2)22= .Difficulty:HardSMP-CCSS:1. Make senseof problemsand persevere in applythe 8 Practice Questions usedaltogether?(A)1920(B)1952(C)1980(D)2 013(E)39322013 AMC8, problem #22 Findthe number of columnsand rows for60toothpickslongand32toothpickshigh. SolutionAnswer (E) totalof(61 32)+(33 60)=3932toothpicksare :HardSMP-CCSS:1. Make senseof problemsandpersevere in solvingthem;7. Look for andmake use :None2310 AMC 8 Practice Questions Continued13-23 AngleABCof ABCis a ABCare , andthearcof.

7 WhatistheradiusofthesemicircleonBC?(A)7( B) (C)8(D) (E)92013 AMC8, problem #23 Findthe area for the circlewithdiameterAB. SolutionAnswer (B):ThecirclewithdiameterABhastwicethear eaofthecorrespondingsemicircle;thusthear eaofthecircleis16 anditsradiusis4. ConsequentlyAB=8. ThecirclewithdiameterAChascircumference1 7 ,soAC= ,172=82+(BC) , :MediumHardSMP-CCSS:1. Make senseof problemsand persevere in applythe