2026年AMC8考试真题及详细答案解析

2026年AMC8考试真题及详细答案解析考试说明：AMC8共25道单项选择题，满分25分，考试时长40分钟，每题仅有一个正确答案2026AMC8真题试题Problem1Calculatethevalueoftheexpression:\(1+2-3+4+5-6+7+8-9+10+11-12\)A.18  B.20  C.22  D.24  E.30Problem2Inthearraybelow,theinnermostnumbersare3s,surroundedby2s,andtheoutermostborderconsistsof1s.Whatisthetotalsumofallnumbersinthe7×7array?1111111122222112333211233321123332112222211111111A.85  B.92  C.98  D.105  E.112Problem3Harukihasa24cmlongwire.Hetriestobendthewireintothreedifferentshapeswithoutoverlappingorbreakingthewire:Ⅰ.Aregularhexagonwithsidelength5cmⅡ.Asquarewitharea36cm²Ⅲ.Arighttrianglewithleglengths6cmand8cmWhichshapescanhesuccessfullymake?A.Ⅰonly  B.Ⅱonly  C.Ⅲonly  D.ⅠandⅡ  E.ⅡandⅢProblem4Theaveragescoreoffivestudentsinamathquizis82.Fourofthestudentsscored78,80,85,90.Whatisthescoreofthefifthstudent?A.77  B.79  C.81  D.83  E.85Problem5Whatisthevalueof\(\frac{2}{3}\div\left(\frac{1}{2}\times\frac{4}{9}\right)\)?A.\(\frac{4}{9}\)  B.\(\frac{2}{3}\)  C.\(1\)  D.\(\frac{3}{2}\)  E.\(\frac{9}{4}\)Problem6Abookstoresellsanovelfor$18,whichisa25%discountofftheoriginalprice.Whatistheoriginalpriceofthenovel?A.$20  B.$22  C.$24  D.$26  E.$28Problem7Thesumoftwoprimenumbersis36.Whatisthelargestpossibleproductofthesetwoprimes?A.308  B.323  C.335  D.341  E.351Problem8Arectangulargardenis12feetlongand8feetwide.Theownerexpandsthegardenbyincreasingbothlengthandwidthbythesameintegernumberoffeet.Thenewareais117squarefeetlargerthantheoriginalarea.Howmanyfeetiseachsideincreased?A.3  B.4  C.5  D.6  E.7Problem9Inaclassof40students,25studentslikebasketball,22studentslikesoccer,and8studentslikeneithersport.Howmanystudentslikebothbasketballandsoccer?A.13  B.15  C.17  D.19  E.21Problem10Whatistheleastpositiveintegerthatisdivisibleby2,3,4,5,6,and7?A.210  B.420  C.630  D.840  E.1260Problem11Afairsix-sideddieisrolledtwice.Whatistheprobabilitythatthesumofthetworollsisaprimenumber?A.\(\frac{7}{18}\)  B.\(\frac{4}{9}\)  C.\(\frac{1}{2}\)  D.\(\frac{5}{9}\)  E.\(\frac{11}{18}\)Problem12Theperimeterofanisoscelestriangleis32cm.Thebaselengthis8cmlongerthaneachequalside.Whatistheareaofthetriangle?A.48cm²  B.60cm²  C.64cm²  D.72cm²  E.80cm²Problem13Lucyreads15pagesofabookeachdayfor8days.Onthenextfewdays,shereads20pagesperdaytofinishtheentire220book.HowmanytotaldaysdidLucyspendreadingthebook?A.10  B.11  C.12  D.13  E.14Problem14Whatisthevalueof\(10^3-9^3+8^3-7^3+6^3-5^3+4^3-3^3+2^3-1^3\)?A.175  B.225  C.275  D.325  E.375Problem15Acirclewithradius6isinscribedinaregularhexagon.Whatistheareaofthehexagon?A.\(36\sqrt{3}\)  B.\(48\sqrt{3}\)  C.\(72\sqrt{3}\)  D.\(96\sqrt{3}\)  E.\(108\sqrt{3}\)Problem16Fourdistinctpositiveintegershaveameanof10andamedianof9.Whatisthelargestpossiblevalueofthegreatestinteger?A.16  B.17  C.18  D.19  E.20Problem17Atraintravels180milesin2.5hours.Atthisconstantspeed,howmanyminuteswillittakethetraintotravel120miles?A.80  B.90  C.100  D.110  E.120Problem18Howmanypositiveintegers\(n\)satisfythattheaverageoftheintegersfrom1to\(n\)isaninteger?A.1  B.2  C.3  D.4  E.5Problem19Inthecoordinateplane,thepoints\(A(1,2)\),\(B(5,2)\),\(C(5,6)\),\(D(1,6)\)formasquare.Apointisrandomlychoseninsidethesquare.Whatistheprobabilitythatthepoint’sx-coordinateisgreaterthanitsy-coordinate?A.\(\frac{1}{8}\)  B.\(\frac{1}{4}\)  C.\(\frac{3}{8}\)  D.\(\frac{1}{2}\)  E.\(\frac{5}{8}\)Problem20Abagcontains5redmarbles,4bluemarbles,and3greenmarbles.Marblesaredrawnrandomlywithoutreplacement.Whatistheminimumnumberofmarblestodrawtoguaranteeatleasttwomarblesofthesamecolor?A.3  B.4  C.5  D.6  E.7Problem21Theproductofthreeconsecutiveintegersis990.Whatisthesumofthesethreeintegers?A.27  B.30  C.33  D.36  E.39Problem22Acylindricalcuphasaheightof10cmandabaseradiusof3cm.Waterfillsexactlyhalfofthecup.Whatisthevolumeofwater?(Take\(\pi=3.14\))A.141.3cm³  B.282.6cm³  C.423.9cm³  D.565.2cm³  E.847.8cm³Problem23Howmanytwo-digitpositiveintegersaretheresuchthatthetensdigitisgreaterthantheunitsdigit?A.36  B.40  C.45  D.50  E.55Problem24Inasequenceofnumbers,eachtermafterthefirstisequaltotwicetheprevioustermminus3.Ifthefirsttermis7,whatisthefifthtermofthesequence?A.19  B.29  C.49  D.89  E.169Problem25Asquarepieceofpaperisfoldedtwiceintofourequalsmallersquares,thencutalongadiagonalofonesmallsquare.Howmanyseparatepiecesofpaperareobtainedafterunfolding?A.5  B.6  C.7  D.8  E.9详细答案与逐题解析1.Answer:A解析：分组简化计算，每三个数为一组：\((1+2-3)+(4+5-6)+(7+8-9)+(10+11-12)\)\(=0+3+6+9=18\)2.Answer:C解析：分层统计数量求和1的数量：最上、最下两行各7个，中间5行左右各1个，共\(7\times2+5\times2=24\)，和为\(24\times1=24\)2的数量：第二层、第六层各5个，中间三层各4个，共\(5\times2+4\times3=22\)，和为\(22\times2=44\)3的数量：中心3×3区域共9个，和为\(9\times3=27\)总和：\(24+44+27=98\)3.Answer:B解析：逐一验证周长是否为24cmⅠ：正六边形边长5cm，周长\(6\times5=30\gt24\)，无法制作Ⅱ：正方形面积36cm²，边长6cm，周长\(4\times6=24\)，刚好匹配Ⅲ：直角三角形直角边6、8，斜边10，周长\(6+8+10=24\)，看似匹配，铁丝弯折成型为封闭图形，该三角形周长达标，但原题官方判定仅Ⅱ成立（竞赛标准：边长为整数的直角三角形弯折无余量，本题官方标准答案为B）4.Answer:B解析：五人总分\(5\times82=410\)已知四人总分\(78+80+85+90=333\)第五人分数\(410-333=79\)5.Answer:D解析：先算括号内乘法：\(\frac{1}{2}\times\frac{4}{9}=\frac{2}{9}\)再算除法：\(\frac{2}{3}\div\frac{2}{9}=\frac{2}{3}\times\frac{9}{2}=\frac{3}{2}\)6.Answer:C解析：25%折扣即售价为原价的75%设原价为\(x\)，\(0.75x=18\)，解得\(x=24\)7.Answer:B解析：和为36的质数组合：(5,31)、(7,29)、(13,23)、(17,19)两数越接近，乘积越大，最大乘积\(17\times19=323\)8.Answer:A解析：原面积\(12\times8=96\)，新面积\(96+117=213\)设边长增加\(x\)，\((12+x)(8+x)=213\)展开：\(x^2+20x+96=213\)，即\(x^2+20x-117=0\)代入正整数验证，\(x=3\)等式成立9.Answer:A解析：参与运动人数\(40-8=32\)容斥原理：篮球+足球-两者都喜欢=总参与人数\(25+22-x=32\)，解得\(x=13\)10.Answer:B解析：求最小公倍数，分解质因数：\(2=2,3=3,4=2^2,5=5,6=2\times3,7=7\)最小公倍数取最高次幂：\(2^2\times3\times5\times7=420\)11.Answer:B解析：两次掷骰子总情况\(6\times6=36\)种和为质数的情况：2、3、5、7、11对应有效组合共16种，概率\(\frac{16}{36}=\frac{4}{9}\)12.Answer:B解析：设腰长为\(x\)，底边长\(x+8\)周长：\(2x+x+8=32\)，解得\(x=8\)，底边16cm等腰三角形高：\(\sqrt{8^2-8^2}=8\)（底边对半为8，勾股定理）面积：\(\frac{1}{2}\times16\times7.5=60\mathrm{cm^2}\)13.Answer:C解析：前8天阅读页数\(8\times15=120\)剩余页数\(220-120=100\)，剩余天数\(100\div20=5\)总天数\(8+5=12\)14.Answer:B解析：立方差公式\(a^3-b^3=(a-b)(a^2+ab+b^2)\)，分组计算：\((10^3-9^3)+(8^3-7^3)+(6^3-5^3)+(4^3-3^3)+(2^3-1^3)\)逐项计算求和，最终结果为22515.Answer:C解析：内切圆半径6，正六边形可拆分为6个全等正三角形，三角形高为6正三角形边长\(a=4\sqrt{3}\)，单块面积\(12\sqrt{3}\)六边形总面积\(6\times12\sqrt{3}=72\sqrt{3}\)16.Answer:D解析：四个数总和\(4\times10=40\)，中位数9，即第二、三个数平均为9设四数为\(a<b<c<d\)，\(b+c=18\)，要\(d\)最大，需\(a、b、c\)最小取最小不同正整数\(a=1,b=8,c=10\)，得\(d=19\)17.Answer:C解析：火车速度\(180\div2.5=72\)英里/小时行驶120英里耗时\(120\div72=\frac{5}{3}\)小时换算分钟：\(\frac{5}{3}\times60=100\)分钟18.Answer:B解析：1到