2023年数学竞赛AMC8试卷（含答案）.docx

2023年AMC8试卷

2023AmericanMathematicsCompetitions8

Problem1

Whatisthevalueofbelowexpression?下面表达式的值是多少?

(8×4+2)-(8+4×2)

(A)0(B)6(C)10(D)18(E)24

Problem2

Asquarepieceofpaperisfoldedtwiceintofourequalquarters,asshownbelow,thencutalongthedashedline.Whenunfolded,thepaperwillmatchwhichofthefollowingfigures?

如下图所示，将一张正方形纸对折两次，变成四等分，然后沿虚线裁剪.问这张纸展开后会是下面哪个图形?

(A)

(D)

Problem3

Windchillisameasureofhowcoldpeoplefeelwhenexposedtowindoutside.Agoodestimateforwindchillcanbefoundusingthiscalculation:

(windchill)=(airtemperature)-0.7×(windspeed),

wheretemperatureismeasuredindegreesFahrenheit(°F)andwindspeedismeasuredinmilesperhour(mph).Supposetheairtemperatureis36°Fandthewindspeedis18mph.Whichofthefollowingisclosesttotheapproximatewindchill?

风寒指数是对人们暴露在室外风中时寒冷感觉的度量.通过下面的计算可以对风寒指数做出很好的估计：

(风寒指数)=(气温)-0.7×(风速),

其中温度以华氏度(F)为单位，风速以英里每小时(mph)为单位.假设气温为36°F,风速为18mph.问以下哪个选项最接近风寒指数?

(A)18(B)23(C)28(D)32(E)35

Problem4

Thenumbersfrom1to49arearrangedinaspiralpatternonasquaregrid,begin-ningatthecenter.Thefirstfewnumbershavebeenenteredintothegridbelow.Considerthefournumbersthatwillappearintheshadedsquares,onthesamediagonalasthenumber7.Howmanyofthesefournumbersareprime?

在正方形方格表上，数1到49从中心开始，按螺旋式方式排列.前面几个数已经填入到下面的方格表中.考虑与数7出现在同一个对角线上的阴影方格中的四个数.问这四个数中有几个质数?

(A)0(B)1(C)2(D)3(E)4

Problem5

Alakecontains250trout,alongwithavarietyofotherfish.Whenamarinebi-

ologistcatchesandreleasesasampleof180fishfromthelake,30areidentifiedastrout.Assumethattheratiooftrouttothetotalnumberoffishist