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2016 AMC8真题含答案

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2016

12016AMC8Problem1Thelongestprofessionaltennismatchlastedatotalof11hoursand5minutes.Howmanyminutesisthat?时间最长的职业网球赛总共持续了11小时5分钟。问一共多少分钟？Problem2Inrectangle,and.Pointisthemidpointof.Whatistheareaof?在矩形ABCD中，AB=6，AD=8，点M是的中点。那么ΔAMC的面积是多少？

Problem3Fourstudentstakeanexam.Threeoftheirscoresareand.Iftheaverageoftheirfourscoresis,thenwhatistheremainingscore?4个学生参加一个考试。其中3个的分数是70，80，90．若他们的平均分是70分，那么剩下那个学生的分数是多少分？2016

2Problem4WhenCheenuwasaboyhecouldrunmilesinhoursandminutes.Asanoldmanhecannowwalkmilesinhours.Howmanyminuteslongerdoesittakeforhimtotravelamilenowcomparedtowhenhewasaboy?当Cheenu还是个孩子时，他3小时30分钟内可以跑15英里，现在他是个老人，4小时内可以走10英里。现在的他和当他还是个孩子时比起来，行过1英里需要多花多少分钟？Problem5Thenumberisatwo-digitnumber.•Whenisdividedby,theremainderis.•Whenisdividedby,theremainderis.Whatistheremainderwhenisdividedby?N是个两位数。·当N除以9，余数为1．·当N除以10，余数为3．当N除以11时，余数是多少？Problem6Thefollowingbargraphrepresentsthelength(inletters)ofthenamesof19people.Whatisthemedianlengthofthesenames?下面的柱状图代表了19个人的名字的长度（字母个数）。那么这些名字长度的中位数是多少？Frequency|频率Namelength|名字长度2016

3Problem7Whichofthefollowingnumbersisnotaperfectsquare?下面哪个数不是完全平方数？Problem8Findthevalueoftheexpression计算下面表达式的值Problem9Whatisthesumofthedistinctprimeintegerdivisorsof?2016的不同质因数之和是多少？Problem10SupposethatmeansWhatisthevalueofif假设表示那么，若，则的值是多少？2016

4Problem11Determinehowmanytwo-digitnumberssatisfythefollowingproperty:whenthenumberisaddedtothenumberobtainedbyreversingitsdigits,thesumis有多少个两位数满足下面的性质：当把这个两位数的十位数字和个位数字调换位置所形成的新的数与原来的数相加，所得的和是132．Problem12JeffersonMiddleSchoolhasthesamenumberofboysandgirls.ofthegirlsandoftheboyswentonafieldtrip.Whatfractionofthestudentsonthefieldtripweregirls?Jefferson中学的男生和女生数目相同。的女生和的男生去郊游。那么这些去郊游的学生中，有多少比例是女生？Problem13Twodifferentnumbersarerandomlyselectedfromthesetandmultipliedtogether.Whatistheprobabilitythattheproductis?从集合中随机选择两个不同的数，并将它们相乘，那么乘积为0的概率是多少？2016

5Problem14Karl'scarusesagallonofgaseverymiles,andhisgastankholdsgallonswhenitisfull.Oneday,Karlstartedwithafulltankofgas,drovemiles,boughtgallonsofgas,andcontinueddrivingtohisdestination.Whenhearrived,hisgastankwashalffull.HowmanymilesdidKarldrivethatday?Karl的汽车每开35英里就需要1加仑汽油，且当他的油缸加满时，可以装14加仑的汽油。一天，Karl开始他的行程前，把油缸加满了汽油，接着开了350英里，之后买了8加仑汽油，然后继续开到目的地。当他到达目的地时，他的油缸只剩下一半汽油。问Karl那天总共开了多少英里？Problem15Whatisthelargestpowerofthatisadivisorof?是的一个因子的最大的2的幂是多少？Problem16AnnieandBonniearerunninglapsarounda-meterovaltrack.Theystartedtogether,butAnniehaspulledaheadbecausesherunsfasterthanBonnie.HowmanylapswillAnniehaverunwhenshefirstpassesBonnie?Annie和Bonnie绕着400米椭圆跑道跑步。他们同时起跑，但是因为Annie的速度比Bonnie快了25％，所以她跑到了Bonnie的前面。当Annie第一次经过Bonnie时，Annie已经跑了多少圈了？2016

6Problem17AnATMpasswordatFred'sBankiscomposedoffourdigitsfromto,withrepeateddigitsallowable.Ifnopasswordmaybeginwiththesequencethenhowmanypasswordsarepossible?Fred银行的取款机密码由0到9中的4个数字组成，且允许重复，如果密码不允许以序列9,1,1开头，那么一共有多少种可能的密码？Problem18InanAll-Areatrackmeet,sprintersenterameterdashcompetition.Thetrackhaslanes,soonlysprinterscancompeteatatime.Attheendofeachrace,thefivenon-winnersareeliminated,andthewinnerwillcompeteagaininalaterrace.Howmanyracesareneededtodeterminethechampionsprinter?在一次全区田径比赛中，共有216个短跑运动员角逐100米冲刺赛。比赛一共有6个赛道，因此一次只允许6个短跑运动员同时比赛。每场比赛结束后，会淘汰掉其中5人，胜者将参与到下一次比赛中。问一共需要多少场比赛才能确定整个比赛最终的冠军？Problem19Thesumofconsecutiveevenintegersis.Whatisthelargestoftheseconsecutiveintegers?25个连续的偶数之和是10,000，问这25个连续的整数中，最大的数是多少？Problem20Theleastcommonmultipleofandis,andtheleastcommonmultipleofandis.Whatistheleastpossiblevalueoftheleastcommonmultipleofand?a和b的最小公倍数是12，b和c的最小公倍数是15，问a和c的最小公倍数的最小可能值是多少？2016

7Problem21Atophatcontains3redchipsand2greenchips.Chipsaredrawnrandomly,oneatatimewithoutreplacement,untilall3oftheredsaredrawnoruntilbothgreenchipsaredrawn.Whatistheprobabilitythatthe3redsaredrawn?一个罐子里装有3个红色筹码和2个绿色筹码。现在将筹码一个个随机抽出且不放回，直到3个红色筹码被全部取出或者2个绿色筹码被全部取出，这时取出动作立即停止，那么取出3个红色筹码的概率是多少？Problem22Rectanglebelowisarectanglewith.Theareaofthe"batwings"(shadedarea)is？如下图所示，在一个3ｘ4的矩形DEFA中，DC=CB=BA=1，则“蝙蝠翅膀形状”的图形（图中阴影部分）的面积是多少？2016

8Problem23Twocongruentcirclescenteredatpointsandeachpassthroughtheothercircle'scenter.Thelinecontainingbothandisextendedtointersectthecirclesatpointsand.Thecirclesintersectattwopoints,oneofwhichis.Whatisthedegreemeasureof?两个圆心分别在点A和点B的全等圆各自通过对方的圆心。连接点A和点B的直线和这2个圆交于点C和点D。这2个圆交于2个点，其中之一是点E．那么的度数是多少？Problem24Thedigits,,,,andareeachusedoncetowriteafive-digitnumber.Thethree-digitnumberisdivisibleby,thethree-digitnumberisdivisibleby,andthethree-digitnumberisdivisibleby.Whatis?数字1，2，3，4，5各使用一次组成一个五位数PQRST，其中三位数PQR能被4整除，三位数QRS能被5整除，三位数RST能被3整除。问P是多少？Problem25Asemicircleisinscribedinanisoscelestrianglewithbaseandheightsothatthediameterofthesemicircleiscontainedinthebaseofthetriangleasshown.Whatistheradiusofthesemicircle?如图所示，一个底边为16，高为15的等腰三角形内有一个半圆与两条腰相切，并且半圆的直径与三角形的底边重合，问这个半圆的半径是多少？2016

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2011 AMC8真题含答案

2011 AMC8真题含答案

2011

12011AMC8Problem1

Margieboughtapplesatacostofcentsperapple.Shepaidwitha5-dollarbill.Howmuch

changedidMargiereceive?

Margie买了3个苹果，每个50美分。她付了5美元，那么她应该找回多少零钱？

Problem2

Karl'srectangularvegetablegardenisfeetbyfeet,andMakenna'sisfeetbyfeet.Which

ofthefollowingstatementsaretrue?

Karl的长方形蔬菜园的尺寸是20英尺ｘ45英尺，Makenna的菜园是25英尺ｘ40英尺。下面

哪句话是对的？

（A）Karl’sgardenislargerby100squarefeet．|Karl的莱园比Makenna的大100平方英尺。

（B）Karl’sgardenislargerby25squarefeet．｜Karl的菜园比Makenna的大25平方英尺。

（C）Thegardensarethesamesize.｜两人的菜园一样大。

（D）Makenna’sgardenislargerby25squarefeet.|Makenna的菜园比Karl的大25平方英尺。

（E）Makenna’sgardenislargerby100squarefeet.|Makenna的菜园比Karl的大100平方英尺。

Problem32011

2Extendthesquarepatternof8blackand17whitesquaretilesbyattachingaborderofblacktiles

aroundthesquare.Whatistheratioofblacktilestowhitetilesintheextendedpattern?

把下图所示的有8块黑色和17块白色方形瓷砖组成的正方形图案，通过围绕着这个大正方形

美国数学竞赛amc8真题及答案

美国数学竞赛amc8真题及答案

美国数学竞赛amc8真题及答案

AMC 8（时间：20XX年11月16日）

一、选择题

1.函数f(x) = x^2 + 4x与g(x) = 2x^2 + 3x + 2交于x =

A．-2 B．-1 C．1 D．2

答案：A (-2)

2.在编写计算机程序时，一行的长度最长不能超过

A．80个字符 B．100个字符 C．120个字符 D．200个字符

答案：A (80个字符)

二、填空题

3. 已知正三角形ABC有AB = 8，BC = 10，则其斜边AC 长为_____

答案：12

4. 一个班有35人，一个年级有295人，那么该年级有多少个班?______

答案：8个班

三、解答题

5. 若反三角形ABC中，∠BAC = 36° ，BC = 4 ，则∠ABC．

解：设∠ABC=x，知ΔABC是等边三角形，则∠BAC = ∠ABC =

36°，∴∠ABC=x=36°，所以∠ABC=36°.

6. 对于以下的函数，

f(x) = 2x^3 - 8x^2 + 5x， 求使f(x)能有最大值的x的取值。

解：f(x)的导数：

f'(x)= 6x^2 - 16x + 5

设f'(x)=0，即：

6x^2 - 16x + 5 = 0

解得x=2,x=5/3

又f(2)>f(5/3)，所以当x=2时，函数f(x)能有最大值。

2017AMC8真题及答案

2017AMC8真题及答案

2017 AMC 8 Problems

Problem 1

Which of the following values is largest?

(A) 2 + 0 4-1 + 7 (B) 2 xO+1 + 7 (C) 2 + 0 x 1 + 7 (D) 2 + 0 + 1 x 7 (E) 2 x 0 x 1 x 7

Problem 2

Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three

candidates. If Brenda received 36 votes, then bow many votes were cast all together?

(A) 70 (B) 84 (C) 100 (D)

106

Problem 3(A) 4 (B) 4据 (C) 8 (D) 8据

Problem 4

When 0.00031 S is multiplied by 7,928,564 the product is dosest to which of the following?

(A) 210 (B) 240 (C) 2100 (D) 2400 (E) 24000

Problem 5

1-2-3-4-5-6-7-8

What is the value of the expression ---------------- - -- -- --------- -- -- --- --- - - —?

1+2+3+4+5+6+7+8

(A) 1020 (B) 1120 (C) 1220 (D) 2240 (E) 3360

2021AMC8考题及答案

2021AMC8考题及答案

2021 AMC 8 考题及答案

Problem 1

Which of the following values is largest?

Problem 2

Alicia, Brenda, and Colby were the candidates in a recent election for

student president. The pie chart below shows how the votes were

distributed among the three candidates. If Brenda received 36 votes,

then how many votes were cast all together?

Problem 3

What is the value of the expression ?

Problem 4

When 0.000315 is multiplied by 7,928,564 the product is closest to

which of the following?

Problem 5

What is the value of the expression

?

Problem 6

If the degree measures of the angles of a triangle are in the ratio

, what is the degree measure of the largest angle of the

triangle?

Problem 7

Let be a 6-digit positive integer, such as 247247, whose first

three digits are the same as its last three digits taken in the same