2020年第36屆美國(guó)數(shù)學(xué)競(jìng)賽試卷（MAA AMC 8）

• 1．Luka is making lemonade to sell at a school fundraiser.His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice.He uses 3 cups of lemon juice.How many cups of water does he need？（　　）
  Luka正在制作檸檬汽水以在學(xué)?；I款活動(dòng)上出售。他的食譜需要的水是糖的4倍，糖是檸檬汁的兩倍。他使用了3杯檸檬汁。他需要多少杯水？（　?。?/div>

  A．6	B．8	C．12	D．18
  E．24
  組卷：4引用：1難度：0.8

  解析
• 2．Four friends do yardwork for their neighbors over the weekend,earning 15，20，25，and40，respectively.They decide to split their earnings equally among themselves.In total how much will the friend who earned＄40 give to the others？（　?。?br />四位朋友在周末為鄰居做園藝工作，分別賺了15、20、25和40美元。他們決定平均分配他們的收入。那位賺了40美元的朋友將給其他人多少錢？（　?。?/div>

  A．＄5	B．＄10	C．＄15	D．＄20
  E．＄25
  組卷：6引用：1難度：0.5

  解析
• 3．Carrie has a rectangular garden that measures 6 feet by 8 feet.She plants the entire garden with strawberry plants.Carrie is able to plant 4 strawberry plants per square foot,and she harvests an average of 10 strawberries perplant.How many strawberries can she expect to harvest？（　?。?br />Carrie有一個(gè)長(zhǎng)6英尺、寬8英尺的長(zhǎng)方形花園。她在整個(gè)花園里種植了草莓植株。Carrie每平方英尺能種植4株草莓植株，而她每株植株平均可收獲10顆草莓。她可以期望收獲多少草莓？（　?。?/div>

  A．560	B．960	C．1120	D．1920
  E．3840
  組卷：2引用：1難度：0.8

  解析
• 4．Three hexagons of increasing size are shown below.Suppose the dot pattern continues so that each successive hexagon contains one more band of dots.How many dots are in the next hexagon？（　?。?br />下面顯示了三個(gè)尺寸逐漸增大的六邊形，假設(shè)點(diǎn)的圖案會(huì)繼續(xù)，以便每個(gè)連續(xù)的六邊形包含更多一圈的點(diǎn)。下一個(gè)六邊形中有多少個(gè)點(diǎn)？（　　）
  

  A．35	B．37	C．39	D．43
  E．49
  組卷：5引用：1難度：0.8

  解析
• 5．Three fourths of a pitcher is filled with pineapple juice.The pitcher is emptied by pouring an equal amount of juice into each of 5 cups.What percent of the total capacity of the pitcher did each cup receive？（　?。?br />一只瓶子的四分之三裝滿了菠蘿汁。將瓶子中的菠蘿汁平均倒入5個(gè)杯子中，每個(gè)杯子中倒入相同的量。每個(gè)杯子收到了瓶子總?cè)萘康陌俜种嗌?？（　　?/div>

  A．5	B．10	C．15	D．20
  E．25
  組卷：14引用：1難度：0.5

  解析
• 6．Aaron,Darren,Karen,Maren,and Sharon rode on a small train that has five cars that seat one person each.Maren sat in the last car.Aaron sat directly behind Sharon.Darren sat in one of the cars in front of Aaron.At least one person sat between Karen and Darren.Who sat in the middle car？（　?。?br />在一輛有5節(jié)車廂，每節(jié)車廂有一個(gè)座位的小火車上，Aaron、Darren、Karen、Maren 和 Sharon 坐了下來(lái)。Maren坐在最后一節(jié)車廂。Aaron坐在Sharon的后面。Darren坐在Aaron前面的一節(jié)車廂里。Karen和Darren之間至少坐了一個(gè)人。誰(shuí)坐在中間的車廂？

  A．Aaron	B．Darren	C．Karen	D．Maren
  E．Sharon
  組卷：4引用：1難度：0.5

  解析
• 7．How many integers between 2020 and 2400 have four distinct digits ar-ranged in increasing order？（For example,2357 is one such integer.）（　?。?br />在2020年到2400年之間，有多少個(gè)整數(shù)的四個(gè)不同數(shù)字按升序排列？（例如，2357就是這樣的一個(gè)整數(shù)。）（　?。?/div>

  A．9	B．10	C．15	D．21
  E．28
  組卷：4引用：1難度：0.5

  解析
• 8．Ricardo has 2020 coins,some of which are pennies（1-cent coins） and the rest of which are nickels（5-cent coins）.He has at least one penny and at least one nickel.What is the difference in cents between the greatest possible and least possible amounts of money that Ricardo can have？（　　）
  Ricardo有2020枚硬幣，其中一部分是便士（1分硬幣），其余的是五分幣（5分硬幣）。他至少有一枚便士和一枚五分幣。Ricardo可能擁有的最大金額和最小金額之間相差多少分？（　?。?/div>

  A．8062	B．8068	C．8072	D．8076
  E．8082
  組卷：1引用：1難度：0.5

  解析

• 24．A large square region is paved with n² gray square tiles,each measuring sinches on a side.A border d inches wide surrounds each tile.The figure below shows the case for n=3.When n=24，the 576 gray tiles cover 64% of the area of the large square region.What is the ratio

  d

  s

  for this larger value of n？（　?。?br />一個(gè)大的正方形區(qū)域用n²個(gè)灰色的正方形瓷磚鋪設(shè)，每塊瓷磚的邊長(zhǎng)為s英寸。每塊瓷磚周圍有d英寸寬的邊框。下圖顯示了n=3的情況。當(dāng)n=24時(shí)，576塊灰色瓷磚覆蓋了大正方形區(qū)域的64%。對(duì)于這個(gè)較大的n值，

  d

  s

  比率是多少？（　?。?/div>

  A． 6 25	B． 1 4	C． 9 25	D． 7 16
  E． 9 16
  組卷：15引用：1難度：0.5

  解析
• 25．Rectangles R₁ and R₂，and squares S₁，S₂ and S₃ shown below,combine to form a rectangle that is 3322 units wide and 2020 units high.What is the side length of S_2?in units？（　?。?br />如下圖所示，矩形R₁和R₂以及正方形S₁、S₂和S₃組合成一個(gè)寬3322單位、高2020單位的矩形。S₂的邊長(zhǎng)是多少單位？（　?。?br />

  A．651	B．655	C．656	D．662
  E．666
  組卷：8引用：1難度：0.5

  解析