2019年第35屆美國(guó)數(shù)學(xué)競(jìng)賽試卷（MAA AMC 8）

• 1．Ike and Mike go into a sandwich shop with a total of 30.00tospend.Sandwichescost4.50 ach and soft drinks cost＄1.00 each.Ike and Mike plan to buy as many sandwiches as they can nd use any remaining money to buy soft drinks.Counting both soft drinks and sandwiches,how many items will they buy？（　　）
  Ike和Mike總共帶著30.00進(jìn)入一個(gè)三明治店。每個(gè)三明治的價(jià)格是4.50，而軟飲料每瓶＄1.00。Ike和Mike計(jì)劃買盡可能多的三明治，并用剩下的錢買軟飲料。計(jì)算軟飲料和三明治在內(nèi)，他們將購(gòu)買多少物品？（　?。?/div>

  A．6	B．7	C．8	D．9
  E．10
  組卷：1引用：1難度：0.8

  解析
• 2．Three identical rectangles are put together to form rectangle ABCD，as shown in the figure below.Given that the length of the shorter side of each of the smaller rectangles is 5 feet,what is the area in square feet of rectangle ABCD？（　?。?br />三個(gè)相同的矩形組合在一起形成了矩形ABCD，如圖所示。每個(gè)小矩形的較短邊的長(zhǎng)度是5英尺，那么矩形ABCD的面積是多少平方英尺？（　?。?/div>

  A．45	B．75	C．100	D．125
  E．150
  組卷：6引用：1難度：0.5

  解析
• 3．Which of the following is the correct order of the fractions

  15

  11

  ，

  19

  15

  ，and

  17

  13

  ，from least to greatest？（　?。?br />以下哪個(gè)是

  15

  11

  ，

  19

  15

  ，

  17

  13

  從小到大的正確排列？（　?。?/div>

  A． 15 11 ＜ 17 13 ＜ 19 15	B． 15 11 ＜ 19 15 ＜ 17 13
  C． 17 13 ＜ 15 19 ＜ 15 11	D． 19 15 ＜ 15 11 ＜ 17 13
  E． 19 15 ＜ 17 13 ＜ 15 11
  組卷：20引用：1難度：0.8

  解析
• 4．Quadrilateral ABCD is a rhombus with perimeter 52 meters.The length of diagonal

  AC

  is 24 meters.What is the area in square meters of rhombus ABCD？（　　）
  菱形ABCD的周長(zhǎng)是52米。對(duì)角線

  AC

  的長(zhǎng)度是24米。那么菱形ABCD的面積是多少平方米？（　　）

  A．60	B．90	C．105	D．120
  E．144
  組卷：5引用：1難度：0.5

  解析
• 5．A tortoise challenges a hare to a race.The hare eagerly agrees and quickly runs ahead,leaving the slow-moving tortoise behind.Confident that he will win,the hare stops to take a nap.Meanwhile,the tortoise walks at a slow steady pace for the entire race.The hare awakes and runs to the finish line,only to find the tortoise already there.Which of the following graphs matches the description of the race,showing the distance d traveled by the two animals over time t from start to finish？（　?。?br />一只烏龜向一只兔子挑戰(zhàn)比賽。兔子欣然同意并迅速跑到前面，把動(dòng)作緩慢的烏龜留在后面。兔子自信地認(rèn)為他會(huì)贏，所以停下來(lái)小睡了一會(huì)兒。與此同時(shí)，烏龜以穩(wěn)定的步伐走完了整個(gè)比賽。兔子醒來(lái)并跑到終點(diǎn)，只是發(fā)現(xiàn)烏龜已經(jīng)到那里了。以下哪個(gè)圖形描述了比賽的描述，顯示了兩只動(dòng)物從開(kāi)始到結(jié)束在時(shí)間t內(nèi)走過(guò)的距離d？（　?。?/div>

  A．	B．
  C．	D．
  E．
  組卷：1引用：1難度：0.8

  解析
• 6．There are 81 grid points（uniformly spaced） in the square shown in the diagram below,including the points on the edges.Point P is the center of the square.Given that point Q is randomly chosen from among the other 80 points,what is the probability that the line PQ is a line of symmetry for the square？（　?。?br />如圖所示的正方形內(nèi)有81個(gè)網(wǎng)格點(diǎn)（均勻分布），包括邊緣上的點(diǎn)。點(diǎn)P是正方形的中心。若從其他80個(gè)點(diǎn)中隨機(jī)選擇定點(diǎn)Q，那么線PQ是正方形的對(duì)稱線的概率是多少？（　?。?/div>

  A． 1 5	B． 1 4	C． 2 5	D． 9 20
  E． 1 2
  組卷：11引用：1難度：0.5

  解析
• 7．Shauna takes five tests,each worth a maximum of 100 points.Her scores on the first three tests are 76，94，and 87.In order to average 81 for all five tests,what is the lowest score she could earn on one of the other two tests？（　　）
  Shauna參加了五次測(cè)試，每次測(cè)試的最高分是100分。她在前三次測(cè)試中的分?jǐn)?shù)分別是76、94和87。為了在所有五次測(cè)試中平均得到81分，她在其他兩次測(cè)試中的最低分是多少？（　?。?/div>

  A．48	B．52	C．66	D．70
  E．74
  組卷：5引用：1難度：0.8

  解析
• 8．Gilda has a bag of marbles.She gives 20% of them to her friend Pedro.Then Gilda gives 10% of what is left to another friend,Ebony.Finally,Gilda gives 25% of what is now left in the bag to her brother Jimmy.What percentage of her original bag of marbles does Gilda have left for herself？（　?。?br />Gilda有一袋玻璃球。她給了她的朋友Pedro 20%的玻璃球。然后Gilda給了她的另一個(gè)朋友Ebony剩下的10%。最后，Gilda給了她的兄弟Jimmy現(xiàn)在袋子里剩下的25%。Gilda還剩下原來(lái)袋子里多少百分比的玻璃球？（　?。?/div>

  A．20	B．33	C．38	D．45
  E．54
  組卷：6引用：1難度：0.5

  解析

• 24．In triangle ABC，point D divides side

  AC

  so that AD：DC=1：2.Let E be the midpoint of

  BD

  and let F be the point of intersection of line BC and line AE.Given that the area of△ABC is 360，what is the area of△EBF？（　?。?br />在三角形ABC中，點(diǎn)D將邊AC分為兩部分，使得AD：DC=1：2。點(diǎn)E是BD的中點(diǎn)，點(diǎn)F是直線BC和直線AE的交點(diǎn)?！鰽BC的面積是360，那么△EBF的面積是多少？（　　）

  A．24	B．30	C．32	D．36
  E．40
  組卷：15引用：1難度：0.5

  解析
• 25．Alice has 24 apples.In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples？（　?。?br />Alice有24個(gè)蘋果。她有多少種方法可以與Becky和Chris分享，使得三個(gè)人中的每一個(gè)都至少有兩個(gè)蘋果？（　?。?/div>

  A．105	B．114	C．190	D．210
  E．380
  組卷：7引用：1難度：0.5

  解析