Math Kangaroo袋鼠數學競賽真題解答（三）

今天我們(men) 給出第三組袋鼠競賽的題目（每個(ge) 年級組一道題），並附上解答。

1-2年級組

A ship was attacked by pirates. One by one they were climbing a rope to get to the ship. The pirate captain was in the middle and he was also the eighth one from the beginning. How many pirates were on the rope?

一艘船被海盜襲擊了。海盜們(men) 一個(ge) 接一個(ge) 地沿著一條繩子攀爬到船上。海盜首領的位置在正中間，他是第8個(ge) 爬上船的。共有多少個(ge) 海盜沿著這條繩子爬上船？

3-4年級組

There are 5 ladybugs (see fig.). Two ladybugs are friends with each other if the numbers of spots that they have differ exactly by 1. On Kangaroo Day each of the ladybugs sent to each of her friends one SMS greeting. How many SMS greetings were sent?

有5隻瓢蟲（見圖）。如果兩(liang) 隻瓢蟲背上的黑點數量剛好相差1，那麽(me) 它們(men) 就是朋友。在袋鼠日那天，每隻瓢蟲都給它的朋友發了一條祝福短信。它們(men) 一共發了多少條短信？

5-6年級組

Lucy and her mother were both born in January. Today, March 19 2015, Lucy adds the year of her birth, the year of her mother's birth, her age, and her mother's age. What result does she get?

Lucy和她媽媽都是在一月份出生的。今天是2015年3月19日，Lucy把她自己的出生年份、她媽媽的出生年份、她自己的歲數和她媽媽的歲數都加在一起。請問計算結果是多少？

7-8年級組

A square with area 30 is divided in two by a diagonal and then into triangles, as shown. The areas of some of these triangles are given in the diagram. Which part of the diagonal is the longest?

如下圖，一個(ge) 正方形的麵積是30平方厘米，被它的一條對角線分成兩(liang) 個(ge) 三角形，每個(ge) 三角形又被分成更小的三角形。其中一些三角形的麵積已經在圖中標示出來了。對角線的哪個(ge) 小段長度最長？

--------   分割線   --------

下麵是第三組題目的參考答案和解析。

1-2年級組

A ship was attacked by pirates. One by one they were climbing a rope to get to the ship. The pirate captain was in the middle and he was also the eighth one from the beginning. How many pirates were on the rope?

一艘船被海盜襲擊了。海盜們(men) 一個(ge) 接一個(ge) 地沿著一條繩子攀爬到船上。海盜首領的位置在正中間，他是第8個(ge) 爬上船的。共有多少個(ge) 海盜沿著這條繩子爬上船？

【答案：D】因為(wei) 海盜首領排在第8位，所以他前麵有7個(ge) 人。因此他後麵也有7個(ge) 人。7+1+7=15。

3-4年級組

There are 5 ladybugs (see fig.). Two ladybugs are friends with each other if the numbers of spots that they have differ exactly by 1. On Kangaroo Day each of the ladybugs sent to each of her friends one SMS greeting. How many SMS greetings were sent?

有5隻瓢蟲（見圖）。如果兩(liang) 隻瓢蟲背上的黑點數量剛好相差1，那麽(me) 它們(men) 就是朋友。在袋鼠日那天，每隻瓢蟲都給它的朋友發了一條祝福短信。它們(men) 一共發了多少條短信？

【答案：C】五隻瓢蟲的朋友數量依次為(wei) ：2，1，1，1，1。

5-6年級組

Lucy and her mother were both born in January. Today, March 19 2015, Lucy adds the year of her birth, the year of her mother's birth, her age, and her mother's age. What result does she get?

Lucy和她媽媽都是在一月份出生的。今天是2015年3月19日，Lucy把她自己的出生年份、她媽媽的出生年份、她自己的歲數和她媽媽的歲數都加在一起。請問計算結果是多少？

【答案：C】Lucy的出生年份和她的年齡之和正好是今年的年份，即2015。類似地，她媽媽的出生年份和年齡之和也等於(yu) 2015。

7-8年級組

A square with area 30 is divided in two by a diagonal and then into triangles, as shown. The areas of some of these triangles are given in the diagram. Which part of the diagonal is the longest?

如下圖，一個(ge) 正方形的麵積是30平方厘米，被它的一條對角線分成兩(liang) 個(ge) 三角形，每個(ge) 三角形又被分成更小的三角形。其中一些三角形的麵積已經在圖中標示出來了。對角線的哪個(ge) 小段長度最長？

【答案：D】容易求得，未標注麵積的兩(liang) 個(ge) 三角形，上麵的三角形麵積為(wei) 4平方厘米，下麵的麵積為(wei) 6平方厘米。進而根據等高三角形的麵積比等於(yu) 底邊長度的比，求得對角線的五個(ge) 小段的長度之比為(wei) 2：3：1：5：4。