Math Kangaroo袋鼠数学竞赛真题解答(三)

今天我们给出第三组袋鼠竞赛的题目(每个年级组一道题),并附上解答

1-2年级组

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?

一艘船被海盗袭击了。海盗们一个接一个地沿着一条绳子攀爬到船上。海盗首领的位置在正中间,他是第8个爬上船的。共有多少个海盗沿着这条绳子爬上船?

袋鼠数学竞赛题选(三)

3-4年级组

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只瓢虫(见图)。如果两只瓢虫背上的黑点数量刚好相差1,那么它们就是朋友。在袋鼠日那天,每只瓢虫都给它的朋友发了一条祝福短信。它们一共发了多少条短信?

袋鼠数学竞赛题选(三)

5-6年级组

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和她妈妈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、她妈妈的出生年份、她自己的岁数和她妈妈的岁数都加在一起。请问计算结果是多少?

袋鼠数学竞赛题选(三)

7-8年级组

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?

如下图,一个正方形的面积是30平方厘米,被它的一条对角线分成两个三角形,每个三角形又被分成更小的三角形。其中一些三角形的面积已经在图中标示出来了。对角线的哪个小段长度最长?

袋鼠数学竞赛题选(三)

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下面是第三组题目的参考答案和解析

1-2年级组

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?

一艘船被海盗袭击了。海盗们一个接一个地沿着一条绳子攀爬到船上。海盗首领的位置在正中间,他是第8个爬上船的。共有多少个海盗沿着这条绳子爬上船?

袋鼠数学竞赛题选(四)

【答案:D】因为海盗首领排在第8位,所以他前面有7个人。因此他后面也有7个人。7+1+7=15。

3-4年级组

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只瓢虫(见图)。如果两只瓢虫背上的黑点数量刚好相差1,那么它们就是朋友。在袋鼠日那天,每只瓢虫都给它的朋友发了一条祝福短信。它们一共发了多少条短信?

袋鼠数学竞赛题选(四)

【答案:C】五只瓢虫的朋友数量依次为:2,1,1,1,1。

5-6年级组

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和她妈妈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、她妈妈的出生年份、她自己的岁数和她妈妈的岁数都加在一起。请问计算结果是多少?

袋鼠数学竞赛题选(四)

【答案:C】Lucy的出生年份和她的年龄之和正好是今年的年份,即2015。类似地,她妈妈的出生年份和年龄之和也等于2015。

7-8年级组

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?

如下图,一个正方形的面积是30平方厘米,被它的一条对角线分成两个三角形,每个三角形又被分成更小的三角形。其中一些三角形的面积已经在图中标示出来了。对角线的哪个小段长度最长?

袋鼠数学竞赛题选(四)

【答案:D】容易求得,未标注面积的两个三角形,上面的三角形面积为4平方厘米,下面的面积为6平方厘米。进而根据等高三角形的面积比等于底边长度的比,求得对角线的五个小段的长度之比为2:3:1:5:4

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