适合年会开场的歌曲-福州高考

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外国语学校小升初英语奥数训练题
第一部分
1155
，则这三个素数中最大的是多少？
2006
1155
1. The sum of the reciprocals of three prime numbers is, so what is the greatest
2006
one among the three prime numbers?




414
2、有一个分数，它的分子加2，可以约简 为；它的分母减2，可以约简为。
725
这个分数是多少？
4
2. There is a fraction. If its numerator adds 2, it can be reduced to be; if its
7
14
denominator subtracts 2, it can be reduced to be. So what is this fraction?
25



11020
3、一个数分别除以
1，，，所得的商都是自然数。这个数最小是多少？
142149
11020
3. A number is divided by
1
, and respectively and the quotients are all
142149
natural numbers. So what is the minimum value of this number?


4、一片竹 林，去年不开花的竹子比开花的2倍还多55棵，今年又多了100棵
开花，这时开花的竹子恰好是不开 花的4倍，这片竹林有多少棵竹子？
4. There is a bamboo forest. Last year, the non-blooming bamboos were two times
and 55 more than the blooming bamboos. With another 100 bamboos blooming this
year, the blooming bamboos are four times as many as the non-blooming bamboos.
So, how many bamboos are there in this forest?
（红色的地方我有点不确定，葛老师您看看应该怎么翻）



1 11111
5、从

中去掉两个分数，余下的分数之和为1。这两个分
24681012
数是哪两个分数？
1、三个素数的倒数之和是

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111111

to make the sum of remaining
24681012
fractions to be 1. So what are these two fractions?



6、一个整数与它的倒数的和等于20.05，这个整数是多少？它的倒数是多少？
6. The sum of an integer and its reciprocal is 20.05, so what is this integer and what is
its reciprocal?



7、四个非零自然数的和为38，这四个自然数的乘积的是小值是多少？最大值是
多少？
7. The sum of four nonzero natural numbers is 38, so what can the minimum product
of these four natural numbers be? And what can the maximum product be?



8、已知a是质数，b是偶数，且a
2
+b=2008，则a+b+1结果是多少？
8. It is known that a is a prime number and b is an even number and that a
2
+b=2008,
so what is the result of a+b+1?


5. Take out two fractions from
9、一个质数p，使得p+ 2，p+4同时都是质数。则
111

的结果是多
pp2p4
少？
9. There is a prime number p, which can make p+2 and p+4 to be prime numbers as
well. So what is the result of
111

?
pp2p4





10、 彼此不等且大 于0的偶数a，b，c，d满足a+b+c+d=20，这样的偶数组
（a，b，c，d）共有多少组？
10. There are four different even numbers a, b, c and d, which are all greater than 0. If
they should satisfy the equation of a+b+c+d=20, how many groups of such even
numbers (a, b, c, d) are there?

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11、 在一个两位数的中间加上一个0，得到的新数比原来大8倍，原来的两
位数是多少？
11. Add a “0” to the middle place of a double-digit number, so that the new three-digit
number is 8 times more than the original number. So what is the original double-digit
number?



12、 如图，从A到B有多少条不同的路线？（只能向上或向左走）
B

















A
12. As shown in the picture, how many different ways are there to go from A to B?
(One can only walk up or towards left)



13、 小马虎在考试中做一道计算题时，将一个数乘9错算成除以9，接着又< br>将加上30错算成减去30，结果得18，如果按正确的运算顺序，所得的结果
是多少？
13. When doing a calculation in an exam, a careless student made some mistakes.
Rather than multiplying a number by 9 and then adding 30, he divided the number by
9 and then subtracted 30, so that the result was 18. If he did the calculation correctly,
what would the result be?




5
14、 袋里有若干个球，其中红 球占，后来又往袋里放了6个红球，这时红
12
1
球占总数的。现在袋里有多少个球？
2
5
14. There are some balls in a bag and the red balls account for of the total
12

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amount. After adding another 6 red balls into the bag, the red balls account for
1
of
2
the total amount. So how many balls are there in the bag now?



15、 有1567名同学排成一排玩游戏，从 排头到排尾按顺序说“我”“最”“棒”
3个字（每人说一个字），再从排尾到排头重新按顺序说这3个 字，其中有多
少人两次都说“我”这个字？
15. 1567 students stand in a row to play games, speaking “I’m” “the” “best” from the
head of the row to the end of the row (each student speaks one word at a time) and
then speaking these three words from the end of the row to the head of it. So, how
many students speak “I’m” twice?


第二部分

1、一条船顺水航行48千米，再逆水航行16千米，共用了5小时；这条 船顺水
航行32千米，再逆水航行24千米，也用了5小时。求这条船在静水中的速
度。
1. It takes a boat 5 hours to sail 48 km downstream and 16 km upstream. And it also
takes the boat 5 hours to sail 32 km downstream and 24 km upstream. So what is the
speed of this boat in still water?



3
2、有一所学校，男生占学生总人数的，学生总人数与男生人数都是三 位数，
5
组成这两个三位数的六个数字正好是1、2、3、4、5、6。问：这所学校有多少学生？
3
2. In a school, boy students account for of all the students. It is known that the
5
number of all the students and the number of boys are both three-digit numbers and
the six digits making up these two three-digit numbers are 1, 2, 3, 4, 5 and 6. So how
many students are there in this school?



3、六个小朋友在一起做游戏。他们每人想一相整数写在卡片上交给老师，老师
用不同的方式把 其中5人写的数加在一起，得到以下6个数：87、92、98、
99、104、110。那么卡片上写 的数中最接近平均数的是什么数？
3. Six children play games. Each of them writes down an integer on a card and gives
the card to a teacher. The teacher adds up any 5 of the six numbers in different ways

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and gets the following six numbers: 87, 92, 98, 99, 104 and 110. So what number on
the six cards is closest to the average number?



4、现在一副去掉大小王的扑克牌，共52张。把它们洗匀后，分成A、B两组，
各26张。请问：在 1000次洗牌中，A组中的黑牌数和B组中的红牌数，有
几次会完全相同？
4. There is a set of playing cards, a total of 52 cards, which does not include the big
king and the little king. After being shuffled, the cards are divided into A and B
groups, 26 cards in each group. So in 1000 times of shuffle, how many times will the
number of black cards in Group A be exactly equal to the number of red cards in
Group B?



5、给10位学生发铅笔，每人 3支还剩下一些，每人4支又不够。如果剩下的
和不够的同样多，那么共有多少支铅笔？
5. Divide pencils among 10 students. There will be some pencils left if each student is
given 3 pencils and it will not be enough to give each student 4 pencils. Given that the
number of the pencils left is equal to the number of the insufficient pencils, how
many pencils are there totally?



6、甲、乙、丙丁进行象棋比赛 ，每两人之间要赛一盘。规定胜一盘得2分，平
一盘各得1分，输一盘不得分。甲、乙、丙共得10分， 丁得多少分？
6. A, B, C and D play chess and every two people need to compete once. It is ruled
that winning will bring 2 marks, a draw will bring 1 mark and losing will bring no
marks. A, B and C altogether get 10 marks, so how many marks does D get?



7、甲、乙两人卖商品，甲 的比乙多10个，可是全部卖出后的收入都是15元。
如果甲的商品按乙的价格出售可卖18元，那么， 甲、乙各有多少个商品？
7. A and B sell commodities. A has 10 more commodities than B, but both of them
gain a profit of 15 yuan after selling out their commodities. If A sells his commodities
according to B’s price, he will get 18 yuan. So how many commodities do A and B
have respectively?



8、有20包花生给一只猴子吃， 一包只能吃一天，但不能连续两天都吃（即今
天吃了，明天就不能吃），且间隔的天数彼此不同。那么， 这20包花生至少

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要多少天才能吃完？
8. 20 bags of peanuts will be used to feed a monkey and one bag of peanuts can only
last for one day. The monkey cannot eat peanuts every two continuous days (if it eats
peanuts today, it cannot eat them tomorrow) and the interval days should be different.
So how many days at least will it take the monkey to eat up these 20 bags of peanuts?



9、在1到100这100个自然数中，找出3个自然数，使它们的倒数和为1。
9. Find out 3 natural numbers among 100 natural numbers from 1 to 100, so that the
sum of these three numbers’ reciprocals is 1.



1
10、 有一个边长为1分米的正方形，甲先划去正方形面积的，乙接着划去3
111
剩下面积的，然后甲又划去剩下面积的，乙再划去剩下面积的，……，
2 32
依次类推。如果两人分别划了三次，此时这个正方形还剩下多少平方分米没
有被划去？
1
10. There is a square whose sides are 1 dm. A first cuts off of the square and B
3
11
cuts off of the remaining area. Then A cuts off of the remaining area and B
23
1
cuts off of the area left,……After A and B cut the square in the same manner for
2
three times, how many square decimeters is the area left?





11、 3个六面体都是按照相同的规律涂有红、黄、蓝、白、黑、绿6种颜色
（如图）。黄色对面是（ ）色，白色对面是（ ）色，红色对面是（ ）
色。


白 绿 黄

红

黄 红
黑
白 蓝


11. As shown below, 3 hexahedrons are painted with 6 colors of red, yellow, blue,
white, black and green according to the same rule. So the color opposite yellow is
( ), the color opposite white is ( ) and the color opposite red is ( ).

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white green yellow

red

yellow red
black
white blue





12、 大毛、二毛、三毛每天早晨都要在运动场上进行长 跑训练。一天，他们
在200米跑道的同一起跑线上同时起跑，当三毛正好跑完一圈时，二毛超过
1
三毛圈，大毛超过三毛半圈，这天早晨他们共跑了15圈。如果他们始终
4
以各人 的速度跑步，那么他们每人各跑了几圈？
12. A, B and C took long- distance running training on the playground every morning.
One day, they started at the same time from the same starting line of the 200-meter
1
runway. When C finished a circle, B was circle ahead of C and A was half circle
4
ahead of C. They altogether ran 15 circles. If they kept running with constant speeds,
how many circles did they run respectively?

第三部分
16、 一个三位数，如果它的每 一位数字都不超过另一个三位数对应数位上的
数字，那么就称它被另一个三位数“吃掉”。又规定“任何 数都可以被它相
同的数吃掉”。比如，241被342“吃掉”，123被123“吃掉”，但是240 和
223互相都不能被“吃掉”。现请你设计出6个三位数，它们中的任何一个都
不能被另外5 个“吃掉”，并且它们的百位数字只允许取1，2；十位数字只
允许取1，2，3；个位数字只允许取1 ，2，3，4，那么这6个三位数之和是
多少？
There is a three- digit number. If every digit of it does not exceed its counterpart of
another three-digit number, then,

we can say that it is eaten by the later three-digit
number. It is also the rule that any number can be eaten by itself. For example, 241 is
eaten by 342 and 123 is eaten by 123. But 240 and 223 can not be eaten by each other.
Now please conceive six three-digit numbers and make sure that none of them can be
eaten by the other five. In addition, their hundreds digits can only be 1 or 2, their tens
digits can only be 1, 2 or 3, and their ones digits can only be chosen from 1, 2, 3 and
4. Then, what is the sum of the six three-digit numbers?

17、 小王骑自行车，小张骑摩托车，他们同时从A、B两地相向而行 ，在距
3
中点10千米处相遇。已知小王骑车的速度是小张的，求A、B两地间的距
5
离。
Xiao Wang is riding a bike and Xiao Zhang is riding a motorcycle. They move face to
face from A and B respectively at the same time. They meet at the place which is 10

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kilometers away from the midpoint. Given that Xiao Wang’s speed is three fifths of
that of Xiao Zhang. What is the distance between A and B?

18、 小刚骑车从8路 汽车的起点站出发，沿着8路车的行驶路线前进。当他
骑了1650米时，一辆8路公共汽车从起点站出 发，每分钟行450米。这辆
汽车在行驶过程中每行5分钟停靠一站，停车时间为1分钟。已知小刚骑车
2
速度是汽车行驶速度的，这辆车出发后多少分钟追上小刚？
3
3. Xiao Gang starts from the origin station of No.8 bus by bike and goes along the
route of No.8 bus. When he covers 1650 meters, a No.8 bus sets out from the origin
station and moves 450 meters per minute. This bus pulls up for one minute at one
bus stop every five minutes. Given that Xiao Gang’s speed is two thirds of that of
the bus, how many minutes will it take the bus to catch up with Xiao Gang after its
departure?

19、 甲、乙两筐水果重量相等，如果从甲筐取出6千克 水果放入乙筐，这时，
1
甲筐比乙筐少，甲筐原有水果多少千克？
4
4. There are two baskets of fruits, A and B, with the same weight. If one takes out 6
kilograms of fruits from A and put them into B, then, the fruits in A is a quarter less
than those in B. How many kilograms of fruits are there in A in the first place?

20、 下面的每个图形中的数字都存在一定的规律，请找一找，再算出第四个
图形中的“？”表示的数是多少？
8 13 12 6 22 3 43 5

12 13 14 ?

5 3 4 2 9 5 11 6
5. There exists a certain regularity of the numbers in the following pictures. Please
find the regularity and figure out the number indicated by a question mark in the
fourth picture.

21、
如果一个整数等于它各个数位上数的和的3倍，那么这个数会是多少？

6. If an integer is three times as large as the sum of the figures in its digit positions,
then, what is the number?

22、 有两个大小不同 的正方形A、B，如下图，B的中心与A的一个顶点重合，
1
重叠部分的面积是A面积的，你能 知道正方形A的边长是B的多少倍吗？
9
7. Square A and square B are different in size. As is shown in the following picture,
the center of B and one of the vertexes of A overlap each other. The area of the
overlapped part is one ninth of that of A. Do you know how many times the side of A
is as long as that of B?

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23、
B
A上题中，如果A与B以下图的方式重叠时，那么重叠部分面积又是B面
积的几分之几？



A



B

8. In the above problem, if A and B overlap like the following picture, then, what
portion is the area of the overlapped part to that of B in terms of fraction?
24、 图1中有8个面积都是4平方厘米的正三角形，依次叠放在同一条 直线
上，从左到右，每个三角形底边的中点恰好与下一个三角形的一个顶点重合，
那么由这8个 三角形所盖住的面积是多少平方厘米？




9. There are eight identical regular triangles in the following picture. Each area is 4
cm
2
. They overlap one another on the same straight line. From left to right the
midpoint of the base line of every triangle overlaps with one of the vertexes of the
next triangle. What is the area covered by the eight triangles in square centimeters?

25、 下图中有10个边长都是2厘米的正方形，依次地排 在一条直线上，而
且正方形的一个顶点，正好是下一个正方形的中心，那么由这10个正方形
所 盖住的面积是多少？



In the following picture, ten squares with the same side length of 2 cm are arranged
on one straight line in order. One of the vertexes of one square is just the center of the
next one. What is the area covered by the ten squares?

26、 有一个3×3的方格 ，能否通过若干次操作，使得方格中的所有数变为0？
（其中一次操作是指将表中一行的3个数或一列的 3个数同时加上或减去同
一个数），如果能请给出一种操作方案，如果不能，请说明理由。

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11. There is a 3×3 grid. Can you turn all the numbers in the grid into 0
1 1 2
after several operations? (The operation is to add or minus the same
3 7 8
number to or from the three numbers in one row or in one column at the
2 6 7
same time.) If you can, please give one plan, and if not, please give your
reason.

27、 上题中，其他条件不变，能否通过若干次操作，使得方格中的所有数变
为1呢？
12. In the above problem, if we keep the other conditions unchanged, can you turn all
the numbers in the grid into 1 after several operations?
28、 将一张长 方形纸片连续对折，对折的次数越多，折痕的条数也就越多，
请问对折8次后，折痕有多少条？（向同一 个方向对折）
13. If one folds a piece of rectangular paper continuously, the more times he folds
the paper, the more creases there are on the paper. After it has been folded 8
times, how many creases are there on the paper? (Please fold it in the same
direction.)

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必记词汇
insufficient [,insə'fiʃənt] adj. 不足的
draw [drɔ:] n. 平局；抽签 v. 抽
proportion [prə'pɔ:ʃən] n. 比例
hexahedron [,heksə'hedrən] n. 六面体

补充词汇
shuffle ['ʃʌfl] n. 洗牌 v. 洗牌
compete [kəm'pi:t] v. 竞争；对抗
interval ['intəvəl] n. 间隔；间距

'
词组句型
account for 占…比例；对….做出解释
sell out 卖完；卖光
eat up吃光
constant speed 恒速；匀速
ahead of 在…之前