习题14.1.1-1.2.3.4题. 查看更多

 

题目列表(包括答案和解析)

在某次数学竞赛中每解出一道难题得3分,每解出一道普通题得2分,此外,对于每道未能解出的普通题要扣去1分.某人解出了10题,一共得了14分.则该次数学竞赛中一共有
 
道普通题.

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观察下列解题过程
计算:1+5+52+53+…+524+525
解:设S=1+5+52+53+…+524+525
则5S=5+52+53+…+524+525+526
②-①的:4S=526-1,∴S=
526-14

你能用你学到的方法计算下面的题吗?
1+3+32+33+…+39+310

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观察下列各式:
1
1×2
=1-
1
2
1
2×3
=
1
2
-
1
3
1
3×4
=
1
3
-
1
4
,…
(1)请依据以上的式子填写下列各题:
1
8×9
=
1
8
-
1
9
1
8
-
1
9

1
n(n+1)
=
1
n
-
1
n+1
1
n
-
1
n+1
.(n为正整数)
(2)根据上面各式所归纳的规律计算下题:
1
1×2
+
1
2×3
+
1
3×4
+…+
1
2008×2009
+
1
2009×2010

(3)拓展延伸:
如果a=1,b=3,计算下题:
1
ab
+
1
(a+1)(b+1)
+
1
(a+2)(b+2)
+…+
1
(a+98)(b+98)

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小明和小红回答6道题的分数如下:
问题 1 2 3 4 5 6 7 8
小明 5 8 10 13 15 18
小红 9 11 12 14 15 17
按这样的规律,回答8道题后的情况是什么?(  )

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完形填空 (20分)
The famous British inventor George Stephenson was born in 1781 and died in 1848. one of his _21_ important inventions was the train. He _22_his first train when he was forty-four years old. When he was experimenting with the _23_ engine on the train, he met with _24_ from the government, newspapers and the gentlemen in the country. They said that the noise and the smoke would _25_ cows, horses and sheep, that the _26_ would hurtle(炸飞) or that the hot coals from it would _27_their houses. At that time, _28_ people believed what they said.
George Stephenson _29_ the people that the train could go on small _30_, could pull carriages _31_goods and passengers and there was _32_ to them. It was a very _33_ matter for him to _34_ them believe. However, after _35_, he was able to do it; and the first train that _36_ by Stephenson himself _37_ what he had said.
The first day _38_ the people along the way _39_ the noises of the train _40_ and saw it running quickly to them, they ran back home as quickly as they could and closed their doors tightly, for they thought it a genius. They did not dare to come out until it had passed.
【小题1】
A.veryB.a lotC.mostD.much
【小题2】made   B. bought   C. introduced   D. did
【小题3】
A.electricalB.atomicC.steamD.beautiful
【小题4】
A.successB.troublesC.peopleD.pleasure
【小题5】
A.killB.buyC.interestD.take away
【小题6】
A.smokeB.noiseC.driverD.engine
【小题7】
A.pull downB.blow awayC.set fire toD.pass
【小题8】
A.mostB.fewC.only a fewD.the rich
【小题9】
A.saidB.spokeC.toldD.warned
【小题10】 A.reads    B. rivers    C. steam    D rails
【小题11】
A.short ofB.full ofC.empty ofD.without
【小题12】
A.no great dangerB.dangerousC.a lot of dangerD.few danger
【小题13】
A.easyB.difficultC.pleasantD.light
【小题14】
A.getB.causeC.makeD.force
【小题15】
A.sometimesB.some timeC.a few timesD.sometime
【小题16】
A.was soldB.were drivenC.was pulledD.was driven
【小题17】
A.believedB.seemedC.sensedD.proved
【小题18】
A.ofB.whenC.whileD.for
【小题19】
A.caught sight ofB.listened toC.heardD.thought
【小题20】
A.nearbyB.in the distanceC.on the farD.from the distance

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