2007年全国高中数学联赛江苏赛区复赛试卷试题

2007年全国高中数学联赛江苏赛区复赛试卷试题 - 学进去中小学试卷试题库

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【单选】1．已知为偶函数，且，当时，.若，，则等于.
A．27 B．3 C． D．
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】2．从集合中任取两个元素作为椭圆方程中的m、n.则能组成落在矩形区域内的椭圆的个数是.
A．43 B．72 C．86 D．9
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】3．函数的图像大致是图中的.
A． B．
C． D．
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】4．设表示不超过x的最大整数，Z表示整数集，方程的解集为M，则有.
A． B．
C． D．M与Z互不包含
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】5．已知不等式对于任意正实数x、y恒成立.则正实数a的最小值为（）.
A．2 B．4 C．6 D．8
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】6．A、B两位同学各有3张卡片，现以投掷均匀硬币的形式进行游戏.当出现正面向上时，A赢得B—张卡片，否则，B赢得A—张卡片.若某人已赢得所有卡片，则游戏终止.那么，恰好掷完5次硬币时游戏终止的概率是.
A． B． C． D．
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】7．在△ABC中，角A、B、C的对边分别为、、，且，则角B的大小是 _________.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】8．掷一次硬币，出现正面与背面的概率都是.当第n次投掷出现正面时，令；当第n次投掷出现背面时，令.又记，则的概率是____.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】9．如图.在多面体ABCDEF中，已知四边形ABCD是边长为3的正方形，EF∥AB，.若该多面体的体积为，则与AC的距离为____.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】10．给定平面上的五个点A、B、C、D、E，任意三点不共线.由这些点连成4条线，每点至少是一条线段的端点，不同的联结方式有____种.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】11．已知，.则等于____.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】12．已知双曲线的左顶点为A，右焦点为
A．设P为第一象限中双曲线上的任意一点.若总有，则双曲线的离心率e等于________.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】13．在数列中，已知，对于任意正整数n，有（M为常数，且为整数）.求M的最小值.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】14．设顶点为P的抛物线交x轴正半轴于点A、B交y轴正半轴于点C，过A、B、C三点，恰好与y轴相切.求证：PA丄DA.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】15．已知数列.
（1）n是什么数时，是整数？
（2）如果n是奇数，并且是整数，那么，n是多少？
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】16．如图，在梯形ABCD中，AD∥BC，BC=BD=1，AB=AC，CD<1，且∠BAC+∠BDC=180°.求CD的长.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】17．已知n为正整数.求证: .
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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【单选】18．如图，依顺时针方向，从1开始，走1步到2，再走2步到3，最后走3步到4.对于大于1的自然数n，能否将1至n排在圆周上，使得从1开始，走一步到，再走步到，……最后，走步到?这里是1，2，1…，n的一个排列.
- A Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- B 我是超长选项我是超长选项我是超长选项我
- C Monday1 Monday 1Monday 1Monday 1onday 1Mond1 Monday1
- D Tuesday
正确答案：B，您的答案：B,回答错误。

【解析】
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean euismod bibendum laoreet. Proin gravida dolor sit amet lacus accumsan et viverra justo commodo. Proin sodales pulvinar tempor. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nam fermentum, nulla luctus pharetra vulputate, felis tellus mollis orci, sed rhoncus sapien nunc eget odio.

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A．	B．
C．	D．

A．	B．
C．	D．M与Z互不包含

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