1989年四川省高中数学联合竞赛试卷试题 - 学进去中小学试卷试题库

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【单选】1．异面直线、分别在平面、内，若，则直线必定是（）
A．分别与、相交 B．与、都不相交
C．至少与、中之一相交 D．至多与、中之一相交
- 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．设动点到点的距离与到直线的距离之比为2,则的轨迹方程为()
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】3．的充要条件是（）
A． B．或
C． D．<或
- 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．函数的图象(图中实线部分)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】5．已知,,且,是的整数部分,则等于( )
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】6．设,且,那么______.
- 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．设椭圆的两个焦点为,其短轴上的一个顶点为A,那么的外接圆的方程为______.
- 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】8．若一圆台的上底周长为4,下底周长为9,平行于底的截面周长是上、下底周长的比例中项,则这个截面分圆台的高所成的两段的比为______.
- 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】9．设关于的方程无实根,那么函数的反函数是______.
- 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】10．已知由幂函数构成的集合A中,奇函数有10个,定义在区间上的增函数有8个,图象过原点的函数有12个,那么集合A的元素最多有______个.
- 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: .求证:
(1)若,且,则
(2)当时,.
- 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.

添加错题本
【单选】12．如图,已知三棱柱的底面是边长为2的正三角形,侧棱与下底面相邻的两边AB,AC均成45度的角.

(1)求点到平面B₁BCC₁的距离.
(2)试问,当为多长时,点到平面与到平面的距离相等.
- 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．设G是紧夹在平行线与之间的任一凸区域(即其边界上任意两点之间所连线段都包含于它的区域),其边界与和都有公共点．平行于的直线将G分为如图所示的两部分,且l与和之间的距离分别为a和b.
(1)G为怎样的图形时;两部分的面积之比达到最大?并说明理由.
(2)试求的最大值.
- 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．已知数列满足，满足.证明：.
- 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.

添加错题本

A．分别与、相交	B．与、都不相交
C．至少与、中之一相交	D．至多与、中之一相交

A．	B．
C．.	D．.

A．	B．或
C．	D．<或

A．	B．
C．	D．

答题卡