2015年全国初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．已知，，满足，，则（）．
A．0 B．3 C．6 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】2．若抛物线与轴只有一个公共点，且过点，，则（）
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．矩形中，，，、分别为矩形外的两点，，，则（）
A． B．15 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．已知为坐标原点，位于第一象限的点在反比例函数的图象上，位于第二象限的点在反比例函数的图象上，且，则的值为（）
A． B． C．1 D．2
- 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．已知实数，满足关系式，则的最小值为（）
A． B． C．1 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．设是小于100的正整数且使是15的倍数，则符合条件的所有正整数的和是（）
A．285 B．350 C．540 D．635
- 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．设实数，，满足：，，则（）
A．12 B．9 C．6 D．3
- 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．已知实数满足关系式，则的最大值为（）
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】9．设是小于100的正整数且使是6的倍数，则符合条件的所有正整数的和是（）
A．784 B．850 C．1536 D．1634
- 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．设，是一元二次方程的两根，则的值为__________.
- 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】11．从三边长均为整数且周长为24的三角形中任取一个，它是直角三角形的概率为__________.
- 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】12．已知锐角的外心为，交于，、分别为、的外心，若，，则__________.
- 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．将数字1，2，3，…，34，35，36填在的方格中，每个方格填一个数字，要求每行数字从左到右是从小到大的顺序，则第三列所填6个数字的和的最小值为______．
- 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】14．三边长均为整数且周长为24的三角形的个数为__________．
- 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】15．、两点在以为直径的半圆周上，平分，，，则的长为__________．
- 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】16．在圆周上按序摆放和为15的五个互不相等的正整数，，，，，使得最小，则这个最小值为___________．
- 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】17．关于的方程有且仅有一个实数根，求实数的取值范围．
- 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，圆内接四边形的对角线、交于点，且，．过点作，交的延长线于点，的平分线分别交、于点、．

（1）证明：；
（2）如果，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.

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【单选】19．设正整数，满足：关于的方程至少有一个正整数解，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.

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【单选】20．若正数，满足，求的最小值．
- 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.

添加错题本
【单选】21．如图，圆内接四边形的对角线、交于点，且，.过点作，交的延长线于点，的平分线分别交、于点、．

（1）证明：；
（2）如果，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.

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【单选】22．若关于的方程至少有一个正整数根，求满足条件的正整数的值．
- 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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