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【330308】2020年湖北省随州市中考数学试题

时间:2025-02-09 10:50:10 作者: 字数:28405字

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 随州市2020年初中毕业升学考试数学试题

一、选择题(本大题共10小题,每小题3分,共30分,每小题给出的四个选项中,有且只有一个是正确的)

1.2020的倒数是( )

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】C

【解析】

【分析】

根据倒数的定义解答.

【详解】2020的倒数是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故选:C.

【点睛】此题考查倒数的定义,熟记倒数的定义是解题的关键.

2.如图,直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 分别交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 两点,若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的度数是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】C

【解析】

【分析】

如图:先运用两直线平行、同位角相等得到∠3=∠1=60°,然后再根据邻补角的性质得到∠3+∠2=180°,最后计算即可.

【详解】解:如图:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,∠1=60°

∴∠3=∠1=60°

∵∠3+∠2=180°

∴∠2=180°-∠3=180°-60°=120°

故答案为C

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】本题考查了平行 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 性质和邻补角的性质,掌握平行线的性质(两直线平行、同位角相等)是正确解答本题的关键.

3.随州7月份连续5天的最高气温分别为:2930323034(单位:℃),则这组数据的众数和中位数分别为(

A. 3032 B. 3130 C. 3031 D. 3030

【答案】D

【解析】

【分析】

根据众数和中位数的求解答案来判断即可.

【详解】解:∵7月份连续5天的最高气温分别为:2930303234(单位:℃)

这组数据的众数是:30

中位数:30

故选:D

【点睛】本题考查了众数和中位数,注意有偶数个数时中位数就是中间两个数的平均数,而个数有奇数个时,中位数就是中间的一个数.

4.一个几何体的三视图如图所示,则该几何体为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

A. 圆柱 B. 圆锥 C. 四棱柱 D. 四棱锥

【答案】A

【解析】

【分析】

主视图、左视图、俯视图是分别从物体正面、左面和上面看所得到的图形,从而得出答案.

【详解】俯视图为圆的几何体为球,圆柱,再根据其他视图,可知此几何体为圆柱.

故选:A

【点睛】本题考查由三视图确定几何体的形状,主要考查学生空间想象能力.

5. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的计算结果为(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】B

【解析】

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 分析】

先把分母因式分解,再把除法转换为乘法,约分化简得到结果.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故选:B

【点睛】本题主要考查了分式的除法,约分是解答的关键.

6.我国古代数学著作《孙子算经》中有“鸡兔同笼”问题:“今有鸡兔同笼,上有三十五头,下有九十四足,问鸡兔各几何”.设鸡有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 只,兔有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 只,则根据题意,下列方程组中正确的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】A

【解析】

【分析】

根据“上有三十五头”和“下有九十四足”两个等量关系列二元一次方程组即可.

【详解】解:设鸡有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 只,兔有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

根据上有三十五头,可得x+y=35

下有九十四足,2x+4y=94

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故答案为A

【点睛】本题考查了二元一次方程组的应用,弄清题意、找准等量关系是解答本题的关键.

7.小明从家出发步行至学校,停留一段时间后乘车返回,则下列函数图象最能体现他离家的距离( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> )与出发时间( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> )之间的对应关系的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】B

【解析】

【分析】

根据已知条件,确定出每一步的函数图形,再把图象结合起来即可求出结果.

【详解】解:小明从家出发步行至学校,可以看作是一条缓慢上升的直线;

中间停留一段时间,可以看作与水平方向平行的直线;

从学校乘车返回家,可以看作是一条迅速下降的直线;

结合四个选项,B符合题意;

故选:B

【点睛】本题主要考查了函数的图象问题,在解题时要根据实际情况确定出函数的图象是解题的关键.

8.设边长为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的等边三角形的高、内切圆的半径、外接圆的半径分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则下列结论不正确的是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】C

【解析】

【分析】

将图形标记各点,即可从图中看出长度关系证明A正确,再由构造的直角三角形和30°特殊角证明B正确,利用勾股定理求出rR,即可判断CD

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

如图所示,标上各点,AOROBrABh

从图象可以得出AB=AO+OB,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> A正确;

三角形为等边三角形,

∴∠CAO=30°

根据垂径定理可知∠ACO=90°

AO=2OC,即R=2rB正确;

Rt△ACO中,利用勾股定理可得:AO2=AC2+OC2,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

B中关系可得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

所以C错误,D正确;

故选:C

【点睛】本题考查圆与正三角形的性质结合,关键在于巧妙利用半径和构建直角三角形.

9.将关于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 变形为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,就可以将 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 表示为关于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的一次多项式,从而达到“降次”的目的,又如 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> …,我们将这种方法称为“降次法”,通过这种方法可以化简次数较高的代数式.根据“降次法”,已知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的值为(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】C

【解析】

【分析】

先求得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 即可得出答案.

【详解】∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

原式= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故选:C

【点睛】本题考查了一元二次方程的解,解题的关键是会将四次先降为二次,再将二次降为一次.

10.如图所示,已知二次函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的图象与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 轴交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 两点,与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 轴的正半轴交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,顶点为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则下列结论:① <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ;② <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ;③当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 是等腰三角形时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的值有2个;④当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 是直角三角形时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> .其中正确的有(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

A. 1 B. 2 C. 3 D. 4

【答案】B

【解析】

【分析】

根据二次函数对称轴的位置可判断;②把两个点代入解析式可得到方程组,解出BC的关系即可;③由图象可知, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,从而得以判断;④根据直角三角形的

【详解】∵二次函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的图象与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 轴交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 两点,

二次函数的对称轴为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故①正确;

二次函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的图象与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 轴交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 两点,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故②错误;

由图象可知,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 是等腰三角形时,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,只能是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,故a有两个值,

故③正确;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 是直角三角形,

分两种情况 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

得到的a有两个值,

故④错误;

故答案选B

【点睛】本题主要考查了二次函数图象与系数之间的关系,准确分析判断是解题的关键.

二、填空题(本大题共有6小题,每小题3分,共18分,只需要将结果直接填写在答题卡对应题号处的横线上)

11.计算: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> _____

【答案】4

【解析】

【分析】

分别进行乘方运算和开根号,相加即可.

【详解】原式=1+3=4

故答案为4

【点睛】本题主要考查了实数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 运算,准确进行幂的运算是解题的关键.

12.如图,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的角平分线,若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的度数为_____

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】30°

【解析】

【分析】

根据圆周角定理求出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,再由角平分线的性质可得到结果;

【详解】∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的角平分线,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故答案为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】本题主要考查了圆周角定理的应用,准确运用角平分线的性质是解题的必要步骤.

13.幻方是相当古老的数学问题,我国古代的《洛书》中记载了最早的幻方---九宫图.将数字1~9分别填入如图所示的幻方中,要求每一横行、每一竖行以及两条斜对角线上的数字之和都是15,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的值为______

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】9

【解析】

【分析】

本题首先根据每一横行数字之和为15求出第一个方格数字,继而根据对角线斜边数字和为15求出最后一格数字,最后根据每一竖行数字之和为15求出m

【详解】设第一方格数字为x,最后一格数字为y,如下图所示:

由已知得:x+7+2=15,故x=6

因为x+5+y=15,将x=6代入求得y=4

又因 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 2+m+y=15,将y=4代入求得m=9

故答案为:9

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】本题考查新题型,本质是一元一次方程的求解,理清题意,按照图示所给信息逐步列方程求解即可.

14.如图, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 中,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的中点,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的中点,若随机向 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 内投一粒米,则米粒落在图中阴影部分的概率为____

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【解析】

【分析】

根据三角形的中位线定理建立面积之间的关系,按规律求解,再根据概率公式进行求解即可.

【详解】根据三角形中位线定理可得第二个三角形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 各边长都等于最大三角形各边的一半,并且这两个三角形相似,

那么第二个△DEF的面积= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> △ABC的面积

那么第三个△MPN的面积= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> △DEF的面积= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> △ABC的面积

若随机向 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 内投一粒米,则米粒落在图中阴影部分的概率为:  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】本题考查了三角形的中位线定理,概率公式,解决本题的关键是利用三角形的中位线定理得到第三个三角形的面积与第一个三角形的面积的关系,以及概率公式.

15.如图,直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 与双曲线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 在第一象限内交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 两点,与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 轴交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 为线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的中点,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的面积为3,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的值为____

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】2

【解析】

【分析】

A点坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> C点坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,求出B点坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,根据B点在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,整理得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,再根据三角形面积公式得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 可得k的值.

【详解】解:设A点坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> C点坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 恰为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的中点,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 点的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 点在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的图象上,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故答案为:2

【点睛】本题考查了反比例函数与一次函数的交点问题,反比例函数图象上点的坐标特征,解题时注意:反比例函数与一次函数的交点坐标同时满足两个函数的解析式.

16.如图,已知矩形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 分别在边 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上,沿着 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 折叠矩形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,使点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 分别落在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 处,且点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 在线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上(不与两端点重合),过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,给出下列判断:① <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ;②折痕 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的长度的取值范围为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ;③当四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 为正方形时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的中点;④若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则折叠后重叠部分的面积为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> .其中正确的是_____.(写出所有正确判断的序号).

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】①②③④

【解析】

【分析】

由题意,逐一判定,①由折叠的性质以及等腰三角形三线合一的性质即可判定;②根据题意点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 在线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上(不与两端点重合),假设F分别在CD两点,即可得出其取值范围;③由相似三角形、正方形的性质以及勾股定理构建方程,即可判定;④由相似三角形以及勾股定理,得出梯形MEFN的面积和△MEO的面积,即可得解;

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

由折叠性质,得,BG=FGBN=FN

BF⊥MN

∵∠BIH=∠MIG <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

∴∠HBI=∠GMI

∵∠MHN=∠BCF=90°

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故①结论正确;

假设FC重合时,MN取得最小值,即为3

假设FD重合时,MN取得最大值,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

MH=3BC=4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 在线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上(不与两端点重合)

折痕 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的长度的取值范围为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故②结论正确;

四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 为正方形

MH=HC=3

BH=1

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (不符合题意,舍去)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的中点

故③结论正确;

④∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> AB=CD=3

DF=1CF=2

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

BG=GF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

HN= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

∵△FGN∽△MHN

GN= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

BH=BC-HN-NC=4- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> - <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> =1

∵∠EMO=∠CNF,∠MEO=∠NCF=90°

MEO∽△NCF

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

EO= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

折叠后重叠部分的面积为:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故④结论正确;

故答案为:①②③④.

【点睛】此题主要考查矩形的折叠性质以及相似三角形的综合运用,熟练掌握,即可解题.

三、解答题(本大题共8小题,共72分,解答应写出必要的演算步骤、文字说明或证明过程)

17.先化简,再求值: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,其中 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【解析】

【分析】

先根据整式的乘法法则化简整式,再将字母的值代入结果计算求值即可.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 时,

原式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】本题主要考查了整式的混合运算----化简求值,解答本题的关键是明确整式化简求值的方法.

18.已知关于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

1)求证:无论 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 取何值,此方程总有两个不相等的实数根;

2)若方程有两个实数根 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的值.

【答案】1)见解析;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【解析】

【分析】

1)求出△的值即可证明;

2),根据根与系数的关系得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,得到关于m的方程,然后解方程即可.

【详解】(1)证明:依题意可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故无论m取何值,此方程总有两个不相等的实数根.

2)由根与系数的关系可得:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】本题考查了利用一元二次方程根的判别式证明根的情况以及一元二次方程ax2+bx+c=0a≠0)的根与系数的关系:x1x2是一元二次方程ax2+bx+c=0a≠0)的两根时,x1+x2=− <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> x1x2= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

19.根据公安部交管局下发的通知,自202061日起,将在全国开展“一带一盔”安全守护行动,其中就要求骑行摩托车、电动车需要佩戴头盔.某日我市交警部门在某个十字路口共拦截了50名不带头盔的骑行者,根据年龄段和性别得到如下表的统计信息,根据表中信息回答下列问题:

年龄 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (岁)

人数

男性占比

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

4

50%

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

60%

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

25

60%

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

8

75%

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

3

100%



1)统计表中 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的值为_______

2)若要按照表格中各年龄段的人数来绘制扇形统计图,则年龄在“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ”部分所对应扇形的圆心角的度数为_______

3)在这50人中女性有______人;

4)若从年龄在“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ”的4人中随机抽取2人参加交通安全知识学习,请用列表或画树状图的方法,求恰好抽到2名男性的概率.

【答案】110;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ;(318;(4P(恰好抽到2名男性) <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【解析】

【分析】

1)用50-4-25-8-3可求出m的值;

2)用360°乘以年龄在“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ”部分人数所占百分比即可得到结论;

3)分别求出每个年龄段女性人数,然后再相加即可;

4)年龄在“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ”的4人中,男性有2人,女性有2人,分别用A1A2表示男性,用B1B2表示女性,然后画出树状图表示出所有等可能结果数,以及关注的事件数,然后利用概率公式进行求解即可.

【详解】解:(1m=50-4-25-8-3=10

故答案为:10

2360°× <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

3)在这50人中女性人数为:

4×1-50%+10×1-60%+25×1-60%+8×1-75%+3×1-100%

=2+4+10+2+0

=18

故答案为:18

4)设两名男性用 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 表示,两名女性用 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 表示,根据题意:

可画出树状图:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

或列表:

2

1

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>


 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>


 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>


 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>




由上图(或上表)可知,共有12种等可能的结果,符合条件的结果有2种,

P(恰好抽到2名男性) <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】此题考查了列表法或树状图法求概率以及频数分布表.用到的知识点为:概率=所求情况数与总情况数之比.

20.如图,某楼房 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 顶部有一根天线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,为了测量天线的高度,在地面上取同一条直线上的三点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,在点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 处测得天线顶端 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的仰角为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,从点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 走到点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,测得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 米,从点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 测得天线底端 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的仰角为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,已知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 在同一条垂直于地面的直线上, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 米.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

1)求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 之间的距离;

2)求天线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的高度.(参考数据: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,结果保留整数)

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 之间的距离为30米;(2)天线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的高度约为27米.

【解析】

【分析】

1)根据题意,∠BAD=90°,∠BDA=45°,故AD=AB,已知CD=5,不难算出AC之间的距离.

2)根据题意,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,利用三角函数可算出AE的长,又已知AB,故EB即可求解.

【详解】(1)依题意可得,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 米,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 米, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> .

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 之间的距离为30米.

2)在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 米,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (米),

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 米, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 米.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> .并精确到整数可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 米.

即天线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的高度约为27米.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】(1)本题主要考查等腰直角三角形的性质,掌握等腰直角三角形的性质是解答本题的关键.

2)本题主要考查三角函数的灵活运用,正确运用三角函数是解答本题的关键.

21.如图,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,以斜边 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上的中线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 为直径作 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的另一个交点为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

1)求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的切线;

2)若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的直径为5 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的长.

【答案】1)见解析;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【解析】

【分析】

1)欲证明MN为⊙O的切线,只要证明OM⊥MN
2)连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,分别求出
BD=5BE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 求解即可.

【详解】(1)证明:连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 是斜边 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上的中线,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的切线.

2)连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,易知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

由(1)可知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,故M <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的中点,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】本题考查切线的判定和性质,等腰三角形的性质,解直角三角形等知识;熟练掌握切线的判定定理是解题的关键.

22.2020年新冠肺炎疫情期间,部分药店趁机将口罩涨价,经调查发现某药店某月(按30天计)前5天的某型号口罩销售价格 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (元/只)和销量 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (只)与第 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 天的关系如下表:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

1

2

3

4

5

销售价格 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (元/只)

2

3

4

5

6

销量 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (只)

70

75

80

85

90



物价部门发现这种乱象后,统一规定各药店该型号口罩的销售价格不得高于1/只,该药店从第6天起将该型号口罩的价格调整为1/只.据统计,该药店从第6天起销量 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (只)与第 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 天的关系为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 为整数),已知该型号口罩的进货价格为0.5/只.

1直接写出该药店该月前5天的销售价格 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 和销量 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 之间的函数关系式;

2)求该药店该月销售该型号口罩获得的利润 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (元)与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的函数关系式,并判断第几天的利润最大;

3)物价部门为了进一步加强市场整顿,对此药店在这个月销售该型号口罩的过程中获得的正常利润之外的非法所得部分处以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 倍的罚款,若罚款金额不低于2000元,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的取值范围为______

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> x为整数, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> x为整数;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,第5天时利润最大;(3 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【解析】

【分析】

1)根据表格数据,px的一次函数,qx的一次函数,分别求出解析式即可;

2)根据题意,求出利润wx的关系式,再结合二次函数的性质,即可求出利润的最大值.

3)先求出前5天多赚的利润,然后列出不等式,即可求出m的取值范围.

【详解】(1)观察表格发现px的一次函数,qx的一次函数,

p=k1x+b1

x=1p=2x=2p=3分别代入得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

所以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

经验证p=x+1符合题意,

所以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> x为整数;

q=k2x+b2

x=1q=70x=2q=75分别代入得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

所以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

经验证 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 符合题意,

所以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> x为整数;

2)当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> x为整数时,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> x为整数时,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

即有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> x为整数时,售价,销量均随x的增大而增大,

故当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (元)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> x为整数时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (元);

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,可知第5天时利润最大.

3)根据题意,

5天的销售数量为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (只),

5天多赚的利润为:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> (元),

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的取值范围为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】此题考查二次函数的性质及其应用,一次函数的应用,不等式的应用,也考查了二次函数的基本性质,另外将实际问题转化为求函数最值问题,从而来解决实际问题.

23.勾股定理是人类最伟大的十个科学发现之一,西方国家称之为毕达哥拉斯定理.在我国古书《周髀算经》中就有“若勾三,股四,则弦五”的记载,我国汉代数学家赵爽为了证明勾股定理,创制了一幅“弦图”(如图1)后人称之为“赵爽弦图”,流传至今.

1)①请叙述勾股定理;

勾股定理的证明,人们已经找到了400多种方法,请从下列几种常见的证明方法中任选一种来证明该定理;(以下图形均满足证明勾股定理所需的条件)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

2)①如图456,以直角三角形的三边为边或直径,分别向外部作正方形、半圆、等边三角形,这三个图形中面积关系满足 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的有_______个;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

如图7所示,分别以直角三角形三边为直径作半圆,设图中两个月形图案(图中阴影部分)的面积分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,直角三角形面积为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,请判断 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的关系并证明;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

3)如果以正方形一边为斜边向外作直角三角形,再以该直角三角形的两直角边分别向外作正方形,重复这一过程就可以得到如图8所示的“勾股树”.在如图9所示的“勾股树”的某部分图形中,设大正方形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的边长为定值 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,四个小正方形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的边长分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,已知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 变化时,回答下列问题:(结果可用含 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的式子表示)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> _______

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的关系为_______ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的关系为_______

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【答案】1)①如果直角三角形的两条直角边分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,斜边为c,那么 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,(或者:在直角三角形中,两条直角边的平方和等于斜边的平方.);②证明见解析;(2)①3,②结论 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ;(3)① <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,② <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【解析】

【分析】

1)①根据所学的知识,写出勾股定理的内容即可;

根据题意,利用面积相等的方法,即可证明勾股定理成立;

2)①根据题意,设直角三角形的三边分别为abc,利用面积相等的方法,分别求出面积的关系,即可得到答案;

利用三角形的面积加上两个小半圆的面积,然后减去大半圆的面积,即可得到答案;

3)①由(1)(2)中的结论,结合勾股定理的应用可知, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,同理可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,利用解直角三角形以及勾股定理,即可得到答案.

【详解】解:(1)①如果直角三角形的两条直角边分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,斜边为c,那么 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

(或者:在直角三角形中,两条直角边的平方和等于斜边的平方.)

证明:

在图1中,大正方形的面积等于四个全等的直角三角形的面积与中间小正方形面积的和.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

化简得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

在图2中,大正方形的面积等于四个全等的直角三角形的面积与中间小正方形面积的和.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,化简得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

在图3中,梯形的面积等于三个直角三角形的面积的和.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,化简 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

2)①根据题意,则如下图所示:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

在图4中,直角三角形的边长分别为abc,则

由勾股定理,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

在图5中,三个扇形的直径分别为abc,则

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

在图6中,等边三角形的边长分别为abc,则

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

满足 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的有3个,

故答案为:3

结论 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

3)①如图9,正方形ABCDEFM中,对应的边长分别为abcdefm,则有

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

由(1)(2)中的结论可知,面积的关系为:A+B=EC+D=FE+F=M

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

②∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

由解直角三角形和正方形的性质,则

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

同理: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【点睛】本题考查了求扇形的面积,解直角三角形,勾股定理的证明,以及正方形的性质,解题的关键是掌握勾股定理的应用,注意归纳推理等基础知识,考查运算求解能力、推理论证能力、归纳总结能力,是中档题.

24.如图,在平面直角坐标系中,抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的对称轴为直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,其图象与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 轴交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 和点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 轴交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

1)直接写出抛物线的解析式和 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的度数;

2)动点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 同时从 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 点出发,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 以每秒3个单位的速度在线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上运动,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 以每秒 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 个单位的速度在线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 上运动,当其中一个点到达终点时,另一个点也随之停止运动.设运动的时间为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 秒,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,再将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 顺时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,设点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 落在点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的位置,若点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 恰好落在抛物线上,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的值及此时点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的坐标;

3)在(2)的条件下,设 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 为抛物线上一动点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 轴上一动点,当以点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 为顶点的三角形与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 相似时,请直接写出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 及其对应的点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的坐标.(每写出一组正确的结果得1分,至多得4分)

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ;(2t= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> D点坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 3 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

【解析】

【分析】

1)根据抛物线的对称轴以及点B坐标可求出抛物线表达式;

2)过点N <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> E,过点D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> F,证明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,从而得到点D坐标,代入抛物线表达式,求出t值即可;

3)设点Pm <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ),当点Py轴右侧,点Qy轴正半轴,过点PPR⊥y轴于点R,过点DDS⊥x轴于点S,根据△CPQ∽△MDB,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,从而求出m值,再证明△CPQ∽△MDB,求出CQ长度,从而得到点Q坐标,同理可求出其余点P和点Q坐标.

【详解】解:(1)∵抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 的对称轴为直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则b=-3a

抛物线经过点B40),

16a+4b+1=0,将b=-3a代入,

解得:a= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> b= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

抛物线的解析式为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

y=0,解得:x=4-1

x=0,则y=1

A-10),C01),

tan∠CAO= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

2)由(1)易知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

过点N <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> E,过点D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> F

∵∠DMN=90°

∴∠NME+∠DMF=90°,又∠NME+∠ENM=90°

∴∠DMF=∠ENM

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> AAS),

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

由题意得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,又 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

故可解得:t= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 0(舍),

经检验,当t= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 时,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 均未到达终点,符合题意,

此时D点坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

3)由(2)可知:D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> t= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 时,M <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 0),B40),C01),

设点Pm <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ),

如图,当点Py轴右侧,点Qy轴正半轴,

过点PPR⊥y轴于点R,过点DDS⊥x轴于点S

PR=mDS= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

若△CPQ∽△MDB

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,解得:m=0(舍)或15(舍),

故点P的坐标为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

∵△CPQ∽△MDB

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

当点P <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ,解得:CQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

Q坐标为(0 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> ),

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

同理可得:点P和点Q的坐标为:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1031/" title="随州" class="c1" target="_blank">随州</a> .

【点睛】本题是二次函数综合题,考查了二次函数的图像和性质,二次函数表达式,全等三角形的判定和性质,相似三角形的性质,难度较大,计算量较大,解题时注意结合函数图像,找出符合条件的情形.