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【330346】2020年山东省青岛市中考数学试题

时间:2025-02-09 11:00:12 作者: 字数:31253字
简介:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 山东省青岛市2020年中考数学真题

(考试时间:120分钟;满分:120分)

说明:

1.本试题分第I卷和第II卷两部分,共24题,第I卷为选择题,共8小题,24分;

II卷为填空题、作图题、解答题,共16小题,96分.

2.所有题目均在答题卡上作答,在试题上作答无效.

I卷(共24分)

一、选择题(本大题共8小题,每小题3分,共24分)

1.4的绝对值是(

A. 4 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> C. 4 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【答案】A

【解析】

【分析】

根据绝对值的概念计算即可.(绝对值是指一个数在坐标轴上所对应点到原点的距离叫做这个数的绝对值.

【详解】根据绝对值的概念可得-4的绝对值为4.

【点睛】错因分析:容易题.选错的原因是对实数的相关概念没有掌握,与倒数、相反数的概念混淆.

2.下列四个图形中,中心对称图形是(

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【答案】D

【解析】

【分析】

根据中心对称图形的概念结合各图形的特点求解.

【详解】解:A、不是中心对称图形,不符合题意;

B、不是中心对称图形,不符合题意;

C、不是中心对称图形,不符合题意;

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 中心对称图形,符合题意.

故选:D

【点睛】本题考查了中心对称图形与轴对称图形的概念.判断中心对称图形是要寻找对称中心,图形旋转180度后与原图形重合.

3.2020623日,中国第55颗北斗导航卫星成功发射,顺利完成全球组网.其中支持北斗三号新信号的22纳米工艺射频基带一体化导航定位芯片,已实现规模化应用,22纳米=0.000000022米,将0.000000022用科学记数法表示为(

A. 22×108 B. 2.2×10-8 C. 0.22×10-7 D. 22×10-9

【答案】B

【解析】

【分析】

科学记数法的形式是: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 10 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 取决于原数小数点的移动位数与移动方向, <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 是小数点的移动位数,往左移动, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为正整数,往右移动, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为负整数。本题小数点往右移动到 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的后面,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【详解】解:0.000000022 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

故选 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【点睛】本题考查 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 知识点是用科学记数法表示绝对值较小的数,关键是在理解科学记数法的基础上确定好 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的值,同时掌握小数点移动对一个数的影响.

4.如图所示的几何体,其俯视图是(

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【答案】A

【解析】

【分析】

根据俯视图的定义即可求解.

【详解】由图形可知,这个几何体的俯视图为

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

故选A

【点睛】此题主要考查俯视图的判断,解题的关键是熟知俯视图的定义.

5.如图,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 先向上平移1个单位,再绕点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 按逆时针方向旋转 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,则点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的对应点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的坐标是(

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

A. 04 B. 2-2 C. 3-2 D. -14

【答案】D

【解析】

【分析】

根据平移的规律找到A点平移后对应点,然后根据旋转的规律找到旋转后对应点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,即可得出 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的坐标.

【详解】解:如图所示:A的坐标为(42),向上平移1个单位后为(43),再绕点P逆时针旋转90°后对应 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 点的坐标为(-14).
故选: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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【点睛】本题考查了根据平移变换和旋转变换作图,熟练掌握平移的规律和旋转的规律是解题的关键.

6.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的直径,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【答案】B

【解析】

【分析】

先根据圆周角定理得到∠ <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,再根据等弧所对的弦相等,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,最后根据同弧所对的圆周角等于圆心角的一半,得到∠CAD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,∠BAG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,即可求解.

【详解】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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的直径

∴∠ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

故选:B

【点睛】此题主要考查圆周角定理和弧、弦及圆周角之间的关系,熟练掌握圆周角定理和三者之间的关系是解题关键.

7.如图,将矩形 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 折叠,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 重合,折痕为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的长为(

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【答案】C

【解析】

【分析】

先证明 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 再求解 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 利用轴对称可得答案.

【详解】解:由对折可得: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> BC=8

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

由对折得: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

故选C

【点睛】本题考查的是矩形的性质,等腰三角形的判定,勾股定理的应用,轴对称的性质,掌握以上知识是解题的关键.

8.已知在同一直角坐标系中二次函数 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 和反比例函数 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的图象如图所示,则一次函数 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的图象可能是(

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【答案】B

【解析】

【分析】

根据反比例函数图象和二次函数图象位置可得出:a﹤0b﹥0c﹥0,由此可得出 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 0,一次函数图象与y轴的交点在y轴的负半轴,对照四个选项即可解答.

【详解】由二次函数图象可知:a﹤0,对称轴 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 0

a﹤0b﹥0

由反比例函数图象知:c﹥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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 0,一次函数图象与y轴的交点在y轴的负半轴,

对照四个选项,只有B选项符合一次函数 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的图象特征.

故选:

【点睛】本题考查反比例函数 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 图象、二次函数的图象、一次函数的图象,熟练掌握函数图象与系数之间的关系是解答的关键·

第Ⅱ卷(共96分)

二、填空题(本大题共6小题,每小题3分,共18分)

9.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的结果是___

【答案】4

【解析】

【分析】

根据二次根式的混合运算计算即可.

【详解】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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> .

故答案为4.

【点睛】本题考查二次根式的混合运算,熟练掌握运算顺序和运算法则是解题关键.

10.某公司要招聘一名职员,根据实际需要,从学历、经验和工作态度三个方面对甲、乙两名应聘者进行了测试.测试成绩如下表所示.如果将学历、经验和工作态度三项得分按2:1:3的比例确定两人的最终得分,并以此为依据确定录用者,那么__________将被录用(填甲或乙)

应聘者

项目

学历

9

8

经验

7

6

工作态度

5

7




【答案】

【解析】

【分析】

直接根据加权平均数比较即可.

【详解】解:甲得分: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

乙得分: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

故答案为:乙.

【点睛】此题主要考查加权平均数,正确理解加权平均数的概念是解题关键.

11.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 是反比例函数 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 图象上的一点, <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 垂直于 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 轴,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的面积为6.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 也在此函数的图象上,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【解析】

【分析】

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的面积可得 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的值,再把 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 代入解析式即可得到答案.

【详解】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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的面积为6

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

经检验: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 符合题意.

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【点睛】本题考查的是反比例函数的性质, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的几何意义,掌握以上知识是解题的关键.

12.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为常数)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 轴交点的个数是__________

【答案】2

【解析】

【分析】

求出∆的值,根据∆的值判断即可.

【详解】解:∵∆=4(k-1)2+8k=4k2+4>0

抛物线与 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 轴有2个交点.

故答案为:2

【点睛】本题考查了二次函数与坐标轴的交点问题,二次函数y=ax2+bx+cabc为常数,a≠0)的图象与x轴的交点横坐标是一元二次方程ax2+bx+c=0的根.当∆=0时,二次函数与x轴有一个交点,一元二次方程有两个相等的实数根;当∆>0时,二次函数与x轴有两个交点,一元二次方程有两个不相等的实数根;当∆<0时,二次函数与x轴没有交点,一元二次方程没有实数根.

13.如图,在正方形 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 中,对角线 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的延长线上,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,则点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的距离为__________

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【解析】

【分析】

先根据正方形的性质与中位线定理得到CD,FG的长,故可求出AEDF的长,再等面积法即可得到AH的长,故可求解.

【详解】如图,过点AAH⊥DF的延长线于点H

正方形ABCD中,对角线ACBD交于点O

OAC中点

F点是AE中点,

OF是△ACE的中位线,

CE=2OF=6

G点是AD的中点,

FG是△ADE的中位线,

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> =1

CD=CE-DE=4,

AD=CD=4

Rt△ADE中,AD=4,DE=2

AE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

DF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> AE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

S△AFD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> AD·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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> FD·AH

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ×4×1= <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ×AH

AH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

ADF的距离为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【点睛】此题主要考查正方形内的线段求解,解题的关键是熟知正方形的性质、中位线定理、勾股定理及三角形的面积公式.

14.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 边上的一点,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为圆心的半圆分别与 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 相切于点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的长为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,则图中阴影部分的面积为__________

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【解析】

【分析】

连接OMONOA,易证得∠MON=60º,即∠MOE+∠NOF=120º <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,再由弧长公式求得半径OM,然后证得Rt△AMO≌Rt△ANO,即∠AOM=30º,进而解得AM,则可得 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,代入相关数值即可解得阴影面积·

【详解】如图,连接OMONOA,设半圆分别交BC于点EF

OM⊥ABON⊥AC

∴∠AMO=∠ANO=90º

∵∠BAC=120º

∴∠MON=60º

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的长为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

OM=3

Rt△AMORt△ANO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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

Rt△AMO≌Rt△ANO(HL)

∴∠AOM=∠AON= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ∠MON=30º

AM=OM·tan30º= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

∵∠MON=60º

∴∠MOE+∠NOF=120º

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

图中阴影面积为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【点睛】本题考查了切线的性质定理、弧长公式、HL定理、锐角的三角函数定义、扇形面积的计算等知识,解答的关键是熟练掌握基本图形的性质,会根据图形和公式进行推理、计算.

三、作图题(本大题满分4分)

请用直尺、圆规作图,不写作法,但要保留作图痕迹

15.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ..

求作: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,使它经过点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,并且圆心 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的平分线上,

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【答案】见详解.

【解析】

【分析】

要作圆,即需要先确定其圆心,先作∠A的角平分线,再作线段BC的垂直平分线相交于点O,即O点为圆心.

【详解】解:根据题意可知,先作∠A的角平分线,

再作线段BC的垂直平分线相交于O

即以O点为圆心,OB为半径,作圆O

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【点睛】此题主要考查了学生对确定圆心的作法,要求学生熟练掌握应用.

四、解答题(本大题共9小题,共74分)

16.1)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 2)解不等式组: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ;(2x>3

【解析】

【分析】

1)先算括号里,再把除法转化为乘法,然后约分化简即可;

2)先分别解两个不等式,求出它们的解集,再求两个不等式解集的公共部分即可得到不等式组的解集.

【详解】解:(1)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

解①得,x≥-1

解②得,x>3

不等式组的解集是x>3

【点睛】本题考查了分式的混合运算,一元一次不等式组的解法,熟练掌握分式的运算法则是解(1)的关键,掌握解一元一次不等式组得步骤是解(2)的关键.

17.小颖和小亮都想去观看“垃圾分类”宣传演出,但只有一张入场券,于是他们设计了一个“配紫色”游戏: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 是两个可以自由转动的转盘,每个转盘都被分成面积相等的几个扇形、同时转动两个转盘,如果其中一个转盘转出了红色,另一个转盘转出了蓝色,那么可以配成紫色.若配成紫色,则小颖去观看,否则小亮去观看.这个游戏对双方公平吗?请说明理由.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【答案】这个游戏对双方公平,理由见解析

【解析】

【分析】

画出树状图,求出配成紫色的概率即可求解.

【详解】解:这个游戏对双方公平,理由如下:

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

由树状图可知,所有可能发生的组合有6种,能配成紫色的组合有3种,

P(紫色)= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

这个游戏对双方公平.

【点睛】本题考查的是游戏公平性的判断.判断游戏公平性就要计算每个事件的概率,概率相等就公平,否则就不公平.画出树状图,求出他们各自获胜的概率是解答本题的关键.

18.如图,在东西方向的海岸上有两个相距6海里的码头 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> .某海岛上的观测塔 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 距离海岸5海里,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 处测得 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 位于南偏西 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 方向.一艘渔船从 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 出发,沿正北方向航行至 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 处,此时在 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 处测得 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 位于南偏东 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 方向,求此时观测塔 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 与渔船 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 之间的距离(结果精确到0.1海里).

(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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【答案】4.3海里

【解析】

【分析】

过点AAE⊥BD,过点CCF⊥AE,由正切函数与正弦函数的定义,以及矩形的性质,即可求解.

【详解】过点AAE⊥BD,过点CCF⊥AE,则四边形CDEF是矩形,

∵∠BAE=22°AE=5(海里),

BE=AE∙tan22°=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> =2(海里),

DE=BD-BE=6-2=4(海里),

四边形CDEF是矩形,

CF=DE=4(海里),

AC=CF÷sin67°=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ≈4.3(海里).

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【点睛】本题主要考查解直角三角形的实际应用,熟练掌握锐角三角函数的定义,是解题的关键.

19.某校为调查学生对海洋科普知识的了解情况,从全校学生中随机抽取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 名学生进行测试,测试成绩进行整理后分成五组,并绘制成如下的频数直方图和扇形统计图.

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

请根据图中信息解答下列问题:

1)补全频数直方图;

2)在扇形统计图中,“70~80”这组的百分比 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> __________

3)已知“80~90”这组的数据如下:818384858586868687888889.抽取的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 名学生测试成绩的中位数是__________分;

4)若成绩达到80分以上(含80分)为优秀,请你估计全校1200名学生对海洋科普知识了解情况为优秀的学生人数.

【答案】1)见解析;(220%;(3845分;(4672

【解析】

【分析】

1)先求出样本容量,再用用本容量减去已知各部分的频数,即可求出“90~1000”这组的频数,从而补全频数直方图;

2)用“70~80”这组的频数除以样本容量即可;

3)根据中位数的定义求解即可;

4)用1200乘以80分以上人数所占的比例即可.

【详解】解:(18÷16=50人,

50-4-8-10-12=16人,

补全频数直方图如下:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

2m= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> =20%;

3)∵“50~80”分的人数已有22人,

2526名的成绩分别是是84分,85分,

中位数是 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 分;

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 人.

优秀人数是672人.

【点睛】此题主要考查了频数分布直方图、扇形统计图的综合和利用统计图获取信息的能力;利用统计图获取信息时,必须认真观察、分析、研究统计图,才能作出正确的判断和解决问题.也考查了利用样本估计总体.

20.为让更多的学生学会游泳,少年宫新建一个游泳池,其容积为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,该游泳池有甲、乙两个进水口,注水时每个进水口各自的注水速度保持不变,同时打开甲、乙两个进水口注水,游泳池的蓄水量 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 与注水时间 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 之间满足一次函数关系,其图象如图所示.

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

1)根据图象求游泳池的蓄水量 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 与注水时间 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 之间的函数关系式,并写出同时打开甲、乙两个进水口的注水速度;

2)现将游泳池的水全部排空,对池内消毒后再重新注水.已知单独打开甲进水口注满游泳池所用时间是单独打开乙进水口注满游泳池所用时间的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 倍.求单独打开甲进水口注满游泳池需多少小时?

【答案】1y=140t+100140m3/h;(28h

【解析】

【分析】

1)用待定系数法即可求出yt的函数关系式,然后求出注满水池用的时间,进而可求出同时打开甲、乙两个进水口的注水速度;

2)设甲的注水速度是x m3/h,则乙的注水速度是(140-x) m3/h,根据单独打开甲进水口注满游泳池所用时间是单独打开乙进水口注满游泳池所用时间的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 倍列方程求解即可.

【详解】解:(1)设y=kt+100,把(2380)代入得,

2k+100=380

解得

k=140

y=140t+100

y=480时,

480=140t+100

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

(480-100)÷ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> =140m3/h

y=140t+100,同时打开甲、乙两个进水口的注水速度是140m3/h

2)设甲的注水速度是x m3/h,则乙的注水速度是(140-x) m3/h,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

解得x=60

经检验x=60符合题意,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> (h)

单独打开甲进水口注满游泳池需8h

【点睛】本题考查了一次函数的应用,分式方程的应用,掌握待定系数法是解(1)的关键,找出数量关系列出方程是解(2)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 中,对角线 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 相交于点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 分别在 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的延长线上,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 时,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 什么特殊四边形?请说明理由.

【答案】1)见解析(2)菱形,见解析

【解析】

【分析】

1)利用SAS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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 即可求解;

2)先证明四边形 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 是平行四边形,再证明对角线互相垂直即可得到为菱形.

【详解】(1)∵四边形ABCD是平行四边形,

AD=BC,∠ADB=∠CBD

又∵∠ADB+∠ADE=180°,∠CBF+∠CBD=180°

∴∠ADE=∠CBF

在△ADE和△CBF

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

∴△ADE≌△CBF

2)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 是菱形

理由如下:

如图,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

由(1)得△ADE≌△CBF

CF=AE, ∠E=∠F

AE∥CF

AE <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> CF

四边形AFCE是平行四边形

BD平分∠ABC时,∠ABD=∠CBD

又∵AD∥CB

∴∠ADB=∠DBC

∴∠ABD=∠ABD

AD=AB=BC

∴△ABC为等腰三角形

由等腰三角形性质三线合一可得AC⊥EF

平行四边形AFCE是菱形

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【点睛】此题主要考查特殊平行四边形的性质与判定,解题的关键是熟知菱形的判定定理.

22.某公司生产 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房成本是每个425元.图①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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房的一面墙,它由长方形和抛物线构成,长方形的长 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,宽 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,抛物线的最高点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的距离为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

1)按如图①所示的直角坐标系,抛物线可以用 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 表示,求该抛物线的函数表达式;

2)现将 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房改造为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房.如图②,在抛物线与 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 之间的区域内加装一扇长方形窗户 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 上,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 在抛物线上,窗户的成本为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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,求每个 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房的成本是多少?(每个 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房的成本=每个 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房的成本+一扇窗户 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的成本)

3)根据市场调查,以单价650元销售(2)中的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房,每月能售出100个,而单价每降低10元,每月能多售出20个.公司每月最多能生产160 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房.不考虑其他因素,公司将销售单价 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> (元)定为多少时,每月销售 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 型活动板房所获利润 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> (元)最大?最大利润是多少?

【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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 25003n=620时,w最大=19200

【解析】

【分析】

1)根据图形及直角坐标系可得到D,E的坐标,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 即可求解;

2)根据N点与M点的横坐标相同,求出N点坐标,再求出矩形FGMN的面积,故可求解;

3)根据题意得到w关于n的二次函数,根据二次函数的性质即可求解.

【详解】(1)由题可知D2,0),E0,1

代入到 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

抛物线的函数表达式为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

2)由题意可知N点与M点的横坐标相同,把x=1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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,得y= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

N1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

MN= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> m

S四边形FGMN=GM×MN=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

则一扇窗户的价格为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ×50=75

因此每个B型活动板的成本为425+75=500元;

3)根据题意可得w=(n-500)100+20× <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> =-2n-6002+20000,

一个月最多生产160个,

100+20× <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ≤160

解得n≥620

-20

n≥620时,wn的增大而减小

n=620时,w最大=19200元.

【点睛】此题主要考查二次函数的综合运用,解题的关键是熟知待定系数法、二次函数的图像与性质.

23.实际问题:

某商场为鼓励消费,设计了投资活动.方案如下:根据不同的消费金额,每次抽奖时可以从100张面值分别为1元、2元、3元、…、100元的奖券中(面值为整数),一次任意抽取2张、3张、4张、…等若干张奖券,奖券的面值金额之和即为优惠金额.某顾客获得了一次抽取5张奖券的机会,小明想知道该顾客共有多少种不同的优惠金额?

问题建模:

123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数,这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数之和共有多少种不同的结果?

模型探究:

我们采取一般问题特殊化的策略,先从最简单的情形入手,再逐次递进,从中找出解决问题的方法.

探究一:

1)从1233个整数中任取2个整数,这2个整数之和共有多少种不同的结果?

表①

所取的2个整数

12

13

23

2个整数之和

3

4

5


如表①,所取的2个整数之和可以为345,也就是从35的连续整数,其中最小是3,最大是5,所以共有3种不同的结果.

2)从12344个整数中任取2个整数,这2个整数之和共有多少种不同的结果?

表②

所取的2个整数

12

13

14

23

24

34

2个整数之和

3

4

5

5

6

7


如表②,所取的2个整数之和可以为34567,也就是从37的连续整数,其中最小是3,最大是7,所以共有5种不同的结果.

3)从123455个整数中任取2个整数,这2个整数之和共有______种不同的结果.

4)从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取2个整数,这2个整数之和共有______种不同的结果.

探究二:

1)从12344个整数中任取3个整数,这3个整数之和共有______种不同的结果.

2)从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取3个整数,这3个整数之和共有______种不同的结果.

探究三:

123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取4个整数,这4个整数之和共有______种不同的结果.

归纳结论:

123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数,这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数之和共有______种不同的结果.

问题解决:

100张面值分别为1元、2元、3元、…、100元的奖券中(面值为整数),一次任意抽取5张奖券,共有______种不同的优惠金额.

拓展延伸:

1)从123,…,3636个整数中任取多少个整数,使得取出的这些整数之和共有204种不同的结果?(写出解答过程)

2)从345,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数,这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数之和共有______种不同的结果.

【答案】探究一:(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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ;(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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数);探究二:(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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ;探究三: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 归纳结论: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> );问题解决: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ;拓展延伸:(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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个或 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个;(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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【解析】

【分析】

探究一:

3)根据(1)(2)的提示列表,可得答案;

4)仔细观察(1)(2)(3)的结果,归纳出规律,从而可得答案;

探究二:

1)仿探究一的方法列表可得答案;

2)由前面的探究概括出规律即可得到答案;

探究三:

根据探究一,探究二,归纳出从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取4个整数的和的结果数,

再根据上面探究归纳出从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数,这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数之和的结果数;

问题解决:

利用前面的探究计算出这5张奖券和的最小值与最大值,从而可得答案;

拓展延伸:

1)直接利用前面的探究规律,列方程求解即可,

2)找到与问题等价的模型,直接利用规律得到答案.

【详解】解:探究一:

3)如下表:

取的2个整数

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

2个整数之和

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>


所取的2个整数之和可以为3456789也就是从39的连续整数,其中最小是3,最大是9,所以共有7种不同的结果.

4)从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取2个整数,这2个整数之和的最小值是3,和的最大值是 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 所以一共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种.

探究二:

1)从12344个整数中任取3个整数,如下表:

取的3个整数

1,2,3

1,2,4

1,3,4

2,3,4

3个整数之和

6

7

8

9


12344个整数中任取3个整数,这3个整数之和共有4种,

2)从123455个整数中任取3个整数,

3个整数之和的最小值是6,和的最大值是12,

所以从123455个整数中任取3个整数,这3个整数之和共有7种,

从而从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取3个整数,

3个整数之和的最小值是6,和的最大值是 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

所以一共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种,

探究三:

123455个整数中任取4个整数, 4个整数之和最小是 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 最大是 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

所以这4个整数之和一共有5种,

1234566个整数中任取4个整数, 4个整数之和最小是 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 最大是 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

所以这4个整数之和一共有9种,

123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取4个整数,

4个整数之和的最小值是10,和的最大值是 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

所以一共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种不同的结果.

归纳结论:

由探究一,从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取2个整数,这2个整数之和共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种.

探究二,从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取3个整数,这3个整数之和共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种,

探究三,从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取4个整数,这4个整数之和共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种不同的结果.

从而可得:

123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数,这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数之和共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种不同的结果.

问题解决:

100张面值分别为1元、2元、3元、…、100元的奖券中(面值为整数),

一次任意抽取5张奖券,这5张奖券和的最小值是15,和的最大值是490

共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种不同的优惠金额.

拓展延伸:

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数,这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数之和共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种不同的结果.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

123,…,3636个整数中任取29个或7个整数,使得取出的这些整数之和共有204种不同的结果.

2)由探究可知:从345,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数,等同于从123,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数,

所以:从345,…, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为整数,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> )这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数中任取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数,这 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 个整数之和共有 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 种不同的结果.

【点睛】本题考查的是学生自主探究,自主归纳的能力,同时考查了一元二次方程的解法,掌握自主探究的方法是解题的关键.

24.已知:如图,在四边形 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,延长 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 出发,沿 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 方向匀速运动,速度为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ;同时,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 出发,沿 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 方向匀速运动,速度为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> .设运动时间为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

解答下列问题:

1)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为何值时,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的垂直平分线上?

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为矩形时,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的值;

3)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,设四边形 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的函数关系式;

4)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 在运动过程中,是否存在某一时刻 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的平分线上?若存在,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的值;若不存在,请说明理由.

【答案】1 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ;(2t=3;3St的函数关系式为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ;(4)存在,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,

【解析】

【分析】

1)要使点M在线段CQ的垂直平分线上,只需证CM=MQ即可;

2)由矩形性质得PH=QN,由已知和AP=2tMQ=t,解直角三角形推导出PHQN,进而得关于t的方程,解之即可;

3)分别用t表示出梯形GHFM的面积、△QHF的面积、△CMQ的面积,即可得到St的函数关系式;

4)延长ACEFT,证得AT⊥EF,要使点P在∠AFE的平分线上,只需PT=PH,分别用t表示PTPH,代入得关于t的方程,解之即可.

【详解】(1)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的垂直平分线上,理由为:

由题意,CE=2CM∥BF

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

解得:CM= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

要使点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的垂直平分线上,

只需QM=CM= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

2)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

AC=10EF=10sin∠PAH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> cos∠PAH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> sin∠EFB= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

Rt△APH中,AP=2t

PH=AP·sin∠PAH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

Rt△ECM中,CE=2,CM= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,由勾股定理得:EM= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

Rt△QNF中,QF=10-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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

QN=QF·sin∠EFB=( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 为矩形,

PH=QN

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

解得:t=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

3)如图,过QQN⊥AFN

由(2)中知QN= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> AH=AP·cos∠PAH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

BH=GC=8- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

GM=GC+CM= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> HF=HB+BF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

St的函数关系式为: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

4)存在,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

证明:如图,延长ACEFT

AB=BF <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> BC=BF,  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

∴△ABC≌△EBF

∴∠BAC=∠BEF

∵∠EFB+∠BEF=90º

∴∠BAC+∠EFB=90º

∴∠ATE=90ºPT⊥EF

要使点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> 的平分线上,只需PH=PT

Rt△ECM中,CE=2,sin∠BEF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

CT=CE·sin∠BEF = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

PT=10+ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> ,又PH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a>

【点睛】本题属于四边形的综合题,考查了解直角三角形、锐角三角函数、垂直平分线、角平分线、矩形的性质、全等三角形的判定与性质、多边形的面积等知识、解答的关键是认真审题,分析相关知识,利用参数构建方程解决问题,是中考常考题型.