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【330366】2020年四川省自贡市中考试卷

时间:2025-02-09 11:10:45 作者: 字数:26267字

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 2020年自贡中考数学

满分:150 时间:120分钟

.选择题(共12个小题,每小题4分,共48分;在每题给出的四个选项中,只有一项是符合题目要求的)

1.如图, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的度数为

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

A. 40° B. 50° C. 55° D. 60°

【答案】B

【解析】

【分析】

利用平行线的性质与对顶角相等即可求出.

【详解】两平行线同位角相等,再根据对顶角相等即可得到答案.

故答案为B

【点晴】本题主要考查了平行线的性质与对顶角的性质,熟练掌握平行线的性质是解题关键.

2.522日晚,中国自贡第26届国际恐龙灯会开始网络直播,有着近千年历史自贡灯会进入“云游”时代,70余万人通过“云观灯”感受“天下第一灯”的璀璨,人数700000用科学记数法表示为(

A.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> B.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> C.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> D.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】C

【解析】

【分析】

根据科学记数法规定 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,要求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,即可得解.

【详解】由题意,得

700000= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

故选:C.

【点睛】此题主要考查科学记数法的应用,熟练掌握,即可解题.

3.如图所示的几何体的左视图是(

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

A.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> B.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> C.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> D.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】C

【解析】

【分析】

找到从几何体左面看得到的平面图形即可.

【详解】解:从几何体左面看得到两列正方形的个数分别为13
故选:C

【点睛】考查三视图的相关知识;掌握左视图是从几何体左面看得到的平面图形是解决本题的关键.

4.关于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的一元二次方程 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 有两个相等的实数根,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的值为(

A.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> B.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> C.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> D.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】A

【解析】

【分析】

由题意,根据一元二次方程根的判别式值为零,求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 可解.

【详解】解:由一元二次方程有两个相等实根可得,判别式等于0可得, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

故应选A

【点睛】本题考查了一元二次方程根的情况与判别式△的关系,解答时注意△=0⇔方程有两个相等的实数根.

5.在平面直角坐标系中,将点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 向下平移3个单位长度,所得点的坐标是(

A.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> B.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> C.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> D.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】D

【解析】

【分析】

根据点的平移规律为上加下减,左减右加即可求解.

【详解】解:点的平移规律为上加下减,左减右加,可得横坐标不变,纵坐标减31-3=-2

故答案为D

【点睛】本题考查点的坐标平移规律,根据“上加下减,左减右加”即可求解.

6.下列图形中,是轴对称图形,但不是中心对称图形的是(

A.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> B.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> C.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> D.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】A

【解析】

【分析】

根据轴对称图形与中心对称图形的概念对各图形分析判断后利用排除法求解.

【详解】解:A、图形不是中心对称轴图形,是轴对称图形,此选项正确;
B、图形是中心对称轴图形,不是轴对称图形,此选项错误;
C、图形是中心对称轴图形,也是轴对称图形,此选项错误;
D、图形不是中心对称轴图形,也不是轴对称图形,此选项错误;
故选:A

【点睛】本题考查了中心对称图形与轴对称图形的概念:轴对称图形的关键是寻找对称轴,图形两部分沿对称轴折叠后可重合;中心对称图形是要寻找对称中心,旋转180度后与原图重合.

7.对于一组数据 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,下列说法正确的是(

A. 中位数是5 B. 众数是7 C. 平均数是4 D. 方差是3

【答案】C

【解析】

【分析】

分别计算该组数据的众数、平均数、中位数及方差后,选择正确的答案即可.

【详解】将数据按从小到大排列为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,平均值 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,众数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 3,中位数为3,方差为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

故选:C

【点睛】本题是一道有关统计的综合题,具体考查了平均数、众数、中位数及方差的知识,解题时分别计算出众数、中位数、平均数及方差后找到正确的选项即可.

8.如果一个角的度数比它的补角的度数2倍多30°,那么这个角的度数是(

A <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 50° B. 70° C. 130° D. 160°

【答案】C

【解析】

【分析】

根据互为补角的定义结合已知条件列方程求解即可.

【详解】解:设这个角是 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,则它的补角是: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

根据题意,得:

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

解得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

即这个角的度数为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

故选:C

【点睛】此题考查了补角的知识,熟悉相关性质定义是解题的关键.

9.如图,在 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 中, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,以点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 为圆心, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 长为半径画弧,交 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ; <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的度数为

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

A. 50° B. 40° C. 30° D. 20°

【答案】D

【解析】

【分析】

由作图过程可知BC=BD,根据等边对等角得到∠BCD=∠BDC=70°,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的度数即可求解.

【详解】∵∠A=50°,可得∠B=40°

∵BC=BD

∴∠BCD=∠BDC

∵∠B+∠BCD+∠BDC=180°

∴∠BCD=70°

∴∠ACD=90°-70°=20°

故选:D

【点睛】本题考查了等腰三角形的性质等内容,解题的关键是通过题目描述,得到BC=BD

10.函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的图象如图所示,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的大致图象为

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

A.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> B.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> C.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> D.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】D

【解析】

【分析】

根据反比例函数过一、三象限可确定出k的符号,根据二次函数图像的对称轴可以确定出a,b的符号,进而求解.

【详解】解:∵反比函数过一三象限,∴ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

由二次函数开口向下可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

又二次函数的对称轴 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,∴ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 同号,∴ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

一次函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 经过第一、二、三象限,

故答案为D

【点睛】本题考查了一次函数和二次函数图象 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 知识,解题的关键是掌握一次和二次函数的图象性质,此类题属于中考常考题型.

11.某工程队承接了80万平方米的荒山绿化任务,为了迎接雨季的到来,实际工作时每天的工作效率比原计划提高了35%,结果提前40天完成了这一任务;设实际工作时每天绿化的面积为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 万平方米,则下面所列方程中正确的是(

A.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> B.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

C.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> D.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】A

【解析】

【分析】

根据题意分别表示实际工作和原计划工作所用的时间,再以时间为等量构造方程即可;

【详解】解:由题意可得原计划的工作效率为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,所以原计划的工作时间为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,实际的工作时间为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,所以原计划的时间减去实际的时间为40天,则可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

故选:A

【点睛】本题考查了由实际问题列出分式方程,解题关键是找准等量关系,正确列出分式方程.

12.如图,在平行四边形 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 中, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 是锐角, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的中点,连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ;若 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的长为(

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

A.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> B.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> C.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> D.  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】B

【解析】

【分析】

延长EFDA交于G,连接DE,先证明△AFG≌△BFE,进而得到BE=AGFGE的中点,结合条件BF⊥GE进而得到BF是线段GE的垂直平分线,得到GD=DE,最后在Rt△AED中使用勾股定理即可求解.

【详解】解:延长EFDA交于G,连接DE,如下图所示:

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∵FAB的中点,∴AF=BF

四边形ABCD是平行四边形,

∴AB∥BC,∴∠GAB=∠EBF

且∠GFA=∠EFB,∴△AFG≌△BFE(ASA)

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

GF=EF,且∠DFE=90°知,

DF是线段GE的垂直平分线,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

Rt△GAE中, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

Rt△AED中, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,解得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

故选:B

【点睛】本题考查了三角形全等的判定与性质、平行四边形的性质、勾股定理等知识点,能正确作出辅助线是解题的关键.

第Ⅱ卷 非选择题 (共102分)

注意事项:必须使用0.5毫米黑色墨水铅签字笔在答题卡上题目所指示区域内作答,作图题可先用铅笔绘出,确认后用0.5毫米黑色墨水铅签字笔描清楚,答在试题卷上无效.

.填空题(6个小题,每题4分,共24)

13.分解因式: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> =

【答案】 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【解析】

试题分析:要将一个多项式分解因式的一般步骤是首先看各项有没有公因式,若有公因式,则把它提取出来,之后再观察是否是完全平方公式或平方差公式,若是就考虑用公式法继续分解因式.因此,

先提取公因式3后继续应用完全平方公式分解即可: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

考点:提公因式法和应用公式法因式分解.

14. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 最接近的自然数是 ________

【答案】2

【解析】

【分析】

先根据 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 得到 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,进而得到 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,因为14更接近16,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 最接近的自然数是2

【详解】解: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∵14接近16

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 更靠近4

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 最接近的自然数是2

故答案为:2

【点睛】本题考查无理数的估算,找到无理数相邻的两个整数是解题的关键.

15.某中学新建食堂正式投入使用,为提高服务质量,食堂管理人员对学生进行了“最受欢迎菜品”的调查统计,以下是打乱了的调查统计顺序,请按正确顺序重新排序 (只填番号)_________________

①.绘制扇形图;②.收集最受学生欢迎菜品的数据;③.利用扇形图分析出受欢迎的统计图;④.整理所收集的数据.

【答案】②④①③

【解析】

【分析】

根据统计的一般顺序排列即可.

【详解】统计的一般步骤,一般要经过收集数据,整理数据,绘制统计图表,分析图表得出结论,

故答案为:②④①③.

【点睛】本题考查统计的一般步骤,一般要经过收集数据,整理数据,绘制统计图表,分析图表得出结论.

16.如图,我市在建高铁的某段路基横断面为梯形 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 长为6米,坡角 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 45° <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的坡角 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 30°,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的长为 ________ (结果保留根号)

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【解析】

【分析】

CCE⊥ABEDF⊥ABF,分别在Rt△CEBRt△DFA中使用三角函数即可求解.

【详解】解:过CCE⊥ABEDF⊥ABF,可得矩形CEFDRt△CEBRt△DFA

∵BC=6

∴CE= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴DF=CE= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

故答案为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【点睛】此题考查了解直角三角形的应用-坡度坡角问题,难度适中,解答本题的关键是构造直角三角形和矩形,注意理解坡度与坡角的定义.

17.如图,在矩形 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 中, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 上的一点,连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 进行翻折,恰好使点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 落在 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的中点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 处,在 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 上取一点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,以点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 为圆心, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的长为半径作半圆与 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 相切于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ; <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,则图中阴影部分的面积为 ____

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> .

【解析】

【分析】

连接OG,证明△DOG∽△DFC,得出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,设OG=OF=r,进而求出圆的半径,再证明△OFQ为等边三角形,则可由扇形的面积公式和三角形的面积公式求出答案.

【详解】解:连接OG,过O点作OH⊥BCH点,设圆OBC交于Q点,如下图所示:

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

设圆的半径为r

∵CD是圆的切线,

∴OG⊥CD

∴△DOG∽△DFC

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,由翻折前后对应的线段相等可得DF=DA=4

∵FBC的中点,∴CF=BF=2,代入数据:

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴∠ODG=30°,∴∠DFC=60°

OF=OQ,∴△OFQ是等边三角形,

∴∠DOQ=180°-60°=120°

同理△OGQ也为等边三角形,

∴OH= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,且S扇形OGQ=S扇形OQF

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> .

故答案为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> .

【点睛】本题考查了扇形面积的计算,切线的性质,翻折变换,熟练掌握基本图形的性质是解题的关键.

18.如图, 直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴交于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,与双曲线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 在第三象限交于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 两点,且  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ;下列等边三角形 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,……的边 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,……在 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴上,顶点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ……在该双曲线第一象限的分支上,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> = ____,前25个等边三角形的周长之和为 _______

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】 (1).  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> (2). 60

【解析】

【分析】

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 设直线与 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴的交点为H,先求解 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的坐标,得到∠HAO=30°,用含 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的代数式表示 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,联立函数解析式利用根与系数的关系得到关于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的方程,从而可得第一空的答案;过 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 分别向 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴作垂线,垂足分别为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 先根据等边三角形的性质与反比例函数的性质求解 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的边长,依次同法可得后面等边三角形的边长,发现规律,再前25个等边三角形的周长之和即可.

【详解】解:设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 设直线与 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴的交点为H

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴H <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ),又A0b),

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴tan∠HAO= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,∴∠HAO=30°

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴AB=2BMAC=2CN,∵BM= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴AB= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> AC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

联立 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

得到 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,由已知可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

反比例函数的解析式为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 分别向 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴作垂线,垂足分别为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

由等边三角形的性质得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> (舍去)

经检验: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 符合题意,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的边长为4

同理设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

解得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> (舍去)

经检验: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 符合题意,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的边长为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

同理可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的边长为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的边长为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

25个等边三角形的周长之和为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>


故答案为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【点睛】本题考查的是反比例函数的性质,考查一元二次方程的根与系数的关系,等边三角形的性质的应用,锐角三角函数的应用,同时考查与反比例函数相关的规律题,掌握以上知识是解题的关键.

.解答题(8个题,共78)

19.计算: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【解析】

【分析】

根据实数的绝对值、零指数幂和负指数幂的知识进行计算即可.

【详解】解:原式= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【点睛】本题考查了实数的绝对值、零指数幂、和负指数幂的性质,解答关键是根据相关运算法则进行计算.

20.先化简,再求值: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,其中 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 为不等式组 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的整数解.

【答案】 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【解析】

【分析】

根据分式的运算法则化简式子,再解不等式组得到不等式组的整数解,代入即可.

【详解】解: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

解不等式组可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,即 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 为整数,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,代入 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【点睛】本题考查分式的化简求值、不等式组的整数解,解题的关键是取值时,注意分式的分母不能为0

21.如图,在正方形 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 中,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 边的延长线上,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 边的延长线上,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 相交于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

求证: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】证明见解析.

【解析】

【分析】

利用正方形的性质证明:AB=BC=CD,∠ABE=∠BCF=90°,再证明BE=CF,可得三角形的全等,利用全等三角形的性质可得答案.

【详解】证明:∵四边形ABCD为正方形,

∴AB=BC=CD,∠ABE=∠BCF=90°

又∵CE=DF

∴CE+BC=DF+CDBE=CF

在△BCF和△ABE中,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> SAS),

∴AE=BF

【点睛】本题考查的是正方形的性质,三角形全等的判定与性质,掌握以上知识是解题的关键.

22.某校为了响应市政府号召,在“创文创卫”活动周中,设置了“ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> :文明礼仪; <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> :环境保护; <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ;卫生保洁; <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> :垃圾分类 ”四个主题,每个学生选一个主题参与;为了解活动开展情况,学校随机抽取了部分学生进行调查,并根据调查结果绘制了如下条形统计图和扇形统计图.

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

⑴.本次调查的学生人数是 人, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> =

⑵.请补全条形统计图;

⑶.学校要求每位同学从星期一至星期五选择两天参加活动,如果小张同学随机选择连续两天,其中有一天是星期一的概率是 ;小李同学星期五要参加市演讲比赛,他在其余四天中随机选择两天,其中一天是星期三的概率是

【答案】16030;(2)画图见解析;(3 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【解析】

【分析】

(1)B的人数是12人,所占的百分比为20%即可求出总的学生人数,再用18除以总人数即可得到m的值;

(2)总人数减去ABD的人数即可得到C的人数;

(3)采用列举的形式,将所有可能的情况按照从星期一到星期五的顺序列出来,然后再用符合题意要求的情况除以总的情况即可得到概率.

【详解】(1 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

本次调查的学生人数为60人, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,故m=30

故答案为:60m=30.

2C的人数为:60-18-12-9=21(),补全图形如下所示:

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

3)星期一到星期五连续的两天为(星期一、星期二),(星期二、星期三),(星期三、星期四),(星期四、星期五)共4种情况,

符合题意的只有(星期一、星期二)这一种情况,故概率为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

在星期一到星期四任选两天的所有情况如下:(星期一、星期二),(星期一、星期三),(星期一、星期四),(星期二、星期三)、(星期二、星期四),(星期三、星期四)共6种情况,

其中有一天是星期三的情况有:(星期一、星期三),(星期二、星期三),(星期三、星期四)共3种情况,所以概率是 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> .

故答案为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> .

【点睛】本题考查了列表法、扇形统计图、条形统计图以及概率公式:通过列表法或树状图法展示所有等可能的结果求出n,再从中选出符合事件AB的结果数目m,然后根据概率公式求出事件AB的概率.

23.甲、乙两家商场平时以同样价格出售相同 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 商品,新冠疫情期间,为了减少库存,甲、乙两家商场打折促销,甲商场所有商品按9折出售,乙商场对一次购物中超过100元后的价格部分打8折.

⑴. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> (单位:元)表示商品原价, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> (单位:元)表示实际购物金额,分别就两家商场的让利方式写出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 关于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的函数关系式;

⑵.新冠疫情期间如何选择这两家商场去购物更省钱?

【答案】1 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ;(2)当购买商品原价金额小于200时,选择甲商场更划算;当购买商品原价金额等于200时,选择甲商场和乙商场购物一样划算;当购买商品原价金额大于200时,选择乙商场更划算.

【解析】

【分析】

1)根据题意,可以分别写出两家商场对应的 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 关于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的函数解析式;

2)根据(1)中函数关系式,可以得到相应的不等式,从而可以得到新冠疫情期间如何选择这两家商场去购物更省钱.

【详解】解:(1)由题意可得,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 时, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 时, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

由上可得, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

2)由题意可知,当购买商品原价小于等于100时,甲商场打9折,乙商场不打折,所以甲商场购物更加划算;

当购买商品原价超过100元时,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,即 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 此时甲商场花费更低,购物选择甲商场;

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,即 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,此时甲乙商场购物花费一样;

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,即 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 时,此时乙商场花费更低,购物选择乙商场;

综上所述:当购买商品原价金额小于200时,选择甲商场更划算;当购买商品原价金额等于200时,选择甲商场和乙商场购物一样划算;当购买商品原价金额大于200时,选择乙商场更划算.

【点睛】本题考查一次函数的应用、一元一次不等式的应用,解答本题的关键是明确题意,利用一次函数的性质和不等式的性质解答.

24.我国著名数学家华罗庚说过“数缺形时少直观,形少数时难入微”;数形结合是解决数学问题的重要思想方法.例如,代数式 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的几何意义是数轴上 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 所对应的点与2所对应的点之间的距离;因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的几何意义就是数轴上 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 所对应的点与 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 所对应的点之间的距离.

⑴. 发现问题:代数式 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的最小值是多少?

⑵. 探究问题:如图,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 分别表示的是 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的几何意义是线段 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的长度之和

当点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 在线段 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 上时, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ;当点点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 在点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的左侧或点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的右侧时  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 最小值是3

⑶.解决问题:

①. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的最小值是

②.利用上述思想方法解不等式: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

③. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 为何值时,代数式 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的最小值是2

【答案】6;② <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ;③ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【解析】

【分析】

(3)①根据绝对值的几何意义可知,变成数轴上的点到-2的距离和到4的距离之和的最小值;

根据题意画出相应的图形,确定出所求不等式的解集即可;

根据原式的最小值为2,得到3左边和右边,且到3距离为2的点即可.

【详解】解:(3)①A表示的数为4B表示的数为-2P表示的数为x

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 表示数轴上的点P4的距离,用线段PA表示,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 表示数轴上的点P-2的距离,用线段PB表示,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的几何意义表示为PA+PB,当P在线段AB上时取得最小值为AB

且线段AB的长度为6

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的最小值为6.

故答案为:6.

A表示-3B表示1P表示x

线段AB的长度为4,则,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的几何意义表示为PA+PB

不等式的几何意义是PA+PBAB

∴P不能在线段AB上,应该在A的左侧或者B的右侧,

即不等式的解集为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

故答案为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

A表示-aB表示3P表示x

则线段AB的长度为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的几何意义表示为PA+PB,当P在线段AB上时PA+PB取得最小值,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

故答案为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> .

【点睛】此题考查了解一元一次不等式,数轴,绝对值,以及数学常识,掌握绝对值的几何意义,学会分类讨论是解决本题的关键.

25.如图,⊙ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的外接圆, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 为直径,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 是⊙ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 外一点,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,延长 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 交⊙ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

⑴.证明: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> = <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

⑵. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,证明: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 是⊙ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的切线;

⑶.在⑵的条件下,连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 交⊙ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ; <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的长.

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】1)证明过程见解析;(2)证明过程见解析;(3 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【解析】

【分析】

1)连接CO,易证△PCO≌△PAO,得PO为∠APC的角平分线,根据条件证出F为优弧 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 中点,即可证明 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> = <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

2)因为AB是直径,所以∠ACB=90°,由tan∠ABC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 可求得∠ABC的正弦和余弦,设⊙O的半径为r,则AB=2r,根据三角函数表示出BCAC的长度,由勾股定理表示出OD的长度,易得PA=PC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> PO=PD+OD=3r,由 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 可得PA⊥OA,即可证明 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 是⊙ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的切线;

3)连接AE,过EEN⊥PDN,过BBH⊥PFH,由(2)可得, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> PB= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,证出△PEA∽△PAB,可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,证出四边形BCDH是矩形,得BH=CD= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,在Rt△BPHRt△PEN中表示出sin∠BPH,可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ND=PD-PN= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,在Rt△NED中,DE= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,代入r=3即可

【详解】解:(1)证明:如图,连接CO

在△PCO和△PAO中,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴△PCO≌△PAOSSS),

∴∠CPO=∠APO,即PO为∠APC的角平分线,

∵PA=PC

∴CD=ADPF⊥AC

∵AC为⊙O的弦,PF过圆心O

∴F为优弧 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 中点,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> = <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

2)证明:∵AB是⊙O的直径,且弦AB所对圆周角为∠ACB

∴∠ACB=90°

∵tan∠ABC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴sin∠ABC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> cos∠ABC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

设⊙O的半径为r,则AB=2r

∴BC=ABcos∠ABC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> AC=ABsin∠ABC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∵PA=PC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> AB

∴PA=PC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴PO=PD+OD=3r

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,即PA⊥OA

又∵OA是⊙O半径,

∴PA是⊙O的切线;

3)由(2)可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

Rt△PBA中, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,连接AE,可得∠AEB=90°

∴∠PEA=∠PAB=90°,又∠APE=∠APB

∴△PEA∽△PAB

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

EEN⊥PDN,过BBH⊥PFH,如图所示,

∴∠BCD=∠CDF=∠BHD=90°

四边形BCDH是矩形,

∴BH=CD= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

Rt△BPH中,sin∠BPH= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

Rt△PEN中,sin∠BPH= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,∴ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴ND=PD-PN= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

Rt△NED中,DE= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴DE= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【点睛】此题考查了圆的综合应用,用到的知识点是矩形的判定、相似三角形的判定与性质、勾股定理以及解直角三角形等知识,此题综合性很强,难度较大,注意数形结合思想应用.

26.在平面直角坐标系中,抛物线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴相交于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,交 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 抛物线的顶点,对称轴与 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴交于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

⑴.求抛物线的解析式;

⑵.如图1,连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 是线段 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 上方抛物线上的一动点, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ;过点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 于点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> . <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴上一动点,当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 取最大值时.

①. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的最小值;

②.如图2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 点是 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴上一动点,请直接写出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的最小值.

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【答案】1 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ;(2)① <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ;② <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【解析】

【分析】

1)直接利用待定系数法,把A,B两点代入解析式即可求出.

2)利用配方法求出M点,求出直线AM的解析式,从而可以得出经过点E且与直线AM平行的直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 解析式,再根据当直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 与抛物线只有一个交点时,EF取最大值,利用根的判别式可求出E点和D点的坐标,再根据当P,B,D三点共线时,PD+PC有最小值,利用勾股定理即可求出.

3)利用添加辅助线,对线段OQ进行转化,再根据三点共线求出最小值.

【详解】1)将A-3,0)、B1,0)代入二次函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 得,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 解之得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,∴二次函数的解析式为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

2)①将二次函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 配方得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴M-1,4

设直线AM的解析式为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,将 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 代入直线可得,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 解得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

直线AM的解析式为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

E作直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,平行于直线AM,且解析式为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∵E在直线AM上方的抛物线上,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

当直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> AM距离最大时,EF取得最大值,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 与抛物线只有一个交点时,EF取得最大值,

将直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的解析式代入抛物线得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

由题意可得,△= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,经计算得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,将 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 代入二次方程可得,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,即E点的横坐标为-2,将 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 代入抛物线得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

又∵ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,将 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 代入直线AM

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∴BC两点关于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴对称,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,当PBD三点不共线时 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

PBD三点共线时, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

PBD三点共线时PC+PD取得最小值,

Rt△BHD中。DH=2BH=3,∴BD= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的最小值为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

Q作直线平行于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴,并在 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴右侧该直线上取一点G,使得,

QG= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> ,当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 三点共线时,

DQ+QG取得最小值,设Q0y),则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

∵QG∥ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 轴,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a> 的最小值为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1083/" title="自贡" class="c1" target="_blank">自贡</a>

【点晴】本题主要考查了二次函数综合应用,利用待定系数求解析式,根的判别式求点的坐标,利用三点共线求最值的问题.