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【330356】2020年四川省甘孜市中考试卷

时间:2025-02-09 11:06:26 作者: 字数:23247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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 四川省甘孜州2020年中考数学试题

一、选择题(本大题共10个小题,每小题3分,共30分,每小题均有四个选项,其中只有一项符合题目要求)

1.气温由-5℃上升了4℃时的气温是(

A. 1℃ B. 1℃ C. 9℃ D. 9℃

【答案】A

【解析】

【分析】

根据题意列出算式,计算即可.

【详解】解:根据题意,得-5+4=-1
则气温由-5℃上升了4℃时的气温是-1℃
故选:A

【点睛】此题考查了有理数的加法,熟练掌握运算法则是解本题的关键.

2.如图摆放的下列几何体中,左视图是圆的是(

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】C

【解析】

【分析】

分别找到四个立体图形的左视图即可,左视图是从左面看所得到的平面图形.

【详解】解:A、正方体的左视图是正方形,不符合题意;
B、圆柱的左视图是矩形,不符合题意;
C、球的三视图都是圆,符合题意;
D、圆锥的左视图是等腰三角形,不符合题意;
故选:C

【点睛】此题主要考查了简单几何体的三视图,关键是掌握左视图所看的位置.

3.月球与地球之间的平均距离约为38.4万公里,38.4万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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】B

【解析】

【分析】

用科学记数法表示较大的数时,一般形式为 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 为整数,据此判断即可.

【详解】解:38.4 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

故选: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【点睛】本题考查了用科学记数法表示较大的数,科学记数法的表示形式为 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,确定 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的值是解题的关键.确定n的值时,要看把原数变成a时,小数点移动了多少位,n的绝对值与小数点移动的位数相同.当原数绝对值>1时,n是正数;当原数的绝对值<1时,n是负数.

4.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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中,自变量 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的取值范围是(

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】C

【解析】

【分析】

根据分母不等于0列式计算即可得解.

【详解】解:由题意,得x+3≠0
解得x≠-3
故选:C

【点睛】本题考查了函数自变量的范围,一般从三个方面考虑:
1)当函数表达式是整式时,自变量可取全体实数;
2)当函数表达式是分式时,考虑分式的分母不能为0
3)当函数表达式是二次根式时,被开方数非负.

5.在平面直角坐标系中,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 轴对称的点是(

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】A

【解析】

【分析】

根据“关于x轴对称的点,横坐标相同,纵坐标互为相反数'解答即可.

【详解】解: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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 轴对称的点的坐标是 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

故选:A

【点睛】本题考查了关于x轴、y轴对称的点的坐标,解决本题的关键是掌握对称点的坐标规律:

(1)关于x轴对称的点,横坐标相同,纵坐标互为相反数;

(2)关于y轴对称的点,纵坐标相同,横坐标互为相反数.

6.分式方程 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的解为(

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】D

【解析】

【分析】

根据解分式方程的步骤解答即可.

【详解】解:方程变形得 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> .

方程的两边同乘(x-1,3=x-1.

解得x=4.
经检验,x=4是原方程的解.
故选:D

【点睛】本题主要考查了解分式方程,熟练掌握把分式方程转化为整式方程是解答本题的关键.

7.如图,菱形ABCD中,对角线ACBD相交于点OEAB的中点.若菱形ABCD的周长为32,则OE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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

A. 3 B. 4 C. 5 D. 6

【答案】B

【解析】

【分析】

利用菱形的对边相等以及对角线互相垂直,进而利用直角三角形斜边上的中线等于斜边的一半得出答案.

【详解】解:∵四边形ABCD是菱形,
∴AC⊥BDAB=BC=CD=AD
∴∠AOB=90°
又∵AB+BC+CD+AD=32
∴AB=8
Rt△AOB中,OE是斜边上的中线,
∴OE=
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> AB=4
故选:B

【点睛】本题考查了菱形的性质、直角三角形斜边上的中线的性质.注意:直角三角形斜边上的中线等于斜边的一半.

8.下列运算中,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】C

【解析】

【分析】

根据同底数幂的乘除法、幂的乘方以及合并同类项法则即可逐一排除.

【详解】解: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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,故A错误;

Ba2a2不是同类项,不能合并,故B错误;

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,故C正确;

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,故D错误;

故选:C

【点睛】本题考查了同底数幂的乘除法、幂的乘方以及合并同类项,解题的关键是熟悉基本的运算法则.

9.如图,等腰△ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中,点DE分别在腰ABAC上,添加下列条件,不能判定 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】B

【解析】

【分析】

根据全等三角形的判定方法逐项判断即得答案.

【详解】解: A、若添加 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,由于AB=AC,∠A是公共角,则可根据SAS判定 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,故本选项不符合题意;

B、若添加 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,不能判定 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,故本选项符合题意;

C、若添加 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,由于AB=AC,∠A是公共角,则可根据AAS判定 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,故本选项不符合题意;

D、若添加 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,∵AB=AC,∴∠ABC=∠ACB,∴∠ABE=∠ACD,由于∠A是公共角,则可根据ASA判定 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,故本选项不符合题意.

故选:B

【点睛】本题考查了全等三角形的判定和等腰三角形的性质,属于基本题型,熟练掌握全等三角形的判定方法是解题的关键.

10.如图,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的图象与 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 轴交于 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> B两点,下列说法错误的是(

 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> B. 图象的对称轴为直线 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

C. B的坐标为 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 时,yx的增大而增大

【答案】D

【解析】

【分析】

根据二次函数的图象和性质依次对各选项进行判断即可.

【详解】解:由图可知二次函数的图象的开向下,所以a<0,A选项正确;

因为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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

所以图象的对称轴为直线 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,故B选项正确;

因为二次函数的对称轴为直线 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> A,B两点是抛物线与x轴的交点,

所以A,B两点到对称轴的距离相等,

B点坐标为(b,0,则有b-(-1)=(-1)-(-3),

解得b=1,

所以B点坐标为(-1,0.

C选项正确;

由图形可知当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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> -1,yx的增大而增大,当-1<x<0时,yx的增大而减小,故D选项错误.

故选:D.

【点睛】本题考查二次函数的图象与性质,解题的关键是熟练运用二次函数的图象与系数的关系,本题属于基础题型.

二、填空题(本大题共4个小题,每小题4分,共16分)

11. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> _______

【答案】5

【解析】

【分析】

根据数轴上某个数与原点的距离叫做这个数的绝对值的定义求解.

【详解】解:在数轴上,点﹣5到原点的距离是5,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

故答案为:5

【点睛】本题考查绝对值的概念.

12.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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中,过点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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,垂足为E,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】50°

【解析】

【分析】

由平行四边形的性质得出∠B=∠EAD=40°,由角的互余关系得出∠BCE=90°-∠B即可.

【详解】解:∵四边形ABCD是平行四边形,
ADBC
∴∠
B=∠EAD=40°
CEAB
∴∠
BCE=90°-∠B=50°
故答案为:50°

【点睛】本题考查了平行四边形的性质和三角形的内角和;熟练掌握平行四边形的性质,求出∠B的度数是解决问题的关键.

13.某班为了解同学们一周在校参加体育锻炼的时间,随机调查了10名同学,得到如下数据:

锻炼时闭(小时)

5

6

7

8

人数

1

4

3

2


则这10名同学一周在校参加体育锻炼时间的平均数是__________小时.

【答案】6.6

【解析】

【分析】

根据加权平均数的定义解答即可.

【详解】解:这10名同学一周在校参加体育锻炼时间的平均数= <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 小时.

故答案为:6.6

【点睛】本题考查了加权平均数的计算,属于基础题型,熟练掌握计算的方法是解题关键.

14.如图,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的直径,弦 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 于点H,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,则OH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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】3

【解析】

【分析】

连接OC,由垂径定理可求出CH的长度,在Rt△OCH中,根据CH和⊙O的半径,即可由勾股定理求出OH的长.

【详解】连接OC

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

Rt△OCH中,OC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> AB=5CH= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> CD=4

由勾股定理,得: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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>
即线段OH的长为3

故答案为:3

【点睛】本题考查了垂径定理:平分弦的直径平分这条弦,并且平分弦所对的两条弧.也考查了勾股定理.

三、解答题:(本大题共6个小题,共54分)

15.1)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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

2)解不等式组: <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】11;(2-3x≤5

【解析】

【分析】

1)原式根据二次根式的性质、特殊角三角函数值以及零指数幂的运算法则分别化简各项,然后再合并;

2)分别求出不等式组中每个不等式的解集,然后再取它们的公共部分即可得到不等式组的解集.

【详解】(1)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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

=1

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

解不等式①得,x-3

解不等式②得,x≤5

所以,不等式组的解集为:-3x≤5

【点睛】本题主要考查了实数的混合运算以及求不等式组的解集,解答此题的关键是熟练掌握运算法则,确定不等式组的解集就熟练掌握口诀“大大取大,小小取小,大小小大中间找,小小大大找不了(无解)”.

16.化简: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【解析】

 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 分析】

括号内先通分,化为同分母分式后,根据分式的运算法则计算可得.

【详解】 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【点睛】本题主要考查了分式的加减乘除混合运算,解题的关键是熟练掌握异分母分式加减运算法则.

17.热气球的探测器显示,从热气球A处看大楼BC顶部C的仰角为30°,看大楼底部B的俯角为45°,热气球与该楼的水平距离AD60米,求大楼BC的高度.(结果精确到1米,参考数据: <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】这栋楼的高度约为95米.

【解析】

【分析】

利用正切函数分别在Rt△ABDRt△ACD中求得BDCD的长即可.

【详解】由题意可知 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 米,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ()

答:这栋楼的高度约为95米.

【点睛】本题考查了解直角三角形的应用,准确确定直角三角形,灵活运用相关知识是解此题的关键.

18.如图,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的图象与反比例函数 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的图象相交于 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> B两点.

 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

1)求反比例函数的解析式;

2)求点B的坐标.

【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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【解析】

【分析】

1)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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 代入一次函数 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中,求出m,再将点A代入反比例函数 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 即可;

2)联立一次函数与反比例函数解析式,解方程组即可解答.

【详解】解:(1)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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 代入一次函数 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中得:

 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,代入反比例函数 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中得: <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

解得:k=4

反比例函数解析式为 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

2)联立一次函数与反比例函数解析式得: <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【点睛】本题考查的是反比例函数与一次函数的交点问题,掌握函数图象上点的坐标特征是解题的关键.

19.为了解同学们最喜欢一年四季中的哪个季节,数学社在全校随机抽取部分同学进行问卷调查,根据调查结果,得到如下两幅不完整的统计图.

 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

根据图中信息,解答下列问题:

1)此次调查一共随机抽取了________名同学;扇形统计图中,“春季”所对应的扇形的圆心角的度数为________

2)若该学校有1500名同学,请估计该校最喜欢冬季的同学的人数;

3)现从最喜欢夏季的3名同学ABC中,随机选两名同学去参加学校组织的“我爱夏天”演讲比赛,请用列表或画树状图的方法求恰好选到AB去参加比赛的概率.

【答案】1120108°;(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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 名;(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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【解析】

【分析】

1)由“夏季”的人数除以占的百分比得出调查学生的总数即可;求出“春季”占的比例,乘以 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 即可得到结果;
2)用全校学生数×最喜欢冬季的人数所占比例即可;
3)首先根据题意画出树状图,然后由树状图求得所有等可能的结果与选出的2名学生中恰好有AB的情况,再利用概率公式即可求得答案.

【详解】(1)根据题意得:18÷15%=120(名);

春季”占的角度为36÷120×360°=108°
故答案为:120108°

2)该校最喜欢冬季的同学的人数为:1500 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> (名);

3)画树状图得:
 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>
共有6种等可能的结果,恰好选到AB的有2种情况,

故恰好选到AB的概率是: <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【点睛】本题考查了用列表法或画树状图法求概率以及条形统计图与扇形统计图的知识.列表法或画树状图法可以不重复不遗漏的列出所有可能的结果,列表法适合于两步完成的事件,树状图法适合两步或两步以上完成的事件.用到的知识点为:概率=所求情况数与总情况数之比.

20.如图,AB是⊙O的直径,C为⊙O上一点,AD和过点C的切线互相垂直,垂足为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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

1)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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

2)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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,求CD的长.

【答案】(1)见解析;(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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> .

【解析】

【分析】

1)连接OC,根据切线 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 性质,判断出AD∥OC,再应用平行线的性质,即可推得 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

(2)连接BC,通过证明△ADC <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> △ACB,可求出AD的长,再在Rt△ADC中,通过勾股定理可求出CD的长.

【详解】解:(1)证明:如图,连接OC
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>
∵CD是⊙O的切线,
∴OC⊥CD
∵AD⊥CD
∴AD∥OC
∴∠DAC=∠ACO
∵OA=OC
∴∠CAB=∠ACO
∴∠DAC=∠CAB.
(2)如图,连接BC

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∵AB是⊙O的直径,

∴∠ACB=90°.

∵AD⊥CD

∴∠ADC=90°.

∴∠ADC=∠ACB.

由(1)知∠DAC=∠CAB

∴△ADC <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> △ACB.

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,则可设AD=2x,AB=3x,x>0,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> .

解得x=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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∴AD=4.

Rt△ADC中,由勾股定理,得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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> .

【点睛】此题主要考查了切线的性质和应用,以及平行线的性质和应用,要熟练掌握,解答此题的关键是要明确:若出现圆的切线,必连过切点的半径,得出垂直关系.

四、填空题(本大题共5个小题,每小题4分,共20分)

21.在单词 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> (数学)中任意选择-一个字母,选中字母“ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ”的概率为______

【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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【解析】

【分析】

由题意可知总共有11个字母,求出字母 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的个数,利用概率公式进行求解即可.

【详解】解:共有 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 个字母,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 个,

所以选中字母“ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ”的概率为 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> .

【点睛】本题考查概率的求法,如果一个事件有n种可能,而且这些事件的可能性相同,其中事件A出现m种结果,那么事件A的概率PA= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> .

22. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,则代数式 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的值为________

【答案】5

【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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 化为 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的形式,再整体代入求值即可.

【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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

故答案为:5

【点睛】本题考查了求代数式的值,运用整体的数学思想是解决问题的关键.

23.三角形的两边长分别为47,第三边的长是方程 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的解,则这个三角形的周长是________

【答案】17

【解析】

【分析】

先利用因式分解法求解得出x的值,再根据三角形三边之间的关系判断能否构成三角形,从而得出答案.

【详解】解:解方程 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> x1=2x2=6
x=2时,2+4=6<7,不能构成三角形,舍去;
x=6时,2+67,能构成三角形,此时三角形的周长为4+7+6=17.
故答案为:17

【点睛】本题主要考查解一元二次方程的能力,熟练掌握解一元二次方程的几种常用方法:直接开平方法、因式分解法、公式法、配方法,结合方程的特点选择合适、简便的方法是解题的关键.

24.如图,有一张长方形片ABCD <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> .点ECD上一点,将纸片沿AE折叠,BC的对应边 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 恰好经过点D,则线段DE的长为________cm

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】5

【解析】

【分析】

根据折叠的性质得到线段和角相等,然后在Rt△ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中,由勾股定理求出 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的长,则可得出 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的长,再在Rt△ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 利用勾股定理进行计算即可求DE的长.

【详解】解:∵四边形ABCD是长方形,

∴AD=BC=10,CD=AB=8,∠B=∠C=90°.

根据折叠的性质, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> =8-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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> =∠B=90°.

Rt△ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,由勾股定理,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> =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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> =10-6=4.

Rt△ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,由勾股定理,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> .

8-DE2+42=DE2.

解得DE=5.

故答案是:5.

【点睛】本题考查了折叠的性质,矩形的性质,勾股定理,熟练运用折叠的性质是本题的关键.

25.如图,在平面直角坐标系 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的图象与反比例函数 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的图象交于AB两点,若点P是第一象限内反比例函数图象上一点,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的面积是 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的面积的2倍,则点P横坐标________

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【答案】2

【解析】

【分析】

联立方程组 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 求出AB两点坐标,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,过P <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 轴,过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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 轴,过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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 轴,交BFF点,交PE于点E,分别求出梯形BFEP、△APE、△ABF、△AOB、△ABP的面积,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的面积是 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的面积的2倍列方程求解即可.

【详解】联立方程组 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,过P <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 轴,过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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 轴,过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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 轴,交BFF点,交PE于点E,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

对于y=x+1,当x=0时,y=1;当y=0时,x=-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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,整理得, <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 是原方程的解,

∵x0

∴x=2

P的横坐标为:2

故答案为:2

【点睛】本题主要考查了反比例函数与一次函数的交点问题,解题时注意:反比例函数与一次函数的图象的交点坐标满足两函数的解析式.

五、解答题(本大题共3个小题,共30分)

26.某商品的进价为每件40元,在销售过程中发现,每周的销售量y(件)与销售单价x(元)之间的关系可以近似看作一次函数 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,且当售价定为50/件时,每周销售30件,当售价定为70/件时,每周销售10件.

1)求kb的值;

2)求销售该商品每周的利润w(元)与销售单价x(元)之间的函数解析式,并求出销售该商品每周可获得的最大利润.

【答案】1k=-1b=80;(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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,最大利润为400元.

【解析】

【分析】

1)将“当售价定为50/件时,每周销售30件,当售价定为70/件时,每周销售10件”代入一次函数 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,即可解答;

2)根据利润=销售量×(销售单价-进价),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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,再根据二次函数的性质得到利润最大为400元即可.

【详解】解:(1)由题意可得,当x=50时,y=30;当x=70时,y=10

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中得:

 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∴k=-1b=80

2)由(1)可知,y=-x+80

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∵y=-x+80≥0

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∵-10

x=60时,w有最大值,此时w=400

即最大利润为400元.

【点睛】本题考查了待定系数法求一次函数解析式以及二次函数的实际应用,解题的关键是根据题意列出函数关系式,并熟悉二次函数的性质.

27.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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 绕点C顺时针旋转得到 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,点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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 线段AB上,连接BE

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

1)求证:DC平分 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

2)试判断BEAB的位置关系,并说明理由:

3)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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 的值.

【答案】1)见解析;(2BE⊥AB,理由见解析;(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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【解析】

【分析】

1)根据旋转的性质可得AC=CD,∠A=∠CDE,再由等腰三角形的性质得到∠A=∠ADC即可证明∠ADC=∠CDE

2)根据旋转的性质得到∠ACD=∠BCECB=CEAC=CD,从而得出∠CAD=∠ADC=∠CBE=∠CEB,再根据∠ACB=90°即可得到∠ABE=90°

3)设BD=BE=a,根据勾股定理计算出AB=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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,表达出AD,再证明△ACD∽△BCE,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 即可.

【详解】解:(1)由旋转可知:AC=CD,∠A=∠CDE

∴∠A=∠ADC

∴∠ADC=∠CDE,即DC平分∠ADE

2BE⊥AB

理由:由旋转可知,∠ACD=∠BCECB=CEAC=CD

∴∠CAD=∠ADC=∠CBE=∠CEB

又∵∠ACB=90°

∴∠CAD+∠ABC=90°

∴∠CBE+∠ABC=90°

即∠ABE=90°

∴BE⊥AB

3)∵∠ABE=90°BD=BE

BD=BE=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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

又∵AB=DE

∴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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,则AD= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

由(2)可知,∠ACD=∠BCE,∠CAD=∠ADC=∠CBE=∠CEB

∴△ACD∽△BCE

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∴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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

【点睛】本题考查了旋转的综合应用以及相似三角形的性质与判定、锐角三角函数的定义,解题的关键是熟练掌握旋转的性质,并熟记锐角三角函数的定义.

28.如图,在平面直角坐标系 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 中,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 分别交x轴、y轴于AB两点,经过AB两点的抛物线 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> x轴的正半轴相交于点 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

1)求抛物线的解析式;

2)若P为线段AB上一点, <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,求AP的长;

3)在(2)的条件下,设My轴上一点,试问:抛物线上是否存在点N,使得以APMN为顶点的四边形为平行四边形?若存在,求出点N的坐标;若不存在,请说明理由.

【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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ;(3)存在,点N的坐标为( <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> )

【解析】

【分析】

1)利用直线 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> y轴的交点求得点B的坐标,然后把点BC的坐标代入 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> ,即可求解;

2)先求得点A的坐标,证得△PAO <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> △CAB,利用对应边成比例即可求解;

3)分点NAB的上方或下方两种情况进行讨论,根据平行四边形的性质和等腰直角三角形的性质,利用三角形全等,即可求解.

【详解】(1)令 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

B的坐标为(03)

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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 经过点B (03)C (10)

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

抛物线的解析式为: <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

2)令 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

A的坐标为( <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 0)

∴OA=3OB=3OC=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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∴△PAO <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> △CAB

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

3)存在,

过点PPDx轴于点D

∵OA=3OB=3,∠AOB= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∴∠BAO=∠ABO= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∴△PAD为等腰直角三角形,

 <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∴PD=AD=2

P的坐标为( <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 2)

NAB的上方时,过点NNEy轴于点E,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

四边形APMN为平行四边形,

∴NM∥APNM=AP= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∴∠NME=∠ABO= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

∴△NME为等腰直角三角形,

∴Rt△NME <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> Rt△APD

∴NE=AD=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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

N的坐标为( <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> 3)

NAB的下方时,过点NNFy轴于点F,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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

同理可得:Rt△NMF <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/261/" title="考试" class="c1" target="_blank">考试</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> Rt△APD

∴NF=AD=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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a>

N的坐标为( <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> )

综上,点N的坐标为( <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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</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/1107/" title="甘孜" class="c1" target="_blank">甘孜</a> )

【点睛】本题是二次函数的综合问题,解题的关键是掌握待定系数法求二次函数与一次函数的解析式、二次函数的性质、平行四边形的性质、等腰直角三角形的性质、全等三角形的判定和性质等知识点.正确作出图形是解题的关键.