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【330357】2020年四川省广元市中考数学真题

时间:2025-02-09 11:06:38 作者: 字数:25254字

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 四川省广元市2020年中考数学真题

一、选择题(每小题4分,共40分)每小题给出的四个选项中,只有一个是符合题意的.

1. 2的绝对值是(

A. 2 B.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> C.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> D.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】A

【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,在数轴上,点﹣2到原点的距离是2,所以﹣2的绝对值是2,故选A


2.下列运算正确的是(

A.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> B.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> C.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> D.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】B

【解析】

【分析】

分别利用幂的乘方和积的乘方、完全平方公式,同底数幂的乘法法则计算即可.

【详解】解:A、原式=4a4b2,故选项错误;

B、原式=a2,故选项正确;

C、原式=a2+2ab+b2,故选项错误;

D、原式=a7,故选项错误;

故选B.

【点睛】此题考查了幂的乘方和积的乘方、完全平方公式,同底数幂的乘法,熟练掌握运算法则是解本题的关键.

3.如图所示的几何体是由5个相同的小正方体组成,其主视图为(

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

A.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> B.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> C.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> D.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】D

【解析】

【分析】

根据从正面看得到的图形是主视图,可得答案.

【详解】解:从正面看第一层是一个小正方形,第二层是三个小正方形,

主视图为:

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

故选:D

【点睛】本题考查了简单组合体的三视图,从正面看得到的图形是主视图.

4.2019年某中学举行的冬季阳径运动会上,参加男子跳高的15名运动员的成绩如表所示:

成绩(m

1.80

1.50

1.60

1.65

1.70

1.75

人数

1

2

4

3

3

2


这些运动员跳高成绩的中位数和众数分别是(

A.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> B.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

C.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> D.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】D

【解析】

【分析】

首先根据这组数据的个数是奇数,则处于中间位置的数就是这组数据的中位数,判断出这些运动员跳高成绩的中位数即可;然后找出这组数据中出现次数最多的数,则它就是这些运动员跳高成绩的众数,据此解答即可.

【详解】解:∵15÷27…1,第8名的成绩处于中间位置,

男子跳高的15名运动员的成绩处于中间位置的数是1.65m

这些运动员跳高成绩的中位数是1.65m

男子跳高的15名运动员的成绩出现次数最多的是1.60m

这些运动员跳高成绩的众数是1.60m

综上,可得这些运动员跳高成绩的中位数是1.65m,众数是1.60m

故选:D

【点睛】此题主要考查了众数和中位数,要熟练掌握,解答此题的关键是要明确众数和中位数的含义和求法.

5.如图,a∥b,MN分别在a,b上,P为两平行线间一点,那么∠1+∠2+∠3= .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

A. 180° B. 360° C. 270° D. 540°

【答案】B

【解析】

【分析】

首先作出PA∥a,根据平行线性质,两直线平行同旁内角互补,可以得出∠1+∠2+∠3的值.

【详解】解:过点PPA∥a

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>
∵a∥b
PA∥a
∴a∥b∥PA

∴∠1+∠MPA=180°
,∠3+∠APN=180°
∴∠1+∠MPA+∠3+∠APN=180°+180°=360°

∴∠1+∠2+∠3=360°

故选B

【点睛】此题主要考查了平行线的性质,作出PA∥a是解决问题的关键.

6.按照如图所示的流程,若输出的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,则输入的m为(

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

A. 3 B. 1 C. 0 D. -1

【答案】C

【解析】

【分析】

根据题目中的程序,利用分类讨论的方法可以分别求得m的值,从而可以解答本题.

【详解】解:当m2-2m≥0时,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,解得m=0

经检验,m=0是原方程的解,并且满足m2-2m≥0
m
2-2m0时,
m-3=-6
,解得m=-3,不满足m
2-2m0,舍去.
故输入的m0
故选:C

【点睛】本题考查有理数的混合运算,解答本题的关键是明确有理数混合运算的计算方法.

7.下列各图是截止2020618日的新冠肺疫情统计数据,则以下结论错误的是(

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

A. 1显示印度新增确诊人数大约是伊朗的两倍.每百万人口的确诊人数大约是伊朗的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

B. 1显示俄罗斯当前的治愈率高于四班牙

C. 2显示海外新增确诊人数随时间的推移总体呈增长趋势

D. 3显示在2-3月之间,我国现有确诊人数达到最多

【答案】A

【解析】

【详解】略

8.关于x的不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的整数解只有4个,则m的取值范围是(

A.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> B.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> C.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> D.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】C

【解析】

【分析】

不等式组整理后,表示出不等式组的解集,根据整数解共有4个,确定出m的范围即可.

【详解】解:不等式组整理得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解集为mx3

由不等式组的整数解只有4个,得到整数解为210-1

-2≤m<-1

故选:C

【点睛】本题主要考查对解一元一次不等式,不等式的性质,解一元一次不等式组,一元一次不等式组的整数解等知识点的理解和掌握,能根据不等式组的解集得到-2≤m<-1是解此题的关键.

9.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的两条互相垂直的直径,点P从点O出发,沿 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的路线匀速运动,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> (单位:度),那么y与点P运动的时间(单位:秒)的关系图是(

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

A.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> B.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> C.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> D.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】B

【解析】

【分析】

根据图示,分三种情况:(1)当点P沿O→C运动时;(2)当点P沿C→B运动时;(3)当点P沿B→O运动时;分别判断出y的取值情况,进而判断出y与点P运动的时间x(单位:秒)的关系图是哪个即可.

【详解】解:(1)当点P沿O→C运动时,

当点P在点O的位置时,y90°

当点P在点C的位置时,

OAOC

y45°

y90°逐渐减小到45°

2)当点P沿C→B运动时,

根据圆周角定理,可得

y≡90°÷245°

3)当点P沿B→O运动时,

当点P在点B的位置时,y45°

当点P在点O的位置时,y90°

y45°逐渐增加到90°

故选:B

【点睛】此题主要考查了动点问题的函数图象和圆周角定理,解答此类问题的关键是通过看图获取信息,并能解决生活中的实际问题,用图象解决问题时,要理清图象的含义即学会识图.

10.规定: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 给出以下四个结论:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ;(3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ;(4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 其中正确的结论的个数为(

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

【答案】C

【解析】

【分析】

根据题目所规定的公式,化简三角函数,即可判断结论.

【详解】解:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,故此结论正确;

2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,故此结论正确;

3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

故此结论正确;

4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

故此结论错误.

故选:C

【点睛】本题属于新定义问题,主要考查了三角函数的知识,解题的关键是熟练掌握三角函数的基础知识,理解题中公式.

二、填空题(每小题4分,共20分)把正确答案直接填写在答题卡对应题目的横线上.

11.近年来,四川省加快推进商业贸易转型升级,2019年,四川全省商业贸易服务业增加值达4194亿元,用科学计数法表示______________元.

【答案】4.194×1011

【解析】

【分析】

科学记数法的表示形式为a×10n的形式,其中1≤|a|10n为整数.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.当数绝对值大于10时,n是正数;当原数的绝对值小于1时,n是负数.

【详解】解:将4194亿元用科学记数法表示为4.194×1011元.
故答案为:4.194×10
11

【点睛】此题考查科学记数法的表示方法.科学记数法的表示形式为a×10n的形式,其中1≤|a|10n为整数,表示时关键要正确确定a的值以及n的值.

12.在如图所示的电路图中,当随机闭合开关 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 中的两个时,能够让灯泡发光的概率为________

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【解析】

【分析】

分析电路图知:要让灯泡发光, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 必须闭合,同时 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 中任意一个关闭时,满足条件,从而求算概率.

【详解】分析电路图知:要让灯泡发光, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 必须闭合,同时 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 中任意一个关闭时,满足:

一共有: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 三种情况,满足条件的有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 两种,

能够让灯泡发光的概率为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【点睛】本题考查概率运算,分析出所有可能的结果,寻找出满足条件的情况是解题关键.

13.关于x的分式方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的解为正数,则m的取值范围是_____________

【答案】m<2m≠0

【解析】

【分析】

首先解方程求得方程的解,根据方程的解是正数,即可得到一个关于m的不等式,从而求得m的范围.

【详解】解:去分母得:m+4x-2=0

解得:x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

关于x的分式方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的解是正数,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 0

m<2

2x-1≠0

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

m≠0

m的取值范围是m<2m≠0

故答案为:m<2m≠0

【点睛】本题主要考查了分式方程的解的符号的确定,正确求解分式方程是解题的关键.

14.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 内接于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 于点H,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的半径为7,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ______

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【解析】

【分析】

作直径AD,连接BD,根据圆周角定理得到∠ABD90°,∠D=∠C,证明△ABD∽△AHC,根据相似三角形的性质解答即可.

【详解】解:作直径AD,连接BD

AD为直径,

∴∠ABD90°,又AH⊥BC

∴∠ABD=∠AHC

由圆周角定理得,∠D=∠C

∴△ABD∽△AHC

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解得,AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

故答案 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【点睛】本题考查的是三角形的外接圆和外心的概念和性质,掌握圆周角定理、相似三角形的判定和性质是解题的关键.

15.如图所示, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 均为等边三角形,边长分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> BCD三点在同一条直线上,则下列结论正确的________________.(填序号)

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 为等边三角形  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> CM平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】①②③⑤

【解析】

【分析】

根据等边三角形的性质得CACBCDCE,∠ACB60°,∠DCE60°,则∠ACE60°,利用“SAS”可判断△ACD≌△BCE,则ADBE

E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,根据等边三角形求出EDCN的长,即可求出BE的长;

由等边三角形的判定得出△CMN是等边三角形;

证明△DMC∽△DBA,求出CM长;

证明MFCG四点共圆,由圆周角定理得出∠BMC=∠FGC60°,∠CMD=∠CFG60°,得出∠BMC=∠DMC,所以CM平分∠BMD.

【详解】解:连接MCFG,过点EEN⊥BD,垂足 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> N

①∵△ABC和△CDE都是等边三角形,

CACBCDCE,∠ACB60°,∠DCE60°

∴∠ACE60°

∴∠ACD=∠BCE120°

在△ACD和△BCE中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

∴△ACD≌△BCESAS),

ADBE;①正确;

②∵△CDE都是等边三角形,且边长为3cm.

CN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> cmEN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> cm.

BC=5cm.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,②正确;

③∵△ACD≌△BCE

∴∠CAD=∠CBE

在△ACG和△BCF中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

∴△ACG≌△BCFASA),

CGCF

而∠GCF60°

∴△CMN是等边三角形,③正确;

⑤∵∠EMD=∠MBD+∠MDB=∠MAC+∠MDB60°=∠FCG

MFCG四点共圆,

∴∠BMC=∠FGC60°,∠CMD=∠CFG60°

∴∠BMC=∠DMC

CM平分∠BMD,⑤正确;

④∵∠DMC=∠ABD,∠MDC=∠BDA

∴△DMC∽△DBA

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

CM= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> .④错误.

故答案为:①②③⑤.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【点睛】本题考查了全等三角形的判定和性质,等边三角形的判定与性质,熟练掌握等边三角形的性质,证明三角形全等是解题的关键.

三、解答题(共90分)要求写出必要的解答步骤或证明过程

16.计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【答案】-2

【解析】

【分析】

直接利用特殊角的三角函数值、绝对值的性质、零指数幂的性质、负整数指数幂的性质分别代入化简即可.

【详解】解:原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

=-2

【点睛】此题主要考查了实数运算,正确化简各数是解题关键.

17.先化简,再求值: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,其中a是关于x的方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的根.

【答案】a2+2a+116

【解析】

【分析】

首先将括号里面通分,进而因式分解各项,化简求出即可.

【详解】解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

=a2+2a+1

a是关于x的方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的根,

a2-2a-3=0

a=3a=-1

a2+a≠0

a≠-1

a=3

原式=9+6+1=16.

【点睛】此题主要考查了分式的化简求值以及一元二次方程的解,正确化简分式是解题关键.

18.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> O为对角线AC的中点,过O的一条直线交AD于点E,交BC于点F

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

1)求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

2)若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 面积为2,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的面积.

【答案】1)见解析;(216.

【解析】

【分析】

1)由平行四边形的性质得出AD∥BC,得出∠EAO=∠FCO,由ASA即可得出结论;

2)由于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> O为对角线AC的中点,得出△AEO∽△ADC,根据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的面积为2,可得△ADC的面积,进而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的面积.

【详解】解:(1)∵四边形ABCD是平行四边形,

AD∥BC

∴∠EAO=∠FCO

OAC的中点,

OAOC

在△AOE和△COF中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

∴△AOE≌△COFASA);

2)∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> =12O为对角线AC的中点,

AO:AC=1:2

∵∠EAO=∠DAC

∴△AEO∽△ADC

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的面积为2

∴△ADC的面积为8

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的面积为16.

【点睛】本题考查了平行四边形的性质与判定、全等三角形的判定与性质、相似三角形面积比,要熟练掌握全等三角形的判定和相似三角形的判定.

19.广元市某中学举行了“禁毒知识竞赛”,王老师将九年级(1)班学生成绩划分为ABCDE五个等级,并绘制了图1、图2两个不完整的统计图,请根据图中的信息解答下列问题:

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

1)求九年级(1)班共有多少名同学?

2)补全条形统计图,并计算扇形统计图中的“C”所对应的圆心角度数;

3)成绩为A类的5名同学中,有2名男生和3名女生;王老师想从这5名同学中任选2名同学进行交流,请用列表法或画树状图的方法求选取的2名同学都是女生的概率.

【答案】150;(2)见解析,108°;(3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【解析】

【分析】

1)由B的人数和其所占的百分比即可求出总人数;

2C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 人数可知,而总人数已求出,进而可求出其所对应扇形的圆心角的度数;根据求出的数据即可补全条形统计图;

3)列表得出所有等可能的情况数,找出刚好抽到2名同学都是女生的情况数,即可求出所求的概率.

【详解】解:(1)由题意可知总人数=10÷20%50名;

2)补全条形统计图如图所示:

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

扇形统计图中C等级所对应扇形的圆心角=15÷50×100%×360°108°

3)列表如下:

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

得到所有等可能的情况有20种,其中恰好抽中2名同学都是女生的情况有6种,

所以恰好选到2名同学都是女生的概率= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【点睛】此题考查了列表法与树状图法,用到的知识点为:概率=所求情况数与总情况数之比.

20.某网店正在热销一款电子产品,其成本为10/件,销售中发现,该商品每天的销售量y(件)与销售单价x(元/件)之间存在如图所示的关系:

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

1)请求出yx之间的函数关系式;

2)该款电子产品的销售单价为多少元时,每天销售利润最大?最大利润是多少元;

3)由于武汉爆发了“新型冠状病毒”疫情,该网店店主决定从每天获得的利润中抽出300元捐赠给武汉,为了保证捐款后每天剩余利润不低于450元,如何确定该款电子产品的销售单价?

【答案】1) y=−10x300;(220元时,最大利润为1000元;(3)单价每件不低于15元,且不高于25.

【解析】

【分析】

1)利用待定系数法求解可得;

2)设该款电子产品每天的销售利润为w元,根据“总利润=每件的利润×销售量”可得函数解析式,配方成顶点式后利用二次函数的性质求解可得;

3)设捐款后每天剩余利润为z元,根据题意得出z=−10x2400x−3000−300=−10x2400x−3300,求出z450时的x的值,求解可得.

【详解】解:(1)设 与 的函数关系式为 ykxb

将(20100),(2550)代入 ykxb

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

yx的函数关系式为 y=−10x300

2)设该款电子产品每天的销售利润为w元,

由题意得 w=(x−10)•y

=(x−10)(−10x300

=−10x2400x−3000

=−10x−2021000

∵−100

x20时,w有最大值,w最大值为1000

答:该款电子产品销售单价定为20元时,每天销售利润最大,最大销售利润为1000元;

3)设捐款后每天剩余利润 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  元,

由题意可得 z=−10x2400x−3000−300=−10x2400x−3300

z450,即−10x2400x−3300450

x2−40x3750

解得x115x225

∵−100

当该款电子产品的销售单价每件不低于15元,且不高于25元时,可保证捐款后每天剩余利润不低于450 元.

【点睛】本题主要考查二次函数的应用,解题的关键是掌握待定系数法求函数解析式,理解题意找到题目蕴含的相等关系,并据此得出函数解析式.

21.如图,公路MN为东西走向,在点M北偏东36.5°方向上,距离5千米处是学校A;在点M北偏东45°方向上距离 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 千米处是学校B.(参考数据: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ).

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

1)求学校AB两点之间的距离

2)要在公路MN旁修建一个体育馆C,使得AB两所学校到体育馆C的距离之和最短,求这个最短距离.

【答案】1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> km;2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> km.

【解析】

【分析】

1)过点ACD//MNBE⊥MN,在Rt△ACM中求出CMAC,在Rt△MBE中求出BEME,继而得出ADBD的长度,在Rt△ABD中利用勾股定理可得出AB的长度.

2)作点B关于MN的对称点G,连接AGMN于点P,点P即为站点,求出AG的长度即可.

【详解】(1)过点ACD//MNBE⊥MN,如图:

Rt△ACM中,∠CMA36.5°AM5km

sin36.5° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 0.6

CA3MC4km

Rt△MBE中,∠NMB45°MB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> km

sin45° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

BE6ME6km

ADCD−CAME−CA3kmBDBE−DEBE−CM2km

Rt△ABD中,AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> km

2)作点B关于MN的对称点G,连接AGMN于点P,连接PB,点P即为站点,

此时PAPBPAPGAG,即AB两所学校到体育馆C的距离之和最短为AG

Rt△ADG中,AD=3DG=DE+EG=DE+BE=4+6=10,∠ADG=90°

AG <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> km

答:最短距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> km

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【点睛】本题考查了解直角三角形的知识,解答本题的关键是构造直角三角形,利用三角函数值求解相关线段的长度,难度较大.

22.如图所示,一次函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的图象与反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的图象交于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

1)求反比例函数和一次函数的解析式;

2)在x轴上存在一点C,使 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 为等腰三角形,求此时点C的坐标;

3)根据图象直接写出使一次函数的值大于反比例函数的值的x的取值范围.

【答案】1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ;(3-12<x<0x>3

【解析】

【分析】

1)因为反比例函数过AB两点,所以可求其解析式和n的值,从而知B点坐标,进而求一次函数解析式;

2)分三种情况:OA=OCAO=ACCA=CO,分别求解即可;

3)根据图像得出一次函数图像在反比例函数图像上方时x的取值范围即可.

【详解】解:(1)把A34)代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

m12

反比例函数是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

Bn-1)代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> n=−12

A34)、B-12,−1)分别代入ykxb中:

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

一次函数的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

2)∵A34),△AOC为等腰三角形,OA= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

分三种情况:

OA=OC时,OC=5

此时点C的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

AO=AC时,∵A34),点C和点O关于过A点且垂直于x轴的直线对称,

此时点C的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

CA=CO时,点C在线段OA的垂直平分线上,

AAD⊥x轴,垂足为D

由题意可得:OD=3AD=4AO=5,设OC=x,则AC=x

在△ACD中,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解得:x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

此时点C的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

综上:点C的坐标为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

3)由图得:

当一次函数图像在反比例函数图像上方时,

-12<x<0x>3

即使一次函数的值大于反比例函数的值的x的取值范围是:-12<x<0x>3.

【点睛】本题考查了反比例函数与一次函数的交点,待定系数法求函数解析式,等腰三角形的性质,利用了数形结合及分类讨论的思想.

23. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> OA平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> BC于点O,以O为圆心,OC长为半径作圆交BC于点D

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

1)如图1,求证:AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的切线;

2)如图2AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 相切于点E,连接CEOA于点F

试判断线段OACE的关系,并说明理由.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的值.

【答案】1)见解析;(2)①OA垂直平分CE,理由见解析;② <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【解析】

【分析】

1)过点OOG⊥AB,垂足为G,利用角平分线的性质定理可得OG=OC,即可证明;

2)①利用切线长定理,证明OE=OC,结合OE=OC,再利用垂直平分线的判定定理可得结论;

根据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 求出OFCF,再证明△OCF∽△OAC,求出AC,再证明△BEO∽△BCA,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,设BO=xBE=y,可得关于xy的二元一次方程组,求解可得BOBE,从而可得结果.

【详解】解:(1)如图,过点OOG⊥AB,垂足为G

OA平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> BC于点O

OG=OC

G <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 上,

AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 相切;

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

2)①OA垂直平分CE,理由是:

连接OE

AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 相切于点EAC <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 相切于点C

AE=AC

OE=OC

OA垂直平分CE

②∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

FC=2OF,在△OCF中,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解得:OF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,则CF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

由①得:OA⊥CE

则∠OCF+∠COF=90°,又∠OCF+∠ACF=90°

∴∠COF=∠ACF,而∠CFO=∠ACO=90°

∴△OCF∽△OAC

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解得:AC=6

AB与圆O切于点E

∴∠BEO=90°AC=AE=6,而∠B=∠B

∴△BEO∽△BCA

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,设BO=xBE=y

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,即BO=5BE=4

tanB= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

【点睛】本题考查了圆的综合,切线的判定和性质,相似三角形的判定和性质,二元一次方程组的应用,有一定难度,解题要合理选择相似三角形得出结论.

24.如图,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 分别与x轴,y轴交于点AB两点,点COB的中点,抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 经过AC两点.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

1)求抛物线的函数表达式;

2)点D是直线AB下方的抛物线上的一点,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,求点D的坐标;

3)点P为抛物线上一点,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 是以AB为直角边的直角三角形,求点P到抛物线的对称轴的距离.

【答案】1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ;(2)(2-3);(3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> .

【解析】

【分析】

1)由直线解析式求出AB坐标,然后得出C点坐标,再用待定系数法求出抛物线解析式;

2)过点DDE⊥x轴,交直线AB于点E,设Dm <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ),利用S△ABD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 得出方程,解出m值即可;

3)分点A是直角顶点和点B是直角顶点,结合图像,表示出△ABP三边长度,利用勾股定理得出方程,求解即可.

【详解】解:(1)直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 中,

x=0,则y=10,令y=0,则x=5

A50),B010),

COB中点,

C05),将AC代入抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 中,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ,解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

抛物线表达式为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

2)联立: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

直线AB与抛物线交于点(-112)和(50),

D是直线AB下方抛物线上的一点, Dm <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ),

-1m5

过点DDE⊥x轴,交直线AB于点E

Em-2m+10),

DE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

S△ABD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

解得:m=2

D的坐标为(2-3);

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

3)抛物线表达式为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

∵△APB是以AB为直角边的直角三角形,

设点Pn <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> ),∵A50),B010),

AP2= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> BP2= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> AB2=125

当点A为直角顶点时,

BP2= AB2+ AP2

解得:n= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 5(舍),

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

当点B为直角顶点时,

AP2= AB2+ BP2

解得:n= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

而抛物线对称轴为直线x=3

3- <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> -3= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> 3- <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>

综上:点P到抛物线对称轴的距离为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1158/" title="广元" class="c1" target="_blank">广元</a> .

【点睛】本题是二次函数综合题,主要考查了一次函数图象上坐标点的特征,待定系数法求二次函数解析式,三角形面积的铅垂高表示法,解一元二次方程,勾股定理,相似三角形的判定与性质等重要知识点,综合性强,难度较大.