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【349974】年重庆市中考数学试题A卷

时间:2025-03-05 22:10:08 作者: 字数:29470字
简介:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 重庆市初中学业水平暨高中招生考试

数学试题(A卷)

一、选择题

1.下列各数中,最小的数是(

A. 3 B. 0 C. 1 D. 2

【答案】A

【解析】

【分析】

有理数的大小比较法则:正数大于0,负数小于0,正数大于一切负数;两个负数,绝对值大的反而小.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

最小的数是-3

故选:A

【点睛】本题考查有理数的大小比较,属于基础应用题,只需熟练掌握有理数的大小比较法则,即可完成.

2.下列图形是轴对称图形的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】A

【解析】

【分析】

根据轴对称图形的概念对各选项分析判断即可得解.

【详解】解:A、是轴对称图形,故本选项正确;

B、不是轴对称图形,故本选项错误;

C、不是轴对称图形,故本选项错误;

D、不是轴对称图形,故本选项错误;

故选:A

【点睛】本题考查了轴对称图形的概念,轴对称图形的关键是寻找对称轴,图形两部分折叠后可重合.

3.在今年举行的第127广交会上,有近26000家厂家进行云端销售.其中数据26000用科学记数法表示为(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】C

【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.当原数绝对值>10时,n是正数;当原数的绝对值<1时,n是负数.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故选:C

【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.

4.把黑色三角形按如图所示的规律拼图案,其中第个图案中有1个黑色三角形,第个图案中有3个黑色三角形,第个图案中有6个黑色三角形,,按此规律排列下去,则第个图案中黑色三角形的个数为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

A. 10 B. 15 C. 18 D. 21

【答案】B

【解析】

【分析】

根据前三个图案中黑色三角形的个数得出第n个图案中黑色三角形的个数为1+2+3+4+……+n,据此可得第个图案中黑色三角形的个数.

【详解】解:∵第个图案中黑色三角形的个数为1

个图案中黑色三角形的个数31+2

个图案中黑色三角形的个数61+2+3

……

个图案中黑色三角形的个数为1+2+3+4+515

故选:B

【点睛】本题主要考查图形的变化规律,解题的关键是根据已知图形得出规律:第n个图案中黑色三角形的个数为1+2+3+4+……+n

5.如图,AB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的切线,A切点,连接OAOB,若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的度数为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

A. 40° B. 50° C. 60° D. 70°

【答案】D

【解析】

【分析】

根据切线的性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,再根据三角形内角和求出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> .

【详解】AB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的切线

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故选D.

【点睛】本题考查切线的性质,由切线得到直角是解题的关键.

6.下列计算中,正确的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】C

【解析】

【分析】

根据同类二次根式的概念与二次根式的乘法逐一判断可得答案.

【详解】解:A <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 不是同类二次根式,不能合并,此选项计算错误;

B2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 不是同类二次根式,不能合并,此选项计算错误;

C <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,此选项计算正确;

D2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 与﹣2不是同类二次根式,不能合并,此选项错误;

故选:C

【点睛】本题主要考查二次根式的混合运算,解题的关键是掌握二次根式的乘法法则与同类二次根式的概念.

7.解一元一次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,去分母正确的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】D

【解析】

【分析】

根据等式的基本性质将方程两边都乘以6可得答案.

【详解】解:方程两边都乘以6,得:

3x+1)=62x

故选:D

【点睛】本题主要考查解一元一次方程,解题的关键是掌握解一元一次方程的步骤和等式的基本性质.

8.如图,在平面直角坐标系中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的顶点坐标分别是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,以原点为位似中心,在原点的同侧画 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,使 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 成位似图形,且相似比为21,则线段DF的长度为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> B. 2 C. 4 D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】D

【解析】

【分析】

AC的横纵坐标都乘以2得到DF的坐标,然后利用两点间的距离公式计算线段DF的长.

【详解】解:∵以原点为位似中心,在原点的同侧画△DEF,使△DEF与△ABC成位似图形,且相似比为21

A12),C31),

D24),F62),

DF <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故选:D

【点睛】本题考查了位似变换:在平面直角坐标系中,如果位似变换是以原点为位似中心,相似比为k,那么位似图形对应点的坐标的比等于kk

9.如图,在距某居民楼AB楼底B点左侧水平距离60mC点处有一个山坡,山坡CD的坡度(或坡比) <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,山坡坡底C点到坡顶D点的距离 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,在坡顶D点处测得居民楼楼顶A点的仰角为28°,居民楼AB与山坡CD的剖面在同一平面内,则居民楼AB的高度约为(

(参考数据: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

A. 76.9m B. 82.1m C. 94.8m D. 112.6m

【答案】B

【解析】

【分析】

构造直角三角形,利用坡比的意义和直角三角形的边角关系,分别计算出DEECBEDFAF,进而求出AB

【详解】解:如图,由题意得,∠ADF28°CD45BC60

Rt <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> DEC中,

山坡CD的坡度i10.75

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

DE4x,则EC3x

由勾股定理可得CD5x

CD45,即5x45

x9

EC3x27DE4x36FB

BEBC+EC60+2787DF

Rt <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ADF中,

AFtan28°×DF0.53×8746.11

ABAF+FB46.11+3682.1

故选:B

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【点睛】本题考查直角三角形的边角关系,掌握坡比的意义和直角三角形的边角关系是正确计算的前提.

10.若关于x的一元一次不等式结 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的解集为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ;且关于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的分式方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 有正整数解,则所有满足条件的整数a的值之积是(

A. 7 B. 14 C. 28 D. 56

【答案】A

【解析】

【分析】

不等式组整理后,根据已知解集确定出a的范围,分式方程去分母转化为正整数方程,由分式方程有非负整数解,确定出a的值,求出之和即可.

【详解】解:解不等式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,解得x≤7

不等式组整理的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

由解集为x≤a,得到a≤7

分式方程去分母得:y−a3y−4y−2,即3y−2a

解得:y <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

y为正整数解且y≠2,得到a17

1×77

故选:A

【点睛】此题考查了分式方程的解,以及解一元一次不等式组,熟练掌握运算法则是解本题的关键.

11.如图,三角形纸片ABC,点DBC边上一点,连接AD,把 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 沿着AD翻折,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> DEAC交于点G,连接BEAD于点F. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的面积为2,则点FBC的距离为( )

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】B

【解析】

【分析】

首先求出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ABD的面积.根据三角形的面积公式求出DF,设点FBD的距离为h,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> BDh <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> BFDF,求出BD即可解决问题.

【详解】解:∵DGGE

SADGSAEG2

SADE4

由翻折可知, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ADB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ADEBEAD

SABDSADE4,∠BFD90°

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> AF+DF)•BF4

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 3+DF)•24

DF1

DB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

设点FBD的距离为h

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> BDh <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> BFDF

h <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故选:B

【点睛】本题考查翻折变换,三角形的面积,勾股定理二次根式的运算等知识,解题的关键是灵活运用所学知识解决问题,学会利用参数构建方程解决问题.

12.如图,在平面直角坐标系中,矩形ABCD的对角线AC的中点与坐标原点重合,点Ex轴上一点,连接AE.若AD平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的图象经过AE上的两点AF,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的面积为18,则k的值为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

A. 6 B. 12 C. 18 D. 24

【答案】B

【解析】

【分析】

先证明OBAE,得出SABE=SOAE=18,设A的坐标为(a <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ),求出F点的坐标和E点的坐标,可得SOAE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ×3a× <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> =18,求解即可.

【详解】解:如图,连接BD

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

四边形ABCD为矩形,O为对角线,

AO=OD

∴∠ODA=OAD

又∵AD为∠DAE的平分线,

∴∠OAD=EAD

∴∠EAD=ODA

OBAE

SABE=18

SOAE=18

A的坐标为(a <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ),

AF=EF

F点的纵坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

代入反比例函数解析式可得F点的坐标为(2a <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ),

E点的坐标为(3a0),

SOAE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ×3a× <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> =18

解得k=12

故选:B

【点睛】本题考查了反比例函数和几何综合,矩形的性质,平行线的判定,得出SABE=SOAE=18是解题关键.

二、填空题

13.计算: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> __________

【答案】3

【解析】

【分析】

根据零指数幂及绝对值计算即可.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故答案为3

【点睛】本题比较简单,考查含零指数幂的简单实数混合运算,熟记公式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 是关键.

14.若多边形的内角和是外角和的2倍,则该多边形是_____边形.

【答案】

【解析】

【分析】

设这个多边形的边数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,根据内角和公式和外角和公式,列出等式求解即可.

【详解】设这个多边形的边数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>
 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>
解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>
故答案为:六.

【点睛】本题考查了多边形的内角和与外角和,是基础知识要熟练掌握内角和公式和外角和公式.

15.现有四张正面分别标有数字﹣1123的不透明卡片,它们除数字外其余完全相同,将它们背而面朝上洗均匀,随机抽取一张,记下数字后放回,背面朝上洗均匀,再随机抽取一张记下数字,前后两次抽取的数字分别记为mn,则点Pmn)在第二象限的概率为__________

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【解析】

【分析】

画树状图展示所有16种等可能的结果数,利用第二象限内点的坐标特征确定点Pmn)在第二象限的结果数,然后根据概率公式求解.

【详解】解:画树状图为:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

共有16种等可能的结果数,其中点Pmn)在第二象限的结果数为3

所以点Pmn)在第二象限的概率= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【点睛】本题考查了列表法与树状图法:利用列表法或树状图法展示所有等可能的结果n,再从中选出符合事件AB的结果数目m,然后利用概率公式计算事件A或事件B的概率.也考查了点的坐标.

16.如图,在边长为2的正方形ABCD中,对角线AC的中点为O,分别以点AC为圆心,以AO的长为半径画弧,分别与正方形的边相交.则图中的阴影部分的面积为__________.(结果保留 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【解析】

【分析】

根据图形可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,由正方形的性质可求得扇形的半径,利用扇形面积公式求出扇形的面积,即可求出阴影部分面积.

【详解】由图可知,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

四边形ABCD是正方形,边长为2

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

OAC的中点,

OA= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【点睛】本题考查了求阴影部分面积,扇形面积公式,正方形的性质,解题的关键是观察图形得出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

17.AB两地相距240 km,甲货车从A地以40km/h的速度匀速前往B地,到达B地后停止,在甲出发的同时,乙货车从B地沿同一公路匀速前往A地,到达A地后停止,两车之间的路程ykm)与甲货车出发时间xh)之间的函数关系如图中的折线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 所示.其中点C的坐标是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,点D的坐标是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,则点E的坐标是__________

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【解析】

【分析】

先根据CD段的求出乙货车的行驶速度,再根据两车的行驶速度分析出点E表示的意义,由此即可得出答案.

【详解】设乙货车 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 行驶速度为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

由题意可知,图中的点D表示的是甲、乙货车相遇

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> C的坐标是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,点D的坐标是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 此时甲、乙货车行驶的时间为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,甲货车行驶的距离为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,乙货车行驶的距离为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 乙货车从B地前往A地所需时间为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

由此可知,图中点E表示的是乙货车行驶至A地,EF段表示的是乙货车停止后,甲货车继续行驶至B

则点E的横坐标为4,纵坐标为在乙货车停止时,甲货车行驶的距离,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

即点E的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【点睛】本题考查了一次函数的实际应用,读懂函数图象是解题关键.

18.火锅是重庆的一张名片,深受广大市民的喜爱.重庆某火锅店采取堂食、外卖、店外摆摊(简称摆摊)三种方式经营,6月份该火锅店堂食、外卖、摆摊三种方式的营业额之比为352.随着促进消费政策的出台,该火锅店老板预计7月份总营业额会增加,其中摆摊增加的营业额占总增加的营业额的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,则摆摊的营业额将达到7月份总营业额的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,为使堂食、外卖7月份的营业额之比为85,则7月份外卖还需增加的营业额与7月份总营业额之比是__________

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【解析】

【分析】

先根据题意设出相应的未知数,再结合题目的等量关系列出相应的方程组,最后求解即可求得答案.

【详解】解:设6月份该火锅店堂食、外卖、摆摊三种方式的营业额分别为3k5k2k7月份总增加的营业额为m,则7月份摆摊增加的营业额为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> m,设7月份外卖还需增加的营业额为x

7月份摆摊的营业额是总营业额的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,且7月份的堂食、外卖营业额之比为85

7月份的堂食、外卖、摆摊三种方式的营业额之比为857

7月份的堂食、外卖、摆摊三种方式的营业额分别为8a5a7a

由题意可知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【点睛】本题主要考查了三元一次方程组的应用,根据题意设出相应的未知数,结合题目中的等量关系列出方程组是解决本题的关键.

三、解答题

19.计算:(1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【解析】

【分析】

1)利用完全平方公式和整式乘法展开后合并同类型即可;

2)先把分子分母因式分解,然后按顺序计算即可;

【详解】1)解:原式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

2)解:原式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【点睛】本题考查整式的运算和分式的混合运算,熟记运算法则是解题的关键.

20.为了解学生掌握垃圾分类知识的情况,增强学生环保意识,某学校举行了垃圾分类人人有责的知识测试活动,现从该校七、八年级中各随机抽取20名学生的测试成绩(满分10分,6分及6分以上为合格)进行整理、描述和分析,下面给出了部分信息.

七年级20名学生的测试成绩为:

7879765910985876797106

七、八年级抽取的学生的测试成绩的平均数、众数、中位数、8分及以上人数所占百分比如下表所示:

年级

平均数

众数

中位数

8分及以上人数所占百分比

七年级

7.5

a

7

45%

八年级

7.5

8

b

c


八年级20名学生的测试成绩条形统计图如图:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

根据以上信息,解答下列问题:

1)直接写出上述表中的abc的值;

2)根据以上数据,你认为该校七、八年级中哪个年级学生掌握垃圾分类知识较好?请说明理由(写出一条理由即可);

3)该校七、八年级共1200名学生参加了此次测试活动,估计参加此次测试活动成绩合格的学生人数是多少?

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ;(2)八年级学生掌握垃圾分类知识较好,理由:根据以上数据,七、八年级的平均数相同,八年级的众数、中位数、8分及以上人数所占百分比比七年级的高;(3)估计参加此次测试活动成绩合格的人数有1080

【解析】

【分析】

1)七年级20名学生的测试成绩的众数找出现次数最多的即可得出a的值,由条形统计图即可得出八年级抽取的学生的测试成绩的中位数,八年级8分及以上人数除以总人数20人即可得出c的值;

2)分别比较七年级和八年级 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 平均数、众数、中位数、8分及以上人数所占百分比即可得出结论;

3)用七八年级的合格总人数除以总人数40人,得到这两个年级测试活动成绩合格的百分比,再乘以1200即可得出答案.

【详解】解:(1)七年级20名学生的测试成绩的众数是:7

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

由条形统计图可得,八年级抽取的学生的测试成绩的中位数是: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

八年级8分及以上人数有10人,所占百分比为:50%

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

2)八年级学生掌握垃圾分类知识较好,理由:根据以上数据,七、八年级的平均数相同,八年级的众数、中位数、8分及以上人数所占百分比比七年级的高;

3)七年级合格人数:18人,

八年级合格人数:18人,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 人,

答:估计参加此次测试活动成绩合格的人数有1080人.

【点睛】本题考查了平均数,众数,中位数,条形统计图等知识,熟练掌握平均数的求法,众数、中位数的概念是解决本题的关键.

21.如图,在平行四边形ABCD中,对角线ACBD相交于点O,分别过点AC <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,垂足分别为EFAC平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

1)若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的度数;

2)求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ;(2)见解析

【解析】

【分析】

1)利用三角形内角和定理求出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,利用角平分线的定义求出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,再利用平行线的性质解决问题即可.

2)证明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 可得结论.

【详解】(1)解: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 是平行四边形,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

2)证明: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 是平行四边形,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【点睛】本题考查平行四边形的性质,全等三角形的判定和性质等知识,解题的关键是熟练掌握相关的知识点.

22.在初中阶段的函数学习中,我们经历了列表、描点、连线画函数图象,并结合图象研究函数性质的过程.以下是我们研究函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 性质及其应用的部分过程,请按要求完成下列各小题.

1)请把下表补充完整,并在图中补全该函数图象;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

5

4

3

2

1

0

1

2

3

4

5

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>


 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

3

0

3

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>


 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>


2)根据函数图象,判断下列关于该函数性质的说法是否正确,正确的在相应的括号内打“√”,错误的在相应的括号内打×”

该函数图象是轴对称图形,它的对称轴为y轴;( )

该函数在自变量的取值范围内,有最大值和最小值,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,函数取得最大值3;当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,函数取得最小值-3( )

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,yx的增大而减小;当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,yx的增大而增大;( )

3)已知函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的图象如图所示,结合你所画的函数图象,直接写出不等式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的解集(保留1位小数,误差不超过0.2).

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ;(2)①× ;(3x10.3x1.8

【解析】

【分析】

1)代入x=3x=-3即可求出对应的y值,再补全函数图象即可;

2)结合函数图象可从增减性及对称性进行判断;

3)根据图象求解即可.

【详解】解:(1)当x=-3时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

x=3时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

函数图象如下:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

2)①由函数图象可得它是中心对称图形,不是轴对称图形;

故答案为:×

结合函数图象可得:该函数在自变量的取值范围内,有最大值和最小值,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,函数取得最大值3;当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,函数取得最小值-3

故答案为:

观察函数图象可得:当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,yx的增大而减小;当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,yx的增大而增大;

故答案为:

3 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

故该不等式的解集为: x10.3x1.8

【点睛】本题主要考查一次函数的图象和性质,一次函数与一元一次不等式,会用描点法画出函数图象,利用数形结合的思想得到函数的性质是解题的关键.

23.在整数的除法运算中,只有能整除与不能整除两种情况,当不能整除时,就会产生余数,现在我们利用整数的除法运算来研究一种数——“差一数

定义:对于一个自然数,如果这个数除以5余数为4,且除以3余数为2,则称这个数为差一数

例如: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,所以14差一数

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,但 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,所以19不是差一数

1)判断4974是否为差一数?请说明理由;

2)求大于300且小于400的所有差一数

【答案】149不是差一数 74差一数,理由见解析;(2314329344359374389

【解析】

【分析】

1)直接根据差一数的定义计算即可;

2)根据差一数的定义可知被5除余4的数个位数字为49;被3除余2的数各位数字之和被3除余2,由此可求得大于300且小于400的所有差一数

【详解】解:(1)∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

49不是差一数

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

74差一数

2)∵差一数这个数除以5余数为4

差一数这个数的个位数字为49

大于300且小于400的符合要求的数为304309314319324329334339344349354359364369374379384389394399

差一数这个数除以3余数为2

差一数这个数的各位数字之和被3除余2

大于300且小于400的所有差一数314329344359374389

【点睛】此题主要考查了带余数的除法运算,本题用逐步增加条件的方法依此找到满足条件的所有数是解决本题的关键.

24.为响应把中国人的饭碗牢牢端在自己手中的号召,确保粮食安全,优选品种,提高产量,某农业科技小组对AB两个玉米品种进行实验种植对比研究.去年AB两个品种各种植了10亩.收获后AB两个品种的售价均为2.4/kg,且B品种的平均亩产量比A品种高100千克,AB两个品种全部售出后总收入为21600元.

1)求AB两个品种去年平均亩产量分别是多少千克?

2)今年,科技小组优化了玉米的种植方法,在保持去年种植面积不变的情况下,预计AB两个品种平均亩产量将在去年的基础上分别增加a%2a%.由于B品种深受市场欢迎,预计每千克售价将在去年的基础上上涨a%,而A品种的售价保持不变,AB两个品种全部售出后总收人将增加 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,求a的值.

【答案】1A品种去年平均亩产量是400B品种去年平均亩产量是500千克;(210

【解析】

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 分析】

1)设AB两个品种去年平均亩产量分别是xy千克,根据题意列出方程组,解方程组即可得到答案;

2)根据题意分别表示A品种、B品种今年的收入,利用总收入等于A品种、B品种今年的收入之和,列出一元二次方程求解即可得到答案.

【详解】1)设AB两个品种去年平均亩产量分别是xy千克,由题意得

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

答:AB两个品种去年平均亩产量分别是400500千克

2)根据题意得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

a%=m,则方程化为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

整理得10m2-m=0

解得:m1=0(不合题意,舍去),m2=0.1

所以a%=0.1,所以a=10

答:a <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 值为10

【点睛】本题考查的是二元一次方程组的应用,一元二次方程的应用,掌握列方程或方程组解应用题的方法与步骤是解题的关键.

25.如图,在平面直角坐标系中,已知抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 与直线AB相交于AB两点,其中 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

1)求该抛物线的函数表达式;

2)点P为直线AB下方抛物线上的任意一点,连接PAPB,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 面积的最大值;

3)将该抛物线向右平移2个单位长度得到抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,平移后的抛物线与原抛物线相交于点C,点D为原抛物线对称轴上的一点,在平面直角坐标系中是否存在点E,使以点BCDE为顶点的四边形为菱形,若存在,请直接写出点E的坐标;若不存在,请说明理由.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 面积最大值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ;(3)存在, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【解析】

【分析】

1)将点AB的坐标代入抛物线表达式,即可求解;

2)设 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,求得解析式,过点Px轴得垂线与直线AB交于点F,设点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,即可求解;

3)分BC为菱形的边、菱形的的对角线两种情况,分别求解即可.

【详解】解:(1)∵抛物线过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

2)设 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,将点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

过点Px轴得垂线与直线AB交于点F

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

设点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

由铅垂定理可得

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 面积最大值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

3)(3)抛物线的表达式为:yx24x−1=(x22−5

则平移后的抛物线表达式为:yx2−5

联立上述两式并解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,故点C14);

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

设点D2m)、点Est),而点BC的坐标分别为(01)、(14);

BC为菱形的边时,

C向右平移1个单位向上平移3个单位得到B,同样DE)向右平移1个单位向上平移3个单位得到ED),

21sm3t2−1sm−3t

当点DE的下方时,则BEBC,即s2+(t121232

当点DE的上方时,则BDBC,即22+(m121232

联立①③并解得:s1t24(舍去4),故点E12);

联立②④并解得:s-3t-4± <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,故点E-3-4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> )或(-3-4− <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> );

BC为菱形的的对角线时,

则由中点公式得:1s−24−1mt

此时,BDBE,即22+(m12s2+(t12

联立⑤⑥并解得:s1t3

故点E13),

综上,点E的坐标为:(12)或 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 或(13).

存在, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【点睛】本题考查的是二次函数综合运用,涉及到一次函数的性质、菱形的性质、图形的平移、面积的计算等,其中(3),要注意分类求解,避免遗漏.

26.如图,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,点DBC边上一动点,连接AD,把AD绕点A逆时针旋转90°,得到AE,连接CEDE.点FDE的中点,连接CF

1)求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

2)如图2所示,在点D运动的过程中,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 时,分别延长CFBA,相交于点G,猜想AGBC存在的数量关系,并证明你猜想的结论;

3)在点D运动的过程中,在线段AD上存在一点P,使 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的值最小.当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 的值取得最小值时,AP的长为m,请直接用含m的式子表示CE的长.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【答案】1)证明见解析;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ;(3 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【解析】

【分析】

1)先证△BAD≌△CAE,可得∠ABD=∠ACE45°,可求∠BCE90°,由直角三角形的性质和等腰直角三角形的性质可得结论;

2)由(1)得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,推出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,然后根据现有条件说明

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,点ADCE四点共圆,F为圆心,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 中,推出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,即可得出答案;

3)设点P存在,由费马定理可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,设PD <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

得出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,得出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,解出a,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 即可得出答案.

【详解】解:(1)证明如下:∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 中,FDE中点(同时 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ), <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 为等腰直角三角形,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

2)由(1)得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

FDE中点,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

在四边形ADCE中,有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

ADCE四点共圆,

FDE中点,

F为圆心,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a> 中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

FCG中点,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

3)设点P存在,由费马定理可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

PD <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1009/" title="重庆" class="c1" target="_blank">重庆</a>

【点睛】本题是几何变换综合题,考查了全等三角形的判定和性质,等腰直角三角形的性质,旋转的性质,锐角三角函数等知识,灵活运用所学知识是解本题的关键.



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