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【330311】2020年湖北省咸宁市中考数学试题

时间:2025-02-09 10:51:07 作者: 字数:26734字

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 湖北省咸宁市2020年中考数学试题

一、精心选一选(本大题共8小题,每小题3分,满分24分.在每小题给出的四个选项中只有一项是符合题目要求的,请在答题卷上把正确答案的代号涂黑)

1.早在两千多年前,中国人就已经开始使用负数,并运用到生产和生活中,比西方早一千多年,下列各式计算结果为负数的是(

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】C

【解析】

【分析】

各式计算得到结果,即可作出判断.

【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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> =1,故选项不符合;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> =5,故选项不符合;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> =-6,故选项符合;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,故选项不符合;

故选C.

【点睛】此题考查了有理数的混合运算,熟练掌握运算法则是解本题的关键.

2.中国互联网络信息中心数据显示,随着二胎政策全面开放,升学就业竞争压力的不断增大,满足用户碎片化学习需求的在线教育用户规模持续增长,预计2020年中国在线教育用户规模将达到305000000人.将305000000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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】B

【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:305000000用科学记数法表示为3.05×108
故选:B

【点睛】此题考查了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.

3.下列计算正确的是(

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】B

【解析】

【分析】

利用合并同类项,同底数幂的乘法和除法,幂的乘方和积的乘方运算法则计算即可.

【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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,故选项不符合;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,故选项符合;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,故选项不符合;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,故选项不符合;

故选B.

【点睛】本题考查了合并同类项,同底数幂的乘法和除法,幂的乘方和积的乘方运算,掌握运算法则是关键.

4.如图是由5个完全相同的小正方体组成的几何体,则该几何体的左视图是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】A

【解析】

【分析】

根据主视图、左视图、俯视图是分别从物体正面、侧面和上面看所得到的图形,从而得出该几何体的左视图.

【详解】解:该几何体的左视图是:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

故选A.

【点睛】本题考查了三视图,考验学生的思考能力和对几何体三种视图的空间想象能力.

5.如图是甲、乙两名射击运动员某节训练课的5次射击成绩的折线统计图,下列判断正确的是(

 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

A. 乙的最好成绩比甲高 B. 乙的成绩的平均数比甲小

C. 乙的成绩的中位数比甲小 D. 乙的成绩比甲稳定

【答案】D

【解析】

【分析】

根据折线统计图得出甲乙成绩的各项数据,从而判断各选项.

【详解】解:由图可知:

甲运动员的成绩为:671089

乙运动员的成绩为:89878

A、甲的最好成绩为10环,乙的最好成绩为9环,故选项错误;

B、甲的成绩平均数为:(6+7+10+8+9÷5=8

乙的成绩平均数为:(8+9+8+7+8÷5=8

一样大,故选项错误;

C、甲的成绩的中位数为8,乙的成绩的中位数为8,一样大,故选项错误;

D、甲 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 成绩的方差为 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> =2

乙的成绩的方差为 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> =0.4

0.42,所以乙的成绩比甲稳定,故选项正确;

故选D.

【点睛】本题考查了平均数、中位数、方差,关键是根据甲乙的成绩计算出各项数据.

6.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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,则图中阴影部分 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 面积为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】D

【解析】

【分析】

根据圆周角定理得出∠AOB=90°,再利用S阴影=S扇形OAB-S△OAB算出结果.

【详解】解:∵∠C=45°

∴∠AOB=90°

OA=OB=2

S阴影=S扇形OAB-S△OAB= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

故选D.

【点睛】本题考查了圆周角定理,扇形面积计算,解题的关键是得到∠AOB=90°.

7.在平面直角坐标系 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 中,对于横、纵坐标相等的点称为“好点”.下列函数的图象中不存在“好点”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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】B

【解析】

【分析】

根据“好点”的定义判断出“好点”即是直线y=x上的点,再各函数中令y=x,对应方程无解即不存在“好点”.

【详解】解:根据“好点”的定义,好点即为直线y=x上的点,令各函数中y=x

Ax=-x,解得:x=0,即“好点”为(00),故选项不符合;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,无解,即该函数图像中不存在“好点”,故选项符合;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,经检验 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 是原方程的解,即“好点”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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> )和(- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> - <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ),故选项不符合;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,解得:x=03,即“好点”为(00)和(33),故选项不符合;

故选B.

【点睛】本题考查了函数图像上的点的坐标,涉及到解分式方程,一元二次方程,以及一元一次方程,解题的关键是理解“好点”的定义.

8.如图,在矩形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> E <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 的中点,将 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 沿直线 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 翻折,点B落在点F处,连结 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】C

【解析】

【分析】

根据折叠的性质得到∠AEB=∠AEF,再根据点EBC中点可得EF=EC,可得∠EFC=∠ECF,从而推出∠ECF=∠AEB,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 即可得到结果.

【详解】解:由折叠可得:AB=AF=2BE=EF,∠AEB=∠AEF

EBC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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

BE=CE=EF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

∴∠EFC=∠ECFAE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

∵∠BEF=∠AEB+∠AEF=∠EFC+∠ECF

∴∠ECF=∠AEB

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

故选C.

【点睛】本题考查了矩形的性质和折叠的性质,以及余弦的定义,解题的关键是利用折叠的性质得到∠ECF=∠AEB.

二、细心填一填(本大题共8小题,每小题3分,满分24分.请把答案填在答题卷相应题号的横线上)

9.A在数轴上的位置如图所示,则点A表示的数的相反数是________

 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】-3

【解析】

【分析】

A在数轴上表示的数是3,根据相反数的含义和求法,判断出点A表示的数的相反数是多少即可.

【详解】解:∵点A在数轴上表示的数是3
A表示的数的相反数是-3
故答案为:-3

【点睛】此题主要考查了在数轴上表示数的方法,以及相反数的含义和求法,要熟练掌握.

10.因式分解: <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> __________

【答案】mx-12

【解析】

【分析】

先提取公因式m,再利用完全平方公式进行因式分解即可.

【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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【点睛】本题考查了因式分解的问题,掌握完全平方公式是解题的关键.

11.如图,请填写一个条件,使结论成立:∵__________,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】1=∠4(答案不唯一)

【解析】

【分析】

根据平行线的判定添加条件即可.

【详解】解:如图,

若∠1=∠4,则a∥b

故答案为:∠1=∠4(答案不唯一)

【点睛】本题考查了平行线的判定,可围绕截线找同位角、内错角和同旁内角解答.

12.若关于x的一元二次方程 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 有实数根,则n的取值范围是__________

【答案】n≥0

【解析】

【分析】

根据平方的非负性可得结果.

【详解】解:∵关于x的一元二次方程 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 有实数根,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

n≥0

故答案为:n≥0

【点睛】本题考查了一元二次方程的解,掌握根的判别方法是解题的关键.

13.某校开展以“我和我的祖国”为主题的“大合唱”活动,七年级准备从小明,小东、小聪三名男生和小红、小慧两名女生中各随机选出一名男生和一名女生担任领唱,则小聪和小慧被同时选中的概率是________

【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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【解析】

【分析】

先画树状图展示所有6种等可能的结果数,再找出小聪和小慧被同时选中的结果数,然后根据概率公式求解.

【详解】解:画树状图如下:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

可知:共有6种等可能的结果,其中小聪和小慧同时被选中的情况有1种,

小聪和小慧被同时选中的概率是 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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展示所有等可能的结果数,再找出某事件所占有的结果数,然后根据概率公式计算这个事件的概率.

14.如图,海上有一灯塔P,位于小岛A北偏东60°方向上,一艘轮船从北小岛A出发,由西向东航行 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 到达B处,这时测得灯塔P在北偏东30°方向上,如果轮船不改变航向继续向东航行,当轮船到达灯塔P的正南方,此时轮船与灯塔P的距离是________ <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> .(结果保留一位小数, <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】20.8

【解析】

【分析】

证明△ABP是等腰三角形,过PPD⊥AB,从而求得PD的长即可.

【详解】解:过PPD⊥ABD

AB=24

∵∠PAB=90°-60°=30°,∠PBD=90°-30°=60°

∴∠BPD=30°

∴∠APB=30°,即∠PAB=∠APB
∴AB=BP=24

在直角△PBD中,PD=BP•sin∠PBD=24×
 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ≈20.8.

故答案为:20.8.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【点睛】本题主要考查了解直角三角形的应用,正确作出垂线,转化为直角三角形的计算是解决本题的关键.

15.按一定规律排列的一列数: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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,…,若abc表示这列数中的连续三个数,猜想abc满足的关系式是__________

【答案】bc=a

【解析】

【分析】

根据题目中的数字,可以发现相邻的数字之间的关系,从而可以得到abc之间满足的关系式.

【详解】解:∵一列数: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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,…,
可发现:第n个数等于前面两个数的商,
abc表示这列数中的连续三个数,
∴bc=a

故答案为:bc=a

【点睛】本题考查数字的变化类,解答本题的关键是明确题意,发现题目中数字的变化规律,求出abc之间的关系式.

16.如图,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 是边长为2的正方形,点E是边 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 上一动点(不与点BC重合), <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 交正方形外角的平分线 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 于点F,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 于点G,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,有下列结论:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 的面积的最大值为1

其中正确结论的序号是_____________.(把正确结论的序号都填上)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】①②③

【解析】

【分析】

证明∠BAE=∠CEG,结合∠B=∠BCD可证明△ABE∽△ECG,可判断①;在BA上截取BM=BE,证明△AME≌△ECF,可判断②;可得△AEF为等腰直角三角形,证明∠BAE+∠DAF=45°,结合∠BAE=∠CEF,∠FCH=45°=∠CFE+∠CEF,可判断③;设BE=x,则BM=xAM=AB-BM=2-x,根据△AME≌△ECF,求出△AME面积的最大值即可判断④.

【详解】解:∵四边形ABCD为正方形,

∴∠B=∠BCD=90°

∵∠AEF=90°

∴∠AEB+∠CEG=90°,又∠AEB+∠BAE=90°

∴∠BAE=∠CEG

∴△ABE∽△ECG,故①正确;

BA上截取BM=BE

四边形ABCD为正方形,
∴∠B=90°
BA=BC
∴△BEM
为等腰直角三角形,
∴∠BME=45°

∴∠AME=135°

∵BA-BM=BC-BE

∴AM=CE

∵CF
为正方形外角平分线,
∴∠DCF=45°

∴∠ECF=135°=∠AME

∵∠BAE=∠FEC

∴△AME≌△ECF
ASA),

AE=EF,故②正确;

∴△AEF为等腰直角三角形,

∴∠EAF=∠EFA=45°

∴∠BAE+∠DAF=45°

而∠BAE=∠CEF,∠FCH=45°=∠CFE+∠CEF

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,故③正确;

BE=x,则BM=xAM=AB-BM=2-x
S
△AME= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> •x•2-x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

x=1时,S△AME有最大值 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>
而△AME≌△ECF
∴S
△AME=S△CEF
∴S
△CEF有最大值 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,所以④错误;

综上:正确结论的序号是:①②③.

故答案为:①②③.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【点睛】本题考查了全等三角形的判定和性质,相似三角形的判定,等腰直角三角形的判定和性质,正方形的性质,二次函数的最值,解题的关键是添加辅助线,灵活运用全等三角形的知识解决线段的问题.

三、专心解一解(本大题共8小题,满分2分.请认真读题,冷静思考,解答题应写出必要的文字说明、证明过程或演算步骤,请把解题过程写在答题卷相应题号的位置)

17.1)计算: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

2)解不等式组: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【答案】10;(2-3x-2

【解析】

【分析】

1)根据实数的混合运算法则计算即可;

2)分别解得两个不等式的解集,再合并即可.

【详解】解:(1)原式= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

=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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

解不等式①得:x-2

解不等式②得:x-3

不等式组的解集为:-3x-2.

【点睛】本题考查了实数的混合运算与解不等式组,以及特殊角的三角函数值,解题的关键是掌握运算法则.

18.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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 中,以点B为圆心, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 长为半径画弧,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 于点E,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 上截取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

1)求证: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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 是菱形;

2)请用无刻度的直尺 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 内找一点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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> (标出点P的位置,保留作图痕迹,不写作法)

【答案】1)见解析;(2)见解析

【解析】

【分析】

1)根据四边形ABCD为平行四边形,得出AF∥BE,由作图过程可知AF=BE,结合AB=BE即可证明;

2)利用菱形对角线互相垂直的性质,连接AEBF,交点即为点P.

【详解】解:(1)根据作图过程可知:AB=BEAF=BE

四边形ABCD为平行四边形,

AF∥BE

AF=BE

四边形ABEF为平行四边形,

AB=BE

平行四边形ABEF为菱形;

2)如图,点P即为所作图形,

 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

四边形ABEF为菱形,则BF⊥AE

∴∠APB=90°.

【点睛】本题考查了菱形的判定和性质,平行四边形的性质,解题的关键是利用相应的性质进行画图.

19.如图,已知一次函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 与反比例函数 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 的图象在第一、三象限分别交于 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 两点,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

1)求一次函数和反比例函数的解析式;

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 的面积为______

3)直接写出 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> x的取值范围.

【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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ;(28;(3-2x0x6.

【解析】

【分析】

1)把A代入反比例函数,根据待定系数法即可求得m,得到反比例函数 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 解析式,然后将 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 代入,求得a,再根据待定系数法求得一次函数的解析式即可;

2)求出一次函数图像与x轴交点坐标,再利用面积公式计算即可;

3)根据图象得到一次函数图像在反比例函数图像上方时的x取值范围.

【详解】解:(1)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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 代入反比例函数 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 得:

m=6

反比例函数的解析式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 点在反比例函数 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 图像上,

-3a=6,解得a=-2

B-2-3),

一次函数y1=kx+b的图象经过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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

一次函数的解析式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,一次函数的解析式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

y=0,解得:x=4,即一次函数图像与x轴交点为(40),

S△AOB= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

故答案为:8

3)由图象可知:

 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 时,即一次函数图像在反比例函数图像上方,

x的取值范围是:-2x0x6.

【点睛】此题是考查一次函数与反比例函数的交点问题、待定系数法求一次函数解析式,待定系数法求反比例函数解析式,待定系数法求函数解析式是中学阶段求函数解析式常用的方法,一定要熟练掌握并灵活运用.

20.随着科技 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 进步和网络资源的丰富,在线阅读已成为很多人选择的阅读方式.为了解同学们在线阅读情况,某校园小记者随机调查了本校部分同学,并统计他们平均每天的在线阅读时间t(单位: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ),然后利用所得数据绘制成如下不完整的统计图表.

在线阅读时间频数分布表

组别

在线阅读时间t

(人数)

A

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

4

B

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

8

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

16

E

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

根据以上图表,解答下列问题:

1)这次被调查的同学共有______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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ______ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> _____

2)求扇形统计图中扇形D的圆心角的度数;

3)若该校有950名学生,请估计全校有多少学生平均每天的在线阅读时间不少于 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ?

【答案】150208;(2115.2°;(3722

【解析】

【分析】

1)根据B组人数和所占百分比求出被调查的学生总数,再根据C组所占百分比求出a值,最后根据A组人数求出所占百分比;

2)求出D组所占百分比,再乘以360°即可;

3)用样本中在线阅读时间不少于 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 的总人数除以50,再乘以全校总人数即可.

【详解】解:(1)∵B组的人数为8人,所占百分比为16%

被调查的同学共有8÷16%=50人,

a=50×40%=20人,4÷50×100%=8%

m=8

故答案为:50208

2)(1-40%-16%-8%-4%×360°=115.2°

则扇形统计图中扇形D的圆心角的度数为:115.2°

3950× <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> =722人,

全校有722学生平均每天的在线阅读时间不少于 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> .

【点睛】本题考查频数分布表、扇形统计图、用样本估计总体,解答本题的关键是明确题意,利用数形结合的思想解答.

21.如图,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,点O <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 上,以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 为半径的半圆O <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 于点D,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 于点E,过点D作半圆O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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

1)求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

2)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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,求半圆O的半径长.

【答案】1)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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【解析】

【分析】

1)连接OD,根据切线的性质得到∠BDF+∠ADO=90°,再结合∠ADO=∠OAD,推出∠BDF=∠B,即可;

2)过FFG⊥BDG,先利用三角函数求出BG=DG,再过点OOH⊥ADH,在△AOH中,求出AO即可.

【详解】解:(1)连接OD

DF和半圆相切,

OD⊥DF

∴∠BDF+∠ADO=90°

∵∠ADO=∠OAD

∴∠OAD+∠BDF=90°,又∠C=90°

∴∠OAD+∠B=90°

∴∠BDF=∠B

BF=DF

2)过FFG⊥BDG,则GF垂直平分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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

BF=DF=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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,∠C=90°

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

cos∠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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,解得:BG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> =DG

AD=AB-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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

过点OOH⊥ADH

AH=DH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> AD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

cos∠BAC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

AO= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

即半圆O的半径长为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> .

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【点睛】本题考查了切线的性质,相似三角形的判定和性质,等腰三角形的判定和性质,解直角三角形,解题的关键是正确寻找相似三角形,学会添加常用辅助线,属于中考常考题型.

22.518日,我市九年级学生安全有序开学复课.为切实做好疫情防控工作,开学前夕,我市某校准备在民联药店购买口罩和水银体温计发放给每个学生.已知每盒口罩有100只,每盒水银体温计有10支,每盒口罩价格比每盒水银体温计价格多150元.用1200元购买口罩盒数与用300元购买水银体温计所得盒数相同.

1)求每盒口罩和每盒水银体温计的价格各是多少元?

2)如果给每位学生发放2只口罩和1支水银体温计,且口罩和水银体温计均整盒购买.设购买口罩m盒(m为正整数),则购买水银体温计多少盒能和口罩刚好配套?请用含m的代数式表示.

3)在民联药店累计购医用品超过1800元后,超出1800元的部分可享受8折优惠.该校按(2)中的配套方案购买,共支付w元,求w关于m的函数关系式.若该校九年级有900名学生,需要购买口罩和水银体温计各多少盒?所需总费用为多少元?

【答案】1)每盒口罩和每盒水银体温计的价格各是200元,50元;(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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,需要购买口罩18盒,水银体温计90盒,所需总费用为6840.

【解析】

【分析】

1)设每盒水银体温计的价格是x元,根据用1200元购买口罩盒数与用300元购买水银体温计的盒数相同列出方程,求解即可;

2)先用m表示出需要水银体温计的支数,再表示出水银体温计的盒数;

3)分当m≤4时,当m4时,分别得出关系式,再合并,根据若该校九年级有900名学生求出口罩的盒数m,从而得到体温计的盒数以及总费用.

【详解】解:(1)设每盒水银体温计的价格是x元,则每盒口罩的价格是x+150元,

根据题意可得: <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

解得:x=50

经检验:x=50是原方程的解,

50+150=200元,

每盒口罩和每盒水银体温计的价格各是200元,50元;

2)∵购买口罩m盒,

共有口罩100m个,

给每位学生发放2只口罩和1支水银体温计,

需要发放 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 支水银体温计,

需要购买 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 盒水银体温计;

3)由题意可得:

200m+5m×50=1800

解得:m=4

若未超过1800元,即当m≤4时,

w=200m+5m×50=450m

若超过1800元,即当m4时,

w=200m+5m×50-1800×0.8+1800=360m+360

w关于m的函数关系式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

若该校九年级有900名学生,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> =900

解得:m=18

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> =6840

答:需要购买口罩18盒,水银体温计90盒,所需总费用为6840.

【点睛】本题考查了分式方程的实际应用,一次函数的实际应用,解题的关键是理解题意,弄清口罩盒数与体温计盒数的配套关系.

23.定义:有一组对角互余的四边形叫做对余四边形.

理解:

1)若四边形 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 是对余四边形,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 的度数之和为______

证明:

2)如图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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 的直径,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 上, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 相交于点D

求证: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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 是对余四边形;

 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

探究:

3)如图2,在对余四边形 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,探究线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 之间有怎样的数量关系?写出猜想,并说明理由.

【答案】190°270°;(2)见解析;(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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,理由见解析

【解析】

【分析】

1)分当∠A和∠C互余时,当∠B和∠D互余时,两种情况求解;

2)连接BO,得到∠BON+∠BOM=180°,再利用圆周角定理证明∠C+∠A=90°即可;

3)作△ABD的外接圆O,分别延长ACBCDC,交圆OEFG,连接DFDEEF,先证明GF是圆O的直径,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,再证明△ABC∽△FEC,△ACD∽△GCE,△BCD∽△GCF,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,从而得出 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,根据△ABC为等边三角形可得AB=AC=BC,从而得到 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> .

【详解】解:(1)∵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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 是对余四边形,

当∠A和∠C互余时,

A+∠C=90°

当∠B与∠D互余时,

B+∠D=90°

则∠A+∠C=360°-90°=270°

故答案为:90°270°

2)如图,连接BO

可得:∠BON=2∠C,∠BOM=2∠A

而∠BON+∠BOM=180°

2∠C+2∠A=180°

∴∠C+∠A=90°

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 是对余四边形;

 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

3)∵四边形ABCD为对于四边形,∠ABC=60°

∴∠ADC=30°

如图,作△ABD的外接圆O,分别延长ACBCDC,交圆OEFG,连接DFDEEF

则∠AEF=∠ABC=60°,∠AEG=∠ADG=30°

∴∠AEF+∠AEG=90°,即∠FEG=90°

GF是圆O的直径,

AB=BC

∴△ABC为等边三角形,

∵∠ABC=∠AEF,∠ACB=∠ECF

∴△ABC∽△FEC,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

同理,△ACD∽△GCE,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

BCD∽△GCF,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

AB=BC=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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> .

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【点睛】本题考查了相似三角形的判定和性质,四边形的新定义问题,圆周角定理,等边三角形的判定和性质,多边形内角和,解题的关键是理解对余四边形的概念,结合所学知识求证.

24.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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 平面直角坐标系中,直线 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> x轴交于点A,与y轴交于点B,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 过点B且与直线相交于另一点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

1)求抛物线的解析式;

2)点P是抛物线上的一动点,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 时,求点P的坐标;

3)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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> x轴的正半轴上,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> y轴正半轴上的一动点,且满足 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

mn之间的函数关系式;

m在什么范围时,符合条件的N点的个数有2个?

【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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 或(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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> )或(-2-3);(3)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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ;②0m <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

【解析】

【分析】

1)利用一次函数求出AB的坐标,结合点C坐标,求出二次函数表达式;

2)当点Px轴上方时,点P与点C重合,当点Px轴下方时,APy轴交于点Q,求出AQ表达式,联立二次函数,可得交点坐标,即为点P

3)①过点CCD⊥x轴于点D,证明△MNO∽△NCD,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,整理可得结果;

作以MC为直径的圆E,根据圆E与线段OD的交点个数来判断M的位置,即可得到m的取值范围.

【详解】解:(1)∵直线 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> x轴交于点A,与y轴交于点B

x=0,则y=2,令y=0,则x=4

A40),B02),

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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 经过B02), <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

抛物线的表达式为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

2)当点Px轴上方时,点P与点C重合,满足 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

当点Px轴下方时,如图,APy轴交于点Q

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

BQ关于x轴对称,

Q0-2),又A40),

设直线AQ的表达式为y=px+q,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

直线AQ的表达式为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,联立得:

 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ,解得:x=3-2

P的坐标为(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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> )或(-2-3),

综上,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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 时,点P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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 或(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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> )或(-2-3);

 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

3)①如图,∠MNC=90°,过点CCD⊥x轴于点D

∴∠MNO+∠CND=90°

∵∠OMN+∠MNO=90°

∴∠CND=∠OMN,又∠MON=∠CDN=90°

∴△MNO∽△NCD

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

整理得: <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

如图,∵∠MNC=90°

MC为直径画圆E

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

N在线段OD上(不含OD),即圆E与线段OD有两个交点(不含OD),

My轴正半轴,

当圆E与线段OD相切时,

NE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> MC,即NE2= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> MC2

M0m), <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

E <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> ),

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

解得:m= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

当点M与点O重合时,如图,

此时圆E与线段OD(不含OD)有一个交点,

 <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/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a>

0m <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> 时,圆E与线段OD有两个交点,

m的取值范围是:0m <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> <a href="/tags/1032/" title="咸宁" class="c1" target="_blank">咸宁</a> .

【点睛】本题是二次函数综合,考查了求二次函数表达式,相似三角形的判定和性质,圆周角定理,一次函数表达式,难度较大,解题时要充分理解题意,结合图像解决问题.