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【327986】广西玉林市2021年中考数学真题

时间:2025-01-20 20:55:22 作者: 字数:18846字
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绝密·启用前

广西玉林市2021年中考数学真题

题号

总分

得分





注意事项:

1.答题前填写好自己的姓名、班级、考号等信息

2.请将答案正确填写在答题卡上



评卷人

得分




一、选择题

1.计算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的值( )
A
1
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
C
3
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

2.我市今年中考报名人数接近101000人,将数据101000用科学记数法表示是( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

3.如图是某几何体的三视图,则该几何体是( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
A
.圆锥
B
.圆柱
C
.长方体
D
.三棱柱

4.下列计算正确的是( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

5.甲、乙两人进行飞镖比赛,每人各投6次,他们的成绩如下表(单位:环):

678899

56 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 9910


如果两人的比赛成绩的中位数相同,那么乙的第三次成绩 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是( )
A
6
B
7
C
8
D
9

6.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 底边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 上的高为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 底边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 上的高为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,则有( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
D
.以上都有可能

7.学习圆的性质后,小铭与小熹就讨论起来,小铭说:“被直径平分的弦也与直径垂直”,小熹说:“用反例就能说明这是假命题” .下列判断正确的是( )
A
.两人说的都对
B
.小铭说的对,小燕说的反例不存在
C
.两人说的都不对
D
.小铭说的不对,小熹说的反例存在

8.一个不透明的盒子中装有2个黑球和4个白球,这些球除颜色外其他均相同,从中任意摸出3个球,下列事件为必然事件的是( )
A
.至少有1个白球
B
.至少有2个白球
C
.至少有1个黑球
D
.至少有2个黑球

9.已知关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的一元二次方程: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 有两个不相等的实数根 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,则( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

10.一个四边形顺次添加下列中的三个条件便得到正方形:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
a.两组对边分别相等 b.一组对边平行且相等
c.一组邻边相等 d.一个角是直角
顺次添加的条件:①acdbdcabc
则正确的是:( )
A
.仅①
B
.仅③
C
.①②
D
.②③

11.观察下列树枝分杈的规律图,若第 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 个图树枝数用 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 表示,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

12.图(1),在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 从点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 出发,沿三角形的边以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> /秒的速度逆时针运动一周,图(2)是点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 运动时,线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的长度 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> )随运动时间 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> (秒)变化的关系图象,则图(2)中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 点的坐标是( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

评卷人

得分




二、填空题

13.4的相反数是____

14.实数8的立方根是_____

15.方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的解是______

16.如图,某港口 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 位于东西方向的海岸线上,甲、乙轮船同时离开港口,各自沿一固定方向航行,甲、乙轮船每小时分别航行12海里和16海里,1小时后两船分别位于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 处,且相距20海里,如果知道甲船沿北偏西 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 方向航行,则乙船沿_____方向航行.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

17.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是等腰三角形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 过原点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,底边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 轴双曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 两点,过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 轴交双曲线于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的值是______
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

18.如图、在正六边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 中,连接线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 交于点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,分别延长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> .有以下结论:① <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ;② <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ;③ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的重心、内心及外心均是点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ;④四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 绕点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 逆时针旋转 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 与四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 重合.则所有正确结论的序号是______
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

评卷人

得分




三、解答题

19.计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

20.先化简再求值: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 使反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的图象分别位于第二、四象限.

21.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 上, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
1)求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
2)若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的值.

22.2021年是中国共产党建党100周年华诞.“五一”后某校组织了八年级学生参加建党100周年知识竞赛,为了了解学生对党史知识的掌握情况,学校随机抽取了部分同学的成绩作为样本,把成绩按不及格、合格、良好、优秀四个等级分别进行统计,并绘制了如下不完整的条形统计图与扇形统计图:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

请根据图中提供的信息解答下列问题:
1)根据给出的信息,将这两个统计图补充完整(不必写出计算过程);
2)该校八年级有学生650人,请估计成绩未达到“良好”及以上的有多少人?
3)“优秀”学生中有甲、乙、丙、丁四位同学表现突出,现从中派2人参加区级比赛,求抽到甲、乙两人的概率.

23.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 与等边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 分别交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是直径,过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
1)求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的切线;
2)连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的切线时,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的半径 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 与等边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的边长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 之间的数量关系.

24.某市垃圾处理厂利用焚烧垃圾产生的热能发电,有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 两个焚烧妒,每个焚烧炉每天焚烧垃圾均为100吨,每焚烧一吨垃圾, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉比 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉多发电50度, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉每天共发电55000度.
1)求焚烧一吨垃圾, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉和 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉各发电多少度?
2)若经过改进工艺,与改进工艺之前相比每焚烧一吨垃圾, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉和 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉的发电量分别增加 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> % <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> %,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉每天共发电至少增加 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> %,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的最小值.

25.如图,在四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 中,对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,分别交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
1)求证:四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是菱形:
2)设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的长.

26.已知抛物线: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> )与 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 轴交点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的左侧),顶点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

1)求点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的坐标及抛物线的对称轴;
2)若直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 与抛物线交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 关于原点对称,求抛物线的解析式;
3)如图,将(2)中的抛物线向上平移,使得新的抛物线的顶点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 上,设直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 轴的交点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,原抛物线上的点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 平移后的对应点为点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,求点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的坐标.

参考答案

1.A

【解析】
根据有理数的加法法则进行计算即可.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
故选:A

2.B

【解析】
科学记数法的表示形式为a×10n的形式,其中1≤|a|10n整数.确定n值时,要看把原数a,小数点移了多少位,n绝对值与小数点移的位数相同.当原数绝对值10n是正数;当原数的绝对值1n数.
解:101000= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
B

3.C

【解析】
根据常见几何体的三视图逐一判断即可.
解:A、圆锥的主视图和左视图都是等腰三角形,俯视图是圆,不符合题意;
B
、圆柱的主视图和左视图是矩形,但俯视图是圆,不符合题意;
C
、长方体的主视图、左视图及俯视图都是矩形,符合题意;

D
、三棱柱的主视图和左视图是矩形,但俯视图是三角形,不符合题意;
故选:C

4.D

【解析】
根据合并同类项的法则,积的乘方,同底数幂的除法即可作出判断.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,故选项错误;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,故选项错误;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,则选项错误;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 、正确.
故选 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

5.B

【解析】
根据中位数的求法可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后求解即可.
解:由题意得:甲乙两人的中位数都为第三次和第四次成绩的平均数,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
故选B

6.A

【解析】
分别过点AAEBC于点EPFQR于点F,然后根据形及三角函数可直接行排除选项
解:分别过AAEBC于点EPFQR于点F,如所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
意得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
A

7.D

【解析】
根据垂径定理可直接进行排除选项.
解:由垂径定理的推论“平分弦(不是直径)的直径垂直于弦,并且平分弦所对的弧”可知:
小铭忽略了垂径定理中的“弦不能是直径”这一条件,因为一个圆中的任意两条直径都互相平分,但不垂直,所以小铭说法错误,小熹所说的反例即为两条直径的情况下;
故选D

8.A

【解析】
根据事件发生的可能性大小判断相应事件的类型即可.
解:一个不透明的袋子中只有2个黑球和4个白球,这些球除颜色外无其他差别,随机从袋子中一次摸出3个球,
A
3个球中至少有1个白球,是必然事件,故本选项符合题意;
B
3个球中至少有2个白球,是随机事件,故本选项不符合题意;
C
3个球中至少有1个黑球,是随机事件,故本选项不符合题意;
D
3个球中至少有2个黑球,是随机事件,故本选项不符合题意;
故选:A

9.D

【解析】
根据题意及一元二次方程根的判别式可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后再根据一元二次方程根与系数的关系可进行求解.
解:∵关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的一元二次方程: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 有两个不相等的实数根 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
由韦达定理可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
只有D选项正确;
故选D

10.C

【解析】
根据题意及正方形的判定定理可直接进行排除选项.
解:①由两组对边分别相等可得该四边形是平行四边形,添加一组邻边相等可得该四边形是菱形,再添加一个角是直角则可得该四边形是正方形;正确,故符合题意;
由一组对边平行且相等可得该四边形是平行四边形,添加一个角是直角可得该四边形是矩形,再添加一组邻边相等则可得该四边形是正方形;正确,故符合题意;
ab都为平行四边形的判定定理,故不能判定该四边形是正方形,故错误,不符合题意;
正确的有①②;
故选C

11.B

【解析】
根据题目中的图形,可以写出前几幅图中树枝分杈的数量,从而可以发现树枝分杈的变化规律,进而得到规律 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,代入规律求解即可.
解:由图可得到:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
则: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
故答案选:B

12.C

【解析】
由图象及题意易得AB=8cmAB+BC=18cmBC=10cm,当x=13s,点PBC的中点,而根据直角三角形斜线定理可求解.
解:由意及象可得:
当点P线AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> AP不断增大,当到达点BAP最大,所以此AP=AB=8cm
当点P线BC,由象可知线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 先随运动时间 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的增大而减小,再随运动时间 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的增大而增大,当到达点CAB+BC=18cm,即BC=10cm,由象可知当时间为13sBP=13-8=5cm,此PBC的中点,如所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 点的坐 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
C

13.-4

【解析】
根据符号相反且绝对值相等的两个数互为相反数进行解答.
解:4的相反数是-4
故答案为:-4

14.2

【解析】
根据立方根的定义解答.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,∴8的立方根是2.故答案为2

15.x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

【解析】
先去分母,再解整式方程,检验即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,两边同乘2x-2
去分母得, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
解整式方程得,x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
经检验x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是原分式方程的解;
故答案x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

16.北偏东50°(或东偏北40°

【解析】
由题意易得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 海里,PB=16海里, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,所以APB=90°而可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后问题可求解.
解:由意得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 海里,PB=1×16=16海里, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 海里,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∴∠APB=90°
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
乙船沿北偏50°(或偏北40°)方向航行;
故答案北偏50°(或偏北40°).

17.3

【解析】
设点A标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ),根据已知条件可得到点B标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ),点C标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ),然后得到点D得坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ),表示出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的面解出k即可.
解:A标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是等腰三角形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 原点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,底 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
B标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ),点C标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 交双曲线于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
D标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
故答案 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

18.①②③

【解析】
由题意易得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,进而可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,则有四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是矩形,然后可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 为等边三角形,最后可得答案.
解:∵六边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是正六边形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
在△DEF中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
同理可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是矩形,
同理可 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是矩形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是平行四形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ASA),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是菱形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∴∠NAM=60°
∴△NAM是等三角形,
AM=MN
AB=3
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∵∠MAB=30°ACG=90°
∴∠G=60°
∴△ADG是等三角形,
ACBD交于点M
由等三角形的性及重心、内心、外心可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的重心、内心及外心均是点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
OF,如所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

易得FOA=60°
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 时针 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 与四 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 重合,
上所述:正确结论的序号是①②③
故答案①②③

19.1

【解析】
先算算术平方根,零指数幂,负整数指数幂以及特殊角三角函数值,再算加减法,即可求解.
解:原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
=
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

20. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

【解析】
由题意易得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后对分式进化简,然后再求解即可.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 使反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的图象分别位于第二、四象限,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
=
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
=
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

21.1)见详解;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

【解析】
1)由题意易得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后问题可求证;
2)由(1)及题意易得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后根据相似三角形的面积比与相似比的关系可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后问题可求解.
1)证明:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
2)解:由(1)可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

22.1)图见详解;(2)成绩未达到“良好”及以上的有195人;(3)抽到甲、乙两人的概率为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

【解析】
1)由统计图可得不及格的人数为2人,所占百分比为5%,则可求出随机抽取的总人数,然后问题可求解;
2)由(1)可直接列式进行求解即可;
3)由题意可画出树状图,然后再进行求解概率即可.
解:(1)由题意得:
2÷5
=40人,
∴“
良好”的人数为40-2-10-12=16人,
优秀”所占百分比为12÷40×100=30%,“合格”所占百分比为10÷40×100=25%,
则补全统计图如图所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

故答案为3025
2)由(1)可得:
650×
5+25%)=195(人);
答:成绩未达到“良好”及以上的有195
3)由题意可得:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

抽到甲、乙两人的概率为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

23.1)见详解;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

【解析】
1)连接OD,由意易得A=B=60°AOD三角形,而可得ODBC,然后可得CFD=FDO=90°,最后问题可求
2DE,由(1)及意易得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> FDE=60°FDE是等三角形,而可得DE=DF,然后易得CDF≌△AEDAE=CD=2r,最后问题可求解.
1明:OD,如所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∴∠A=B=60°
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∴△AOD三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
ODBC
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∴∠CFD=FDO=90°
OD是半径,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的切线
2)解:DE,如所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
由(1)可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的切线FDO=90°AOD三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的切线
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∴△FDE是等三角形,
DE=DF
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是直径,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∴△CDF≌△AEDAAS),
AE=CD=2r
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

24.1)焚烧一吨垃圾, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉和 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 焚烧炉各发电300250度;(2a最小值为11

【解析】
1B炉每吨发电x度,A炉每吨发电x+50)度,根据意列出方程,求解即可.
2)根据(1)中的数据,表示出改后的发电量,列出不等式并求解即可.
1B炉每吨发电x度,A炉每吨发电x+50)度,
100
x+50+100x=55000
解方程得x=250
B炉每吨发电250度,A炉每吨发电300度;
2)由(1)可知改AB发电量分别为3001+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> %),2501+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> %),
根据意列式:100×3001+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> %+100×2501+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> %55000+55000× <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> %
解不等式得:a≥11
a的最小值为11

25.1)见详解;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

【解析】
1)由题意易得四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是平行四边形,则有ABCD,然后可DOF≌△BOE问题可求解;
2)由意易得AD=4AB=8ABD=30°DAB=60°而可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是等三角形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是等三角形,然后可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,最后根据三角函数行求解即可.
1明: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是平行四形,
ABCD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∴△DOF≌△BOEASA),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是平行四形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是菱形;
2)由(1)可得四 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是菱形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
∴∠ABD=30°DAB=60°
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是等三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 是等三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

26.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,对称轴为直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ;(3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>

【解析】
1)令y=0 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后行求解即可,最后利用抛物线对公式行求解即可;
2MN的横坐别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,由意可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后利用一元二次方程根与系数的关系行求解即可;
3)由(2)及意易得抛物线向上平移了4度得到新的抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,然后 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 而根据两点距离公式可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,最后求解即可.
解:(1)令y=0 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 在点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的左
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
抛物线轴为线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
2立直线与抛物线的解析式可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,化得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
MN的横坐别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 关于原点称,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
根据一元二次方程根与系数的关系可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
抛物线的解析式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
3)由(2)可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> ,化为顶点式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
将(2)中的抛物线向上平移,使得新的抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 上,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
新抛物线是由抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 向上平移了4度得到,
线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a> 的交点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
由两点距离公式可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1161/" title="玉林" class="c1" target="_blank">玉林</a>