当前位置:首页 > 中考 > 数学试卷

【327659】2022年广西贵港市中考数学真题

时间:2025-01-20 19:56:23 作者: 字数:20229字
简介:

绝密·启用前

2022年广西贵港市中考数学真题

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.-2的倒数是( )
A
-2
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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
D
2

2.一个圆锥如右图所示放置,对于它的三视图,下列说法正确的是(       
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
A
.主视图与俯视图相同
B
.主视图与左视图相同
C
.左视图与俯视图相同
D
.三个视图完全相同

3.一组数据351465的众数和中位数分别是(       
A
54.5
B
4.54
C
44.5
D
55

4.据报道:芯片被誉为现代工业的掌上明珠,芯片制造的核心是光刻技术,我国的光刻技术水平已突破到 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

5.下例计算正确的是(       
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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

6.若点 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 与点 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 关于y轴对称,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的值是(       
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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
C
1
D
2

7. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 是一元二次方程 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的一个根,则方程的另一个根及m的值分别是(       
A
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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
B
00
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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 0

8.下列命题为真命题的是(       
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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
B
.同位角相等
C
.三角形的内心到三边的距离相等
D
.正多边形都是中心对称图形

9.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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的外接圆, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的直径,点P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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 上,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的度数是(       
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

10.如图,某数学兴趣小组测量一棵树 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的高度,在点A处测得树顶C的仰角为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,在点B处测得树顶C的仰角为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,且ABD三点在同一直线上,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,则这棵树 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的高度是(       
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

11.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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 网格正方形中,每个小正方形的边长为1,顶点为格点,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的顶点均是格点,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

12.如图,在边长为1的菱形 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,动点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 边上(与点AB均不重合),点F在对角线 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 相交于点G,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,则下列结论错误的是(       
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的最小值为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

评卷人

得分




二、填空题

13. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 在实数范围内有意义,则实数x的取值范围是________

14.因式分解: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ________

15. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 2这三个数中任取两个不同的数,作为点的坐标,则该点落在第三象限的概率是___

16.如图,将 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 绕点A逆时针旋转角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,点B的对应点D恰好落在 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 边上,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,则旋转角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的度数是______
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

17.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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,以点A为圆心、 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 为半径画弧交 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 于点E,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,则图中阴影部分的面积是_______
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

18.已知二次函数 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,图象的一部分如图所示,该函数图象经过点 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> .对于下列结论: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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ;④ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> );⑤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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 均在该函数图象上,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> .其中正确结论的个数共有_______个.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>

评卷人

得分




三、解答题

19.1)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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
2)解不等式组: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>

20.尺规作图(保留作图痕迹,不要求写出作法):
如图,已知线段mn.求作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,使 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

21.如图,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 与反比例函数 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的图像相交于点A和点 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,与x轴的正半轴相交于点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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(1)
k的值;
(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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,若点C为线段 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的中点,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的面积.

22.在贯彻落实“五育并举”的工作中,某校开设了五个社团活动:传统国学(A)科技兴趣(B)、民族体育(C)、艺术鉴赏(D)、劳技实践(E),每个学生每个学期只参加一个社团活动,为了了解本学期学生参加社团活动的情况,学校随机抽取了若干名学生进行调查,并将调查结果绘制成如下两幅尚不完整的统计图,请根据统计图提供的信息,解答下列问题:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(1)
本次调查的学生共有________人;
(2)
将条形统计图补充完整;
(3)
在扇形统计图中,传统国学(A)对应扇形的圆心角度数是_______
(4)
若该校有2700名学生,请估算本学期参加艺术鉴赏(D)活动的学生人数.

23.为了加强学生的体育锻炼,某班计划购买部分绳子和实心球,已知每条绳子的价格比每个实心球的价格少23元,且84元购买绳子的数量与360元购买实心球的数量相同.
(1)
绳子和实心球的单价各是多少元?
(2)
如果本次购买的总费用为510元,且购买绳子的数量是实心球数量的3倍,那么购买绳子和实心球的数量各是多少?

24.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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,点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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 边的中点,点O <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 边上,⊙ <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 经过点C且与 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 边相切于点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的切线;
(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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的半径及 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的长.

25.如图,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 经过 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 两点,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> x轴相交于点CP是直线 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 上方的抛物线上的一个动点, <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 轴交 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 于点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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(1)
求该抛物线的表达式;
(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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 轴交 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 于点E,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的最大值;
(3)
若以APD为顶点的三角形与 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 相似,请直接写出所有满足条件的点P,点D的坐标.

26.已知:点CD均在直线l的上方, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 都是直线l的垂线段,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的右侧, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 相交于点O
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(1)
如图1,若连接 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的形状为______ <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的值为______
(2)
若将 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 沿直线l平移,并以 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 为一边在直线l的上方作等边 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
如图2,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 重合时,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的长;
如图3,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 时,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 并延长交直线l于点F,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> .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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

参考答案

1.B

【解析】
根据倒数的定义(两个非零数相乘积为1,则说它们互为倒数,其中一个数是另一个数的倒数)求解.
解:-2的倒数是- <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故选:B

2.B

【解析】
根据三视图的定义即可求解.
解:主视图为等腰三角形,左视图为等腰三角形,俯视图为有圆心的圆,
故主视图和左视图相同,主视图俯视图和左视图与俯视图都不相同,
故选:B

3.A

【解析】
把这组数按照从小到大的顺序排列,第34两个数的平均数是中位数,在这组数据中出现次数最多的是5,从而得到这组数据的众数.
解:把这组数按照从小到大的顺序排列为:134556
34两个数的平均数是 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
所以中位数是4.5
在这组数据中出现次数最多的是5,即众数是5
故选:A

4.C

【解析】
绝对值小于1的正数也可以利用科学记数法表示,一般形式为a×10-n,与较大数的科学记数法不同的是其所使用的是负整数指数幂,指数由原数左边起第一个不为零的数字前面的0的个数所决定.
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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
∴28nm=2.8×10
-8m
故选:C

5.D

【解析】
分别根据合并同类项、单项式除以单项式、同底数幂的乘法、幂的乘方法则进行计算即可求解.
解:A. 2aa=a,故原选项计算错误,不符合题意;
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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,不是同类项不能合并,故原选项计算错误,不符合题意;
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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,故原选项计算错误,不符合题意;
D.
(-a3)2=a6,故原选项计算正确,符合题意.
故选:D

6.A

【解析】
根据关于y轴对称的点,纵坐标相同,横坐标互为相反数解答即可.
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 与点 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 关于y轴对称,
a=-2b=-1
a-b=-1
故选A

7.B

【解析】
直接把 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 代入方程,可求出m的值,再解方程,即可求出另一个根.
解:根据题意,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 是一元二次方程 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的一个根,
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
方程的另一个根是 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故选:B

8.C

【解析】
根据判断命题真假的方法即可求解.
解: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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,故A为假命题,故A选项错误;
当两直线平行时,同位角才相等,故B为假命题,故B选项错误;
三角形的内心为三角形内切圆的圆心,故到三边的距离相等,故C为真命题,故C选项正确;
三角形不是中心对称图形,故D为假命题,故D选项错误,
故选:C

9.C

【解析】
根据圆周角定理得到 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,然后利用互余计算出∠A的度数,从而得到 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的度数.
解:∵AB是⊙O的直径,
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故选:C

10.A

【解析】
CD=x,在RtADC中,∠A=45°,可得CD=AD=xBD=16-x,在RtBCD中,用∠B的正切函数值即可求解.
CD=x,在RtADC中,∠A=45°
CD=AD=x
BD=16-x
RtBCD中,∠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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故选A

11.C

【解析】
过点CAB的垂线,构造直角三角形,利用勾股定理求解即可.
解:过点CAB的垂线交AB于一点D,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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
每个小正方形的边长为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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故选:C

12.D

【解析】
先证明△BAF≌△DAFCBE,△ABC是等边三角形,得DF=CE,判断A项答案正确,由∠GCB+∠GBC=60゜,得∠BGC=120゜,判断B项答案正确,证△BEG <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> CEB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,即可判断C项答案正确,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> BC=1,得点G在以线段BC为弦的弧BC上,易得当点G在等边△ABC的内心处时,AG取最小值,由勾股定理求得AG= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,即可判断D项错误.
解:∵四边形ABCD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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
AB=AD=BC=CD,∠BAC=∠DAC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> BAD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
∴△
BAF≌△DAFCBE,△ABC是等边三角形,
DF=CE,故A项答案正确,
ABF=∠BCE
∵∠
ABC=∠ABF+∠CBF=60゜,
∴∠
GCB+∠GBC=60゜,
∴∠
BGC=180-60=180-(∠GCB+∠GBC=120゜,故B项答案正确,
∵∠
ABF=∠BCE,∠BEG=∠CEB
∴△
BEG∽△CEB
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,故C项答案正确,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> BC=1,点G在以线段BC为弦的弧BC上,
当点G在等边△ABC的内心处时,AG取最小值,如下图,
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>    
∵△ABC是等边三角形,BC=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/1016/" title="贵港" class="c1" target="_blank">贵港</a> AF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> AC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,∠GAF=30゜,
AG=2GFAG2=GF2+AF2
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 解得AG= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,故D项错误,
故应选:D

13. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>

【解析】
二次根式要有意义,则二次根式内的式子为非负数.
解:由题意得:
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故答案为: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

14.a(a+1)(a-1)

【解析】
先找出公因式 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,然后提取公因式,再利用平方差公式分解因式即可.
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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故答案为: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> .

15. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>

【解析】
列举出所有情况,看在第三象限的情况数占总情况数的多少即可.
解:∵从 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 2这三个数中任取两个不同的数,作为点的坐标,
所有的点为:( <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ),共6个点;在第三象限的点有( <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ),共2个;
该点落在第三象限的概率是 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故答案为: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

16. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>

【解析】
先求出 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,由旋转的性质,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,即可求出旋转角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的度数.
解:根据题意,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
由旋转的性质,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
旋转角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的度数是50°
故答案为:50°

17. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>

【解析】
过点DDFAB于点F,根据等腰直角三角形的性质求得DF,从而求得EB,最后由S阴影=SABCDS扇形ADESEBC结合扇形面积公式、平行四边形面积公式、三角形面积公式解题即可.
解:过点DDFAB于点F
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
AD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>
DF=ADsin45°= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>
AE=AD=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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
EB=ABAE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>
S阴影=SABCDS扇形ADESEBC
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故答案为: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

18.3

【解析】
根据抛物线与x轴的一个交点(-2,0)以及其对称轴 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,求出抛物线与x轴的另一个交点(1,0),代入可得: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,再根据抛物线开口朝下,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,再结合二次函数的图象和性质逐条判断即可.
抛物线的对称轴为: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,且抛物线与x轴的一个交点坐标为(-2,0)
抛物线与x轴的另一个坐标为(1,0)
代入(-2,0)(1,0)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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,故③正确;
抛物线开口朝下,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,故①错误;
抛物线与x轴两个交点,
y=0时,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 有两个不相等的实数根,
方程的判别式 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,故②正确;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,故④正确;
抛物线的对称轴为: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,且抛物线开口朝下,
可知二次函数 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 时,yx的增大而减小,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,故⑤错误,
故正确的有:②③④,
故答案为:3

19.14;(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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

【解析】
1)根据绝对值的意义、零指数幂、负整数指数幂的运算法则以及特殊角的三角函数值进行计算即可;
2)先分别求解出不等式①和不等式②的解集,再找这个两个解集的公共部分即可.
1)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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
2)解不等式①,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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
解不等式②,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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
不等式组的解集为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

20.见解析

【解析】
作直线ll上一点A;过点Al的垂线;在l上截取 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ;作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ;即可得到 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
解: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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 为所求.
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
注:(1)作直线ll上一点A
2)过点Al的垂线;
3)在l上截取 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>
4)作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>

21.(1)6
(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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

【解析】
1)直接把点C的坐标代入反比例函数的解析式,即可求出答案;
2)由题意,先求出点A的坐标,然后求出直线AC的解析式,求出点B的坐标,再求出 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的面积即可.
(1)
解:∵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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 在反比例函数 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的图象上,
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(2)
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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 是线段 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的中点,点Bx轴上,
A的纵坐标为4
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 上,
A的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
设直线AC <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
B的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

22.(1)90
(2)
见解析
(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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(4)300


【解析】
1)用劳技实践(E)社团人数除以所占的百分比求解;
2)先用总人数分别减去传统国学(A)、科技兴趣(B)、艺术鉴赏(D)、劳技实践(E)社团的人数计算出民族体育(C)社团的人数,再补全条形统计图即可;
3)用360度乘传统国学(A)社团所占的比例来求解;
4)用2700乘艺术鉴赏(D)社团所占的比例来求解.
(1)
解:本次调查的学生人数为:
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> (人).
故答案为:90
(2)
解:民族体育(C)社团人数为: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> (人),
补全条形统计图如下:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(3)
解:在扇形统计图中,传统国学(A)社团对应扇形的圆心角度数是
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故答案为: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(4)
解:该校有2700名学生,本学期参加艺术鉴赏(D)社团活动的学生人数为
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> (人).

23.(1)绳子的单价为7元,实心球的单价为30
(2)
购买绳子的数量为30条,购买实心球的数量为10

【解析】
1)设绳子的单价为x元,则实心球的单价为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 元,根据“84元购买绳子的数量与360元购买实心球的数量相同”列出分式方程,解分式方程即可解题;
2)根据“总费用为510元,且购买绳子的数量是实心球数量的3倍”列出一元一次方程即可解题.
(1)
解:设绳子的单价为x元,则实心球的单价为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 元,
根据题意,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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
解分式方程,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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
经检验可知 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 是所列方程的解,且满足实际意义,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>
答:绳子的单价为7元,实心球的单价为30元.
(2)
设购买实心球的数量为m个,则购买绳子的数量为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 条,
根据题意,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
答:购买绳子的数量为30条,购买实心球的数量为10个.

24.(1)见解析
(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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

【解析】
1)作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,垂足为H,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,先证明 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的平分线,然后由切线的判定定理进行证明,即可得到结论成立;
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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,由勾股定理可求 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的半径为r,然后证明 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,结合勾股定理即可求出答案.
(1)
证明:如图,作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,垂足为H,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的中点,
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>
∴∠
BDC=2∠FAC
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的平分线,
O <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 相切于点E
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的半径,
AC平分∠FABOHAF
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的切线.
(2)
解:如(1)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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
可设 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的半径为r,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
RtAOE中,AO=5OE=3
由勾股定理得 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,又 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 中,由勾股定理得: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

25.(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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(2)
最大值为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

【解析】
1)直接利用待定系数法,即可求出解析式;
2)先求出点C的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,然后证明 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,设点P的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,则点D的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,分别表示出 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,再由二次函数的最值性质,求出答案;
3)根据题意,可分为两种情况进行当 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 时;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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 时;分别求出两种情况的点的坐标,即可得到答案.
(1)
解:(1)∵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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 经过 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 两点,
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
抛物线的表达式为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(2)
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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 表达式为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
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/1016/" title="贵港" class="c1" target="_blank">贵港</a> x轴交于点C
C的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 轴, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 轴,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
设点P的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
则点D的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 有最大值,且最大值为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(3)
解:根据题意,
在一次函数 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 中,令 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
C的坐标为(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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 时,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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
此时点D与点C重合,
D的坐标为(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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 轴,
P的横坐标为2
P的纵坐标为: <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
P的坐标为(23);
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 时,如图,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
设点 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,则点P <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
D的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,点P的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
满足条件的点P,点D的坐标为 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>

26.(1)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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(2)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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ;②见解析

【解析】
1)过点CCHBDH,可得四边形ABHC是矩形,即可求得AC=BH,进而可判断△BCD的形状,ACBD都垂直于l,可得△AOC∽△BOD,根据三角形相似的性质即可求解.
2)①过点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 于点HACBD均是直线l的垂线段,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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,根据等边三角形的性质可得 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,再利用勾股定理即可求解.
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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,根据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 是等边三角形,把 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 旋转得 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,根据30°角所对的直角边等于斜边的一般得到 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,则可得 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,根据三角形相似的性质即可求证结论.
(1)
解:过点CCHBDH,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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
AClDBlCHBD
∴∠
CAB=∠ABD=∠CHB=90°
四边形ABHC是矩形,
AC=BH
又∵BD=2AC
∴AC=BH=DH
,且CH⊥BD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 的形状为等腰三角形,
ACBD都垂直于l
∴△
AOC∽△BOD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
故答案为: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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
(2)
过点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 于点H,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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
ACBD均是直线l的垂线段,
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 是等边三角形,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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 重合,
∴∠
EAD=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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>
又由(1)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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 中,由勾股定理得: <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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> ,如图3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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 是等边三角形,
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a> 是等边三角形,
 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 绕点D顺时针旋转 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 后与 <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/1016/" title="贵港" class="c1" target="_blank">贵港</a> 重合,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</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/1016/" title="贵港" class="c1" target="_blank">贵港</a>