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【327804】2023年广西中考数学真题

时间:2025-01-20 20:18:44 作者: 字数:16893字
简介:

绝密·启用前

2023年广西中考数学真题

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.若零下2摄氏度记为 <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> ,则零上2摄氏度记为(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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>
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>
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>

2.下列数学经典图形中,是中心对称图形的是(       
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>    
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>    
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>    
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>    

3.若分式 <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> 有意义,则x的取值范围是(       
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>
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>
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>
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>

4.如图,点ABC <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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> ,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> 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 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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>
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>
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>

5. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 在数轴上表示正确的是(       
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>    
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>    
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>    
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>    

6.甲、乙、丙、丁四名同学参加立定跳远训练,他们成绩的平均数相同,方差如下: <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,则成绩最稳定的是(       
A
.甲
B
.乙
C
.丙
D
.丁

7.如图,一条公路两次转弯后又回到与原来相同的方向,如果 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,那么 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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>
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>
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>

8.下列计算正确的是(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
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>
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>
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>

9.将抛物线 <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> 向右平移3个单位,再向上平移4个单位,得到的抛物线是(       
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>
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>
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>
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>

10.赵州桥是当今世界上建造最早,保存最完整的中国古代单孔敞肩石拱桥.如图,主桥拱呈圆弧形,跨度约为 <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> ,拱高约为 <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> ,则赵州桥主桥拱半径R约为(       
 <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 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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>
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>
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>

11.据国家统计局发布的《2022年国民经济和社会发展统计公报》显示,2020年和2022年全国居民人均可支配收入分别为3.2万元和3.7万元.设2020年至2022年全国居民人均可支配收入的年平均增长率为x,依题意可列方程为(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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>
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>
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>

12.如图,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> 的图象上点A,分别作x轴,y轴的平行线交 <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> 的图象于BD两点,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 为邻边的矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 被坐标轴分割成四个小矩形,面积分别记为 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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> ,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> 的值为(       
 <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>    
A4
B
3
C
2
D
1

评卷人

得分




二、填空题

13.化简: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ______

14.分解因式:a2 + 5a =________________.

15.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> 的图象经过点 <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> ,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> ______

16.某班开展“梦想未来、青春有我”主题班会,第一小组有2位男同学和3位女同学,现从中随机抽取1位同学分享个人感悟,则抽到男同学的概率是______

17.如图,焊接一个钢架,包括底角为 <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> 的等腰三角形外框和3m高的支柱,则共需钢材约______m(结果取整数).(参考数据: <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>    

18.如图,在边长为2的正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 中,EF分别是 <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> 上的动点,MN分别是 <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> 的中点,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> 的最大值为______
 <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>    

评卷人

得分




三、解答题

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

20.解分式方程: <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>

21.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>    
(1)在斜边 <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> 上求作线段 <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> ,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> ,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>
(要求:尺规作图并保留作图痕迹,不写作法,标明字母)
(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> ,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> 的长.

22.424日是中国航天日,为激发青少年崇尚科学、探索未知的热情,航阳中学开展了“航空航天”知识问答系列活动.为了解活动效果,从七、八年级学生的知识问答成绩中,各随机抽取20名学生的成绩进行统计分析(6分及6分以上为合格),数据整理如下:

学生成绩统计表


七年级

八年级

平均数

7.55

7.55

中位数

8

c

众数

a

7

合格率

b

85%

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>    
根据以上信息,解答下列问题:
(1)
写出统计表中abc的值;
(2)
若该校八年级有600名学生,请估计该校八年级学生成绩合格的人数;
(3)
从中位数和众数中任选其一,说明其在本题中的实际意义.

23.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 相切于点A,延长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 于点C,过点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> ,垂足为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>    
(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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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> 的半径为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> ,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> 的长.

24.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> 是边长为4的等边三角形,点DEF分别在边 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 上运动,满足 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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>
(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> 的长为x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的面积为y,求y关于x的函数解析式;
(3)
结合(2)所得的函数,描述 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的面积随 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的增大如何变化.

25.(综合与实践)
有言道:“杆秤一头称起人间生计,一头称起天地良心”.某兴趣小组将利用物理学中杠杆原理制作简易杆秤.小组先设计方案,然后动手制作,再结合实际进行调试,请完成下列方案设计中的任务.
(
知识背景)如图,称重物时,移动秤砣可使杆秤平衡,根据杠杆原理推导得: <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> .其中秤盘质量 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 克,重物质量m克,秤砣质量M克,秤纽与秤盘的水平距离为l厘米,秤纽与零刻线的水平距离为a厘米,秤砣与零刻线的水平距离为y厘米.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>    
(方案设计)
目标:设计简易杆秤.设定 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,最大可称重物质量为1000克,零刻线与末刻线的距离定为50厘米.
任务一:确定la的值.
(1)
当秤盘不放重物,秤砣在零刻线时,杆秤平衡,请列出关于la的方程;
(2)
当秤盘放入质量为1000克的重物,秤砣从零刻线移至末刻线时,杆秤平衡,请列出关于la的方程;
(3)
根据(1)和(2)所列方程,求出la的值.
任务二:确定刻线的位置.
(4)
根据任务一,求y关于m的函数解析式;
(5)
从零刻线开始,每隔100克在秤杆上找到对应刻线,请写出相邻刻线间的距离.

26.(探究与证明)
折纸,操作简单,富有数学趣味,我们可以通过折纸开展数学探究,探索数学奥秘.
(
动手操作)如图1,将矩形纸片 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 对折,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 重合,展平纸片,得到折痕 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;折叠纸片,使点B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> 上,并使折痕经过点A,得到折痕 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,点BE的对应点分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,展平纸片,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>    
请完成:
(1)
观察图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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,试猜想这三个角的大小关系
(2)
证明(1)中的猜想;
(
类比操作)如图2N为矩形纸片 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 上的一点,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> ,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> 上取一点P,折叠纸片,使BP两点重合,展平纸片,得到折痕 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;折叠纸片,使点BP分别落在 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 上,得到折痕l,点BP的对应点分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,展平纸片,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>    
请完成:
(3)
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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的一条三等分线.

参考答案

1.C

【解析】
根据正负数的实际意义可进行求解.
解:由题意可知零上2摄氏度记为 <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>
故选C

2.A

【解析】
根据中心对称图形的概念:一个图形如果绕某个点旋转180度后能与原图形完全重合的图形;由此问题可求解.
解:选项中符合中心对称图形的只有A选项;
故选A

3.A

【解析】
根据分式有意义的条件可进行求解.
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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
故选A

4.D

【解析】
根据圆周角定理的含义可得答案.
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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
故选:D

5.C

【解析】
在数轴上表示不等式的解集,需要确定“边界点”:若边界点是不等式的解,则用实心圆点,若边界点不是不等式的解,则用空心圆圈;确定“方向”:对边界点a而言, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 向右画, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 向左画.
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> 在数轴上表示为:
 <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>    
故选:C

6.D

【解析】
根据方差可进行求解.
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>
成绩最稳定的是丁;
故选D

7.D

【解析】
根据题意得到 <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> ,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>
解:∵公路两次转弯后又回到与原来相同的方向,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
故选:D

8.B

【解析】
根据合并同类项,同底数幂的乘法,同底数幂的除法,幂的乘方进行计算即可.
A.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,故该选项不符合题意;
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> ,故该选项符合题意;
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> ,故该选项不符合题意;
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> ,故该选项不符合题意;
故选:B

9.A

【解析】
根据“左加右减,上加下减”的法则进行解答即可.
解:将抛物线 <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> 向右平移3个单位,再向上平移4个单位,得到的抛物线的函数表达式为: <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>
故选:A

10.B

【解析】
由题意可知, <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,主桥拱半径R,根据垂径定理,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> ,再利用勾股定理列方程求解,即可得到答案.
解:如图,由题意可知, <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,主桥拱半径R
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 是半径,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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>
故选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>    

11.B

【解析】
2020年至2022年全国居民人均可支配收入的年平均增长率为x,根据题意列出一元二次方程即可.
2020年至2022年全国居民人均可支配收入的年平均增长率为x
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>
故选:B

12.C

【解析】
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,根据坐标求得 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,推得 <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> ,即可求得.
 <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> ,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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> 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>
同理∵BD两点在 <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> 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
故选:C

13.3

【解析】
根据算术平方根的概念求解即可.
解:因为32=9
所以 <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> =3
故答案为:3

14.a(a+5)

【解析】
提取公因式a进行分解即可.
a
2+5a=aa+5).
故答案是:aa+5).

15.1

【解析】
把点 <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> 代入函数解析式进行求解即可.
解:由题意可把点 <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> 代入函数解析式得: <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>
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>
故答案为1

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

【解析】
根据概率公式,即可解答.
解:抽到的同学总共有5种等可能情况,
抽到男同学总共有2种可能情况,
故抽到男同学的概率是 <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>
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>

17.21

【解析】
根据解直角三角形及等腰三角形的性质可进行求解.
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> 是等腰三角形,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
共需钢材约为 <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>
故答案为21

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

【解析】
首先证明出 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的中位线,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> ,然后由正方形的性质和勾股定理得到 <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> ,证明出当 <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> 最大时, <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> 最大,此时 <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> 最大,进而得到当点E和点C重合时, <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> 最大,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> 的长度,最后代入求解即可.
如图所示,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>    
MN分别是 <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> 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的中位线,
 <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>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 是正方形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 最大时, <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> 最大,此时 <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> 最大,
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> 上的动点,
当点E和点C重合时, <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> 最大,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> 的长度,
此时 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的最大值为 <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>
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>

19.6

【解析】
根据有理数的混合运算法则求解即可.
 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>

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

【解析】
去分母转化为整式方程,求出整式方程的解得到x的值,经检验即可得到分式方程的解.
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>
去分母得, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
移项,合并得, <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>
检验: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> 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>
所以原分式方程的解为 <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>

21.(1)图见详解
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>

【解析】
1)以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> 长为半径画弧,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> 于点O,则问题可求解;
2)根据含30度直角三角形的性质可得 <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> ,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,进而问题可求解.
1)解:所作线段 <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> 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>    
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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,即点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> 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>

22.(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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
(2)510

(3)
用中位数的特征可知七,八年级学生成绩的集中趋势,表示了七,八年级学生成绩数据的中等水平.

【解析】
1)根据中位数,众数的定义求解即可,根据合格率=合格人数÷总人数即可求得;
2)根据八年级抽取人数的合格率进行求解即可;
3)根据中位数和众数的特征进行说明即可.
1)根据八年级的成绩分布可得:5分的有3人,6分的有2人,7分的有5人,8分的有4人,9分的有3人,10分的有3人,
故中位数是 <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>
根据扇形统计图可得:5分的有 <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> 人,6分的有 <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> 人,7分的有 <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> 人,8分的有 <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> 人,9分的有 <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> 人,10分的有 <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> 人,
故众数是8
合格人数为: <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> 人,
故合格率为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
2)八年级学生成绩合格的人数为: <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> 人,
即若该校八年级有600名学生,该校八年级学生成绩合格的人数有510人.
3)根据中位数的特征可知七,八年级学生成绩的集中趋势和七,八年级学生成绩数据的中等水平.

23.(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>

【解析】
1)首先根据切线的性质得到 <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> ,然后根据角平分线的性质定理得到 <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> 即可证明;
2)首先根据勾股定理得到 <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> ,然后求得 <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> ,最后利用 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,代入求解即可.
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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 相切于点A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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> 的半径为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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>

24.(1)见详解
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
(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> 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> 的面积随 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的增大而增大,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> 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> 的面积随 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的增大而减小

【解析】
1)由题意易得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,然后根据“ <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> ”可进行求证;
2)分别过点CF <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,垂足分别为点HG,根据题意可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,然后可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,由(1)易得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,进而问题可求解;
3)由(2)和二次函数的性质可进行求解.
1)证明:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 是边长为4的等边三角形,
 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
2)解:分别过点CF <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,垂足分别为点HG,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>    
在等边 <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> 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的长为x,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
同理(1)可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的面积为y
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
3)解:由(2)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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 时,yx的增大而增大,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> 时,yx的增大而减小;
即当 <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> 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> 的面积随 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的增大而增大,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> 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> 的面积随 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的增大而减小.

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>
(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>
(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>
(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>
(5)
相邻刻线间的距离为5厘米

【解析】
1)根据题意可直接进行求解;
2)根据题意可直接代值求解;
3)由(1)(2)可建立二元一次方程组进行求解;
4)根据(3)可进行求解;
5)分别把 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 代入求解,然后问题可求解.
1)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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
2)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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
3)解:由(1)(2)可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
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>
4)解:由任务一可知: <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
5)解:由(4)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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ;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> 时,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
相邻刻线间的距离为5厘米.

26.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
(2)
见详解
(3)
见详解

【解析】
1)根据题意可进行求解;
2)由折叠的性质可知 <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,然后可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> ,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 是等边三角形,进而问题可求证;
3)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> ,根据等腰三角形性质证明 <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> ,根据平行线的性质证明 <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> ,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> ,得出 <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> ,即可证明 <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>
1)解:由题意可知 <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>
2)证明:由折叠的性质可得: <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 是矩形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
3)证明: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> ,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>
由折叠的性质可知: <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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
折痕 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 为矩形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> 的一条三等分线.