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【327649】2022广东省广州市中考数学真题

时间:2025-01-20 19:55:07 作者: 字数:20778字
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2022广东省广州市中考数学真题

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得分





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评卷人

得分




一、选择题

1.如图是一个几何体的侧面展开图,这个几何体可以是(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
A
.圆锥
B
.圆柱
C
.棱锥
D
.棱柱

2.下列图形中,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/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

3.代数式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 有意义时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 应满足的条件为(     
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> -1

4. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 在正比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> )的图象上,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的值为(     
A
-15
B
15
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

5.下列运算正确的是(     
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

6.如图,抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的对称轴为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,下列结论正确的是(     
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
C
.当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的增大而减小
D
.当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的增大而减小

7.实数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 在数轴上的位置如图所示,则 (     
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

8.为了疫情防控,某小区需要从甲、乙、丙、丁 4名志愿者中随机抽取2名负责该小区入口处的测温工作,则甲被抽中的概率是(     
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

9.如图,正方形ABCD的面积为3,点E在边CD上, 且CE = 1,∠ABE的平分线交AD于点F,点MN分别是BEBF的中点,则MN的长为(     
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

10.如图,用若干根相同的小木棒拼成图形,拼第1个图形需要6根小木棒,拼第2个图形需要14根小木棒,拼第3个图形需要22根小木棒……若按照这样的方法拼成的第 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 个图形需要2022根小木棒,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的值为(   
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
A
252
B
253
C
336
D
337

评卷人

得分




二、填空题

11.在甲、乙两位射击运动员的10次考核成绩中,两人的考核成绩的平均数相同, 方差分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,则考核成绩更为稳定的运动员是________(填“甲”、“乙”中的一个)

12.分解因式: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ________

13.如图,在□ABCD中,AD=10,对角线AC BD相交于点OAC+BD=22,则BOC的周长为________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

14.分式方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的解是________

15.如图,在△ABC中,AB=AC,点O在边AC上,以O为圆心,4为半径的圆恰好过点C,且与边AB相切于点D,交BC于点E,则劣弧 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的长是________(结果保留 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

16.如图,在矩形ABCD中,BC=2AB,点P为边AD上的一个动点,线段BP绕点B顺时针旋转60°得到线段BP',连接PP' CP'.当点P' 落在边BC上时,∠PP'C的度数为________; 当线段CP' 的长度最小时,∠PP'C的度数为________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

评卷人

得分




三、解答题

17.解不等式: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

18.如图,点DE在△ABC的边BC上,∠B = ∠CBD = CE,求证:△ABD≌△ACE
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

19.某校在九年级学生中随机抽取了若干名学生参加“平均每天体育运动时间”的调查,根据调查结果绘制了如下不完整的频数分布表和频数分布直方图.
频数分布表

运动时间t/min

频数

频率

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

4

0.1

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

7

0.175

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

a

0.35

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

9

0.225

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

6

b

合计

n

1


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
请根据图表中的信息解答下列问题:
(1)
频数分布表中的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> =________ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> =________ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> =________
(2)
请补全频数分布直方图;
(3)
若该校九年级共有480名学生,试估计该校九年级学生平均每天体育运动时间不低于120 min的学生人数.

20.某燃气公司计划在地下修建一个容积为VV为定值,单位:m3)的圆柱形天然气储存室,储存室的底面积S(单位:m2) 与其深度 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> (单位:m)是反比例函数关系,它的图象如图所示.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(1)
求储存室的容积V的值;
(2)
受地形条件限制,储存室的深度 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 需要满足16≤ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ≤25,求储存室的底面积S的取值范围.

21.已知T= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(1)
化简T
(2)
若关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 有两个相等的实数根,求T的值.

22.如图,AB是⊙O的直径,点C在⊙O上,且AC=8BC=6
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(1)
尺规作图:过点OAC的垂线,交劣弧 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 于点D,连接CD(保留作图痕迹,不写作法);
(2)
在(1)所作的图形中,求点OAC的距离及sin∠ACD 的值.

23.某数学活动小组利用太阳光线下物体的影子和标杆测量旗杆的高度.如图,在某一时刻,旗杆的AB的影子为BC,与此同时在C处立一根标杆CD,标杆CD的影子为CECD = 1.6mBC =5CD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(1)
BC的长;
(2)
从条件①、条件②这两个条件中选择一个作为已知,
求旗杆AB的高度.
条件①:CE = 1.0m; 条件②:从D处看旗杆顶部A的仰角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 54.46°
注:如果选择条件①和条件②分别作答,按第一个解答计分.参考数据:sin54.46°≈0.81cos54.46°≈0.58tan54.46°≈1.40

24.己知直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 经过点(07)和点(16).
(1)
求直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的解析式;
(2)
若点P <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> )在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 上,以P为顶点的抛物线G过点(0-3),且开口向下
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的取值范围;
设抛物线G与直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的另一个交点为Q,当点Q向左平移1个单长度后得到的点Q' 也在G上时,求G <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的图象的最高点的坐标.

25.如图,在菱形ABCD中,∠BAD = 120°AB = 6,连接BD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(1)
BD的长;
(2)
E为线段BD上一动点(不与点BD重合), 点F在边AD上,且BE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> DF
CEAB时,求四边形ABEF的面积;
当四边形ABEF的面积取得最小值时,CE+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> CF的值是否也最小?如果是,求CE+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> CF的最小值;如果不是,请说明理由.

参考答案

1.A

【解析】
由图可知展开侧面为扇形,则该几何体为圆锥.
该几何体的侧面展开图是扇形,所以这个几何体可能是圆锥,
故选:A

2.C

【解析】
根据中心对称图形的概念判断.把一个图形绕某一点旋转180°,如果旋转后的图形能够与原来的图形重合,那么这个图形就叫做中心对称图形.
解:A、不能找到这样的一个点,使图形绕某一点旋转180°后与原来的图形重合,所以不是中心对称图形,故此选项不符合题意;
B
、不能找到这样的一个点,使图形绕某一点旋转180°后与原来的图形重合,所以不是中心对称图形,故此选项不符合题意;
C
、能找到这样的一个点,使图形绕某一点旋转180°后与原来的图形重合,所以是中心对称图形,故此选项符合题意;
D
、不能找到这样的一个点,使图形绕某一点旋转180°后与原来的图形重合,所以不是中心对称图形,故此选项不符合题意;
故选:C

3.B

【解析】
根据分式分母不为0及二次根式中被开方数大于等于0即可求解.
解:由题意可知: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
故选:B

4.D

【解析】
直接把已知点代入,即可求出k的值.
解:∵点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 在正比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的图象上,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
故选:D

5.D

【解析】
根据求一个数的立方根,分式的加减,二次根式的加法,同底数幂的乘法运算,逐项分析判断即可求解.
A.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,故该选项不正确,不符合题意;
B.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ),故该选项不正确,不符合题意;
C.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,该选项不正确,不符合题意;
D.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,故该选项正确,符合题意;
故选D

6.C

【解析】
由图像可知,抛物线开口向上,因此a0.由图像与y轴的交点在y轴负半轴上得c0.根据图像可知,在对称轴左侧yx的增大而减小,在对称轴右侧yx的增大而增大.
抛物线开口向上,因此a0,故A选项不符合题意.
抛物线与y轴的交点在y轴的负半轴上,因此c0,故B选项不符合题意.
抛物线开口向上,因此在对称轴左侧,yx的增大而减小,故C选项符合题意.
抛物线开口向上,因此在对称轴右侧yx的增大而增大,故D选项不符合题意.
故选C

7.C

【解析】
根据数轴上点的位置,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,进而逐项分析判断即可求解.
解:根据数轴上点的位置,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
故选C

8.A

【解析】
根据题意画出树状图,然后求得全部情况的总数与符合条件的情况数目;二者的比值就是其发生的概率.
解:画树状图得:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
一共有12种情况,抽取到甲的有6种,
P(抽到甲)=  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
故选:A

9.D

【解析】
如图,连接EF,先证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 再求解 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 再求解 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 为等腰直角三角形,求解 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 再利用三角形的中位线的性质可得答案.
解:如图,连接EF
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
正方形ABCD的面积为3
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 为等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的中点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
故选D

10.B

【解析】
根据图形的变化及数值的变化找出变化规律,即可得出结论.
解:设第n个图形需要ann为正整数)根小木棒,
观察发现规律:第一个图形需要小木棒:6=6×1+0
第二个图形需要小木棒:14=6×2+2
第三个图形需要小木棒:22=6×3+4,…,
n个图形需要小木棒:6n+2n-1=8n-2
∴8
n-2=2022,得:n=253
故选:B

11.

【解析】
根据方差的定义,方差越小数据越稳定即可求解.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,且平均成绩相同
射击成绩较稳定的运动员是乙,
故答案为:乙.

12. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

【解析】
直接提取公因式3a即可得到结果.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

13.21

【解析】
根据平行四边形对角线互相平分,求出OC+OB的长,即可解决问题.
解:∵四边形ABCD是平行四边形,
AO=OC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ACBO=OD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> BDBC=AD=10,
AC+BD=22
OC+BO=11
BC=10
BOC的周长=OC+OB+BC=16+10=21
故答案为:21

14. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

【解析】
先去分母,将分式方程转化成整式方程求解,再检验即可求解;
解:方程两边同时乘以2x(x+1),得
3(
x+1)=4x
3x+3=4x
x
=3
检验:把x=3代入2x(x+1)=2×3(3+1)=24≠0
原分式方程的解为:x=3
故答案为:x=3

15. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

【解析】
如图,连接ODOE,证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 再证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 再利用弧长公式进行计算即可.
解:如图,连接ODOE
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 与边AB相切于点D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

16.     120°##120度     75°##75

【解析】
由旋转性质及旋转角知△BPP为等边三角形,得到∠PP′B=60°;当点P' 落在边BC上时,∠PP'C=180°-∠PP′B=120°;将线段BA绕点B逆时针旋转60°后点A落在点E,连接BE得到△ABP≌△EBP′(SAS),再证明△ABP为等腰直角三角形,进而得到∠EPB=∠APB=45°
最后当CP′EFH时,CP′有最小值,由此可以求出∠PP'C=∠EPC-∠EPP=90°-15°=75°
解:由线段BP绕点B顺时针旋转60°得到线段BP'可知,△BPP′为等边三角形,
∴∠
PP′B=60°
当点P' 落在边BC上时,∠PP'C=180°-∠PP′B=180°-60°=120°
将线段BA绕点B逆时针旋转60°,点A落在点E,连接BE,设EP′BCG点,如下图所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
则∠ABP=∠ABE-∠PBE=60°-∠PBE,∠EBP′=∠PBP′-∠PBE=60°-∠PBE
∴∠
ABP=∠EBP
BA=BEBP=BP
∴△
ABP≌△EBP′(SAS),
AP=EP,∠E=∠A=90°
由点P' 落在边BC上时,∠PP'C=120°可知,∠EGC=120°
∴∠
CGP′=∠EGB=180°-120°=60°
∴△
EBG于△PCG均为30°60°90°直角三角形,
EG=xBC=2y
BG=2EG=2xCG=BC-BG=2y-2xGP′= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> CG=y-x
EP′=EG+GP′=x+(y-x)=y= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> BC
又已知AB= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> BC
EP′=AB
又由△ABP≌△EBP知:AP=EP
AB=AP
∴△
ABP为等腰直角三角形,
∴∠
EPB=∠APB=45°,∠EPP=60°-∠EPB=60°-45°=15°
CP′EFH时,CP′有最小值,
此时∠PP'C=∠EPC-∠EPP=90°-15°=75°
故答案为:120°75°

17. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

【解析】
先移项合并同类项,然后将未知数系数化为1即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
移项得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
合并同类项得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
不等式两边同除以3得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

18.证明见解析

【解析】
由等腰三角形的判定得出AC=AB,再利用SAS定理即可得出结论.
证明:∵∠B=∠C
AC=AB
ABDACE中,
AB=AC,∠B=∠CBD=CE
∴△
ABD≌△ACESAS

19.(1)140.1540
(2)
补图见解析;
(3)
约有180

【解析】
从频数分布表中得知,频数4占比例为0.1,由此可推出样本容量是40,在求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 后, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 可随之求出,继而(2)可解决;接下来,从样本去估计总体,就是(3)的结果.
(1)
n= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> =40
a=40-4+7+6+9=14
b= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> = 14  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> = 0.15  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> = 40
(2)
补全频数分布直方图如下:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(3)
被抽到的40人中,运动时间不低于120分钟的有9+6=15人,占频率0.225+0.15=0.375
以此估计全年级480人中,大概有480×0.375人,即约有180人.

20.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)
16≤ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ≤25时,400≤S≤625

【解析】
1)利用体积等于等面积乘以深度即可得到答案;
2)先求解反比例函数的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,再利用反比例函数的性质可得答案.
(1)
解:由图知:当深度 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> =20米时,底面积S=5002
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> =5002×20=100003
(2)
由(1)得:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ),S随着 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的增大而减小,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时,S=625; 当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时,S=400
16≤ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ≤25时,400≤S≤625

21.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)
T= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

【解析】
(1)
根据整式的四则运算法则化简即可;
(2)
由方程有两个相等的实数根得到判别式△=4a²-4(-ab+1)=0即可得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,整体代入即可求解.
(1)
解:T= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
=
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)
解:∵方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 有两个相等的实数根,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
T= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

22.(1)作图见解析;
(2)
OAC的距离为3sin∠ACD 的值是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

【解析】
(1)
作线段AC的垂直平分线,由垂径定理推论可知该垂直平分线必经过点O
(2)
由垂径定理得到AF=CF,进而得到OF是△ACB的中位线,由此得到点OAC的距离OF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> BC=3;求出DF=OD-OF=5-3=2CF=4,由勾股定理求出CD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,最后在RtCDF中由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 即得答案.
(1)
解:①分别以AC为圆心,适当长(大于AC长度的一半)为半径作弧,记两弧的交点为E
作直线OE,记OE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 交点为D
连结CD,则线段AC的垂线DE、线段CD为所求图形,如下图所示;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)
解:记ODAC的交点为F, 如下图所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
ODAC
FAC中点,
OF是△ABC的中位线,
OF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> BC=3
OFAC
OF的长就是点OAC的距离;
RtABC中,∵AC=8BC=6
AB=10
OD=OA= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> AB=5
DF=OD-OF=5-3=2
FAC中点,
CF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> AC=4   
RtCDF中,∵DF=2CF=4
CD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
OAC的距离为3sin∠ACD 的值是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

23.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)①
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ;②旗杆AB高度约 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>

【解析】
1)根据BC =5CD,求解即可;
2)①CE=1.0m时,连接DE,则有△DEC∽△ACB,根据相似的性质求解即可;②当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时,作点DAB的垂线段DF,在RtADF中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,进一步可求出AB=AF+FB≈11.20m+1.6m≈12.8m
(1)
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)
解:①CE=1.0m时,连接DE,则有△DEC∽△ACB
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时,作点DAB的垂线段DF
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
则四边形BCDF是矩形,FB=DC=1.6mFD=BC=8.0m
RtADF中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
AB=AF+FB≈11.20m+1.6m≈12.8m
旗杆AB高度约12.8m

24.(1)直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 解析式为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)①
m10,且m≠0;②最高点的坐标为(-29)或(25

【解析】
1)根据待定系数法求出解析式即可;
2)①设G的顶点式,根据点P在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 上得出G的关系式,根据题意得出点(0-3)不能成为抛物线G的顶点,进而得出点P必须位于直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的上方,可求m的取值范围,然后结合点P不能在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 轴上得出答案;
先根据点Q,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的对称,得QQ'=1,可表示点Q <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的坐标,再将点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的坐标的代入关系式,求出a,再将点(0-3)代入可求出m的值,然后分两种情况结合取值范围,求出函数最大值时,最高点的坐标即可.
(1)
解:∵直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 经过点(07)和点(16),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 解析式为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)
解:①设G <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ),
P <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> )在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 上,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
G <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
0-3)不在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 上,
0-3)不能成为抛物线G的顶点,
而以P为顶点的抛物线G开口向下,且经过(0-3),
P必须位于直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的上方,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
另一方面,点P不能在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 轴上,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
所求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 取值范围为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
如图,QQ'关于直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 对称,且QQ'=1
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
Q横坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
而点Q <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 上,∴Q <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ),Q' <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> );
Q' <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> )在G <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 上,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
G <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,或 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
抛物线G过点(0-3),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时,抛物线G <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,对称轴为直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
对应区间为-2≤ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ≤-1,整个区间在对称轴 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的右侧,
此时,函数值 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 随着 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 的增大而减小,如图,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 取区间左端点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 达最大值9,最高点坐标为(-29);
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时,对应区间为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,最高点为顶点P25),如图,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
G在指定区间图象最高点的坐标为(-29)或(25).

25.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)①
四边形ABEF的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ;②最小值为12

【解析】
1)证明△ABC是等边三角形,可得BO=  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,即可求解;
2)过点EAD的垂线,分别交ADBC于点MN, 根据菱形的面积可求出MN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,设BE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,则EN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,从而得到EM=MN-EN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,再由BE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> DF,可得DF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,从而得到四边形ABEF的面积s= SABD - SDEF  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,①当CEAB时,可得点E是△ABC重心,从而得到BE=CE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> BO= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,即可求解;②作CHADH,可得当点EF分别到达点O和点H位置时,CFCE分别达到最小值;再由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,可得当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,即BE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时, s达到最小值,从而得到此时点E恰好在点O的位置,而点F也恰好在点H位置,即可求解.
(1)
解∶连接AC,设ACBD的交点为O,如图,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
四边形ABCD是菱形,
ACBD OA=OCABCDAC平分∠DAB
∵∠
BAD = 120°
∴∠
CAB=60°
∴△
ABC是等边三角形,
BO=ABsin60°= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
BD=2BO= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
(2)
解:如图,过点EAD的垂线,分别交ADBC于点MN
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
∵△
ABC是等边三角形,
AC=AB=6
由(1)得:BD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
菱形ABCD中,对角线BD平分∠ABCABCDBC=AB=6
MNBC
∵∠
BAD=120°
∴∠
ABC=60°
∴∠
EBN=30°
EN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> BE
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
MN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
BE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,则EN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
EM=MN-EN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
S菱形ABCD= ADMN= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
SABD=  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> S菱形ABCD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
BE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> DF
DF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
SDEF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> DF EM= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
记四边形ABEF的面积为s
s= SABD - SDEF = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> - <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
EBD上,且不在端点,∴0BEBD,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
CEAB时,
OBAC
E是△ABC重心,
BE=CE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> BO= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
此时 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
CEAB时,四边形ABEF的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
CHADH,如图,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
COBDCHAD,而点EF分别在BDAD上,
当点EF分别到达点O和点H位置时,CFCE分别达到最小值;
在菱形ABCD中,ABCDAD=CD
∵∠
BAD=120°
∴∠
ADC=60°
∴△
ACD是等边三角形,
AH=DH=3
CH= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> ,即BE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> 时, s达到最小值,
BE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> DF
DF=3
此时点E恰好在点O的位置,而点F也恰好在点H位置,
当四边形ABEF面积取得最小值时,CECF也恰好同时达到最小值,
CE+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> CF的值达到最小,
其最小值为CO+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> CH= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> <a href="/tags/549/" title="广州" class="c1" target="_blank">广州</a> =12