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【328010】山东省东营市2021年中考数学真题

时间:2025-01-20 20:59:26 作者: 字数:19708字
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山东省东营市2021年中考数学真题

题号

总分

得分





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评卷人

得分




一、选择题

1.16的算术平方根是( )
A
4
B
-4
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
D
8

2.下列运算结果正确的是( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

3.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 于点F,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

4.某玩具商店周年店庆,全场八折促销,持会员卡可在促销活动的基础上再打六折.某电动汽车原价300元,小明持会员卡购买这个电动汽车需要花( )元
A
240
B
180
C
160
D
144

5.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,若用科学计算器求AC下列按键顺序正确的是(
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

6.经过某路口的汽车,可能直行,也可能左拐或右拐.假设这三种可能性相同,现有两车经过该路口,恰好有一车直行,另一车左拐的概率为( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

7.已知某几何体的三视图如图所示,则该几何体的侧面展开图圆心角的度数为( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
A
214°
B
215°
C
216°
D
217°

8.一次函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 与二次函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 在同一平面直角坐标系中的图象可能是( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

9.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 中,AB两个点在x的上方,点C的坐是(10),以点C位似中心,在x的下方作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的位似 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,并把 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 边长放大到原来的2倍,B的横坐aB对应 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的横坐是(
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

10.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 是边长为1的等边三角形,DE为线AC上两点,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> DEABBC的平行线相交于点F,分BCAB于点HG有以下结论 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 当点D与点C重合 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,四BHFG菱形,其中正确结论为
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
A
①②③
B
①②④
C
①②③④
D
②③④

评卷人

得分




二、填空题

11.2021511日,第七次全国人口普查数据显示,全国人口比第六次全国人口普查数据增加了7206万人.7206万用科学记数法表示________

12.因式分解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ________

13.如图所示是某校初中数学兴趣小组年龄结构条形统计图,该小组年龄最小为11岁,最大为15岁,根据统计图所提供的数据,该小组组员年龄的中位数为________岁.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

14.不等式组 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的解集是________

15.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 中,EBC的中点,以E为圆心,BE长为半径画弧交线AC于点F,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 扇形BEF的面积为________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

16.某地积极响应“把绿水青山变成金山银山,用绿色杠杆撬动经济转型”发展理念,开展荒山绿化,打造美好家园,促进旅游发展.某工程队承接了90万平方米的荒山绿化任务,为了迎接雨季的到来,实际工作时每天的工作效率比原计划提高了25%,结果提前30天完成了任务.设原计划每天绿化的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 万平方米,则所列方程为________

17.如图,正方形纸片ABCD边长为12,点FAD上一点,将 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 沿CF折叠,点D落在点GDG并延AB于点E.若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> GE长为________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

18.如图,正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> AB与直线l夹锐 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,延 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 交直线l于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,作正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,延 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 交直线l于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,作正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,延 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 交直线l于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,作正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,依此律,则线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

评卷人

得分




三、解答题

19.1)计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
2)化简求值: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

20.为庆祝建党100周年,让同学们进一步了解中国科技的快速发展,东营市某中学九(1)班团支部组织了一次手抄报比赛.该班每位同学从A北斗B5GC东风D快运四个主中任一个自己喜的主统计同学数,制成以下不完整的统计图根据统计图中的信息解答下列问题
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

1)九(1)班共有________名学生;
2全折线统计图
3D对应扇形心角的大小________
4)小明和小ABCD四个主中任一个主用列表或画的方法求出他们选择相同主的概率.

21.如图,以等边三角形ABCBC边为直径画,交AC于点D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 于点FOF,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
1)求DF <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的切线
2)求线OF度.

22.杂交水稻之父”——袁隆平先生所率领的科研团队在增产攻坚第一阶段实现水箱亩产量700公斤的目标,第三阶段实现水稻亩产量1008公斤的目标.
1)如果第二阶段、第三阶段亩产量的增长率相同,求亩产量的平均增长率;
2)按照(1)中亩产量增长率,科研团队期望第四阶段水稻亩产量达到1200公斤,请通过计算说明他们的目标能否实现.

23.如图所示,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 与双曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 交于AB两点,已知点B标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,直线ABx交于点C,与y交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
1)求直线AB的解析式;
2)若点P是第二象限内反比例函数象上的一点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的面2倍,求点P的坐
3)直接写出不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的解集.

24.如图,抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 轴交于AB两点,与 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 交于点C,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> BC两点,AC
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

1)求抛物线的解析式;
2)求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
3)点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 是抛物线上的一点,点D抛物线上位于直线BC上方的一点,D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 交直线BC于点E,点P抛物线对上一点,当线DE度最大,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的最小

25.已知点O线AB的中点,点P是直线l上的任意一点,分别过A和点B作直线l的垂线,垂足分别为C和点D.我垂足与中点之的距离足中距
1[猜想验证]1,当点P与点O重合你猜想、验证后直接写出足中距OCOD的数量关系是________
2[探究]2,当点P线AB上的任意一点足中距OCOD的数量关系是否依然成立,若成立,请给明;若不成立,请说明理由.
3[拓展延伸]3当点P线BA长线上的任意一点足中距OCOD的数量关系是否依然成立,若成立,请给明;若不成立,请说明理由;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 直接写出线ACBDOC的数量关系.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

参考答案

1.A

【解析】
根据算术平方根的定义即可求出结果.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
故选:A

2.B

【解析】
根据合并同类项法则、完全平方公式、积的乘方的运算法则、二次根式的运算法则依次计算各项后即可解答.
选项A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 不是同类项,不能够合并,选项A错误;
选项B,根据完全平方公式可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,选项B正确;
选项C,根据积的乘方的运算法则可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,选项C错误;
选项D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 不能够合并,选项D错误.
故选B

3.D

【解析】
过点EEHCD,由此求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,根据平行线的推得到ABEH,利用平行线的性求出答案.
解:EEHCD,如
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
EHCD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
ABEH
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

4.D

【解析】
根据题意,列出算式,即可求解.
解:300×0.8×0.6=144(元),
故选D

5.D

【解析】
根据正切函数的定义,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,根据计算器的应用,可得答案.
解:由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,得:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
故选:D

6.A

【解析】
画树状图展示所有9种等可能的结果数,找出恰有一车直行,另一车左拐的结果数,然后根据概率公式求解.
解:画树状图为:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
共有9种等可能的结果数,其中恰有一车直行,另一车左拐的结果数为2
所以恰有一车直行,另一车左拐的概率= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
故选A

7.C

【解析】
由已知求得圆锥母线长及圆锥侧面展开图所对的弧长,再由弧长公式求解圆心角的度数.
解:由圆锥的高为4,底面直径为6
可得母线长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
圆锥的底面周长为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
设圆心角的度数为n
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
心角度数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
C

8.C

【解析】
逐一分析四个选项,根据二次函数图象的开口方向以及对称轴与y的位置关系,即可得出ab的正性,由此即可得出一次函数经过的象限,即可得出结论
A.
二次函数象开口向下,y
a0b0
一次函数应该过第二、三、四象限,故本选项错误
B.
二次函数象开口向上,y
a0b0
一次函数应该过第一、三、四象限,故本选项错误
C.
二次函数象开口向下,y
a0b0
一次函数应该过第二、三、四象限,故本选项正确;
D.
二次函数象开口向下,y
a0b0
一次函数应该过第二、三、四象限,故本选项错误
C

9.A

【解析】
设点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的横坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,然后表示出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的横坐标的距离,再根据位似比列式计算即可得解.
设点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的横坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 间的横坐标的差为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 间的横坐标的差为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 放大到原来的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 倍得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> .
故选:A.

10.B

【解析】
AAIBC垂足I,然后ABC的面即可判定;先画出形,然后根据等三角形的性和相似三角形的性即可判定;如BCDB点逆时针60°得到ABN,求NE=DE;再延EAP使AP=CD=ANP=60°NP=AP=CD,然后讨论即可判定;如1,当AE=CD,根据意求得CH=CDAG=CH,再明四BHFG平行四形,最后再明是否菱形.
解:如1, AAIBC垂足I
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 边长为1的等三角形
∴∠BAC=ABC=C=60°CI= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
AI= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
SABC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,正确;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
2,当DC重合
∵∠DBE=30° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 是等三角形
∴∠DBE=ABE=30°
DE=AE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
GE//BD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
BG= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
GF//BD,BG//DF
HF=BG= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,正确;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
3,将BCDB点逆时针60°得到ABN
∴∠1=25=6=60°AN=CD,BD=BN
∵∠3=30°
∴∠2+4=1+4=30°
∴∠NBE=3=30°
BD=BNBE=BE
∴△NBE≌△DBESAS
NE=DE
EAP使AP=CD=AN
∵∠NAP=180°-60°-60°=60°
∴△ANP三角形
∴∠P=60°NP=AP=CD
如果AE+CD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> DE成立,PE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> NE,NEP=90°,但NEP不一定90°,故不成立;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
1,当AE=CD
GE//BC
∴∠AGE=ABC=60°GEA=C=60°
∴∠AGE=AEG=60°
AG=AE
同理:CH=CD
AG=CH
BG//FH,GF//BH
BHFG是平行四
BG=BH
BHFG菱形,故正确.
B

11. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
7206=72060000,根据科学记数法的法则表示还原的数即可
∵7206
=72060000
∴72060000=
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

12. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
先提取公因式b,再利用完全平方公式将括号里的式子进行因式分解即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

13.13

【解析】
直接根据中位数定义求解即可.
解:根据题意排列得:11111212121313
13
13131414141415151515
个数为偶数,中间的两个数为:1313
中位数为13
故答案为:13

14. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
分别求出每一个不等式的解集,再求其解集即可
解不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
解不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 解集 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

15. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
根据三角形内角和、三角形的外角以及等腰三角形性质求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,然后根据扇形面积公式计算.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
EBC的中点,EBEF半径,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
扇形BEF的面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

16. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
原计划每天绿化的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 万平方米,则实际每天绿化的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 万平方米,根据工作时间=工作总量 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 工作效率,结合实际比原计划提前30天完成了这一任务,即可列出关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的分式方程.
设原计划每天绿化的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 万平方米,则实际每天绿化的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 万平方米,
依据题意: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

17. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
因为折叠,则有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,从而可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,利用线段比求出DG,即可求出EG
,  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ABCD是正方形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
折叠, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 垂足H
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> DE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
故答案 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

18. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
利用tan30°计算出30°角所对直角边,乘以2得到斜边,计算3次,找出其中的规律即可.
∵AB
与直线l所夹锐角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
∴∠
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> =30°
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> tan30°= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> =1
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> =1,∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> =30°
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> tan30°= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> .

19.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
1)先化简二次根式、特殊角的正切三角函数、化简绝对值、零指数幂、积的乘方的逆用,再计算实数的混合运算即可得;
2)先计算分式的加法运算,再根据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 代入求值即可得.
解:(1)原式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
2)原式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
原式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

20.150;(2)见解析;(3108°;(4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
1)用B组频数除以所占百分比即可求解;
2)用50减去ABC组频数,求出D组频数,即可全折线统计图
3)用360°乘以D所占百分比即可求解;
4)列表得出所有等可能果,根据概率公式即可求解.
120÷40%=50(人),
故答案50
250-10-20-5=15(人),
全折线统计图
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
故答案 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
4)列表如下:

小明


A

B

C

D

A

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

B

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

C

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

D

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>


由列表可知,一共有16种等可能的果,他们选择相同主果有4种,
所以P(相同主 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

21.1)见解析;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
1)连接OD,先 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 是等三角形得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 即可明;
2)根据三角形中位线的判定与性、直角三角形的性得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,最后运用勾股定理解答即可.
1明:OD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 是等三角形
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 是等三角形
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
OD//AB
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
DF <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的切线
2OD//AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
OD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的中位线
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
由勾股定理,得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

22.120%;(2)能

【解析】
1)设亩产量的平均增长率为x,依意列出关于x的一元二次方程,求解即可;
2)根据(1)求出的平均增算第四亩产量即可.
解:(1设亩产量的平均增x,根据意得:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> (舍去),
答:亩产量的平均增20%
2)第四段的亩产 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> (公斤),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
的目可以实现

23.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ;(2)点P的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ;(3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
1A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 于点E,根据三角函数的性,得点A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,将点A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ;通列二元一次方程并求解,即可得到答案;
2OB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 合(1)的结论,得点B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 意得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ;把 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,得点C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,通过计算即可得到答案;
3)根据(1)和(2)的结论合反比例和一次函数的像,即可得到答案.
1)如A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 于点E
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
双曲线的解析式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
线AB的解析式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
2)如OB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
P的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
3)根据(1)和(2)的结论合点A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 、点B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

24.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ;(2)见解析;(3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
1)先利用直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 得到点B和点C的坐,利用待定系数法求解;
2)根据解析式求得点A的坐,求出两个三角形的边长,根据两组对应边成比例角相等求
3D的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,将线DE用函数关系式表示为顶点式形式,利用函数的性得到当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 线DE度最大,得到点D的坐,再利用轴对称及勾股定理求出答案即可.
1)解:线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 交于点B和点C
B的坐标为40),点C的坐标为02),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
抛物线的解析式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
2抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> x交于点A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
A的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
3D的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
E的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
=
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 线DE度最大.
,点D的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
C和点M关于轴对称,
CD于点P,此 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 最小.
CM交直线DE于点F <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,点F的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 的最小 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

25.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ;(2)仍然成立,证明见解析;(3)①仍然成立,证明见解析;② <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>

【解析】
1)根据三角形全等可得;
2)方法一:过点O作直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,交BD于点F,延ACEF于点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 即可,
方法二:延COBD于点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 即可;
3方法一:O作直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,交BD于点F,延CAEF于点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
方法二:延CODB的延长线于点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
CODB的延长线于点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,根据已知条件得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> O线AB的中点
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
2)数量关系依然成立.
明(方法一):O作直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,交BD于点F,延ACEF于点E
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
CEFD矩形.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
由(1)知, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
明(方法二):延COBD于点E
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
OAB的中点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
3数量关系依然成立.
明(方法一):
O作直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> ,交BD于点F,延CAEF于点E
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
CEFD矩形.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
由(1)知, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> 10
明(方法二):延CODB的延长线于点E
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
OAB的中点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
,延CODB的延长线于点E
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
OAB的中点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a> , <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/996/" title="东营" class="c1" target="_blank">东营</a>