--新人教版八年级学上期末测试题及答案免费下载
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2013--2014新人教版八年级数学上期末测试题
一．选择题（共12小题，满分36分，每小题3分）
1．以下永洁环保、绿色食品、节能、绿色环保四个标志中，是轴对称图形是（
）
A． B． C． D． 2．王师傅用4根木条钉成一个四边形木架，如图．要使这个木架不变形，他至少还要再钉上几根木条？（
）
A． 0根 B． 1根 C． 2根 D． 3根 3．如下图，已知△ABE≌△ACD，∠1=∠2，∠B=∠C，不正确的等式是（
）
A． AB=AC B． ∠BAE=∠CAD C． BE=DC D AD＝DE
4．如图，一个等边三角形纸片，剪去一个角后得到一个四边形，则图中∠α+∠β的度数是（
）
A． 180° B． 220° C． 240° D． 300° 5．下列计算正确的是（
）
A． 2a+3b=5ab B． （x+2）2=x2+4 C． （ab3）2=ab6 D． （﹣1）0=1 6．如图，给出了正方形ABCD的面积的四个表达式，其中错误的是（
）
A． （x+a）（x+a） B． x2+a2+2ax C． （x﹣a）（x﹣a） D． （x+a）a+（x+a）x 7．（3分）下列式子变形是因式分解的是（
）
A． x2﹣5x+6=
x（x﹣5）+6 B． x2﹣5x+6=
（x﹣2）（x﹣3） C． （x﹣2）（x﹣3）=x2﹣5x+6 D． x2﹣5x+6=
（x+2）（x+3） 8．若分式有意义，则a的取值范围是（
）
A． a=0 B． a=1 C． a≠﹣1 D． a≠0 9．化简的结果是（
）
A． x+1 B． x﹣1 C． ﹣x D． x 10．下列各式：①a0=1；②a2?a3=a5；③2﹣2=﹣；④﹣（3﹣5）+（﹣2）4÷8×（﹣1）=0；⑤x2+x2=2x2，其中正确的是（
）
A． ①②③ B． ①③⑤ C． ②③④ D． ②④⑤ 11．随着生活水平的提高，小林家购置了私家车，这样他乘坐私家车上学比乘坐公交车上学所需的时间少用了15分钟，现已知小林家距学校8千米，乘私家车平均速度是乘公交车平均速度的2.5倍，若设乘公交车平均每小时走x千米，根据题意可列方程为（
）
A． B． C． D． 12．如图，已知∠1=∠2，要得到△ABD≌△ACD，从下列条件中补选一个，则错误选法是（
）
A． AB=AC B． DB=DC C． ∠ADB=∠ADC D． ∠B=∠C
二．填空题（共5小题，满分20分，每小题4分）
13．（4分）分解因式：x3﹣4x2﹣12x= _________ ．
14．（4分）若分式方程：有增根，则k= _________ ．
15．（4分）如图所示，已知点A、D、B、F在一条直线上，AC=EF，AD=FB，要使△ABC≌△FDE，还需添加一个条件，这个条件可以是 _________ ．（只需填一个即可）
16．（4分）如图，在△ABC中，AC=BC，△ABC的外角∠ACE=100°，则∠A= _______ 度．
17．（4分）如图，边长为m+4的正方形纸片剪出一个边长为m的正方形之后，剩余部分可剪拼成一个矩形，若拼成的矩形一边长为4，则另一边长为 _________ ．
三．解答题（共7小题，满分64分）
18．先化简，再求值：5（3a2b﹣ab2）﹣3（ab2+5a2b），其中a=，b=﹣．
19．（6分）给出三个多项式：x2+2x﹣1，x2+4x+1，x2﹣2x．请选择你最喜欢的两个多项式进行加法运算，并把结果因式分解．
20．（8分）解方程：．
21．（10分）已知：如图，△ABC和△DBE均为等腰直角三角形．
（1）求证：AD=CE；
（2）求证：AD和CE垂直．
22．（10分）如图，CE=CB，CD=CA，∠DCA=∠ECB，求证：DE=AB．
23．（12分）某县为了落实中央的“强基惠民工程”，计划将某村的居民自来水管道进行改造．该工程若由甲队单独施工恰好在规定时间内完成；若乙队单独施工，则完成工程所需天数是规定天数的1.5倍．如果由甲、乙队先合做15天，那么余下的工程由甲队单独完成还需5天．
（1）这项工程的规定时间是多少天？
（2）已知甲队每天的施工费用为6500元，乙队每天的施工费用为3500元．为了缩短工期以减少对居民用水的影响，工程指挥部最终决定该工程由甲、乙队合做来完成．则该工程施工费用是多少？
24．（12分）在学习轴对称的时候，老师让同学们思考课本中的探究题．如图（1），要在燃气管道l上修建一个泵站，分别向A、B两镇供气．泵站修在管道的什么地方，可使所用的输气管线最短？你可以在l上找几个点试一试，能发现什么规律？
聪明的小华通过独立思考，很快得出了解决这个问题的正确办法．他把管道l看成一条直线（图（2）），问题就转化为，要在直线l上找一点P，使AP与BP的和最小．他的做法是这样的：
①作点B关于直线l的对称点B′．
②连接AB′交直线l于点P，则点P为所求．
请你参考小华的做法解决下列问题．如图在△ABC中，点D、E分别是AB、AC边的中点，BC=6，BC边上的高为4，请你在BC边上确定一点P，使△PDE得周长最小．
（1）在图中作出点P（保留作图痕迹，不写作法）．
（2）请直接写出△PDE周长的最小值： _________ ．
参考答案
一．选择题（共12小题，满分36分，每小题3分）
1．（3分））在以下永洁环保、绿色食品、节能、绿色环保四个标志中，是轴对称图形是（
）
A． B． C． D．
考点： 轴对称图形．314554 分析： 据轴对称图形的概念求解．如果一个图形沿着一条直线对折后两部分完全重合，这样的图形叫做轴对称图形，这条直线叫做对称轴． 解答： 解：A、不是轴对称图形，不符合题意；
B、是轴对称图形，符合题意；
C、不是轴对称图形，不符合题意；
D、不是轴对称图形，不符合题意．
故选B． 点评： 本题主要考查轴对称图形的知识点．确定轴对称图形的关键是寻找对称轴，图形两部分折叠后可重合．
2．（3分）王师傅用4根木条钉成一个四边形木架，如图．要使这个木架不变形，他至少还要再钉上几根木条？（
）
A． 0根 B． 1根 C． 2根 D． 3根
考点： 三角形的稳定性．314554 专题： 存在型． 分析： 根据三角形的稳定性进行解答即可． 解答： 解：加上AC后，原不稳定的四边形ABCD中具有了稳定的△ACD及△ABC，
故这种做法根据的是三角形的稳定性．
故选B．
点评： 本题考查的是三角形的稳定性在实际生活中的应用，比较简单．
3．（3分）如下图，已知△ABE≌△ACD，∠1=∠2，∠B=∠C，不正确的等式是（
）
A． AB=AC B． ∠BAE=∠CAD C． BE=DC D． AD=DE
考点： 全等三角形的性质．314554 分析： 根据全等三角形的性质，全等三角形的对应边相等，全等三角形的对应角相等，即可进行判断． 解答： 解：∵△ABE≌△ACD，∠1=∠2，∠B=∠C，
∴AB=AC，∠BAE=∠CAD，BE=DC，AD=AE，
故A、B、C正确；
AD的对应边是AE而非DE，所以D错误．
故选D． 点评： 本题主要考查了全等三角形的性质，根据已知的对应角正确确定对应边是解题的关键．
4．（3分）如图，一个等边三角形纸片，剪去一个角后得到一个四边形，则图中∠α+∠β的度数是（
）
A． 180° B． 220° C． 240° D． 300°
考点： 等边三角形的性质；多边形内角与外角．314554 专题： 探究型． 分析： 本题可先根据等边三角形顶角的度数求出两底角的度数和，然后在四边形中根据四边形的内角和为360°，求出∠α+∠β的度数． 解答： 解：∵等边三角形的顶角为60°，
∴两底角和=180°﹣60°=120°；
∴∠α+∠β=360°﹣120°=240°；
故选C． 点评： 本题综合考查等边三角形的性质及三角形内角和为180°，四边形的内角和是360°等知识，难度不大，属于基础题
5．（3分）下列计算正确的是（
）
A． 2a+3b=5ab B． （x+2）2=x2+4 C． （ab3）2=ab6 D． （﹣1）0=1
考点： 完全平方公式；合并同类项；幂的乘方与积的乘方；零指数幂．314554 分析： A、不是同类项，不能合并；
B、按完全平方公式展开错误，掉了两数积的两倍；
C、按积的乘方运算展开错误；
D、任何不为0的数的0次幂都等于1． 解答： 解：A、不是同类项，不能合并．故错误；
B、（x+2）2=x2+4x+4．故错误；
C、（ab3）2=a2b6．故错误；
D、（﹣1）0=1．故正确．
故选D． 点评： 此题考查了整式的有关运算公式和性质，属基础题．
6．（3分）如图，给出了正方形ABCD的面积的四个表达式，其中错误的是（
）
A． （x+a）（x+a） B． x2+a2+2ax C． （x﹣a）（x﹣a） D． （x+a）a+（x+a）x
考点： 整式的混合运算．314554 分析： 根据正方形的面积公式，以及分割法，可求正方形的面积，进而可排除错误的表达式． 解答： 解：根据图可知，
S正方形=（x+a）2=x2+2ax+a2，
故选C． 点评： 本题考查了整式的混合运算、正方形面积，解题的关键是注意完全平方公式的掌握．
7．（3分）下列式子变形是因式分解的是（
）
A． x2﹣5x+6=x（x﹣5）+6 B． x2﹣5x+6=（x﹣2）（x﹣3） C． （x﹣2）（x﹣3）=x2﹣5x+6 D． x2﹣5x+6=（x+2）（x+3）
考点： 因式分解的意义．314554 分析： 根据因式分解的定义：就是把整式变形成整式的积的形式，即可作出判断． 解答： 解：A、x2﹣5x+6=x（x﹣5）+6右边不是整式积的形式，故不是分解因式，故本选项错误；
B、x2﹣5x+6=（x﹣2）（x﹣3）是整式积的形式，故是分解因式，故本选项正确；
C、（x﹣2）（x﹣3）=x2﹣5x+6是整式的乘法，故不是分解因式，故本选项错误；
D、x2﹣5x+6=（x﹣2）（x﹣3），故本选项错误．
故选B． 点评： 本题考查的是因式分解的意义，把一个多项式化为几个整式的积的形式，这种变形叫做把这个多项式因式分解，也叫做分解因式．
8．（3分）若分式有意义，则a的取值范围是（
）
A． a=0 B． a=1 C． a≠﹣1 D． a≠0
考点： 分式有意义的条件．314554 专题： 计算题． 分析： 根据分式有意义的条件进行解答． 解答： 解：∵分式有意义，
∴a+1≠0，
∴a≠﹣1．
故选C． 点评： 本题考查了分式有意义的条件，要从以下两个方面透彻理解分式的概念：
（1）分式无意义?分母为零；
（2）分式有意义?分母不为零；
9．（3分）化简的结果是（
）
A． x+1 B． x﹣1 C． ﹣x D． x
考点： 分式的加减法．314554 分析： 将分母化为同分母，通分，再将分子因式分解，约分． 解答： 解：=﹣
=
=
=x，
故选D． 点评： 本题考查了分式的加减运算．分式的加减运算中，如果是同分母分式，那么分母不变，把分子直接相加减即可；如果是异分母分式，则必须先通分，把异分母分式化为同分母分式，然后再相加减．
10．（3分）下列各式：①a0=1；②a2?a3=a5；③2﹣2=﹣；④﹣（3﹣5）+（﹣2）4÷8×（﹣1）=0；⑤x2+x2=2x2，其中正确的是（
）
A． ①②③ B． ①③⑤ C． ②③④ D． ②④⑤
考点： 负整数指数幂；有理数的混合运算；合并同类项；同底数幂的乘法；零指数幂．314554 专题： 计算题． 分析： 分别根据0指数幂、同底数幂的乘法、负整数指数幂、有理数混合运算的法则及合并同类项的法则对各小题进行逐一计算即可． 解答： 解：①当a=0时不成立，故本小题错误；
②符合同底数幂的乘法法则，故本小题正确；
③2﹣2=，根据负整数指数幂的定义a﹣p=（a≠0，p为正整数），故本小题错误；
④﹣（3﹣5）+（﹣2）4÷8×（﹣1）=0符合有理数混合运算的法则，故本小题正确；
⑤x2+x2=2x2，符合合并同类项的法则，本小题正确．
故选D． 点评： 本题考查的是零指数幂、同底数幂的乘法、负整数指数幂、有理数混合运算的法则及合并同类项的法则，熟知以上知识是解答此题的关键．
11．（3分）随着生活水平的提高，小林家购置了私家车，这样他乘坐私家车上学比乘坐公交车上学所需的时间少用了15分钟，现已知小林家距学校8千米，乘私家车平均速度是乘公交车平均速度的2.5倍，若设乘公交车平均每小时走x千米，根据题意可列方程为（
）
A． B． C． D．
考点： 由实际问题抽象出分式方程．314554 分析： 根据乘私家车平均速度是乘公交车平均速度的2.5倍，乘坐私家车上学比乘坐公交车上学所需的时间少用了15分钟，利用时间得出等式方程即可． 解答： 解：设乘公交车平均每小时走x千米，根据题意可列方程为：
=+，
故选：D． 点评： 此题主要考查了由实际问题抽象出分式方程，解题关键是正确找出题目中的相等关系，用代数式表示出相等关系中的各个部分，把列方程的问题转化为列代数式的问题．
12．（3分）如图，已知∠1=∠2，要得到△ABD≌△ACD，还需从下列条件中补选一个，则错误的选法是（
）
A． AB=AC B． DB=DC C． ∠ADB=∠ADC D． ∠B=∠C
考点： 全等三角形的判定．314554 分析： 先要确定现有已知在图形上的位置，结合全等三角形的判定方法对选项逐一验证，排除错误的选项．本题中C、AB=AC与∠1=∠2、AD=AD组成了SSA是不能由此判定三角形全等的． 解答： 解：A、∵AB=AC，
∴，
∴△ABD≌△ACD（SAS）；故此选项正确；
B、当DB=DC时，AD=AD，∠1=∠2，
此时两边对应相等，但不是夹角对应相等，故此选项错误；
C、∵∠ADB=∠ADC，
∴，
∴△ABD≌△ACD（ASA）；故此选项正确；
D、∵∠B=∠C，
∴，
∴△ABD≌△ACD（AAS）；故此选项正确．
故选：B． 点评： 本题考查了三角形全等的判定定理，普通两个三角形全等共有四个定理，即AAS、ASA、SAS、SSS，但SSA无法证明三角形全等．
二．填空题（共5小题，满分20分，每小题4分）
13．（4分）分解因式：x3﹣4x2﹣12x= x（x+2）（x﹣6） ．
考点： 因式分解-十字相乘法等；因式分解-提公因式法．314554 分析： 首先提取公因式x，然后利用十字相乘法求解即可求得答案，注意分解要彻底． 解答： 解：x3﹣4x2﹣12x
=x（x2﹣4x﹣12）
=x（x+2）（x﹣6）．
故答案为：x（x+2）（x﹣6）． 点评： 此题考查了提公因式法、十字相乘法分解因式的知识．此题比较简单，注意因式分解的步骤：先提公因式，再利用其它方法分解，注意分解要彻底．
14．（4分）若分式方程：有增根，则k= 1或2 ．
考点： 分式方程的增根．314554 专题： 计算题． 分析： 把k当作已知数求出x=，根据分式方程有增根得出x﹣2=0，2﹣x=0，求出x=2，得出方程=2，求出k的值即可． 解答： 解：∵，
去分母得：2（x﹣2）+1﹣kx=﹣1，
整理得：（2﹣k）x=2，
当2﹣k=0时，此方程无解，
∵分式方程有增根，
∴x﹣2=0，2﹣x=0，
解得：x=2，
把x=2代入（2﹣k）x=2得：k=1．
故答案为：1或2． 点评： 本题考查了对分式方程的增根的理解和运用，把分式方程变成整式方程后，求出整式方程的解，若代入分式方程的分母恰好等于0，则此数是分式方程的增根，即不是分式方程的根，题目比较典型，是一道比较好的题目．
15．（4分）如图所示，已知点A、D、B、F在一条直线上，AC=EF，AD=FB，要使△ABC≌△FDE，还需添加一个条件，这个条件可以是 ∠A=∠F或AC∥EF或BC=DE（答案不唯一） ．（只需填一个即可）
考点： 全等三角形的判定．314554 专题： 开放型． 分析： 要判定△ABC≌△FDE，已知AC=FE，AD=BF，则AB=CF，具备了两组边对应相等，故添加∠A=∠F，利用SAS可证全等．（也可添加其它条件）． 解答： 解：增加一个条件：∠A=∠F，
显然能看出，在△ABC和△FDE中，利用SAS可证三角形全等（答案不唯一）．
故答案为：∠A=∠F或AC∥EF或BC=DE（答案不唯一）． 点评： 本题考查了全等三角形的判定；判定方法有ASA、AAS、SAS、SSS等，在选择时要结合其它已知在图形上的位置进行选取．
16．（4分）如图，在△ABC中，AC=BC，△ABC的外角∠ACE=100°，则∠A= 50 度．
考点： 三角形的外角性质；等腰三角形的性质．314554 分析： 根据等角对等边的性质可得∠A=∠B，再根据三角形的一个外角等于与它不相邻的两个内角的和列式计算即可得解． 解答： 解：∵AC=BC，
∴∠A=∠B，
∵∠A+∠B=∠ACE，
∴∠A=∠ACE=×100°=50°．
故答案为：50． 点评： 本题主要考查了三角形的一个外角等于与它不相邻的两个内角的和的性质，等边对等角的性质，是基础题，熟记性质并准确识图是解题的关键．
17．（4分）如图，边长为m+4的正方形纸片剪出一个边长为m的正方形之后，剩余部分可剪拼成一个矩形，若拼成的矩形一边长为4，则另一边长为 2m+4 ．
考点： 平方差公式的几何背景．314554 分析： 根据拼成的矩形的面积等于大正方形的面积减去小正方形的面积，列式整理即可得解． 解答： 解：设拼成的矩形的另一边长为x，
则4x=（m+4）2﹣m2=（m+4+m）（m+4﹣m），
解得x=2m+4．
故答案为：2m+4． 点评： 本题考查了平方差公式的几何背景，根据拼接前后的图形的面积相等列式是解题的关键．
三．解答题（共7小题，满分64分）
18．（6分）先化简，再求值：5（3a2b﹣ab2）﹣3（ab2+5a2b），其中a=，b=﹣．
考点： 整式的加减—化简求值．314554 分析： 首先根据整式的加减运算法则将原式化简，然后把给定的值代入求值．注意去括号时，如果括号前是负号，那么括号中的每一项都要变号；合并同类项时，只把系数相加减，字母与字母的指数不变． 解答： 解：原式=15a2b﹣5ab2﹣3ab2﹣15a2b=﹣8ab2，
当a=，b=﹣时，原式=﹣8××=﹣． 点评： 熟练地进行整式的加减运算，并能运用加减运算进行整式的化简求值．
19．（6分）给出三个多项式：x2+2x﹣1，x2+4x+1，x2﹣2x．请选择你最喜欢的两个多项式进行加法运算，并把结果因式分解．
考点： 提公因式法与公式法的综合运用；整式的加减．314554 专题： 开放型． 分析： 本题考查整式的加法运算，找出同类项，然后只要合并同类项就可以了． 解答： 解：情况一：x2+2x﹣1+x2+4x+1=x2+6x=x（x+6）．
情况二：x2+2x﹣1+x2﹣2x=x2﹣1=（x+1）（x﹣1）．
情况三：x2+4x+1+x2﹣2x=x2+2x+1=（x+1）2． 点评： 本题考查了提公因式法，公式法分解因式，整式的加减运算实际上就是去括号、合并同类项，这是各地中考的常考点．
熟记公式结构是分解因式的关键．平方差公式：a2﹣b2=（a+b）（a﹣b）；完全平方公式：a2±2ab+b2=（a±b）2．
20．（8分）解方程：．
考点： 解分式方程．314554 分析： 观察可得最简公分母是（x+2）（x﹣2），方程两边乘最简公分母，可以把分式方程转化为整式方程求解． 解答： 解：原方程即：．（1分）
方程两边同时乘以（x+2）（x﹣2），
得x（x+2）﹣（x+2）（x﹣2）=8．（4分）
化简，得 2x+4=8．
解得：x=2．（7分）
检验：x=2时，（x+2）（x﹣2）=0，即x=2不是原分式方程的解，
则原分式方程无解．（8分） 点评： 此题考查了分式方程的求解方法．此题比较简单，注意转化思想的应用，注意解分式方程一定要验根．
21．（10分）已知：如图，△ABC和△DBE均为等腰直角三角形．
（1）求证：AD=CE；
（2）求证：AD和CE垂直．
考点： 等腰直角三角形；全等三角形的性质；全等三角形的判定．314554 分析： （1）要证AD=CE，只需证明△ABD≌△CBE，由于△ABC和△DBE均为等腰直角三角形，所以易证得结论．
（2）延长AD，根据（1）的结论，易证∠AFC=∠ABC=90°，所以AD⊥CE． 解答： 解：（1）∵△ABC和△DBE均为等腰直角三角形，
∴AB=BC，BD=BE，∠ABC=∠DBE=90°，
∴∠ABC﹣∠DBC=∠DBE﹣∠DBC，
即∠ABD=∠CBE，
∴△ABD≌△CBE，
∴AD=CE．
（2）垂直．延长AD分别交BC和CE于G和F，
∵△ABD≌△CBE，
∴∠BAD=∠BCE，
∵∠BAD+∠ABC+∠BGA=∠BCE+∠AFC+∠CGF=180°，
又∵∠BGA=∠CGF，
∴∠AFC=∠ABC=90°，
∴AD⊥CE．
点评： 利用等腰三角形的性质，可以证得线段和角相等，为证明全等和相似奠定基础，从而进行进一步的证明．
22．（10分）如图，CE=CB，CD=CA，∠DCA=∠ECB，求证：DE=AB．
考点： 全等三角形的判定与性质．314554 专题： 证明题． 分析： 求出∠DCE=∠ACB，根据SAS证△DCE≌△ACB，根据全等三角形的性质即可推出答案． 解答： 证明：∵∠DCA=∠ECB，
∴∠DCA+∠ACE=∠BCE+∠ACE，
∴∠DCE=∠ACB，
∵在△DCE和△ACB中
，
∴△DCE≌△ACB，
∴DE=AB． 点评： 本题考查了全等三角形的性质和判定的应用，主要考查学生能否运用全等三角形的性质和判定进行推理，题目比较典型，难度适中．
23．（12分）（2012?百色）某县为了落实中央的“强基惠民工程”，计划将某村的居民自来水管道进行改造．该工程若由甲队单独施工恰好在规定时间内完成；若乙队单独施工，则完成工程所需天数是规定天数的1.5倍．如果由甲、乙队先合做15天，那么余下的工程由甲队单独完成还需5天．
（1）这项工程的规定时间是多少天？
（2）已知甲队每天的施工费用为6500元，乙队每天的施工费用为3500元．为了缩短工期以减少对居民用水的影响，工程指挥部最终决定该工程由甲、乙队合做来完成．则该工程施工费用是多少？
考点： 分式方程的应用．314554 专题： 应用题． 分析： （1）设这项工程的规定时间是x天，根据甲、乙队先合做15天，余下的工程由甲队单独需要5天完成，可得出方程，解出即可．
（2）先计算甲、乙合作需要的时间，然后计算费用即可． 解答： 解：（1）设这项工程的规定时间是x天，
根据题意得：（+）×15+=1．
解得：x=30．
经检验x=30是方程的解．
答：这项工程的规定时间是30天．
（2）该工程由甲、乙队合做完成，所需时间为：1÷（+）=18（天），
则该工程施工费用是：18×（6500+3500）=180000（元）．
答：该工程的费用为180000元． 点评： 本题考查了分式方程的应用，解答此类工程问题，经常设工作量为“单位1”，注意仔细审题，运用方程思想解答．
24．（12分）在学习轴对称的时候，老师让同学们思考课本中的探究题．
如图（1），要在燃气管道l上修建一个泵站，分别向A、B两镇供气．泵站修在管道的什么地方，可使所用的输气管线最短？
你可以在l上找几个点试一试，能发现什么规律？
聪明的小华通过独立思考，很快得出了解决这个问题的正确办法．他把管道l看成一条直线（图（2）），问题就转化为，要在直线l上找一点P，使AP与BP的和最小．他的做法是这样的：
①作点B关于直线l的对称点B′．
②连接AB′交直线l于点P，则点P为所求．
请你参考小华的做法解决下列问题．如图在△ABC中，点D、E分别是AB、AC边的中点，BC=6，BC边上的高为4，请你在BC边上确定一点P，使△PDE得周长最小．
（1）在图中作出点P（保留作图痕迹，不写作法）．
（2）请直接写出△PDE周长的最小值： 8 ．
考点： 轴对称-最短路线问题．314554 分析： （1）根据提供材料DE不变，只要求出DP+PE的最小值即可，作D点关于BC的对称点D′，连接D′E，与BC交于点P，P点即为所求；
（2）利用中位线性质以及勾股定理得出D′E的值，即可得出答案． 解答： 解：（1）作D点关于BC的对称点D′，连接D′E，与BC交于点P，
P点即为所求；
（2）∵点D、E分别是AB、AC边的中点，
∴DE为△ABC中位线，
∵BC=6，BC边上的高为4，
∴DE=3，DD′=4，
∴D′E===5，
∴△PDE周长的最小值为：DE+D′E=3+5=8，
故答案为：8．
点评： 此题主要考查了利用轴对称求最短路径以及三角形中位线的知识，根据已知得出要求△PDE周长的最小值，求出DP+PE的最小值即可是解题关键．
Delegates, staff: Hello! in the run-up to the Spring Festival, we held one session of four staff representatives Conference 2013-workshop, full back in 2012, careful analysis of the current situation, discuss 2013 development plans.
Here, on behalf of my company 2013 work reports to the General Assembly, for consideration.
Pillar I, 2012 back in 2012, XX power companies adhere to the party's 17 great spirit for guidance, comprehensively implement the scientific concept of development, promoting cost-leadership strategy, standards, focus on implementation, lean management, continuously improve, smooth present safety situation of enterprise management, business management and control scientific and standardized, and the dedication of staff, manage a harmonious and democratic atmosphere of the good situation. Main indicators are as follows:-the battery indicator: power generation totaled 7.815 billion kWh, beyond the annual budget implementation capacity of 315 million kWh, an increase of 757 million kWh.
Sales totaled 7.425 billion kWh, exceeding sales of 330 million kWh the annual Executive budget, an increase of 729 million kWh. --Security measures: unplanned outages 2.5 times.
No personal injury accident occurred, no major accident and above, no major fire accidents without environmental pollution accidents, safety for three consecutive years to maintain stability to good posture.
– Business financial indicators: total profits of 255 million Yuan, beyond the annual budget of 207 million Yuan, beyond the Datang company index 41.89 million Yuan, an increase of 1.76 million Yuan, FCM assessment at grade four.
--Energy: power supply standard coal completing 312.25 g/kWh, down 0.1 g/kWh; integrated auxiliary power consumption ratio in 5.12%, down 0.26%; pollutant emissions performance greatly reduced compared to last year, carbon 0.09 g/kWh, sulfur dioxide 0.104 g/kWh NOx 0.512 g/kWh; dust removal efficiency of more than 99.8%. --Reliability index: equivalent availability factor in 93.47%, increased 7.95% from a year earlier.
Equivalent forced outage rate 0.08%, 0.16% reduction over the same period a year earlier.
Major achievements: first, we should adhere to the two "management system" basis, strengthening technological research, strengthen hidden hazards control and intrinsic safety Enterprise construction took new steps. -The two "management system" for improvement. Focus on promoting the power of the company management system and the application and implementation of the safety loop five-star management system, improve the safety management system, realize the system of safety control. Further regulate security routines, safety supervision and management network role to play to achieve closed-loop. Strengthening the supervision and management of habitual violation of, strengthening the safety supervision of outsourcing contractors. Carried out in spring and autumn of security inspections, flood control and inspection, safety production month, day supervision of production safety and the Olympic Games and other
Delegates, staff: Hello! in the run-up to the Spring Festival, we held one session of four staff representatives Conference 2013-workshop, full back in 2012, careful analysis of the current situation, discuss 2013 development plans.
Here, on behalf of my company 2013 work reports to the General Assembly, for consideration.
Pillar I, 2012 back in 2012, XX power companies adhere to the party's 17 great spirit for guidance, comprehensively implement the scientific concept of development, promoting cost-leadership strategy, standards, focus on implementation, lean management, continuously improve, smooth present safety situation of enterprise management, business management and control scientific and standardized, and the dedication of staff, manage a harmonious and democratic atmosphere of the good situation. Main indicators are as follows:-the battery indicator: power generation totaled 7.815 billion kWh, beyond the annual budget implementation capacity of 315 million kWh, an increase of 757 million kWh.
Sales totaled 7.425 billion kWh, exceeding sales of 330 million kWh the annual Executive budget, an increase of 729 million kWh. --Security measures: unplanned outages 2.5 times.
No personal injury accident occurred, no major accident and above, no major fire accidents without environmental pollution accidents, safety for three consecutive years to maintain stability to good posture.
– Business financial indicators: total profits of 255 million Yuan, beyond the annual budget of 207 million Yuan, beyond the Datang company index 41.89 million Yuan, an increase of 1.76 million Yuan, FCM assessment at grade four.
--Energy: power supply standard coal completing 312.25 g/kWh, down 0.1 g/kWh; integrated auxiliary power consumption ratio in 5.12%, down 0.26%; pollutant emissions performance greatly reduced compared to last year, carbon 0.09 g/kWh, sulfur dioxide 0.104 g/kWh NOx 0.512 g/kWh; dust removal efficiency of more than 99.8%. --Reliability index: equivalent availability factor in 93.47%, increased 7.95% from a year earlier.
Equivalent forced outage rate 0.08%, 0.16% reduction over the same period a year earlier.
Major achievements: first, we should adhere to the two "management system" basis, strengthening technological research, strengthen hidden hazards control and intrinsic safety Enterprise construction took new steps. -The two "management system" for improvement. Focus on promoting the power of the company management system and the application and implementation of the safety loop five-star management system, improve the safety management system, realize the system of safety control. Further regulate security routines, safety supervision and management network role to play to achieve closed-loop. Strengthening the supervision and management of habitual violation of, strengthening the safety supervision of outsourcing contractors. Carried out in spring and autumn of security inspections, flood control and inspection, safety production month, day supervision of production safety and the Olympic Games and other
activities, comprehensive and tamping Safety Foundation ... Troubleshooting, management mechanism, give full play to role of technical supervision and realization of troubleshooting, management, improved process management. This year completed the boiler lower header leakage, boiler pressure, a major risk management, completed 29 of great risks and 3 General problems of governance. Complete chemistry lab construction, thermal control, and complete the boiler scale integrated management, host shafting vibration of 10 scientific and technological projects, such as.
Complete supercritical 630MW on-line simulation system development and application of circulating water MCC standby power transformation, the transformation of desulfurization waste water, the unit water supply system of comprehensive treatment and discharge valve modification of coal mill 5 key technological transformation projects, group health is improved. --Science and technology innovation is further increased. Strengthen the characteristics of supercritical unit major issues, gradually clearing the particularity of supercritical unit and regularity. Developed motor oil time management, switch action times, statistics, coal-aided measurement software, improves the production level of lean management. Increased investment in science and technology, reporting science and technology projects and 14 technical project total cost percentage of the total annual production output of 0.25%. "Large-scale coal-fired power plant flue gas desulfurization, denitrification complete development and application of key technologies" project, won the national science and technology progress second prize. 630MW supercritical units optimized control strategies and the 630MW development and application of on-line simulation system for supercritical units, supercritical 600MW units of turbine driven boiler feed pump set of comprehensive treatment of defects Datang technology respectively one or two and third.
Meanwhile, information technology achievements, the company was named "China power information technology benchmarking enterprises." --Repair and maintenance has improved further. Modify the inspection standards and standards on a regular basis, standardizing work procedures, checking and inspection project. Deepening the BFS++ system, and implements maintenance information shared. Reorganizing RB logic again, and ensure the success of the RB. Innovating the mechanism of maintenance management, implemented a project manager system. Successful completion of two autonomous maintenance, reliability improved steadily. Implementing two c-level maintenance, project themselves 48.7% and 42.3%, respectively. Accomplish two circulating pumps repair and overhaul of four Mills, maintenance teams to get exercise.
Promote the work of energy saving and consumption reducing, complete the unit energy consumption diagnosis, plant water balance test, 10 energy-saving projects.
Second, we should adhere to "three" on the economic benefits of improving, outreach
activities, comprehensive and tamping Safety Foundation ... Troubleshooting, management mechanism, give full play to role of technical supervision and realization of troubleshooting, management, improved process management. This year completed the boiler lower header leakage, boiler pressure, a major risk management, completed 29 of great risks and 3 General problems of governance. Complete chemistry lab construction, thermal control, and complete the boiler scale integrated management, host shafting vibration of 10 scientific and technological projects, such as.
Complete supercritical 630MW on-line simulation system development and application of circulating water MCC standby power transformation, the transformation of desulfurization waste water, the unit water supply system of comprehensive treatment and discharge valve modification of coal mill 5 key technological transformation projects, group health is improved. --Science and technology innovation is further increased. Strengthen the characteristics of supercritical unit major issues, gradually clearing the particularity of supercritical unit and regularity. Developed motor oil time management, switch action times, statistics, coal-aided measurement software, improves the production level of lean management. Increased investment in science and technology, reporting science and technology projects and 14 technical project total cost percentage of the total annual production output of 0.25%. "Large-scale coal-fired power plant flue gas desulfurization, denitrification complete development and application of key technologies" project, won the national science and technology progress second prize. 630MW supercritical units optimized control strategies and the 630MW development and application of on-line simulation system for supercritical units, supercritical 600MW units of turbine driven boiler feed pump set of comprehensive treatment of defects Datang technology respectively one or two and third.
Meanwhile, information technology achievements, the company was named "China power information technology benchmarking enterprises." --Repair and maintenance has improved further. Modify the inspection standards and standards on a regular basis, standardizing work procedures, checking and inspection project. Deepening the BFS++ system, and implements maintenance information shared. Reorganizing RB logic again, and ensure the success of the RB. Innovating the mechanism of maintenance management, implemented a project manager system. Successful completion of two autonomous maintenance, reliability improved steadily. Implementing two c-level maintenance, project themselves 48.7% and 42.3%, respectively. Accomplish two circulating pumps repair and overhaul of four Mills, maintenance teams to get exercise.
Promote the work of energy saving and consumption reducing, complete the unit energy consumption diagnosis, plant water balance test, 10 energy-saving projects.
Second, we should adhere to "three" on the economic benefits of improving, outreach
Delegates, staff: Hello! in the run-up to the Spring Festival, we held one session of four staff representatives Conference 2013-workshop, full back in 2012, careful analysis of the current situation, discuss 2013 development plans.
Here, on behalf of my company 2013 work reports to the General Assembly, for consideration.
Pillar I, 2012 back in 2012, XX power companies adhere to the party's 17 great spirit for guidance, comprehensively implement the scientific concept of development, promoting cost-leadership strategy, standards, focus on implementation, lean management, continuously improve, smooth present safety situation of enterprise management, business management and control scientific and standardized, and the dedication of staff, manage a harmonious and democratic atmosphere of the good situation. Main indicators are as follows:-the battery indicator: power generation totaled 7.815 billion kWh, beyond the annual budget implementation capacity of 315 million kWh, an increase of 757 million kWh.
Sales totaled 7.425 billion kWh, exceeding sales of 330 million kWh the annual Executive budget, an increase of 729 million kWh. --Security measures: unplanned outages 2.5 times.
No personal injury accident occurred, no major accident and above, no major fire accidents without environmental pollution accidents, safety for three consecutive years to maintain stability to good posture.
– Business financial indicators: total profits of 255 million Yuan, beyond the annual budget of 207 million Yuan, beyond the Datang company index 41.89 million Yuan, an increase of 1.76 million Yuan, FCM assessment at grade four.
--Energy: power supply standard coal completing 312.25 g/kWh, down 0.1 g/kWh; integrated auxiliary power consumption ratio in 5.12%, down 0.26%; pollutant emissions performance greatly reduced compared to last year, carbon 0.09 g/kWh, sulfur dioxide 0.104 g/kWh NOx 0.512 g/kWh; dust removal efficiency of more than 99.8%. --Reliability index: equivalent availability factor in 93.47%, increased 7.95% from a year earlier.
Equivalent forced outage rate 0.08%, 0.16% reduction over the same period a year earlier.
Major achievements: first, we should adhere to the two "management system" basis, strengthening technological research, strengthen hidden hazards control and intrinsic safety Enterprise construction took new steps. -The two "management system" for improvement. Focus on promoting the power of the company management system and the application and implementation of the safety loop five-star management system, improve the safety management system, realize the system of safety control. Further regulate security routines, safety supervision and management network role to play to achieve closed-loop. Strengthening the supervision and management of habitual violation of, strengthening the safety supervision of outsourcing contractors. Carried out in spring and autumn of security inspections, flood control and inspection, safety production month, day supervision of production safety and the Olympic Games and other
activities, comprehensive and tamping Safety Foundation ... Troubleshooting, management mechanism, give full play to role of technical supervision and realization of troubleshooting, management, improved process management. This year completed the boiler lower header leakage, boiler pressure, a major risk management, completed 29 of great risks and 3 General problems of governance. Complete chemistry lab construction, thermal control, and complete the boiler scale integrated management, host shafting vibration of 10 scientific and technological projects, such as.
Complete supercritical 630MW on-line simulation system development and application of circulating water MCC standby power transformation, the transformation of desulfurization waste water, the unit water supply system of comprehensive treatment and discharge valve modification of coal mill 5 key technological transformation projects, group health is improved. --Science and technology innovation is further increased. Strengthen the characteristics of supercritical unit major issues, gradually clearing the particularity of supercritical unit and regularity. Developed motor oil time management, switch action times, statistics, coal-aided measurement software, improves the production level of lean management. Increased investment in science and technology, reporting science and technology projects and 14 technical project total cost percentage of the total annual production output of 0.25%. "Large-scale coal-fired power plant flue gas desulfurization, denitrification complete development and application of key technologies" project, won the national science and technology progress second prize. 630MW supercritical units optimized control strategies and the 630MW development and application of on-line simulation system for supercritical units, supercritical 600MW units of turbine driven boiler feed pump set of comprehensive treatment of defects Datang technology respectively one or two and third.
Meanwhile, information technology achievements, the company was named "China power information technology benchmarking enterprises." --Repair and maintenance has improved further. Modify the inspection standards and standards on a regular basis, standardizing work procedures, checking and inspection project. Deepening the BFS++ system, and implements maintenance information shared. Reorganizing RB logic again, and ensure the success of the RB. Innovating the mechanism of maintenance management, implemented a project manager system. Successful completion of two autonomous maintenance, reliability improved steadily. Implementing two c-level maintenance, project themselves 48.7% and 42.3%, respectively. Accomplish two circulating pumps repair and overhaul of four Mills, maintenance teams to get exercise.
Promote the work of energy saving and consumption reducing, complete the unit energy consumption diagnosis, plant water balance test, 10 energy-saving projects.
Second, we should adhere to "three" on the economic benefits of improving, outreach
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