杭州市文澜中学2018八下Unit 3单元检测 (含答案)-最新学习文档

2023-2024学年浙江省杭州市拱墅区文澜中学八年级（下）月考数学试卷（5月份）一、选择题（本题有10小题，每小题3分，共30分）1．（3分）下列四幅图案是四所学校校徽的主体标识，其中是中心对称图形的是（ ）A．B．C．D．2．（3分）下列计算中，正确的是（ ）A．+＝B．＝﹣3C．＝D．3﹣＝23．（3分）如图，在▱ABCD中，CE平分∠BCD交AD于点E，若AE＝2，▱ABCD的周长等于24，则线段AB的长为（ ）A．5B．6C．7D．84．（3分）点点同学对数据26，36，26，46，5■，52进行统计分析，发现其中一个两位数的个位数字被墨水涂污看不到了，则计算结果与被涂污数字无关的是（ ）A．平均数B．中位数C．方差D．标准差5．（3分）若用反证法证明命题“四边形中至少有一个角是钝角或直角”时，则首先应该假设这个四边形中（ ）A．至少有一个角是钝角或直角B．没有一个角是锐角C．每一个角都是钝角或直角D．每一个角是锐角6．（3分）若点A（x1，y1），B（x2，y2），C（x3，y3）都在反比例函数的图象上，且x1＜x2＜0＜x3，则y1，y2，y3的大小关系正确的是（ ）A．y1＜y3＜y2B．y3＜y2＜y1C．y3＜y1＜y2D．y2＜y1＜y37．（3分）已知m，n是方程x2+2x﹣5＝0的两个实数根，则m2﹣mn+3m+n＝（ ）A．6B．7C．8D．98．（3分）如图，已知正方形ABCD的面积为9，AB∥x轴．它的两个顶点B，D是反比例函数（k＞0，x＞0）的图象上两点，若点D的坐标是（m，n），则m﹣n的值为（ ）A．3B．﹣3C．D．9．（3分）如图，在Rt△ABC中，∠ACB＝90°，AC＝3，BC＝4，以其三边为边向形外分别作正方形，然后将整个图形放置于如图所示的长方形中，使点D，E，F；G，H恰好在长方形的边上，则图中阴影部分的面积为（ ）A．B．C．56D．10．（3分）已知关于x的一元二次方程ax2+bx+c＝0，及函数，y2＝cx+b（a，b，c为常数，且ac ≠0），则（ ）A．若方程ax2+bx+c＝0有解，则函数y1，y2的图象一定有交点．B．若方程ax2+bx+c＝0有解，则函数y1，y2的图象一定没有交点．C．若方程ax2+bx+c＝0无解，则函数y1，y2的图象一定有交点．D．若方程ax2+bx+c＝0无解，则函数y1，y2的图象一定没有交点．二.填空题（本题有6小题，每小题3分，共18分）11．（3分）若代数式有意义，则x的取值范围是 ．12．（3分）一个多边形的每一个内角都是120°，则这个多边形是 边形．13．（3分）关于x的方程x2﹣2（a﹣1）x+a2＝0有实数根，则a的取值范围 ．14．（3分）如图，已知△OAB的顶点A、B分别在反比例函数和的图象上，且AB∥x轴．若△OAB的面积为3，则k＝ ．15．（3分）已知在△ABC中，AC＝6cm，点D、E分别是AC、BC的中点，连接DE，在DE上有一点F，EF＝1cm，连接AF，CF，若AF⊥CF，则AB＝ ．16．（3分）如图是一张矩形纸片ABCD，点E为AD中点，点F在BC上，把该纸片沿EF折叠，点A，B 的对应点分别为A′，B′，A′E与BC相交于点G，B′A′的延长线过点C．若，则的值为 ．三.解答题（本题有8小题，共72分）17．（6分）计算：（1）；（2）×．18．（6分）解方程：（1）x（x﹣6）＝5（6﹣x）；（2）2x2﹣4x﹣3＝0．19．（6分）图①、图②均是4×4的正方形网格，每个小正方形的边长均为1，小正方形的顶点称为格点．用直尺在给定的网格中按要求画图，所画图形的顶点均在格点上．（1）在图①中，以线段AB为一边，画一个矩形．（2）在图②中，以点E为顶点，画一个面积最大的正方形．20．（8分）6月5日是世界环境日，某校组织了一次环保知识竞赛，每班选25名同学参加比赛，成绩分别为A、B、C、D四个等级，其中相应等级的得分依次记为10分、9分、8分、7分，学校将某年级的八（1）班和八（2）班的成绩整理并绘制成统计图：根据提供的信息解答下列问题：班级平均分中位数众数方差八（1）班8.76a9 1.06八（2）班8.768b 1.38（1）把八（1）班竞赛成绩统计图补充完整；（2）写出表中a，b的值；（3）依据数据分析表，有同学认为八（2）班的成绩比八（1）班好，但也有同学认为八（1）班的成绩更好，请你写出一条支持八（1）班成绩更好的理由．21．（8分）如图，AE∥BF，AC平分∠BAD，且交BF于点C，BD平分∠ABC，且交AE于点D，连接CD．（1）求证：四边形ABCD是菱形；（2）若AC＝6，BD＝8，过点D作DH⊥BF于点H，求CH的长．22．（10分）已知反比例函数的图象与一次函数y2＝x+b的图象交于点A（a，2），B（﹣2，2b）．（1）求一次函数和反比例函数的表达式．（2）请直接写出当y1≤y2时，x的取值范围．（3）设t≠0，当x＝t时，y1＝m；当x＝t+1时，y1＝n，方方说：“m一定大于n”，你认为方方的说法正确吗？为什么？23．（10分）如图1，在正方形ABCD中，点P是对角线BD上的一点，连结CP．（1）求证：△ADP≌△CDP；（2）如图2，延长AP交线段DC于点Q，交BC的延长线于点G，点M是GQ的中点，连结CM．求证：PC⊥MC；（3）如图3，延长AP交射线DC于点Q，交BC于点G，点M是GQ的中点，连结CM．若，∠BAP＝30°，AB的长度为 ．24．（12分）综合实践：项目主题“亚运主题”草坪设计项目情境为了迎亚运会，同学们参与一块长为40米，宽为30米的矩形“亚运主题”草坪方案设计的项目学习．以下为项目学习小组对草坪设计的研究过程．活动任务一请设计两条相同宽度的小路连接矩形草坪两组对边．小组内同学们设计的方案主要有甲、乙、丙、丁四种典型的方案驱动问题一（1）项目小组设计出来的四种方案小路面积的大小关系？①直观猜想：我认为 ；（请用简洁的语言或代数式表达你的猜想）②具体验证：选择最简单的甲、乙方案，假设小路宽为1米，则甲、乙方案中小路的面积分别为 和 ；③一般验证：若小路宽为x米，则甲、乙方案中小路所占的面积分别为 和 ．活动任务二为施工方便，学校选择甲种方案设计，并要求除小路后草坪面积约为1064平方米．驱动问题二（2）请计算两条小路的宽度是多少？活动任务三为了布置五环标志等亚运元素，将在草坪上的亚运宣传主题墙前，用篱笆围（三边）成面积为100平方米的矩形ABCD，如图．驱动问题三（3）为了使篱笆恰好用完同时围住三面，项目小组的同学对下列问题展开探究，其中矩形宽AB＝x，长BC＝y．①若30米长的篱笆，请用两种不同的函数表示y关于x的函数关系．②数学之星小明提出一个问题：若a米长的篱笆恰好用完，且有两种不同方案可以选择，使得两种方案的宽之和小于15米，甲同学说“篱笆的长可以是28米”，乙同学说“篱笆的长可以是32米”，你认为他们俩的说法对吗？请说明理由．2023-2024学年浙江省杭州市拱墅区文澜中学八年级（下）月考数学试卷（5月份）参考答案与试题解析一、选择题（本题有10小题，每小题3分，共30分）1．（3分）下列四幅图案是四所学校校徽的主体标识，其中是中心对称图形的是（ ）A．B．C．D．【分析】根据中心对称图形的定义：把一个图形绕某一点旋转180°，如果旋转后的图形能够与原来的图形重合，那么这个图形就叫做中心对称图形可得答案．【解答】解：选项A、B、D均不能找到这样的一个点，使图形绕某一点旋转180°后与原来的图形重合，所以不是中心对称图形；选项C能找到这样的一个点，使图形绕某一点旋转180°后与原来的图形重合，所以是中心对称图形；故选：C．【点评】本题主要考查了中心对称图形，解题的关键是找出对称中心．2．（3分）下列计算中，正确的是（ ）A．+＝B．＝﹣3C．＝D．3﹣＝2【分析】直接利用二次根式的加减运算法则计算得出答案．【解答】解：A、+＝+2，无法合并，故此选项错误；B、＝3，故此选项错误；C、＝1，故此选项错误；D、3﹣＝2，正确．故选：D．【点评】此题主要考查了二次根式的加减，正确掌握相关运算法则是解题关键．3．（3分）如图，在▱ABCD中，CE平分∠BCD交AD于点E，若AE＝2，▱ABCD的周长等于24，则线段AB的长为（ ）A．5B．6C．7D．8【分析】利用平行四边形的性质以及角平分线的性质得出∠DEC＝∠DCE，进而得出DE＝DC＝AB求出即可．【解答】解：在▱ABCD中，CE平分∠BCD交AD于点E，∴∠DEC＝∠ECB，∠DCE＝∠BCE，AB＝DC，AD＝BC，∴∠DEC＝∠DCE，∴DE＝DC＝AB，∵ABCD的周长等于24，AE＝2，∴AB+AD＝12，∴AB+AE+DE＝12，∴AB＝5．故选：A．【点评】此题主要考查了平行四边形的性质以及角平分线的性质，得出DE＝DC＝AB是解题关键．4．（3分）点点同学对数据26，36，26，46，5■，52进行统计分析，发现其中一个两位数的个位数字被墨水涂污看不到了，则计算结果与被涂污数字无关的是（ ）A．平均数B．中位数C．方差D．标准差【分析】利用平均数、中位数、方差和标准差的定义对各选项进行判断即可．【解答】解：这组数据的平均数、方差和标准差都与被涂污数字有关，而这组数据的中位数为36与46的平均数，与被涂污数字无关．故选：B．【点评】本题考查了方差：方差描述了数据对平均数的离散程度．也考查了中位数、平均数和标准差的概念．5．（3分）若用反证法证明命题“四边形中至少有一个角是钝角或直角”时，则首先应该假设这个四边形中（ ）A．至少有一个角是钝角或直角B．没有一个角是锐角C．每一个角都是钝角或直角D．每一个角是锐角【分析】反证法的步骤中，第一步是假设结论不成立，反面成立．【解答】解：用反证法证明命题“四边形中至少有一个角是钝角或直角”时，首先应该假设这个四边形中每一个角是锐角，故选：D．【点评】本题考查的是反证法，解此题关键要懂得反证法的意义及步骤．在假设结论不成立时要注意考虑结论的反面所有可能的情况，如果只有一种，那么否定一种就可以了，如果有多种情况，则必须一一否定．6．（3分）若点A（x1，y1），B（x2，y2），C（x3，y3）都在反比例函数的图象上，且x1＜x2＜0＜x3，则y1，y2，y3的大小关系正确的是（ ）A．y1＜y3＜y2B．y3＜y2＜y1C．y3＜y1＜y2D．y2＜y1＜y3【分析】先判断反比例函数的图象所在的象限，再根据x1＜x2＜0＜x3判断y1，y2，y3的大小关系即可．【解答】解：在反比例函数中，﹣6＜0，∴反比例函数的图象在第二、四象限，且在每一象限内，y随x的增大而增大，∵x1＜x2＜0＜x3，∴0＜y1＜y2，y3＜0，∴y3＜y1＜y2，故选：C．【点评】本题考查的是反比例函数图象上点的坐标的特点，根据函数解析式判断出函数图象所在的象限是解题的关键．7．（3分）已知m，n是方程x2+2x﹣5＝0的两个实数根，则m2﹣mn+3m+n＝（ ）A．6B．7C．8D．9【分析】利用根与系数的关系及一元二次方程的解的定义得出m+n＝﹣2，m•n＝﹣5，m2＝5﹣2m，再将m2﹣mn+3m+n变形为两根之积或两根之和的形式，然后代入数值计算即可．【解答】解：∵m、n是方程x2+2x﹣5＝0的两个实数根，∴mn＝﹣5，m+n＝﹣2，m2+2m﹣5＝0，∴m2＝5﹣2m，∴m2﹣mn+3m+n＝（5﹣2m）﹣（﹣5）+3m+n＝10+m+n＝10﹣2＝8．故选：C．【点评】此题主要考查了根与系数的关系及一元二次方程的解的定义，将根与系数的关系与代数式变形相结合解题是一种经常使用的解题方法．8．（3分）如图，已知正方形ABCD的面积为9，AB∥x轴．它的两个顶点B，D是反比例函数（k＞0，x＞0）的图象上两点，若点D的坐标是（m，n），则m﹣n的值为（ ）A．3B．﹣3C．D．【分析】求出AB＝AD＝3，然后表示出点B的坐标，再根据点B，D在反比例函数图象上列式计算即可．【解答】解：∵正方形ABCD的面积为9，∴AB＝AD＝3，∵点D的坐标是（m，n），∴点B的坐标是（m+3，n﹣3），∵点B，D是反比例函数（k＞0，x＞0）的图象上两点，∴mn＝（m+3）（n﹣3），∴m﹣n＝﹣3，故选：B．【点评】本题考查了坐标与图形性质，反比例函数图象上点的坐标特征，正确表示出点B的坐标是解题的关键．9．（3分）如图，在Rt△ABC中，∠ACB＝90°，AC＝3，BC＝4，以其三边为边向形外分别作正方形，然后将整个图形放置于如图所示的长方形中，使点D，E，F；G，H恰好在长方形的边上，则图中阴影部分的面积为（ ）A．B．C．56D．【分析】过点C作CN⊥AB于N，延长AB、BA分别交正方形两边于H、E，证明△ADE≌△CAN得到AE＝CN同理可证△BGM≌△CBN≌△GHP，得到BM＝CN＝GP，GM＝BN，再利用等面积求出CN，利用勾股定理求出BN即可解答．【解答】解：如图所示，过点C作CN⊥AB于N，延长AB、BA分别交正方形两边于M、E，∵∠CNA＝∠DEA＝∠DAC＝90°．∴∠DAE+∠EDA＝∠DAE+∠CAN＝90°．∴∠ADE＝∠CAN，∵AD＝CA，∴△ADE≌△CAN（AAS），∴AE＝CN，同理可证△BGM≌△CBN≌△GHP，∴BM＝CN＝GP，GM＝NB，∵∠ACB＝90°，AC＝3，BC＝4，∴AB＝5，CN＝AE＝BM＝，BN＝＝，∴S阴影＝（+5+）×（5++）﹣32﹣42﹣52﹣×3×4＝，故选：A．【点评】本题考查正方形的性质，全等三角形的判定和性质，勾股定理，熟练掌握以上知识是解题关键．10．（3分）已知关于x的一元二次方程ax2+bx+c＝0，及函数，y2＝cx+b（a，b，c为常数，且ac ≠0），则（ ）A．若方程ax2+bx+c＝0有解，则函数y1，y2的图象一定有交点．B．若方程ax2+bx+c＝0有解，则函数y1，y2的图象一定没有交点．C．若方程ax2+bx+c＝0无解，则函数y1，y2的图象一定有交点．D．若方程ax2+bx+c＝0无解，则函数y1，y2的图象一定没有交点．【分析】令＝cx+b，整理得cx2+bx﹣a＝0，若Δ＝b2﹣4c•（﹣a）＝b2+4ac≥0，函数y1，y2的图象有交点，若Δ＝b2﹣4c•（﹣a）＝b2+4ac＜0，没有交点．【解答】解：令＝cx+b，整理得cx2+bx﹣a＝0，若Δ＝b2﹣4c•（﹣a）＝b2+4ac≥0，函数y1，y2的图象有交点，若Δ＝b2﹣4c•（﹣a）＝b2+4ac＜0，没有交点，若方程ax2+bx+c＝0有解，则b2﹣4ac≥0，无法判定b2+4ac的符号，故A、B不合题意；若方程ax2+bx+c＝0无解，则b2﹣4ac＜0，∴0≤b2＜4ac，∴b2+4ac＞0，∴函数y1，y2的图象一定有交点，故C符合题意，D不合题意．故选：C．【点评】本题是反比例函数与一次函数的交点问题，考查了函数与方程的关系，根的判别式，熟练掌握函数与方程的关系是解题的关键．二.填空题（本题有6小题，每小题3分，共18分）11．（3分）若代数式有意义，则x的取值范围是　x≥2　．【分析】根据式子有意义的条件为a≥0得到x﹣2≥0，然后解不等式即可．【解答】解：∵代数式有意义，∴x﹣2≥0，∴x≥2．故答案为x≥2．【点评】本题考查了二次根式有意义的条件：式子有意义的条件为a≥0．12．（3分）一个多边形的每一个内角都是120°，则这个多边形是　六　边形．【分析】一个多边形的每一个内角都等于120°，根据内角与相邻的外角互补，因而每个外角是60度．根据任何多边形的外角和都是360度，利用360除以外角的度数就可以求出多边形的边数．【解答】解：180﹣120＝60，多边形的边数是：360÷60＝6．则这个多边形是六边形．【点评】已知多边形的内角求边数，可以根据多边形的内角与外角的关系来解决．13．（3分）关于x的方程x2﹣2（a﹣1）x+a2＝0有实数根，则a的取值范围　a≤　．【分析】根据关于x的方程x2﹣2（a﹣1）x+a2＝0有实数根，可知Δ＝[2（a﹣1）]2﹣4a2≥0，然后即可求得a的取值范围．【解答】解：∵关于x的方程x2﹣2（a﹣1）x+a2＝0有实数根，∴Δ＝[2（a﹣1）]2﹣4a2≥0，解得a≤．所以a的取值范围是k≤．故答案为：a≤．【点评】本题考查了一元二次方程ax2+bx+c＝0（a≠0）的根的判别式Δ＝b2﹣4ac，解答本题的关键是明确当Δ＞0，方程有两个不相等的实数根；当Δ＝0，方程有两个相等的实数根；当Δ＜0，方程没有实数根．14．（3分）如图，已知△OAB的顶点A、B分别在反比例函数和的图象上，且AB∥x轴．若△OAB的面积为3，则k＝　3　．【分析】根据题意，设，则，再由AB∥x轴．若△OAB的面积为3，利用平面直角坐标系中三角形面积的求法列方程求解即可得到答案．【解答】解：∵△OAB的顶点A、B分别在反比例函数和的图象上，设，则，∵AB∥x轴．若△OAB的面积为3，∴，解得k＝3，故答案为：3．【点评】本题考查反比例函数与三角形综合，涉及反比例函数图象与性质、平面直角坐标系中三角形面积的求法及解方程等知识，熟练掌握平面直角坐标系中三角形面积的求法是解决问题的关键．15．（3分）已知在△ABC中，AC＝6cm，点D、E分别是AC、BC的中点，连接DE，在DE上有一点F，EF＝1cm，连接AF，CF，若AF⊥CF，则AB＝　8cm　．【分析】根据直角三角形的性质求出DF，进而求出DE，根据三角形中位线定理计算，得到答案．【解答】解：在Rt△AFC中，点D是AC的中点，AC＝6cm，∴DF＝AC＝×6＝3（cm），∵EF＝1cm，∴DE＝DF+EF＝3+1＝4（cm），∵点D，E分别是AC，BC的中点，∴DE是△ABC的中位线，∴AB＝2DE＝2×4＝8（cm），故答案为：8cm．【点评】本题考查的是三角形中位线定理、直角三角形的性质，掌握三角形的中位线平行于第三边，并且等于第三边的一半是解题的关键．16．（3分）如图是一张矩形纸片ABCD，点E为AD中点，点F在BC上，把该纸片沿EF折叠，点A，B 的对应点分别为A′，B′，A′E与BC相交于点G，B′A′的延长线过点C．若，则的值为 ．【分析】设BF＝2m，连接FG，CE，则GC＝3m，由四边形ABCD是矩形，点E为AD中点，得∠A＝∠B＝∠D＝90°，AE＝DE，AB＝DC，BC∥AD，所以∠GFE＝∠AEF，由折叠得A′B′＝AB，B′F＝BF＝2m，∠GEF＝∠AEF，∠B′A′F＝∠A＝90°，所以∠GFE＝∠GEF，A′B′＝DC，∠CA′E＝90°，则GF＝GE，再证明Rt△CA′E≌Rt△CDE，得A′C＝DC，∠A′EC＝∠DEC，可证明∠A′EC ＝∠DEC，则GF＝GE＝GC＝3m，所以AD＝BC＝8m，A′E＝AE＝4m，则A′G＝A′E﹣GE＝m，由勾股定理得AB＝DC＝A′C＝＝2m，则得到问题的答案．【解答】解：设BF＝2m，连接FG，CE，∵＝，∴GC＝3m，∵四边形ABCD是矩形，点E为AD中点，∴∠A＝∠B＝∠D＝90°，AE＝DE，AB＝DC，BC∥AD，∴∠GFE＝∠AEF，由折叠得A′B′＝AB，B′F＝BF＝2m，∠GEF＝∠AEF，∠B′A′F＝∠A＝90°，∴∠GFE＝∠GEF，A′B′＝DC，∠CA′E＝90°，∴GF＝GE，∵∠CA′E＝∠D＝90°，CE＝CE，A′E＝AE＝DE，∴Rt△CA′E≌Rt△CDE（HL），∴A′C＝DC，∠A′EC＝∠DEC，∵∠GCE＝∠DEC，∴∠A′EC＝∠DEC，∴GF＝GE＝GC＝3m，∴AD＝BC＝BF+GF+GE＝2m+3m+3m＝8m，∴A′E＝AE＝AB＝×8m＝4m，∴A′G＝A′E﹣GE＝4m﹣3m＝m，∴AB＝DC＝A′C＝＝＝2m，∴故答案为：．【点评】此题重点考查矩形的性质、轴对称的性质、等腰三角形的判定与性质、全等三角形的判定与性质、勾股定理等知识，正确地作出所需要的辅助线是解题的关键．三.解答题（本题有8小题，共72分）17．（6分）计算：（1）；（2）×．【分析】（1）先把二次根式化为最简二次根式，然后合并即可；（2）先把进行二次根式乘除法，然后合并即可．【解答】解：（1）原式＝4﹣14＝﹣10；（2）原式＝4+2．【点评】本题考查了二次根式的混合运算，熟练掌握运算法则是解题的关键．18．（6分）解方程：（1）x（x﹣6）＝5（6﹣x）；（2）2x2﹣4x﹣3＝0．【分析】（1）先移项得到5x（x﹣3）+2（x﹣3）＝0，然后利用因式分解法解方程；（2）利用配方法解方程．【解答】解：（1）x（x﹣6）＝5（6﹣x），x（x﹣6）+5（x﹣6）＝0，（x﹣6）（x+5）＝0，x﹣6＝0或x+5＝0，所以x1＝6，x2＝﹣5；（2）2x2﹣4x﹣3＝0，x2﹣2x＝，（x﹣1）2＝，x﹣1＝±，所以x1＝1+，x2＝1﹣．【点评】本题主要考查解一元二次方程的能力，熟练掌握解一元二次方程的几种常用方法：直接开平方法、因式分解法、公式法、配方法，结合方程的特点选择合适、简便的方法是解题的关键．19．（6分）图①、图②均是4×4的正方形网格，每个小正方形的边长均为1，小正方形的顶点称为格点．用直尺在给定的网格中按要求画图，所画图形的顶点均在格点上．（1）在图①中，以线段AB为一边，画一个矩形．（2）在图②中，以点E为顶点，画一个面积最大的正方形．【分析】（1）根据矩形的性质按要求作图即可．（2）利用网格，结合勾股定理作边长为的正方形即可．【解答】解：（1）如图①，矩形ABEF即为所求．（2）如图②，正方形AGHK即为所求．【点评】本题考查作图﹣应用与设计作图、平行四边形、菱形、正方形的判定与性质，熟练掌握平行四边形、菱形、正方形的判定与性质是解答本题的关键．20．（8分）6月5日是世界环境日，某校组织了一次环保知识竞赛，每班选25名同学参加比赛，成绩分别为A、B、C、D四个等级，其中相应等级的得分依次记为10分、9分、8分、7分，学校将某年级的八（1）班和八（2）班的成绩整理并绘制成统计图：根据提供的信息解答下列问题：班级平均分中位数众数方差八（1）班8.76a9 1.06八（2）班8.768b 1.38（1）把八（1）班竞赛成绩统计图补充完整；（2）写出表中a，b的值；（3）依据数据分析表，有同学认为八（2）班的成绩比八（1）班好，但也有同学认为八（1）班的成绩更好，请你写出一条支持八（1）班成绩更好的理由．【分析】（1）求出八（1）班C等级的人数，然后补全统计图即可；（2）根据中位数的定义求出a，根据众数的定义求出b的值即可；（3）根据表格中的中位数、众数、平均数和方差进行解答即可．【解答】解：（1）八（1）班C等级的人数为：25﹣6﹣12﹣5＝2（人），补全条形统计图如图所示：（2）将八（1）班25个同学的成绩从小到大进行排序，排在第13位的在B等级中，因此中位数a＝9；八（2）班25个同学的成绩在A等级的人生最多，因此众数b＝10；（3）根据表格中的数据可知，八（1）班25个同学的成绩的中位数比八（1）班25个同学的成绩的中位数大，且八（1）班25个同学的成绩的方差比八（1）班25个同学的成绩的方差要小，说明八（1）班25个同学的成绩较稳定，因此八（1）班成绩更好．【点评】本题主要考查了扇形统计图和条形统计图，求一组数据的中位数和众数，解题的关键是熟练掌握中位数和众数的定义，条形统计图和扇形统计图的特点．21．（8分）如图，AE∥BF，AC平分∠BAD，且交BF于点C，BD平分∠ABC，且交AE于点D，连接CD．（1）求证：四边形ABCD是菱形；（2）若AC＝6，BD＝8，过点D作DH⊥BF于点H，求CH的长．【分析】（1）根据平行线的性质得出∠ADB＝∠DBC，∠DAC＝∠BCA，根据角平分线定义得出∠DAC ＝∠BAC，∠ABD＝∠DBC，求出∠BAC＝∠ACB，∠ABD＝∠ADB，根据等腰三角形的判定得出AB＝BC＝AD，根据菱形的判定得出四边形ABCD是菱形，即可得出答案；（2）根据菱形的性质求出BC＝AB＝5，由菱形的面积等于对角线积的一半和底乘高即可求得结论．【解答】（1）证明：∵AE∥BF，∴∠ADB＝∠DBC，∠DAC＝∠BCA，∵AC、BD分别是∠BAD、∠ABC的平分线，∴∠DAC＝∠BAC，∠ABD＝∠DBC，∴∠BAC＝∠ACB，∠ABD＝∠ADB，∴AB＝BC，AB＝AD，∴AD＝BC，∵AD∥BC，∴四边形ABCD是平行四边形，∵AD＝AB，∴四边形ABCD是菱形；（2）解：∵四边形ABCD是菱形，∴AC⊥BD，AO＝AC＝3，BO＝BD＝4，∴AB＝＝＝5，∴BC＝AB＝5，∵DH⊥BF，∴S菱形ABCD＝BC•DH＝AC•BD，即5DH＝×6×8，∴DH＝，∵CD＝AB＝5，∴CH＝＝＝．【点评】本题主要考查了平行线的性质，等腰三角形的判定，勾股定理，菱形的性质和判定，能通过角的平分线和平行线的性质及等腰三角形的判定证得AB＝BC，AB＝AD是解决问题的关键．22．（10分）已知反比例函数的图象与一次函数y2＝x+b的图象交于点A（a，2），B（﹣2，2b）．（1）求一次函数和反比例函数的表达式．（2）请直接写出当y1≤y2时，x的取值范围．（3）设t≠0，当x＝t时，y1＝m；当x＝t+1时，y1＝n，方方说：“m一定大于n”，你认为方方的说法正确吗？为什么？【分析】（1）根据一次函数y2＝x+b过点B（﹣2，2b）代入求出b，可得点B坐标和一次函数解析式，再代入反比例函数解析式即可；（2）根据两个函数图象的交点，可直接得到y1≤y2时，x的取值范围；（3）根据反比例函数的增减性进行比较即可．【解答】解：（1）∵一次函数y2＝x+b的图象过点B（﹣2，2b），∴﹣2+b＝2b．∴解得b＝﹣2．∴一次函数的关系式为y2＝x﹣2．由B（﹣2，﹣4）在y1＝，∴﹣4＝．∴k＝8．∴反比例函数的表达式y1＝．（2）由题意，点A（a，2）在y1＝上，∴2＝．∴a＝4．∴A（4，2）．∵y1＝与y2＝x﹣2均经过一三象限，交于A（4，2），B（﹣2，﹣4），∴当y1≤y2时，﹣2≤x＜0或x≥4．（3）方方的说法错误，理由如下：∵y1＝，图象分布在一三象限，在每个象限内，y随x的增大而减小．∴当x＝1＞0时，y1＝m＝＝8，x＝t+1＝2，y1＝n＝＝4，∴，∴m＞n，当x＝t＝﹣2＜0时，y1＝m＝＝﹣4，x＝t+1＝﹣1，y1＝n＝＝﹣8，∴＞，∴m＞n．当x＝t＝﹣＜0时，y1＝m＝＝﹣16，x＝t+1＝，y1＝n＝＝16，∴＜，∴m＜n．∴方方的说法错误．【点评】本题考查了反比例函数与一次函数的交点问题，一次函数与反比例函数的交点是两个函数值大小转化的转折点．23．（10分）如图1，在正方形ABCD中，点P是对角线BD上的一点，连结CP．（1）求证：△ADP≌△CDP；（2）如图2，延长AP交线段DC于点Q，交BC的延长线于点G，点M是GQ的中点，连结CM．求证：PC⊥MC；（3）如图3，延长AP交射线DC于点Q，交BC于点G，点M是GQ的中点，连结CM．若，∠BAP＝30°，AB的长度为　3+3　．【分析】（1）由正方形的性质得∠ADP＝∠CDP，AD＝CD，再由SAS证明△ADP≌△CDP即可；（2）由全等三角形的性质得∠DAP＝∠DCP，即∠DCP＝∠DAG，再由平行线的性质得∠DAG＝∠G，则∠DCP＝∠G，然后由直角三角形斜边上的中线性质得CM＝QM，则∠MCQ＝∠MQC，证出∠DCP+∠MCQ＝90°，即可得出结论；（3）由直角三角形斜边上的中线性质得GM＝CM＝QM，则∠MCQ＝∠Q，再证△CGM为等边三角形，得CG＝GM，∠CGM＝∠MCG＝60°，然后证△ABP≌△CBP（SAS），得∠BAP＝∠BCP＝30°，证CG ＝PG，得CG＝PG＝GM＝1，设AB＝x，则BG＝x﹣1，由含30°角的直角三角形的性质得AG＝2BG＝2x﹣2，最后由勾股定理得出方程，解方程即可．【解答】（1）证明：∵BD为正方形ABCD的对角线，∴∠ADP＝∠CDP，AD＝CD，在△ADP和△CDP中，，∴△ADP≌△CDP（SAS）；（2）证明：由（1）得：△ADP≌△CDP，∴∠DAP＝∠DCP，即∠DAG＝∠DCP，∵四边形ABCD为正方形，∴AD//BG，∴∠DAG＝∠G，∴∠DCP＝∠G，∵∠QCG＝90°，M为GQ中点，∴CM＝GQ＝QM，∴∠MCQ＝∠MQC，∵∠G+∠MQC＝90°，∴∠DCP+∠MCQ＝90°，即∠PCM＝90°，∴PC⊥MC；（3）解：∵M为QG的中点，∠QCG＝90°，∴GM＝CM＝QM，∴∠MCQ＝∠Q，∵AB//CQ，∴∠BAP＝∠Q＝30°，∴∠MCQ＝30°，∴∠CMG＝∠Q+∠MCQ＝30°+30°＝60°，∴△CGM为等边三角形，∴CG＝GM，∠CGM＝∠MCG＝60°，∵BD为正方形ABCD的对角线，∴∠ABP＝∠CBP，AB＝BC，在△ABP和△CBP中，，∴△ABP≌△CBP（SAS），∴∠BAP＝∠BCP＝30°，∴∠GPC＝∠CGM﹣∠BCP＝60°﹣30°＝30°，∴∠GPC＝∠BCP，∴CG＝PG，∴CG＝PG＝GM＝PM＝×4＝2，设AB＝x，则BG＝x﹣2，在Rt△ABG中，∠BAG＝30°，∴AG＝2BG＝2x﹣4，由勾股定理得：AG2＝AB2+BG2，即：（2x﹣4）2＝x2+（x﹣2）2，解得：x＝3+3或x＝3﹣3（不合题意舍去），∴AB的长为：3+3．故答案为：3+3．【点评】本题是四边形综合题目，考查了正方形的性质、全等三角形的判定与性质、直角三角形斜边上的中线性质、等腰三角形的性质、含30°角的直角三角形的性质、勾股定理等知识；本题综合性强，熟练掌握正方形的性质和直角三角形斜边上的中线性质，证明△ADP≌△CDP是解题的关键，属于中考常考题型．24．（12分）综合实践：项目主题“亚运主题”草坪设计项目情境为了迎亚运会，同学们参与一块长为40米，宽为30米的矩形“亚运主题”草坪方案设计的项目学习．以下为项目学习小组对草坪设计的研究过程．活动任务一请设计两条相同宽度的小路连接矩形草坪两组对边．小组内同学们设计的方案主要有甲、乙、丙、丁四种典型的方案驱动问题一（1）项目小组设计出来的四种方案小路面积的大小关系？①直观猜想：我认为　四种方案小路面积的大小相等　；（请用简洁的语言或代数式表达你的猜想）②具体验证：选择最简单的甲、乙方案，假设小路宽为1米，则甲、乙方案中小路的面积分别为　69m2　和　69m2　；③一般验证：若小路宽为x米，则甲、乙方案中小路所占的面积分别为　（﹣a2+70a）m2　和　（﹣a2+70a）m2　．活动任务二为施工方便，学校选择甲种方案设计，并要求除小路后草坪面积约为1064平方米．驱动问题二（2）请计算两条小路的宽度是多少？活动任务三为了布置五环标志等亚运元素，将在草坪上的亚运宣传主题墙前，用篱笆围（三边）成面积为100平方米的矩形ABCD，如图．驱动问题三（3）为了使篱笆恰好用完同时围住三面，项目小组的同学对下列问题展开探究，其中矩形宽AB＝x，长BC＝y．①若30米长的篱笆，请用两种不同的函数表示y关于x的函数关系．②数学之星小明提出一个问题：若a米长的篱笆恰好用完，且有两种不同方案可以选择，使得两种方案的宽之和小于15米，甲同学说“篱笆的长可以是28米”，乙同学说“篱笆的长可以是32米”，你认为他们俩的说法对吗？请说明理由．【分析】（1）通过平移知识求解；（2）根据草坪的面积列方程求解；（3）先列出方程，再根据题意得出不等式求解．【解答】解：（1）①直观猜想：我认为：四种方案小路面积的大小相等，故答案为：四种方案小路面积的大小相等；②甲：40×1+30×1﹣1＝69m2；乙：40×30﹣（40﹣1）×（30﹣1）＝1200﹣1131＝69m2，故答案为：69m2，69m2；③甲：40a+30﹣a2＝（﹣a2+70a）m2，乙：40×30﹣（40﹣a）×（30﹣a）＝（﹣a2+70a）m2，故答案为：（﹣a2+70a）m2，（﹣a2+70a）m2；（2）设小路的宽为x m，则（40﹣x）（30﹣x）＝1064，解得：a＝2或a＝68（不合题意，舍去），答：小路的宽为2m；（3）①方法1：∵xy＝100，∴y＝，方法2：∵2x+y＝30，∴y＝30﹣2x；②由题意得：x（a﹣2x）＝100，设方程的两个根分别为x1，x2，则x1+x2＜15，且Δ＞0，。

Unit 3-4周日练习卷词汇1. Tom asks Mary what she is doing for v__________.2. She is busy with b__________ her sister at home today.3. Mr Smith is going to take a trip in E_______ and he will stay there for three weeks.4. Winter holidays will come. Peter is p_______ to Canada’s Great Lakes.5. During the Christmas Holidays, many t______ go to Hong Kong for shopping.6. No one want to r____ their houses to the man, because he is so dirty.7. My father will l_____ for Beijing tomorrow to see the Olympics.8. The air in the c_____ is more fresh than that in the city.9. How long are you going to be a_____ from school for this trip?10. I can’t work on my computer, so I think there must be s____ wrong with it.11. It usually takes10 minutes to w____ from the classroom to the library.12. He s_____ 150 yuan on his new bike yesterday.13. Shanghai is one of the biggest c____ all over the world.14. T_____ a boat to school must be a lot more fun than taking a bus.15. There are sixty m_____ in an hour.16. Greece is an E_____country.17. He decided to work h_____ this year than last year.18. Do remember t_____ walks after supper.19. He p_____ to travel in America next year.20. How f____ can CRH (China Railways High-speed) train run? 200km/h21. It t____ me half an hour to get to school on weekdays.22. I love to go to the countryside on weekend, because I love n_____.23. How f___ is it from his home to school?24. We must wall to the village. There is no other m____ of going there.25. She is worried about her father’s i______. She wants him to see a doctor.26. You can take any different kinds of t_____ to New York, such as bike, car, train and subway.27. Mr Zhang says he just finished m_____ his last movie, and he is p____ to relax at home.28. Summer holiday begins. We must keep staying at home u_____ September 1.29. It takes him two hours to r_____ the bike to school.30. She should eat l___ junk food and more vegetables to keep healthy.31. He always takes w_____ with his lovely dog after supper in the park.32. Is your studying habit the same as h____? If you can, you can get the same good grades.33. I thought about v_______ Italy or Spain this summer.34. I’d like to t_____ to you about your homework after class.35. It’s kind of you to i_____ me to the party, but I can’t go because of my poor marks.完形填空AWhen you go to the seaside, maybe you will notice that the wind very often comes from the sea to the land in the __1__ part of the day, but in the evening, the wind blows in the opposite direction(方向). Why does this happen?In the morning, when the sun __2__, it begins to warm the land __3__ the sea. The land __4__ warm faster than the sea. So while the air above the sea is cool, the air over the land __5__ warmer. The air __6__ the land rises and the cool air from the sea moves __7__ the land.When evening comes, __8__ the sea and the land become cool, but the land cools more __9__ than the sea. The wind now changes __10__ direction.1. A. big B. small C. early D. late2. A. rises B. rise C. to rise D. rose3. A. but B. and C. or D. also4. A. change B. keeps C. gets D. feels5. A. grows B. to grow C. growing D. grew6. A. on B. in C. into D. onto7. A. into B. in C. towards D. on8. A. both B. neither C. either D. all9. A. slowly B. quickly C. fastest D. fastly10. A. it’s B. it C, its D. itselfBSome people believe that dreams can tell them what will happen in the future. __1__ knows why this is so, but there are many stories about people who had derams that __2__. One of these people was a man __3__ John Chapman, who lived in Swaffham in England many years ago.John Chapman dreamt that he was __4__ on London Bridge and a man told him how to become rich. John Chapman was a poor man and he needed __5__, so the next day he decided to leave for London. __6__ was 100 miles from Swaffham to London. He walked for few days and at last he __7__ London Bridge. There were many people on the bridge, but they weren’t__8__ in John Chapman. No one __9__ him. After three days, John Chapman decided to go home, __10__ before he could do this, a shopkeeper came up to him.“I’ve been watching you,” he said. “Are you __11__ someone?”“Yes,” said John. “I had a dream about a ma here. He would help me to get much money.”“Oh,” said the shopkeeper. “You shouldn’t believe in dreams. __12__ I believe in dreams, I’d be in Swaffham right now. I had a dream a few days ago about a man called John Chapman from Swaffham. He had __13__ in his garden, mear an old apple tree.”John Chapman was __14__ by what the shopkkeper said. At once he went home and dug near an old apple tree. He soon found many pieces of gold. He was so happy __15__ he gave some of the gold to his church. For the rest of his life, he was a rich man .1. A. Nobody B. Anybody C. Somebody D. Everybody2. A. came out B. came up C. came true D. came to3. A. said B. spoke C. told D. called4. A. running B. standing C. sleeping D. crying5. A. dream B. future C. money D. apple6. A. This B. It C. That D. Its7. A. reached B. arrived C. got D. went8. A. interest B. interests C. interesting D. interested9. A. listened to B. talked to C. said about D. needed to10. A. after B. and C. but D. or11. A. waiting for B. asking for C. caring for D. looking for12. A. When B. Where C. If D. How13. A. money B. apple C. tree D. gold14. A. angry B. surprised C. happy D. amazed15. A. which B. that C. until D. unless阅读理解AVisitors to Britain are always complaining about English food. But they do not really know what they are talking about because they rarely get a chance to eat it. Most of the restaurants in large towns have foreign owners and serve foreign food When visitors are invited to eat in an English home, their hosts often feel they must offer them something foreign and exotic.Those of us who do know English food realize that at its best it can be really very good. On the other hand it is true to say that it is sometimes terrible. Part of the problem is that we are not really interested in food- we eat to live, we don’t live to eat. So we don’t generally spend the necessary time and effort needed to cook really good meals or ready prepared food which only, needs heating up before eating.You can find the best English food in the country away from large towns, where life is slower and people not in such a hurry. But more visitor come to London, they come because they are interested in shopping and sightseeing. They do not come because of food, so why should they complain about it?1. Visitors to Britain are always complaining about English food because ______.A. they don’t often eat English foodB. they only eat English food in English homeC. they usually eat English food in the restaurantsD. they know little about English food2. When English people have guests they prefer to ______.A. cook some unusual foodB. offer them some prepared foodC. serve them food they are used toD. serve them the English food3. Which of the following statements is right?A. People don’t want to spend time and effort in cookingB. People aren’t really interested in food because they think they live to eat, not eat to liveC. English food is neither good nor terribleD. People like to cook in a quick easy way4. Visitors can find the best English food ______.A. in the restaurants in large townsB. in the countryC. in English homesD. in the restaurants in towns5. The conclusion(结论) suggests ______.A. visitors have the rights to complain about EnglishB. as well as food, people come to shopping and sightseeingC. the criticism(批评) of English food is unfairD. it is impossible to find food English food in towns but it takes times to findBWe have just a small house, with only two bedrooms. You can think why we were worried when Aunt Clara wrote to say that she was coming to stay with her family for the weekend. Her family, I should say, has four boys, are under the age of twelve.I sent off a telegram at once, and explained in it that our house was too small. Aunt Clara called us up the next morning. “I forgot to explain,” she said in her sweetest voice. “The boys will be bringing a couple of tents.”Even so my wife couldn’t make free from fear. It was true that we had a large garden, but there was still the problem of feeding four growing boys. “A nd what if it rains?” she asked.But Saturday morning turned out to be bright and clear when I went to the station to meet Aunt Clara. I tried to squeeze(往车里塞) three of the boys, together with the luggage(行李), into the back of the car. The youngest sat in front, with Aunt Clara and me.“I didn’t see the tents among your luggage.”I turned over and said to David, the eldest boy.“The tents!” said Aunt Clara. “Oh! We left them in the luggage van(车厢).”6. Aunt Clara ______ after she received the telegram.A. wrote another letterB. phonedC. sent a telegramD. came round to see them7. The boys were going to sleep ______.A. outside in the gardenB. with friendsC. downstairsD. on the floor in the living room8. The man’s wife ______.A. was looking forward to the visitB. started cookingC. moved into the gardenD. was still worried9. Aunt Clara arrived by_______.A. carB. planeC. trainD. boat10. From the story, we know that the main problem was _____.A. foodB. timeC. spaceD. noiseCTraffic rules say where, when, how old and how fast you can arrive. These rules help keep traffic moving safely. Rules of the road include traffic control devices,right-of-way, and parking rules.Traffic control devices include traffic signals, signs, pavement markings, and roundabouts.In a traffic signal is not working, come to a complete stop, then yield to traffic as if it were a four-way stop. Go on driving only when you see it is safe, or when a police officer, fire fighter, or traffic control person directs you.Traffic signalsTraffic signals are lights that tell you when or where to stop and go. A green light means you can go if it is safe. A yellow light means you should be careful and a red light means stop.Traffic lights are usually at interactions and they are red, yellow, and green, from top to bottom or left to right. There are some intersections and other locations where there are single green, yellow, or red lights.Traffic signsTraffic signs tell you about traffic rules, dangers, where you are, how to get where you are going, and where services are located. The shape and color of these signs show the type of information they provide.11. How many parts of traffic rules?A. 3B. 4C. 6D. 712. When you see the traffic signals are wrong, you should _______.A. stop your car and change to walk.B. go on driving quickly.C. stop to see first and go on driving until you are safe.D. stop to see first and go on driving until you see the police officer or fire fighter13. What’s the meaning of intersection?A. In the middle of the road.B. On one side of the road.C. At the crossing of two roads.D. On one side of two roads.14. Which is wrong in the following sentences?A. Traffic signals aren’t working sometimes.B. Traffic control devices include traffic rules.C. Traffic signals can be only green.D. Traffic signs can show different traffic information.15. Which picture is the traffic sign?选词填空One day, a traveler in beautiful clothes came into his __6__. The man caught a cold and wanted some __7__. David hoped to be paid more and looked at one of the traveler’s eyes __8__.“Oh, dear!” called out David. “Something is wrong with you because I’ve looked at only one of your eyes! You’ve got a bad heart illness. You should be in __9__ and only I can __1__ you!”“Please look at my right eye, sir.” Said the traveler. “The left is false!”But he __2__ problem. This school __3__ classes at 7:45. He is often late for schooland the teacher was very angry. Yesterday he was late again. “How do you usuallycome to school?” __4__ the teacher. “I usually come to school by bike.” __5__ SunYang. “What time do you usually leave __6__ school?”“I leave home at 7:40.”“Whydon’t you leave home a little __7__?”“I can’t. My mother is ill. She __8__ in bed allday. So I have to __9__ after her and give her the medicine at the right time. So I amoften late for school,” said Sun Yang with __10__ in his eyes. “I’m sorry to hear that.”答案：vacation, babysitting, Europe, planning, tourists, rent, leave, countryside, way, something, walk, spent, cities, Taking, minutes, European, harder, take, plans, fast, takes, nature, far, means, illness, traffic, making, planning, until, ride, less, walks, his, visiting, talk, inviteCABCA ACABCACDBC BADBC ACDBBAAABC CBACD ADDDBdancing, learnt, workmates, look, mind, office, medicine, carefully, hospital, help minutes, has, begins, said, cried, for, earlier, stays, look, tears。

杭州市文澜中学2018年6月八下期末英语总复习-完型拔高练习AOnce there was a king．He was wise but everyone was afraid of him．His face showed the sadness deep in his heart．So there were deep 1___lines（皱纹）on his face．In his country lived a beautiful girl．Everyone seemed to love her，so did the king．Hewanted to 2___her，and finally he decided to speak to her of his love．After he dressed in his best clothes，he looked in the 3___，but he saw a hard face，4___when he tried to smile．“How about wearing a mask（面具）？“he thought．Then he ordered his magician to paint a mask that looked kind and happy and handsome．The magician 5___and said：“But you must keep your own face in the same lines that I paint and be kind to all people from your heart．If not，the mask will break．“The mask looked so 6___that no one new it was not the true face of the king．Months passed，the beautiful lady got married to the king，and the king treated everyone 7___to keep the mask from breaking．At last，the king didn't want to cheat his beautiful wife any more．8___he asked the magician to take the mask off．Surprisingly，he found his face was just like the mask he had worn for so long！This story tells us that a man is what he is in his heart．1．A．ugly B．kind C．beautiful D．peaceful2．A．love B．hate C．kill D．marry3．A．wall B．door C．mirror D．window4．A．yet B．even C．just D．still5．A．looked B．refused C．agreed D．laughed6．A．sad B．happy C．natural D．serious7．A．badly B．kindly C．coldly D．differently8．A．So B．Or C．But D．However．What should we do to keep healthy? One important rule is to exercise 1______ . The Smith family try to exerciseevery day. Mr Smith 2________ exercise in the morning because he must get to work at seven o'clock. But he runsevery evening. He walks a lot, 3_______ . He goes to school on foot every day, and after school he 4________ different sportswith his friends. Mrs Smith goes to a yoga (瑜珈) class 5 _______. But it wasn't always this 6________ . Last year Mr andMrs Smith used to (过去常常) take buses 7_______ , even to the drugstore two blocks away. They wouldn't walk.So they often go to the drugstore. But the Smiths all 8_______ better now. They believe they shouldn't be lazy. We9________ exercise every day, but we should try our best to exercise 10 ______ often as possible.1. A. often B. sometimes C. never2. A. may not B. can not C. should not3. A. also B. either C. too4. A. likes B. plays C. watches5. A. in two weeks B. two or three weeks C. twice a week6. A. way B. kind C. result7. A. somewhere B. everywhere C. nowhere8. A. fell B. feel C. feel like9. A. don't B. mustn't C. needn't10. A. as B. so C. moreThe Goal of the MindIt was an unforgettable night．The noisy Mexico City gradually 1_____．The main Olympic stadium was in darkness．2_______he finished making the scenes that the marathon （马拉松赛跑）winners celebrated the victory，Greenspan，a world famous documentary producer，found the stadium 3______ ．He was leaving for the hotel when he suddenly saw a man running into the stadium．The man ran out of breath．4_______ he didn’t stop．After he got to the goal，he fell down on the ground．Greenspan 5______this was a marathon athlete，so he went over to ask why the athlete ran to the goal with such a difficulty．The young man replied，”That my 6______sent me here is not to let me start of a race in the competition，but to make me 7_______ the game I have fallen behind all other runners，but I have a goal 8______them．I will run to the goal because my motherland is watching me from behind．”Moved by what he said，Greenspan 9_______the most touching scene in the history of the Olympic Games to every Corner of the world．Life should have a 10________of reaching the peak （顶峰），yet the most important is not whether we can reach the peak but whether we have made the greatest efforts﹣to reach the goal in the mind is a success．1.A．slowed down B．calmed down C．put down2.A．Since B．Before C．After3.A．empty B．large C．bright4.A．so B．but C．and5.A．guessed B．hoped C．introduced6.A．coach B．friend C．country7.A．play B．watch C．complete8.A．for B．like C．against9.A．spread B．made C．recorded10.A．decision B．dream C．suggestion．DDo you believe that we can have an important influence on anyone we meet？The right words at just the right time could 1______ someone’s life.When I was 3 years old,my parents discovered I was 2______ .After asking many doctors and parents of other deaf children,they decided not to put me in a special school.Although I seemed outgoing,my self-esteem(自尊心)was quite low.On my first day at school,the other kids 3_______ me because of my hearing aid and the way I talked.I was hurt deeply and I saw myself as a(n) 4_______ kid.Mrs.Green,my 5_______,changed all of that with a single three-word phrase.One morning,she asked the class a question.Sitting at my desk silently,I 6_______ her lips(嘴唇)andr aised my hand right away.She called on me in front of the blackboard.I took a deep breath and 7_______ answered Mrs.Green’s question.I will 8________ forget what happened next.Mrs.Green pointed directly at me.With sparkling(闪光的)eyes and a big smile she cried:”That’s right,Ben!”For the first time in my young life,my confidence(自信)rose.At that moment,I decided that no matter how many 9________ I may face,I can overcome(克服)them.Thanks to those three 10________ words,my whole life changed from that moment.1.A.end B.change C.lose2.A.blind B.deaf C.fat3.A.madefunof B.tookcareof C.madefriendswith4.A.ugly B.smart C.handsome5.A.driver B.doctor C.teacher6.A.read B.touched C.reached7.A.nervously zily C.carelessly8.A.often B.ever C.never9.A.aims B.difficulties C.interests10.A.unkind B.bitter C.simpleEBo a golden retriever won this year’s Dog Hero Award from the Ken L Ration dog food company. Bo acted 1_____ last June. Bo and his owners Rob and Laurie Roberts were going down the Colorado River in a 16-foot boat. The June 2____ was Bo’s first time in a boat.Laurie Roberts said “Things were fine 3_____ a 6-foot wave broke in front of us and filled the boat with water. Another big wave caught us from the back and turned the 4____ over.” Rob was thrown clear but Laurie and Bo were unable to move out 5______ the boat. “Every time I tried to 6______ my head hit the boat ” Laurie said. “I hit the bottom of the river several times. I 7______ I was drowning(溺水).”Rob picked up the story “I reached the land and 8______ Laurie ” he said. “I saw Bo swim out from under the overturned boat. Then he 9_____ and dived(下潜). Soon he came back up pulling Laurie by the hair.” Laurie who was 10______ and breathless tried to catch Bo. But the dog stayed out of reach as is knowing 11_____ of them would drown if Laurie pulled him unde r. 12______ Laurie caught Bo’s tail. He 13______ her 30 yards to the land. Laurie was cut and bleeding but she was 14_______.“If it hadn’t been for Bo 15________ wouldn’t be here.” Laurie told everyone at the Dog Hero awards dinner.1.A. bravely B. strangely C. quietly D. politely2.A. meeting B. match C. trip D. prize3.A. since B. though C. unless D. until4.A. dog B. wave C. boat D. foot5.A. in B. behind C. under D. above6.A. get out B. get down C. get off D. get along7.A. promised B. suggested C. described D. realized8.A. looked after B. looked for C. looked at D. looked into9.A. went ahead B. turn around C. jumped out D. stood up10.A. sad B. sorry C. afraid D. angry11.A. both B. all C. neither D. one12.A. Already B. Often C. Besides D. Finally13.A. followed B. pulled C. led D. pushed14.A. busy B. calm C. safe D. hurt15.A. I B. she C. you D. it答案：A：ADCBC CBAB： ABCBC ABBCAC：BCABA CCBABD：BBAAC AACBCE：ACDCC ADBBC ADBCA。

杭州市文澜中学八年级下册Unit 4 单元检测第一部分听力（共两节，15小题，满分30分）略第二部分阅读理解(共两节，满分40分)第一节(共15小题，每小题2分，满分30分)阅读下列短文，从每题所给的四个选项(A.B.C和D)中选出最佳选项。

AA group of reporters asked a group of 4-to-8-year-old children this question, “What does love mean?”The answers were surprising. The children would answer like they did below.Rebecca --- age 8'When my grandmother hurt her knees , she couldn't bend over and paint her toenails (脚甲) any more. So my grandfather would do it for her all the time, even when his hands hu rt, too. That’s love.”Samantha --- age 6'Love is when someone hurts you, and you get so mad but you don'tshout at her because you know it would hurt her feelings.”Terry --- age 4“Love is what makes you smile when you’re tired.”Bethany --- age 4'I let my big sister pick onme because my Mum says she only picks on me because she l oves me. So I pick on my baby sister because I love her.”Lauren --- age 4“I know my elder sister loves me because she gives me all her old clothes and has to go out andbuy new clothes.”Elaine --- age 5“Love is when Mummy gives Daddy the best piece of chicken.”Clear --- age 5'My Mummy loves me more than anybody. You don'tsee anyone else kissing me to sleep at night.”Jessica --- age 8“You really shouldn’t say ‘I love you’unless you mean it. But if you mean it, you should say it a lot. People forget.”16.Which of the following is NOT true according to the passage?A. Rebecca’s grandmother ever couldn’t bend over.B. Bethany wants to be picked on by any other person.C. If Samantha becomes angry, she will not shout at others.D. Lauren prefers to wear her sister’s old clothes.17.What does Jessica mean about love?A. Too much love is no love.B. You should say love more often.C. You mean what you think.D. Say love more often if you have it.18.What is love according to Terry?A. Love is the care between husband and wife.B. Love is a rest when you are tired.C. Love is what cheers you up when you are tired.D. Love is a kiss from parents.BEveryone has a beautiful memory about school which is hard to forget. Among many thin gs, relationships are the hardest to leave behind. Some schools try to stop students’ pup py love in different ways. Anything about “love” relationship is not allowed. For example, a middle school in Fu'an, Fujian Province forbids boys and girls to sit together for meals a nd forbids boysto look at girls for a long time; a middle school in Luohe, Henan Province sets rules that boysand girls should meet in bright places with at least 5 other classmates , and if they meet in private they will be asked to go home with parents for more than a w eek and even advised to leave school; a middle school in Jinan, Shandong Province forbi ds everyone to send food and gifts to orreceive them form the opposite sex. It also forbid s students to help the opposite sex with bags and coats andrequires a “44 cm” distance between boys and girls.Some students are not satisfied with such rules. “Why should we have strict places for dif ferent sexes to eat? It's not using bathrooms!” Some people who care about the intelligen ce development of the students say that they should be more creative with fewer rules. F or this, I’d liketo say that middle school students are going through puberty (青春期). It’s normal for them tohave some feelings for the opposite sex. Schools should provide corr ect guidance and education instead of giving simple and cruel rules and asking the stude nts to follow.19.We’ve learnt about ________ rules made by schools as examples in this passage.A. 3B. 6C. 9D.1020.Which of the following statements is TRUE according to this passage?A. Not all the students agree with the rules made to stop puppy love.B. In a middle school in Fu’an, boys and girls can’t sit together in class.C. Those rules can help students go through puberty without any difficulties.D. Those rules are useless21. The writer thinks ________.A. it’s necessary to make such strict rulesB. schools needn’t do anything to stop puppy loveC. good guidance and education are better than rules onlyD. such strict rules are the most importantCRob Frenette had problems with bullies(欺辱) at school for eleven years. He was often lonely and scared. When he was fifteen, however, he decided to do something about his problems. He walked into a newspaper office and told them about the bullying. His story went into the newspaper and soon all the TV stations in Canada wanted to talk to him about his experiences. They also wanted to hear his ideas to stop bullying.After that, Rob continued his studies at school, but in his free time he helped other people with bullying problems. With a friend Katie Neu, he made a website called www.bullyingcanada. ca. Visitors to the website can find advice, stories and poems about bullying, in both English and French. When people are upset, they can talk on the phone or online to Rob and his team . Every weekend Rob has to answer e-mails to the website. He also speaks to children, teachers and members of government around the country about bullying.Rob’s most important message is: “When bullies are unkind to you, it isn’t your fault. There’s nothing wrong with you, so you should try to keep trusting yourself. And remember that people care about your problems. You just have to find those people.”One of Rob’s ideas is “Blue Day”, a special day for stopping bullying in schools. Students have to wear blue clothes and in class they learn how to stop bullying. More than 150 Canadian schools now celebrate Blue Day, but Rob won’t stop until there’s a Blue Day in every school in Canada.22. How did Rob often feel at school before he was fifteen?A. Relaxed.B. Unhappy.C. Shocked.D. Tired.23. We can learn from this passage that Rob suffered from bullying since he was ______.A. four.B. sevenC. elevenD. fifteen24. www. bullying canada. ca is a website where people can ______.A. learn how to write poemsB. get advice about bullying problemsC. get blue clothes for freeD. practice both English and French25. The underlined part “those people” in Paragraph 3 means _____.A. people who always bullied others beforeB. people who help others with bullying problemsC. people who are members of the governmentD. people who write e-mails about their problems26. What was the correct order in which these events happened?a. Rob and his friend made a website.b. Rob was bullied at school.c. Rob created “Blue Day”.d. Rob told his story in public.A. b-d-a-cB. a-b-c-dC. b-a-d-cD. c-b-a-dDWhen talking about picking a right school, a mother and teacher gave some pieces of advice.In the latest issue (期) of Youth magazine, the mother shared the school advice she gave her daughters with young people across the country.'I'vetold my daughters many times that I don'twant them to choose a name,” the mother s aid.'Idon'twant them to think, ‘Oh, I should go to these top schools.’ We live in a countrywi th hundreds of excellent universities. So the first question is: what’s going to work for me?”“When it was time to prepare for picking schools, nobody around me believed I could get into Xiamen University. But through hard work I finally made it,” she continued. “So, my s econd pieceof advice is: believe in yourself, no matter what other people might say. Once your goal is set,you only need to try your best to make it come true.”“The last piece of advice is not to be worried even if your dreams don’t come true. As I’ve said above, there are so many good universities out there. So it’s important for everybody to understand that you can always find a university that gives you a great education.”27.The mother shared her advice ________.A. with her studentsB. with her husbandC. in Youth magazineD. in Xiamen University28.To explain her second piece of advice, the mother gave ________.A. a story of her daughtersB. a story of her ownC. some different reasonsD. some different ideas29.We can learn from the last paragraph (自然段) that ________.A. we can realize our dream through hrad workB. the name of the university isn’t the most importantC. it’s not necessary to care what other people might sayD. more than one university can give us a good education30.The best title of the passage may be “________”.A. Colorful University LifeB. Best School EducationC. A Report on University BuildingD. Advice on School Picking第二节任务型阅读（共5小题，满分10分）Florence lived in the countryside of Kenya(肯尼亚）in Africa. When she was 12, the only thing she wanted was to finish school. But for many girls like her, school is only a dream. 31_____ Families will probably spend money educating boys. Many girls have to marry early.But Florence was able to continue her education. 32____ Lisa started an organization to provide many girls with the best education possible. Florence was the first of 320 Kenyan girls among them.33______ During her visit, she heard that many women made and sold baskets. They used the money to send their daughters to school. “Two years later, she started to help sell the Kenyan craft( 工艺品）in the US. In 2019, Lisa began helping girls continue their education.34______ In January, 2019, she started the fourth one. “I want to prepare them for college,” Lisa said.The new high school is called Tembea, which means “to walk”. Florence is walking towards a bright future. 35_______ “Florence is the first in her family to finish high school and college,” said Lisa. “She is an example for all girls in Kenya.”A. School costs money.B. In 1991, Lisa first visited Kenya.C. After that, she helped build three schools.D. She left college in 2019 and is now a teacher.E. It was Lisa Stevens who helped achieve her dream.第三部分英语知识运用（共两节，满分25 分）第一节：完形填空（共10 小题，每小题1 分，满分10 分）通读下面短文，掌握其大意，然后在各题所给的四个选项（A、B、C 和D）中选出一个最佳选项。

2018年杭州市文澜中学八年级下册期末模拟测试卷第一部分听力（共两节， 15题，每小题2分，满分30分）略第二部分阅读理解(共两节，满分40分)第一节(共15小题，每小题2分，满分30分)阅读下列短文，从每题所给的四个选项(A.B.C和D)中选出最佳选项。

AWe know music is very important in our daily life. Do you notice music playing at any of those places when you go somewhere? Today most stores, stations, restaurants and other places play music. You might even hear music in an office or on a farm.Scientists believe that music influences the way people behave(行为). They think that the sound of western classical music makes people feel richer. When a restaurant plays classical music, people spend more money on food and drinks. When the restaurant plays modern music, people spend less money. Without music, people spend less.Scientists also believe that loud, fast music makes people eat faster. Some restaurants play fast music during their busy hours. This makes people eat faster and leave quickly. Restaurants can make more money in this way.Some scientists think that music makes you think and learn better. They say that music helps students to be more active. It is true that people learn better when they are relaxed. And listening to music can help you relax.The next time you hear music somewhere, be careful. It might influence the way you do things.16.According to the text, scientists believe that music can _______.A．Create different feelings for usB．Help us to develop good habitsC．Develop our interest in moneyD．Influence natural environments17.Western classical music makes people feel _________.A．slower B．Something about mannersC．richer D．Something with new styles18.Which type of music below can make people eat faster?A．Light music. B．Rock music. C．Sweet music. D．Soft music.BRachel Carson(1907-1964) was a pioneer of the world’s environmental movement through her writing about the protection of the natural world. Her 1962 book Silent Spring made her well known by many people. It describes the harmful changes in the environment of using toxic(有害的) chemicals on farmland.Carson’s career started as a biologist in the US Bureau of Fisheries. In 1951 she published her first book, The Sea Around Us, which became a bestseller. It made her rich enough to leave her job and devote her life to writing. She was a gifted writer. Her next two books were also about the oceans and both topped the book sales lists.Carson’s book Silent Spring completely change the way America though about nature. It painted a bleak(荒凉的) future for the whole natural world. It led to a nationwide ban(禁止) on the use of a deadly chemical called DDT, and other toxic pesticides(农药) that farmers used for their crops. Many people say the book led to the creation of America’s Environmental Protection Agency.Since her death, Carson’s name has continued to be connected with protecting the environment. There is now a yearly Rachel Carson Book Prize. Norway awards the Rachel Carson Prize to women who have made great contributions to the field of environmental protection. In 1980, 16 years after her death, she was awarded the Presidential Medal of Freedom, the highest civilian honour in America.19. What happened______ to Rachel Carson in 1962?A. She started to write books.B. She gave up working as a biologist.C. Her book The Sea Around Us sold well.D. Her book Silent Spring made her famous.20. What most probably made Rachel Carson leave her job?A. She got an award.B. She published Silent Spring.C. The Sea Around Us brought her enough money.D. The US government took notice of her researches.21. Why is the book Silent Spring important to America’s environmental protection?A. It describes a silent spring.B. It topped the book sales lists.C. It changed how American thought about nature.D. It includes all Carson’s research achievements.CUp to 65% of children don't get as much sleep as they should do, and this can make them nervous and slower at school, scientists say.So how long should young people sleep each night? The answer is between eight and ten hours. If you don't get enough sleep at night, you'll have less energy the next day.But the scientists say many children have missed out on 4,500 hours of sleep by the time they are seven years old. They say that children miss sleep because they have TVs and computers in their rooms,and busy parents don't read to their younger children at night any more. The traditional "bedtime story" helps children to relax and fall asleep peacefully. Children with TVs and computers in their bedrooms were more likely to sleep badly, and to get less than eight hours' sleep. Even losing one hour's sleep a night can mean that children do less well at school.German scientists think that your brain (大脑) keeps working while you are asleep. To show that they were right, they gave two groups of people a problem to work out. One group went to sleep, and the other group stayed awake. The result? The people who slept worked out the answer more quickly.This showed that their brains had been trying to find the answer while the people were asleep. So, make sure you get enough sleep tonight, and you'll be at your best tonight , and you'll be at your best tomorrow!22. What problem do more than a half of students have?A. They don't get on well with their studies.B. They don't have enough sleep at night.C. They don't relax themselves at school.D. They don't follow their school rules23. If you have less energy the next day, you'll probably feel _______.A. sleepy, slow and nervousB. tried, bored and worriedC. afraid, alone and angryD. dull, lazy and crazy24. According to the third paragraph, what has worst influenced many children's sleep?A. Their parents' noise.B. Bedtime stories.C. Too much homeworkD. TV and computers25. The German scientists' experiment showed that _______.A. our study depends on our sleepB. our sleep helps improve our healthC. our brain works while we sleepD. our brain works faster during sleep26. This passage in mainly written for _______.A. parentsB. school teachersC. scientistsD. young studentsDDonna Ashlock, a 14-year-old girl from California, was very sick. She had a bad heart. “Donna needs a new heart,” her doctor said, “she must have a new heart, or she will die soon.”Felipe Carza, 15, was worried about Donna. Felipe was Donna's friend. He liked Donna very much. He liked her freckles, and he liked her smile. Felipe didn't want Donna to die.Felipe talked to his mother about Donna. “I am going to die,” Felipe told his mother, “and I am going to give my heat t o Donna.”Felipe's mother didn't pay much attention to Felipe. “Felipe is just kidding,” she thought, “Felipe is not going to die. He's strong and healthy.”But Felipe was not healthy. He had terrible headaches sometimes. “my head hurts,” he often told his friends. Felipe never told his parents about his headaches.One morning Felipe woke up with a sharp pain in his head. He was dizzy (眩晕的), and he couldn’t breathe. His parents rushed Felipe to the hospital. Doctors at the hospital had terrible news for th em. “Felipe' s brain is dead,” the doctors said, “we can't save him.”The parents were very sad. But they remembered Felipe's words. “Felipe wanted to give his heart to Donna,” they told the doctors.The doctors did several tests. Then they told the paren ts, “we can give Felipe's heart to Donna.”The doctors took out Felipe's heart and rushed the heart to Donna. Other doctors took out Donna's heart and put Felipe's heart in her chest. In a short time the heart began to beat.The operation was a success. Felipe's heart was beating in Donna's chest, but Donna didn't know it. Her parents and doctors didn't tell her. They waited until she was stronger; then they told her about Felipe. “I feel very sad,” Donna said, “but I am thankful to Felipe.”Three months later the operation Donna went back to school. She has to have regular checkups, and she has to take medicine every day. But she is living a normal life.Felipe's brother John says, “Every time we see Donna, we think of Felipe. She has Felipe‘s heart in her. That gives us great peace.”27. We learn from the passage that________ .A. Felipe promised Donna to give her his heartB. Donna needed a new heart instead of her ownC. the doctors asked Felipe's parents to donate his heartD. Felipe never told anyone about his terrible headaches28. Donna knew nothing about Felipe's heart until________ .A. Felipe's parents told her the bad newsB. the operation was going to startC. she was well and strong enoughD. she went back to school29. It is clear that _______.A. Felipe's brother often goes to see Donna in hospitalB. Donna can live a normal life without medicineC. the doctors did several tests during the operationD. the Carza have great peace because of Donna30. Which of the following may probably be the best title for the passageA. The GiftB. The OperationC. The PeaceD. The Illness第二部分阅读理解(共两节，满分40分)第二节(共5小题，每小题2分，满分10分)请从以下选项（A、B、C、D、E和F）中选出符合各段意思的小标题，选项中有一项是多余选项。

八下Test for unit 1-2单选In than 10 years, there will be than 7 billion people in the world.A. fewer, fewerB. fewer, lessC. less, lessD. less, fewer Do you want milk or orange juice?I don’t want . I usually drink coffee.A. the otherB. neitherC. eitherD. bothThe man stood at the side of the road and didn’t know .A. what to do itB. where to doC. how to doD. what to do Everything is reading books Tom. And Tom is reading a science fiction book.A. besidesB. andC. exceptD. withHe seems .A. happilyB. happyC. happinessD. to happy His words me.A. are surprisedB. are surprised atC. surprisesD. surprise There an old man and some children taking walks in the park in 10 minutes.A. isB. will haveC. areD. will be The old man lives , and leads a life.A. lonely, aloneB. alone, lonelyC. lonely, lonelyD. alone, alone His life is better than it is in the past, but not much.A. a lotB. someC. a bitD. far—I bought a new dictionary.—how much did you it?A. payB. spend onC. takeD. costI found easy to read English well.A it is B. this C. that D. itThis coat doesn’t fit him well, as he has a huge body and the coat is small.A. so; suchB. so; soC. such; suchD.such, soI’m sure the baby walk in two months.A. will canB. will able toC. will be able toD. will be Please who broke the window.A. find outB. findC. look forD. look out He’s used to in the afternoon.1A. playB. playsC. playingD. played完型About a week ago, when I was playing basketball at our local park, I noticed a small group of boys picking on a smaller, skinner boy. They were him names and even pushed him to the ground and kicked dirt in his face. I saw that, I walked over to the group.阅读A.Steven Jobs, the designer of Apple Computer, was not clever when he was in school….B.Dear Editor,I’m confused these days. We are taught at home and at school that violence is bad….C.My grandparents can be good fun. They are retired, so they don’t work anymore….单词拼写She is fashionable and likes to wear m dresses.The honest boy is always t to his word.Keep your eyes c while doing and the exercises, children.Listening to the music had a calming I on her. And she fell asleep soon.You’re supposed to make the d for yourself this time. Think it over.Young people like sending short m to friends by using their cell phones.The air on the top of the mountain becomes t than that at the foot.I found that somebody f me on the way home last night. It was scary.You can e the process (过程) of making wine in Wuzhen, the famous water town.You argued with his head teacher and r away from school.2。

Unit 3 What were you doing when the UFO arrived?第三单元测试题（考试时间60分钟，满分100分）一．单项选择（共15小题，计15分）( ) 1. ______ UFO landed on Center Park and ________ alien got out of ________ UFO.A. An; an; theB. A; an; theC. A; a; aD. A; an; a( ) 2. An alien landed ____ the earth ____ Monday morning.A. in , in B .on, on C. in, on D. on, in( ) 3. .W ould you please drive faster? My flight is ________.A. taking offB. getting offC. turning offD. putting off( ) 4. —Do you want ________ sandwich? —Yes, I usually eat a lot when I’m hungry.A. otherB. anotherC. othersD. the other( ) 5. Linda couldn’t see Alice ________.A. somewhereB. everywhereC. nowhereD. anywhere( ) 6. Do you know ______?A. what he happenedB. what the matter is with himC. what happened to himD. what did he happened( ) 7. I was doing my homework _______ the door bell rang.A. whileB. whenC. afterD. before( ) 8. I was ________ to see the police at my home yesterday.A. amazingB. surprisingC. surprisedD. interesting( ) 9. She didn’t come home as _______ as you.A. earlyB. earlierC. very earlyD. the earliest( ) 10. What ________ Ted ________ when you went to him?A. is; doingB. did; doC. was; doingD. Has; done( ) 11. Our teacher asks us too much time reading novels.A. don’t takeB. not to takeC. don’t spendD. not to spend( ) 12. Listen! Can you hear a baby ________? A. cry B. to cry C. crying D. cries( ) 13. The little girl is too young to ________ herself.A. put onB. wearC. have onD. dress( ) 14. —Can you remember _______ when Beijing was made host to the 2008 Olympics?—Sorry, I can’t.A. what are you doingB. what were you doingC. what you are doingD. what you were doing( ) 15. —______ —I was sleeping late.A. When were you born?B. What were you doing at seven yesterday morning?C. What do you do?D. Were you sleeping late?二．完形填空（共10小题，计15分）Billy is a boy of fifteen. His parents died three years ago. One day when he was walking in the street, he 16 a wallet. He returned it to the owner, Mr. Baker. He gave his __17__ to the boy. As the boy had no job, Mr. Baker made him work for him in his 18 Billy worked so hard that Mr. and Mrs. Baker were 19 with him.Mr. Baker loved planting 20 . The week before last, he brought a few trees home, planted them in the 21 himself and watered them every day. Several days 22 , he had to leave for another city. Before he started, he said to Billy, “Take good care of the trees. Some boys near our house always want to steal them.”“Don’t 23 about them, sir.” answered Billy, “I’ll try my best to watch them.” Six days passed and Mr. Baker came back. He asked, 24 anyone ever come to steal the trees?”“No, sir,” said Billy, “To stop someone from stealing the trees, I 25 them up six days ago. I have hidden them for almost a week!”( ) 16. A. found B. bought C. carried D. wanted( ) 17. A. wallet B. pity C. thanks D. excuses( ) 18. A. factory B. office C. town D. home( ) 19. A. pleased B. angry C. strict D. popular( ) 20. A. flowers B. grass C. vegetables D. trees( ) 21. A. garden B. office C. city D. room( ) 22. A. ago B. later C. before D. after( ) 23. A. think B. talk C. learn D. worry( ) 24. A. Did B. Does C. Has D. Will( ) 25.A. sent B. pulled C. put D. picked三．阅读理解（共10小题，计20分）AIn 1954, a British plane was on its way from New York to London. When the plane was flying over an island(岛屿), the captain(机长) and others saw something on the left. It was about five miles away and much lower than their plane.“It became clear,”the captain said, “there was one large object(物体) and six smaller objects.A moment later the smaller objects entered the big object. The big object then became smaller and moved away fast!”The captain later answered a lot of questions from newspaper reporters.“How long did you study the objects?”“They stayed with us for six minutes.”“What shape were the objects?”“The large one was changing its shape all the time, but each of the smaller ones was round(圆的) like a ball.”“Tell us, were you afraid?”“None of the people in the plane were afraid. We tal ked about that, and in fact we felt friendly to the objects.”There are many other reports of UFOs in different parts of the world. It seems that lots of people believe there are UFOs. Only a few people don’t believe in UFOs, but maybe they will in the future.根据短文内容，判断下列各句正（T）误（F）。

杭州市文澜中学八下期末模拟测试卷第一部分听力 (共15小题，每题2分，满分30分) 略第二部分阅读理解(共两节，满分40分)第一节(共15小题，每小题2分，满分30分)阅读下列短文，从每题所给的四个选项(A.B.C和D)中选出最佳选项。

AYears ago, I lived in a building in a large city. The building next door was only a few feet away from mine. There was a woman who lived there, whom I had never met, yet I could see her seated by her window each afternoon, sewing or reading.After several months had gone by, I began to notice that her window was dirty. Everythi ng was unclear through the dirty window. I would say to myself, "I wonder why that woma n doesn't wash her window. It really looks terrible."One bright morning I decided to clean my flat, including washing the window on the insi de.Late in the afternoon when I finished the cleaning, I sat down by the window with a cup of coffee for a rest. What a surprise! Across the way, the woman sitting by her window wa s clearly visible. Her window was clean!Then it dawned on me. I had been criticizing (批评) her dirty window, but all the time I w as watching hers through my own dirty window.That was quite an important lesson for me. How often had I looked at and criticized oth ers through the dirty window of my heart, through my own shortcomings?Since then, whenever I wanted to judge (评判) someone, I asked myself first, "Am I loo king at him through my own dirty window?"Then I try to clean the window of my own world so that I may see the world about me m ore clearly.16. The writer couldn't see everything clearly through the window because_____.A. the woman's window was dirtyB. the writer's window was dirtyC. the woman lived nearbyD. the writer was near-sighted17. The writer was surprised that_____.A. the woman was sitting by her windowB. the woman's window was cleanC. the woman did cleaning in the afternoonD. the woman's window was still terrible18. "It dawned on me" probably means "____".A. I began to understand itB. it cheered me upC. I knew it grew lightD. it began to get darkBHave you ever dreamed about sending a letter to yourself or your friends in the future? W hile express mail represents high speed, there is another type of mail appearing in China as a new business—future mail.“The letter should be sent next …Mother‟s Day‟ and not a day earlier!” Lin Xiaofan, a senior high school student in Hefei, instructs one of the companies offering the service.Lin Xiaofan wrote the letter to her mother in advance to express her love to her mother fo r next Mother‟s Day.“Offering this service makes people slow down and let them understand the meaning of …t ime‟ in another way,” said Zheng Zhimin, manager at a “future mail” company in Hefei. Zh eng thinks “future mail” letters are “reminders of care, friendship and love.”While “future mail” is becoming more and more popular, some people are wondering wha t will happen if the postal address changes or if the company goes broken before the lette rs arrive.Zheng said customers are glad to complete an acceptance form and make an assessme nt (评估) so they can be compensated (赔偿) if their letters or goods are lost or damaged.Most of the business‟ customers are college students and young white-collar workers. Ps ychologists said young Chinese might have a new way to express their feelings through t his service.“Most people put their hopes and wishes in the letter so they can experience the connecti on between the past and the present while they receive the letter. It can help people re-u nderstand the meaning of …time‟”, said Wang Kaiyu, a sociologist in Anhui Province.19. Express mail is a(n) ________way to send your letters.A. slowB. fastC. impossibleD. ancient20. _________ are interested in future mail service now.A. College studentsB. Blue-collar workersC. Old peopleD. Young children21. Through the future mail service, people can________ .A. forget friendshipB. show feelingsC. misund erstand “time”D. make an assessmentCI know my brother better than anyone else in the world. Since the moment of his birth, I‟v e been part of his life. I had spent seven happy years in the world with the attention of tho se around me. But when Rohan was born, life changed. All of a sudden, I had to share m y toys and there were no more bedtime stories or my own choice of food.Finally, I hated this small boy. The poor baby had no idea what had made me so unhapp y. Maybe he found me strange, the only person in this house who did not like him. Whate ver the reason was, he loved following me around. However, I seldom talked to him and always asked him to leave me alone.Then all that changed. I hardly remember everything of that day six years ago, but I do re member that I was feeling very angry. Then I found myself in my brother‟s room. I couldn‟t help reaching my hand through the bars(栏杆)of his bed. At once, he reached his small hand and softly touched mine. And that was all I needed. Through all the unhappiness of the day, that one moment changed everything. How could I hate someone who made me feel so important For the first time, I saw my brother through the eyes of a sister. Sudden ly I realized love from my family was always with me.To this day, I can‟t imagine life without my brother. It is unbelievable(难以置信的)how mu ch I have learned about life from a seven-year-old boy. Above all, Rohan has taught me t hat one should not care only for himself.22.The sister was ________ years old when her brother was born.A.sixB. sevenC. eightD. ten23.The sister used to be the only person in the house who ________.A.didn‟t like the babyB. followed the baby aroundC. often talked to the babyD. fed the baby24.The underlined phrase “that one moment” refers to the time ________.A.when there were no more bedtime stories for the sisterB.when the sister found herself in her brother‟s roomC.when Rohan softly touched his sister‟s handD. when the sister was nervous25.Which of the following is TRUE?A.The sister doesn‟t know her brother very well.B.The sister lives with love from her family all the time.C.The sister remembers everything of that day six years ago.D. The sister is always sad.DHave you heard about "Survival Holidays"? It is for children to go into the lonely place for exciting activities. Now about 1,100 companies are allowed to take children into the great outdoors without their parents.The reason why people like "Survival Holidays" is that they think being close to nature is good for children. Many children in big cities spend all time watching TV and playing com puter games. "Survival Holidays" gives them an important change.Is "Survival Holidays" a wonderful idea? Maybe it is. Children need more free time to play. They need to be left on their own, without adults disturbing(干扰) them. Parents care too much about their children. They like to see the children being busy with activities that are controlled(控制) by adults, which causes many problems. Children don't know what to do when they are in danger. Even something like crossing a small river seems to be a hard c hallenge. Children are not comfortable with danger. Even slight danger like getting their f eet wet or falling down seems very terrible to them.Many people think the survival activities are good for children. Even years later, they will still remember what they have learned. Some have learned to stay calm in dangerous tim es. Some have learned how to keep safe. Others have learned how to work in a team. All these skills will help them a lot in their lives.26.What is "Survival Holidays" according to the passage?A．It is summer holidays. B．It is winter holidays.C．It is a kind of holidays to escape from danger.D．It is a holiday to go into the lonely place for exciting activities.27.Which children may take part in "Survival Holidays"?A．Poor children. B．Rich children.C．Children from cities. D．Children from the countryside.28.What's the main idea of the last paragraph?A．The reasons people dislike "Survival Holidays".B．The advantages of "Survival Holidays".C．The disadvantages of "Survival Holidays".D．The suggestions of taking part in "Survival Holidays".29.In a "Survival Holidays" children can learn the following except _________.A．how to get good gradesB．how to stay calm in different timesC．how to keep safe when they meet dangerD．how to work in a team30.Which of the following is TRUE according to the passage?A．No companies can hold "Survival Holidays".B．Parents can take part in "Survival Holidays" with their children.C．Parents like to keep their children busy with activities controlled by adults. D．Children don't listen to their parents any more after "Survival Holidays".第二节任务型阅读（共5小题，每题2分，满分10分）Inner Voice Helps a lot Throughout Our LivesWhen you couldn't open your mouth till the first two years on the earth, inner voice helps you understand things. Inner voice always shows thoughts and ideas in the body.It justifies （判断） what is right and what is wrong. When we go against inner voice, we usually feel uncomfortable throughout our lives.Sometimes when we are feeling sad, we seem to need some kind of support in spirit. We usually speak to our closest friend or our dearest family member during times of unhappi ness to feel better. After talking to them, we suddenly feel active again, because our inne r voice reminds us to get on with things and leave the things of the past in the memory.Inner voice is always right most of the time, because it knows us better than others and e ven ourselves. It's good to go by inner voice most of the time. Whenever you are trying to smoke, or whenever you are asked to choose one side in an argument, you are always worried about the result. During these times, your inner voice tells you what to do. If you don't follow your inner voice, you might be unhappy in the future. It's our own choice to eit her pay no attention to our inner voice or follow it and search for real happiness.Passage outline Supporting detailsIntroduction to inner voice Before we can talk, inner voice 31_____ understand things, a nd shows thoughts and ideas in the body.Things that inner voice helps us with Inner voice tells us what is right and what is wrong. We usually have an uncomfortable 32 _____ throughout our lives when we go agai nst inner voice.Inner voice reminds us to get on with things and leave the things of the past.33 ____ why we should go by inner voice It knows us better than others and even oursel ves.It tells us 34 ____ to do when we are always worried about the result of our choice.We might be unhappy in the future without 35____ our inner voice.第三部分英语知识运用（共两节，满分 25 分）第一节：完形填空（共 15小题，每小题 1 分，满分 15 分）通读下面短文，掌握其大意，然后在各题所给的四个选项（A、B、C 和 D）中选出一个最佳选项。

浙教版八年级数学下册第三章测试题（附答案）姓名：__________ 班级：__________考号：__________一、单选题（共12题；共24分）1.甲、乙、丙、丁四名同学进行跳高测试，每人10次跳高成绩的平均数都是1.28m，方差分别是s甲2＝0.60，s乙2＝0.62，s丙2＝0.58，s丁2＝0.45，则这四名同学跳高成绩最稳定的是（）A. 甲B. 乙C. 丙D. 丁2.一次数学测试，某小组五名同学的成绩如下表（有两个数据被遮盖）：那么被遮盖的两个数据依次是（）A. 80、2B. 80、C. 78、2D. 78、3.今年，我省启动了“爱护眼睛保护视力”仪式，某小学为了了解各年级戴近视镜的情况，对一到六年级近视的学生进行了统计，得到每个年纪的近视的儿童人数分别为20，30，20，34，36，40，对于这组数据，下列说法错误的是（）A. 平均数是30B. 众数是20C. 中位数是34D. 方差是4.立定跳远是小刚同学体育中考的选考项目之一．某次体育课上，体育老师记录了小刚的一组立定跳远训练成绩如下表：则下列关于这组数据的说法中正确的是（）A. 众数是2.45B. 平均数是2.45C. 中位数是2.5D. 方差是0.485.在一次中学生田径运动会上，参加男子跳高的15名运动员的成绩如下表所示：则这些运动员成绩的中位数、众数分别为（）A. 1.70，1.75B. 1.70，1.70C. 1.65，1.75D. 1.65，1.706.学校准备从甲、乙、丙、丁四个科创小组中选出一组代表学校参加青少年科技创新大赛，各组的平时成绩的平均数（单位：分）及方差s2如表所示：如果要选出一个成绩较好且状态稳定的组去参赛，那么应选的组是（）A. 甲B. 乙C. 丙D. 丁7.在创建平安校园活动中，九年级一班举行了一次“安全知识竞赛”活动，第一小组6名同学的成绩（单位：分）分别是：87，91，93，87，97，96，下列关于这组数据说正确的是（）A. 中位数是90B. 平均数是90C. 众数是87D. 极差是98.某校调查了20名男生某一周参加篮球运动的次数，调查结果如表所示，那么这20名男生该周参加篮球运动次数的平均数是（）A. 3次B. 3.5次C. 4次D. 4.5次9.某班45名同学某天每人的生活费用统计如表：对于这45名同学这天每人的生活费用，下列说法错误的是（）A. 平均数是20B. 众数是20C. 中位数是20D. 极差是2010.数据3，6，7，4，x的平均数是5，则这组数据的中位数是（）A. 4B. 4.5C. 5D. 611.如果一组数据x1，x2，…，x n的方差是4，则另一组数据x1+3，x2+3，…，x n+3的方差是（）A. 4B. 7C. 8D. 1912.已知一组数据的方差为，数据为：－1，0，3，5，x，那么x等于（）A. －2或5.5B. 2或－5.5C. 4或11D. －4或－11二、填空题（共8题；共20分）13.甲、乙两名射击手的50次测试的平均成绩都是8环，方差分别是S甲2=0.4，S乙2=1.2，则成绩比较稳定的是________（填“甲”或“乙”）14.如图是23名射击运动员的一次测试成绩的频数分布折线图，则射击成绩的中位数________。

杭州市文澜中学2019年八下期中任务型阅读练习ATravel Tips for Holidays AbroadEveryone loves holiday abroad. They give us the chance to see some sights, have some fun and rela x. However, holidays aren’t always a great experience. Follow these tips to make sure you enjoy your holiday.1._______Have you packed your passport? Your tickets? Every year, thousands of people miss flights because they've forgotten their passport, they arrive at the airport too late, or even go to the wrong airport.2._______How much do you know about the place you are going to visit? Learning a little about the culture of a country will help you understand the people. Learning a few words of another language can also help you make new friends.3._______Try to reduce the pollution you cause. Travel by train if you can. Flying produces twenty times more carbon dioxide than traveling by train. Of course, it might be impossible to avoid flying, but when you arrive, use buses or trains instead of taxis.4._______You can help a local community a lot by staying in local hotels and eating in local restaurants. This means that your money will go to local people, rather than to a large international company.5._______You don't want to forget your holiday. Make a scrapbook-a book of memories-about your holiday. You can show it to friends, or just use it to remember all the good times you had! And don't forget the new friends you made on holiday. Did you promise to send them pictures or presents? Don't forget to do it! Then next time you go on holiday, you can visit them again.A.Remember the environmentB.Keep a good memory for your holidayC.Travel with your friendsD.Do some researchE.Get organizedF.Help the local populationBHow Can You Create Luck in Everyday LifeYou can probably agree that some people have more good things happening to them. Let's just call that luck. Now, would you like to learn how to be one of these lucky people Here are 5 top tips for creating your own luck.◎See the Good in the PastIt is easy to believe that you never have any luck in everyday life if you don't seem to be getting any breaks. But having had a difficult life gives you unusual lessons and develops courage.◎ 1 _________Some people are already lucky, and they just don't know it. Instead of giving all your attention to what you are short of, look at how lucky you already are. You no doubt have some wonderful friends, family, and a roof over your head.◎ 2 _________Luck doesn't just happen upon us - it comes to us when we're open. Learning a new skill, visiting a new place and trying a new hobby are all great ways of creating your chances.◎ 3 __________You'll never create any luck if you sit there waiting for it to fall into your lap. Take steps towards your goals and dreams and greet every challenge. You will find you create more luck in everyday life.◎ 4 _____________Sometimes people would be prepared to help us out. If you need a hand with dealing with something, rather than wait for someone to offer you a lucky break, go and ask them if they will help you out.A. Try Something NewB. Take Action Right NowC. Ask for Help If NecessaryD. Feel Lucky about What You Have5. Do you feel lucky Why or why not（理由不少于5个单词）________________________________________________________________CWhat can you make with pieces of paper？Look at Chen Yiyan’s works!The 14﹣year﹣old has Origami（折纸） talent at Hangzhou Entel Foreign Language School．Zhejiang．1________But he wasn’t born with this talent．When Chen was a fourth﹣grader，he found his brother’s paper﹣folding book．2__________Following the 50steps shown in the book，he made his first work，a paper peacock，within two hours．Since then，he has read many books about Origami and practices in his spare time．So far，his“fantasy world“has man members，such as monsters and robots．And he made his favorite work last year．3_________Chen used to fold （折叠）paper himself until he met Chen Changnan，an eighth﹣grader at his school，who also loves Origami．They set up a paper﹣folding club last year．With support from school，they host a paper﹣folding class every Wednesday afternoon．The club soon attracted people．Now it has more tan 20 members．4__________On February 14th．The club also held a speech for the kids in wenzhou Children’s Library．“It’s really exciting to develop my hobby and share it with others at the same time．”said Chen，“I hope more and more people get to know Origami and love this art．”A．It’s a paper dragon that invo lved （包含）almost 2019 steps．B．They show their works and teach students how to fold．C．He has folded a“kingdom“with his hands．D．It got him interested in Origami5．The passage mainly tells us__________．A．a paper﹣folding club B．how to fold paperC．a student with Origami talent D．how to develop hobbies．DFlorence lived in the countryside of Kenya(肯尼亚）in Africa. When she was 12, the only thing she wanted was to finish school. But for many girls like her, school is only a dream. 1_____ Families will probably spend money educating boys. Many girls have to marry early.But Florence was able to continue her education. 2____ Lisa started an organization to provide many girls with the best education possible. Florence was the first of 320 Kenyan girls among them.3______ During her visit, she heard that many women made and sold baskets. They used the money to send their daughters to school. “Two years later, she started to help sell the Kenyan craft( 工艺品）in the US. In 2019, Lisa began helping girls continue their education.4______ In January, 2019, she started the fourth one. “I want to prepare them for college,” Lisa said.The new high school is called Tembea, which means “to walk”. Florence is walking towards a bright future. 5_______ “Florence is the first in her family to finish high school and college,” said Lisa. “She is an example for all girls in Kenya.”A. School costs money.B. In 1991, Lisa first visited Kenya.C. After that, she helped build three schools.D. She left college in 2019 and is now a teacher.E. It was Lisa Stevens who helped achieve her dream.EAccording to a new survey, students’ safety has become a big problem. Nearly 50% of students say they are worried about robbery on the way to and from school. Now in main big cities in China , some schools have taught an unusual lesson: self-protection.Students like this lesson because there are no exams or boring classes. And they can learn how to save lives and know how to stop danger before it really happens.Chen Haoyu, a teacher at Beijing No. 25 Middle School, gives young students advice on how to deal with danger.1.___________Keep calm. lf you can not cry for help or run away. Give the robber your money. Try to remember what the robber looks like and tell the police later.2.___________If a car hits you. You should remember the car number. If it is a bicycle, try to call your parents before you let the rider go. This is because you don't know how seriously you are hurt3.___________Don’t stay in high places and stay away from trees.4.____________Get away as fast as yon can. Put wet things on your body and try to find an exit. Do not take the lift.5.____________If you can’t swim, don’t get into the water. Cry out for help.A。

一、选择题1．His son provided the old man ________ all the food and the money he needed.A．for B．with C．to D．at B解析：B【解析】句意：他的儿子为老人提供了他所需要的所有食物和钱。

A. for为了；B. with与……一起；C. to到；D. at在。

provide sb. with sth.=provide sth. for sb.给某人提供某物。

结合句意可知，答案为B。

2．You can't watch TV now.You ________ clean your room first.A．can B．may C．have to D．must have to C解析：C【解析】句意：你现在不能看电视了，你得先打扫你的房间。

A. can能够，可以； B. may可以；C. have to必须，不得不；D. must与have to不能同时出现，结合句意以及语境可知，故答案为C。

3．Would you like to go shopping?—I'd like to，but I have to finish ___ my homework first. A．doing B．to do C．did D．will do A解析：A【解析】句意：你想去购物吗？我很想去，但我得先做完作业。

finish doing sth.做完某事，为固定用法。

故答案为A。

4．There are ___ five new words in this sentence，so it's too difficult for me to understand it. A．at the least B．at all C．at most D．at least D解析：D【解析】句意：这句话至少有五个生词，所以对我来说太难理解了。

杭州市文澜中学八年级下册Unit 2 单元检测第二部分阅读理解(共两节，满分40分)第一节(共15小题，每小题2分，满分30分)阅读下列短文，从每题所给的四个选项(A.B.C和D)中选出最佳选项。

AZhao Hua is a student from a university. He has led a group of university student volunteers since last year. They help children at a primary school with their studies and daily lives.“ When I was a small chi ld,” Zhao said, “ I knew March 5th was a day for people to learn from Lei Feng and help others, but I didn’t know the real meaning of the spirit of Lei Feng. Now when I see the smiling faces of the kids I have helped, I deeply understand Lei Feng. Helping others makes me happy.”Lei Feng（1940—1962）is one of the best-known soldiers in Chinese history. He lost his parents when he was very young. His neighbors brought him up. He died in an accident at the age of 22. He did many good deeds in his short life. For example, he gave his own money t o the parents of another soldier, and bought a ticket for a woman he didn’t know without telling her his name.On March 5th,1963, Chairman Mao called on people to “ Learn from Lei Feng” and made the day“Lei Feng Day”.Today almost 50 years has passed since Lei Feng’s death. Some people say that the spirit of Lei Feng is out. There have been many reports about the coldness (冷漠) of people towards strangers. This has made many Chinese people think deeply about themselves.Many people think we need to promote (提倡) that spirit again. The important thing is that we must be ready to help others and make it a habit.1. Which day is “Lei Feng Day”？A. May 3 rd.B. May 5 th.C. March 3 rd.D. March 5 th.2. Who brought Lei Feng up?A. His parents.B. Chairman Mao.C. His neighbors.D. Soldiers.3. The underlined phrase “good deeds” means _________ in Chinese.A.好人B.好事C. 好梦D. 好主意BZhang Ming, a college student from Shandong, created a 9-page “WeChat guide”. With drawings and simple words, the step-by-step guide explains how to send messages, take pictures and make video calls. Zhang made the guide for his parents. “My parents are getting old. They need an easy way to learn how to use ne w technology.” He said.Zhang’s experience is common nowadays. Worldwide, 40 percent of parents learn about new technologies, including computers, mobile Internet and social media, from their children, according to a study from the International Communication Association in 2019.Parents used to teach their kids about almost everything. Now for the first time, the teachers become the students, and the students turn into the teachers.The change of roles comes from the rapid development of society and technology, says Zhou Xiaohong, a sociology professor from Nanjing University. Zhou said the Internet and other forms of media give children ways to get information besides from asking older generations(长辈). Therefore, in the age of information, it’s possible th at children know more than their parents do.According to the China Internet Network Information Center(CINIC), 56.7 percent of Internet users and 67.2 percent of social media users in China are under the age of 30. The younger generation usually acts as a link between their family and the new environment. But when they teach their parents new technologies, parents can connect to the new world by themselves, noted Zhou.In Zhang Ming’s eyes, teaching his parents about WeChat brings him closer to his parents. “People can communicate more by using new technology. Why should we keep o ur parents out?” said Zhang.1. According to the passage, Zhang’s parents can’t_______with the “WeChat guide”.A. make video callsB. send messagesC. grab the red envelopesD. take pictures2. Why does children know more than their parents do nowadays?A. Because parents teach the children about almost everything.B. Because children can ask more older generations for help.C. Because parents are getting old.D. Because children can get more information by using new technologies.3.What does the underlined word “link” in paragraph 5 mean?A.teacherB.connectionC.treasureD.conversation4.Which of the following is NOT true according to the passage?A.Zhang Ming’s “We Chat guide” is made up of drawings and simple words.B.40% of parents lean about new technologies from their children all over the world on2019.C.56.7% of social media users in China are under 30 according to the CINIC.D.Zhang Ming thinks that we should encourage our parents to use more newtechnologies.CIn London, there has always been a main problem. In order to solve this problem, the government has decided to have a bike revolution (革命). It has decided to provide 6,000 bikes for the people to rent.The government encourages local people to ride bikes in order to solve the traffic problem.More than 12,000 people have agreed to the idea. Some of them ask for more than one key.Although there are not enough bikes, an official (官员) from the government said that they would find some ways to deal with such a shortage.Local people can get these bikes at special docking stations (停靠站). There are about 315 docking stations across the city. About 12,450 keys have already been handed out to the local people, but only 6,000 keys can be used now.Let's see the cost you need to pay. One key costs ￡3, and the cost of using the bike is ￡1 for anhour. The cost per hour increases as the hours increase, so it will cost ￡50 if you rent the bike for 24 hours.The official from the government said they also needed to face a lot of problems, for example, some bikes may be lost. But they said they would try their best to solve all the problems to make sure thesuccess of the program.1. In London, the government has decided to provide bikes for local people to rent in order tosolve _____.A. the traffic problemB. the health problemC. the family problemD. the study problem2. About _____ keys have already been handed out to the local people.A. 315B. 6.000C. 12.450D. 4563. In the passage, the underlined wo rd "shortage" means "_____" in Chinese.A. 挑战B. 缺点C. 短缺D. 消失4. Which of the following is TRUE according to the passage?A. The government provides a bike for each family.B. Local people can get these bikes at special docking stations.C. If you want a key, you need to pay ￡5.D. No one can get the bikes.5. What's the best title for the passage?A. The bike revolution in London.B. The transportation in London.C. The traffic problem in London.D. The scenery in London.DIn Western society, especially in the English-speaking world, the chance for young people to see the other countries and experience life is considered important. Many young people, when they finish school at the age of 18, take a gap year before they go to university.Parents often want their children to grow up a little and see what the real world is like wh en they finish school. Although they are worried about their safety, many think that the ad vantagesof independence and experience are worth the worries. Children are encourage d to be brave, independent and to explore the world on their own or with friends.Young people also want to experience freedom and see what life is like on the other side. This other side could be the other side of the world or just the other side of life. For exam ple, if they have a rich life, they may want to see how people in poor areas live.A gap year after school is also an important chance for young people to spend time thinki ng about what they want to do with their lives. A little bit of growing up and experience wil l help them make their important career decisions, especially when they are unsure about what they want tostudy.Another reason for going straight after school is to get a break from studying before they startthe next few years of university. So anywhere you travel in the world, you will meet y oung European people exploring the world.So much of the world has been travelled and explored. The young people are now lookin g for moreworthy experiences. Some of them work as volunteers to do something for the country they are visiting. Many gap year volunteers are now spending a few months teac hing English in Thailand, helping feed giant pandas in China or building a well(井) in a vill age in Africa.These young people’s wish to explore the world is an expression of the values of the societies that they are part of. Both discovering the world and making a positive difference in it are important parts of the Western mind.1.Which is NOT a reason for young people to take a gap year?A. Young people want to take a break from studying.B. Young people want to be sure about what to study.C. Parents encourage them to be brave and independent.D. Parents encourage them to live a free and wealthy life.2.Now a gap year volunteer might do something more valuable like .A. experiencing different culturesB. helping protect rainforests in BrazilC. making friends with more peopleD. enjoying traditional local food3.By taking a gap year, young people may .A. stay with their parents all the timeB. make money for their further studyC. help change the world for the betterD. change the Western mind completely4.The purpose of writing this article is to .A. show different opinions about gap yearB. offer readers information about gap yearC. discover new ways to take a gap yearD. tell young people when to take a gap year任务型阅读阅读下面文章，然后从文后所给的A--D四个选项中选择正确的小标题，将其序号填入1- 4题，井回答第5题。

浙江省文澜中学初三八年级物理第三章物态变化汇编一、选择题1．如图所示，有三杯水甲、乙、丙放在室温为25℃的同一房间内，一杯是普通自来水，一杯是刚倒的开水，一杯是刚倒的冰水。

请根据图中信息判断甲乙丙分别是（）A．开水、自来水、冰水B．自来水、开水、冰水C．冰水、自来水、开水D．开水、冰水、自来水2．下列温度值最接近实际的是（）A．洗热水澡时的适宜水温约40℃B．让人感觉温暖而舒适的室内温度约37℃C．健康成年人的体温是40℃D．在一个标准大气压下盐水的凝固点是0℃3．在冬季，某地的地下水管破裂了，水喷射出来形成了如图所示的“冰花”。

虽然气温没有回升，过一段时间，发现“冰花”还是变小了。

以下分析正确的是（）A．“冰花”是由空气水蒸气凝华而形成的B．“冰花”变小了主要是冰升华的原因C．“冰花”形成时的气温一定为0℃D．“冰花”变小过程中要放热4．如图所示是“探究某物质熔化和凝固规律”的实验图像，下列说法正确的是（）t 时，该物质处于固液共存状态A．在6minB．在BC段，该物质不吸热C．该物质在CD段是气态D．该物质的凝固点是45℃5．在注射器中吸入少量液态乙醚，用橡皮塞堵住注射孔，向外拉动活塞，液态乙醚会消失，以下四幅图中物态变化的吸放热情况与其相同的是（）A．甲乙B．甲丁C．乙丙D．丙丁6．疫情期间医护人员佩戴护目镜时往往会形成一层水雾覆盖在护目镜内侧，如图所示，下列诗句中加点字的形成与护目镜上的水雾形成相同的是（）A．月落乌啼霜．满天，江枫渔火对愁眠B．露．从今夜白，月是故乡明C．梅须逊雪．三分白，雪却输梅一段香D．冰．合井泉月入闺，金缸青凝照悲啼7．下列有关物态变化的说法，正确的是（）A．冬天北方窗户上的“冰花”，出现在窗户的内侧表面B．深秋时常出现“结霜”现象，结的“霜”是水凝固形成的C．文艺演出时舞台上经常释放“白气”，这是干冰在常温下的升华现象D．夏天用电风扇对着人扇风，人感到凉爽是因为扇风降低了室内的气温8．如图是用水壶烧开水的情景，下列关于离壶嘴较远的地方“白气”比较浓，而靠近壶嘴的地方却没有“白气”的说法正确的是（）A．靠近壶嘴处的温度较高，空气中原有的水蒸气难以液化B．靠近壶嘴处的温度较高，刚冒出的水蒸气难以液化C．液化是需要时间的，刚冒出的水蒸气液化时间太短D．离壶嘴较远处的空气中水蒸气含量较多，所以液化生成的小水珠多9．中央电视台播出的《中国诗词大会》深受学生喜爱，诗句中蕴含了丰富的物理知识，下列对有关诗句的分析正确的是（）A．“可怜九月初三夜，露似珍珠月似弓”——露的形成是熔化现象，需要吸热B．“北风卷地白草折，胡天八月即飞雪”——雪的形成是凝固现象，需要放热C．“月落乌啼霜满天，江枫渔火对愁眠”——霜的形成是凝华现象，需要放热D．“斜月沉沉藏海雾，碣石潇湘无阻路”——雾的形成是液化现象，需要吸热10．在观察“碘锤”中的物态变化之前，查阅资料得知：酒精灯外焰的温度约为800℃，碘的熔点为113.7℃，采用图中的两种方式加热，下面说法错误的是（）A．烧杯内可直接使用100℃的沸水B．甲、乙两图都会发生碘的升华现象C．甲图实验比乙图实验更合理D．乙图碘锤中发生的物态变化比甲图碘锤中多1种11．下列物态变化现象中，属于凝华现象的是（）A．初春，冰雪消融B．盛夏，清晨荷叶上的露珠C．深秋，大雾弥漫D．严冬，玻璃窗上的“冰花”12．下表列出了几种物质在标准大气压下的熔点和沸点，根据数据，下列说法正确的是（）物质氢酒精水银钨铁金熔点/°C-259-117-39341015351064沸点/°C-25378357590027502808B．-39°C时的水银一定是液态C．金掉入铁水中一定会熔化D．钨的沸点高，所以可以用来制作灯丝13．如图甲所示，将质量相等的冰和蜡烛分别装在两个相同的试管中，放入装有水的烧杯中加热，绘制出温度随时间变化的图像如图乙所示，下列说法正确的是（）A．甲图中采用水浴法加热后就没必要用碎冰做实验了B．由图乙可知，B图线对应的物质是冰C．A图线中，2—6min段温度不变，说明此过程不需要吸热D．A图线中，2—6min段表示熔化过程，此过程需要吸热14．夏天，小雨将冰水和热水分别注入常温下的两只透明烧杯中，如图所示。

第 3 章检测题(时间： 100 分钟满分：120分)一、精心选一选(每题 3 分，共 30 分)1 ．某校正九年级 6 个班学生均匀一周的课外阅读时间进行了统计，分别为(单位：h )：3.5 ， 4， 3.5 ， 5， 5， 3.5. 这组数据的众数是 ( B )A． 3 B．C．4 D．52 ．在端午节到来以前，学校食堂介绍了 A ， B， C 三家粽子专卖店，对全校师生爱吃哪家店的粽子作检查，以决定最后向哪家店采买．下边的统计量中，最值得关注的是( D ) A．方差B．均匀数C．中位数 D ．众数13 ．在样本方差的计算公式S2＝[(x 1－ 20) 2＋ (x2－ 20) 2＋＋ (x10－ 20) 2]中，数字 1010与 20 分别表示样本的( A )A．容量，均匀数B．均匀数，容量C．容量，方差 D ．标准差，均匀数4 ．期中考试后，班里有两位同学谈论他们所在小组同学的数学成绩，小明说：“我们构成绩是86 分的同学最多” ，小英说：“我们组的7 位同学成绩排在最中间的恰巧也是86 分”，上边两位同学的话能反应的统计量是( D )A．众数和均匀数B．均匀数和中位数C．众数和方差 D ．众数和中位数5 ．某班组织了一次念书活动，统计了10 名同学在一周内的念书时间，他们一周内的念书时间累计如表，则这10 名同学一周内累计念书时间的中位数是( C )一周内累计的念书时间(小时)581014人数 (个) 1432B．7 C．9 D．106 ．某市 6 月份日均匀气温统计以下图，则在日均匀气温这组数据中，众数和中位数分别是(C)A． 21 ， 21B． 21 ，C．21 ， 22D． 22 ， 227 ．今年，我省启动了“关爱留守小孩工程”．某村小学为了认识各年级留守小孩的数量，对一到六年级留守小孩数目进行了统计，获取每个年级的留守小孩人数分别为10 ，15 ，10 ， 17 ， 18 ， 20. 关于这组数据，以下说法错误的选项是( C )44A．均匀数是15 B．众数是10 C．中位数是17 D ．方差是38 ．某学校举行理科(含数学、物理、化学、生物四科)综合能力竞赛，四科的满分都为100分．甲、乙、丙三人四科的测试成绩以下表，综合成绩依据数学、物理、化学、生物四科测试成绩的 1.2 ∶1 ∶1∶0.8 的比率计分，则综合成绩第一名是( A )学科数学物理化学生物甲95 85 85 60乙80 80 90 80丙70 90 80 95A. 甲B．乙C．丙D．不确立9 ．一组数据 6 ， 4 ，a ， 3， 2 的均匀数是 5，这组数据的标准差为( A )A．2 2 B．5 C．8 D．310 ．在某中学举行的演讲竞赛中，八年级 5 名参赛选手的成绩以下表所示，请你依据表中供给的数据，计算出这 5 名选手成绩的方差为( B )选手 1 号 2 号 3 号 4 号 5 号均匀成绩得分90 95 ■89 88 91A.2 B． 6.8 C． 34 D． 93二、仔细填一填 (每题 3 分，共 24 分)11 ．甲、乙两人进行射击测试，两人 10 次射击成绩的均匀数都是8.5 环，方差分别是：S 甲2＝ 2， S 乙2＝ 1.5 ，则射击成绩较稳固的是__乙 __． (填“甲”或“乙” )12 ．数据 1，2 ，3 ，a 的均匀数是 3 ，数据 4 ，5，a ，6 的众数是5，则 a ＋b ＝ __11 __．1513 ．已知一组数据 3 ，1 ，5 ，x，2，4 的众数是 3 ，那么这组数据的标准差是____．314 ．某大学自主招生考试只考数学和物理，计算综合得分时，按数学占60% ，物理占40% 计算．已知小明数学得分为 95 分，综合得分为 93 分，那么小明物理得分是__90 __分．15．某校抽样检查了七年级学生每日体育锻炼时间，整理数据后制成了以下所示的频数散布表，这个样本的中位数在第__2 __组．组别时间 (小时 ) 频数 (人)第 1 组0 ≤t＜12第 2 组0.5 ≤t＜ 1 24第 3 组 1 ≤t＜18第 4 组 1.5 ≤t＜ 2 10第 5 组 2 ≤t＜ 616. 一组数据 3 ， 4 ， 6 ， 8， x 的中位数是 x，且 x 是知足不等式组x－ 3≥0 ，的整数，5 －x＞ 0，则 x 的值为 __4 __．17 ．两组数据m ， 6 ， n 与 1 ， m ， 2n ， 7 的均匀数都是6 ，若将这两组数据归并成一组数据，则这组新数据的中位数为__7 __．18 ．已知一组数据 1 ，2 ， 3 ，， n( 从左往右数，第 1 个数是 1 ，第 2 个数是 2，第 3 个数是 3 ，依此类推，第n 个数是n) ．设这组数据的各数之和是s，中位数是k，则 s＝__nk __． (用只含有n ， k 的代数式表示)三、耐心做一做(共 66 分 )19 ． (8 分 )在“全民念书月活动”中，小明检查了全班40 名同学本学期计划购置课外书的花销状况，并将结果绘制以下图的统计图．请依据有关信息，解答以下问题：(直接填写结果)(1)此次检查获取的样本数据的众数是__30 元 __；(2)此次检查获取的样本数据的中位数是__50 元__；(3) 若该校共有学生1000 人，依据样本数据，预计本学期计划购置课外书花销50 元的学生有 __250 __人．20 ． (10分)为认识某种电动汽车的性能，对这类电动汽车进行了抽检，将一次充电后行驶的里程数分为 A ， B， C， D 四个等级，此中相应等级的里程挨次为200 千米， 210 千米， 220 千米， 230 千米，获取以下不完好的统计图．依据以上信息，解答以下问题：(1)问此次被抽检的电动汽车共有几辆？并补全条形统计图；(2)预计这类电动汽车一次充电后行驶的均匀里程数为多少千米？1 解：( 1)被抽检的电动汽车共有30 ÷30% ＝ 100 (辆 )，补全条形统计图略(2 )x ＝(10100×200 ＋ 30 ×210 ＋40 ×220 ＋ 20 ×230 )＝ 217 (千米 )21 ． (10 分 )某企业职工的月薪资状况统计以下表：职工人数 2 4 8 20 8 4月薪资 (元 )700060004000350030002700(1)分别计算该企业职工月薪资的均匀数、中位数和众数；(2)你以为用 (1) 上当算出的哪个数据来代表该企业职工的月薪资水平更加适合？请简要说明原因．职工的月薪资水平更加适合，由于3500出现的次数最多，能代表大多数人的薪资水平22 ． (12分)为了推进阳光体育运动的宽泛展开，指引学生走向操场，走进大自然，走到阳光下，踊跃参加体育锻炼，学校准备购置一批运动鞋供学生借用，现从各年级随机抽取了部分学生的鞋号，绘制了以下的统计图①和图②，请依据有关信息，解答以下问题：(1) 本次接受随机抽样检查的学生人数为__40 __，图①中m 的值为__15 __；(2)求本次检查获取的样本数据的众数和中位数；(3) 依据样本数据，若学校计划购置200 双运动鞋，建议购置35 号运动鞋多少双？36 ＋36解： (2 )众数为 35 中位数为＝ 362年级中学生鞋号为35 的人数比率约为30% ，则计划购置200双运动鞋，有200 ×30% ＝60 (双)为 35 号23 ．(12 分 )甲、乙两人是NBA 结盟凯尔特人队的两位明星球员，两人在前五个赛季的罚球命中率以下表所示：甲球员的命中率(%)8786838579乙球员的命中率(%)8785848084(1)分别求出甲、乙两位球员在前五个赛季罚球的均匀命中率；(2)在某场竞赛中，因对方球员技术犯规需要凯尔特人队选派一名队员进行罚球，你以为甲、乙两位球员谁来罚球更好？ (请经过计算说明原因 )解：(1)x 甲＝(87 ＋ 86 ＋ 83 ＋ 85 ＋79 )÷5 ＝ 84 ；x 乙＝ (87 ＋85 ＋ 84 ＋ 80 ＋ 84 )÷5 ＝ 84. 因此甲、乙两位球员罚球的均匀命中率都为84%(2 )S 甲2＝ [( 87 － 84 )2＋ (86 － 84 )2＋ (83 －84 )2＋(85 － 84 )2＋(79 －84 )2]÷5＝8 S 乙2＝ [(87 －84 )2＋(85 － 84 )2＋(84 －84 )2＋(80 － 84 )2＋ (84 － 84 )2 ]÷5 ＝由x甲＝x乙，S甲2＞S乙2可知，乙球员的罚球命中率比较稳固，建议由乙球员来罚球更好24 ． (14 分 )如图， A ， B 两个旅行点从2012 年至 2016 年“五一”的旅行人数变化情况分别用实线和虚线表示．依据图中全部示信息，解答以下问题：(1)B 旅行点的旅行人数相对上一年来说，增加最快的是哪一年？(2) 求 A ，B 两个旅行点从 2012 年至 2016 年旅行人数的均匀数和方差，并从均匀数和方差的角度，用一句话对这两个旅行点的状况进行评论；(3)A 旅行点此刻的门票价钱为每人80 元，为保护旅行点环境和旅客的安全， A 旅行点的最正确招待人数为 4 万人，为控制旅客数目， A 旅行点决定提升门票价钱．已知门票价钱x(元 )与旅客人数 y( 万人 ) 知足函数关系y＝ 5－x4 万.若要使 A 旅行点的旅客人数不超出100人，则门票价钱起码应提升多少？解： (1)B 旅行点的旅行人数相对上一年来说，增加最快的是 2 013年(2 )x A＝1＋ 2＋3＋4＋5 3＋3＋2＋4＋3 1＝ 3(万人 )， x B＝5 ＝3(万人 )．S A2＝×[0＋0＋(－1)2＋125 52＋0 ] ＝ (万人2 )．从 2012 年至 2016 年， A ， B 两个旅行点均匀每年的旅行人数均为3 万5x人，但 A 旅行点较 B 旅行点的旅行人数颠簸大(3 )由题意得 5 －≤4 ，解得 x≥100 ，100100 － 80 ＝ 20 (元 )．答：门票价钱起码应提升20 元初中数学试卷。

一、选择题1．下列命题中，其逆命题是真命题的有（ ）个①全等三角形的对应角相等，② 两直线平行，同位角相等，③等腰三角形的两个底角相等，④正方形的四个角相等．A ．1B ．2C ．3D ．42．如图为某城市部分街道示意图，四边形ABCD 为正方形，点G 在对角线BD 上，GE CD ⊥，GF BC ⊥，1500m AD =，小敏行走的路线为B A G E →→→，小聪行走的路线为B A D E F →→→→．若小敏行走的路程为3100m ，则小聪行走的路程为（ ）A ．3100mB ．4600mC ．5500mD ．6100m 3．如图，Rt ABC ∆中，90BAC AB AC AD BC ︒∠==⊥，，于点D ABC ∠，的平分线分别交AC AD 、于EF 、两点，M 为EF 的中点，AM 的延长线交BC 于点N ，连DM ，下列结论：①DF DN =； ②DMN ∆为等腰三角形；③DM 平分BMN ∠；④AE NC =，其中正确结论的个数是（ ）A ．1个B ．2个C ．3个D ．4个 4．如图，点E 、F 分别在正方形ABCD 的边BC 、CD 上，45EAF ∠=︒，已知6AD =（正方形的四条边都相等，四个内角都是直角），2DF =．则AEF 的面积AEF S =（ ）A ．6B ．12C ．15D ．30 5．已知矩形ABCD ，下列条件中不能判定这个矩形是正方形的是（ ） A ．AC BD ⊥ B ．AC BD = C ．AC 平分BAD ∠ D ．ADB ABD ∠=∠ 6．已知四边形ABCD 是平行四边形，下列结论中不正确的是（ ）A ．当AB BC =时，四边形ABCD 是菱形B ．当AC BD ⊥时，四边形ABCD 是菱形C ．当90ABC ∠=时，四边形ABCD 是矩形D ．当AC BD =时，四边形ABCD 是正方形7．如图，将长方形ABCD 沿对角线BD 折叠，使点C 落在点C ′处，BC ′交AD 于E ，AD ＝8，AB ＝4，则重叠部分（即BDE ）的面积为（ ）A ．6B ．7.5C ．10D ．208．如图，Rt Rt ABC BAD △≌△，BC 、AD 交于点E ，M 为斜边的中点，若CMD α∠=，AEB β∠=．则α和β之间的数量关系为（ ）A ．2180βα-=︒B ．60βα-=︒C ．180αβ+=︒D ．2βα=9．如图，菱形ABCD 中，4AB =，60A ∠=︒，点E 是线段AB 上一点（不与A ，B 重合），作EDF ∠交BC 于点F ，且60EDF ∠=︒，则BEF 周长的最小值是（ ）A ．6B ．43C ．43+D ．423+ 10．如图，矩形纸片ABCD 中，6AB =，10AD =，折叠纸片，使点A 落在BC 边上的点A 处，折痕为PQ ，当点1A 在BC 边上移动时，折痕的端点P 、Q 分别在AB 、AD 边上移动，则当1A B 最小时其值为（ ）A ．2B ．3C ．4D ．511．如图，长方形纸片ABCD ，点E ，M ，N 分别在边AB ，BC ，AD 上，将纸片分别沿EN ，EM 对折，使点A 落在点'A 处，点B 落在点'B 处，若''30A EB ∠=︒，则NEM ∠的度数为（ ）A ．70︒B ．75︒C ．80︒D ．85︒12．如图，矩形纸片ABCD 中，4AB =，3AD =，折叠纸片使AD 边与对角线BD 重合，则折痕为DG 的长为（ ）A 3B 423C ．2D 352二、填空题13．如图，四边形ABCD 为菱形，以AD 为斜边的Rt AED △的面积为3，2DE =，点E ，C 在BD 的同侧，点P 是BD 上的一动点，则PE PC +的最小值是_____________．14．如图，点O 是菱形ABCD 对角线的交点，DE //AC ，CE //BD ，连接OE ，设AC ＝12，BD ＝16，则OE 的长为_____．15．如图，在平行四边形ABCD 中，BE 平分ABC ∠，CF BE ⊥，连接AE ，G 是AB 的中点，连接GF ，若4AE =，则GF =_____．16．如图，在正八边形ABCDEFGH 中，AE 是对角线，则EAB ∠的度数是__________．17．如图，点E 是长方形纸片DC 上的中点，将C ∠过E 点折起一个角，折痕为EF ，再将D ∠过点E 折起，折痕为GE ，且C ，D 均落在GF 上的一点H 处．若1649'∠=︒，则CEF ∠=_______．18．如图，在Rt ABC ∆中，90,6,10ACB AC AB ∠===，过点A 作//,AM CB CE 平分ACB ∠交AM 于点,E Q 是线段CE 上的点，连接BQ ，过点B 作BP BQ ⊥交AM 于点P ，当PBQ ∆为等腰三角形时，AP =________________________．19．如图，90MON ∠=︒，矩形ABCD 的顶点A ，B 分别在边OM ，ON 上，当点B 在边ON 上移动时，点A 随之在边OM 上移动，2AB =，1BC =，运动过程中，点D 到点O 的最大距离为______．20．如图在矩形ABCD 中，对角线,AC BD 相交于点O ，若30,2ACB AB ︒∠==，则BD 的长为_______．三、解答题21．如图，在ABC 中，D 是AB 的中点，AC ＝2，BC ＝22，AB ＝23，延长AC 到E ，使得CE ＝CD ，连接BE ．（1）求证：∠ACB ＝90°；（2）求线段BE 的长度．22．如图，BD 为ABC 的角平分线，E 为AB 上一点，BE BC =，连结DE ． （1）求证：BDC BDE ≅△△；（2）若7AB =，2CD =，90︒∠=C ，求ABD △的面积．23．已知：平行四边形ABCD 中，点M 为边CD 的中点，点N 为边AB 的中点，联结AM 、CN ．（1）求证：AM ∥CN ；（2）过点B 作BH AM ⊥，垂足为H ，联结CH ．求证：△BCH 是等腰三角形．24．如图，在正方形中ABCD ，E 是AB 上一点，F 是AD 延长线上一点，且DF BE =．（1）求证：CE CF =；（2）若点G 在AD 上，且45GCE ︒∠=，判断线段GE BE GD 、、之间的数量关系，并说明理由．25．如图，在矩形ABCD 中，M ，N 分别是AD ，BC 的中点，P ，Q 分别是BM ，DN 的中点．（1）求证：四边形BNDM 是平行四边形．（2）猜想：四边形MPNQ 是哪种特殊的平行四边形？并证明你的猜想．26．如图，在直角ABC 中，90BAC ∠=︒，点D 是BC 上一点，连接AD ，把AD 绕点A 逆时针旋转90°，得到AE ，连接DE 交AC 于点M ．（1）如图1，若2,30,AB C AD BC =∠=︒⊥，求CD 的长；（2）如图2，若45ADB ∠=︒，点N 为ME 上一点，12MN BC =，求证：AN EN CD =+；（3）如图3，若30C ∠=︒，点D 为直线BC 上一动点，直线DE 与直线AC 交于点M ，当ADM △为等腰三角形时，请直接写出此时CDM ∠的度数．【参考答案】***试卷处理标记，请不要删除一、选择题1．B解析：B【分析】先把每一个命题的条件和结论互换就得到它的逆命题，再进行判断即可．【详解】解：“全等三角形的对应角相等”的逆命题是“三组角分别对应相等的两个三角形全等”，逆命题是假命题，故①不符合题意；“两直线平行，同位角相等”的逆命题是“同位角相等，两直线平行”，逆命题是真命题，故②符合题意；“等腰三角形的两个底角相等”的逆命题是“在一个三角形中，有两个角相等的三角形是等腰三角形”，逆命题是真命题，故③符合题意；“正方形的四个角相等”的逆命题是“四个角相等的四边形是正方形”，逆命题是假命题，故④不符合题意；综上：符合题意的有②③．故选：.B【点睛】本题考查的是命题与逆命题，命题真假的判断，正方形的判定方法，掌握由原命题得到逆命题，以及判断命题的真假是解题的关键．2．B解析：B【分析】连接CG ，由正方形的对称性，易知AG=CG ，由正方形的对角线互相平分一组对角，GE ⊥DC ，易得DE=GE ．在矩形GECF 中，EF=CG ．要计算小聪走的路程，只要得到小聪比小敏多走了多少就行．【详解】解：连接GC ，∵四边形ABCD 为正方形，所以AD=DC ，∠ADB=∠CDB=45°，∵∠CDB=45°，GE ⊥DC ，∴△DEG 是等腰直角三角形，∴DE=GE ．在△AGD 和△GDC 中，AD CD ADG CDG DG DG ⎧⎪∠∠⎨⎪⎩＝＝＝，∴△AGD ≌△GDC （SAS ）∴AG=CG ，在矩形GECF 中，EF=CG ，∴EF=AG ．∵BA+AD+DE+EF-BA-AG-GE ，=AD=1500m ．∵小敏共走了3100m ，∴小聪行走的路程为3100+1500=4600（m ），故选：B ．【点睛】本题考查了正方形的性质、全等三角形的性质和判定、矩形的性质及等腰三角形的性质．解决本题的关键是证明AG=EF ，DE=GE ．3．D解析：D【分析】求出BD AD =，DBF DAN ∠=∠，BDF ADN ∠=∠，证明()FBD NAD ASA ≅即可判断①，证明()AFB CNA ASA ≅，推出CN AF AE ==即可判断④，证明()ABM NBM ASA ≅，得AM MN =，由直角三角形斜边的中线的性质推出AM DM MN ==，ADM ABM ∠=∠，即可判断③，根据三角形外角性质求出DNM ∠，证明MDN DNM ∠=∠，即可判断②．【详解】解：∵90BAC ∠=︒，AB AC =，AD BC ⊥，∴45ABC C ∠=∠=︒，AD BD CD ==，90ADN ADB ∠=∠=︒，∴45BAD CAD ∠=︒=∠，∵BE 平分ABC ∠， ∴122.52ABE CBE ABC ∠=∠=∠=︒， ∴9022.567.5BFD AEB ∠=∠=︒-︒=︒，∴67.5AFE BFD AEB ∠=∠=∠=︒，∴AF AE =，AM BE ⊥，∴90AMF AME ∠=∠=︒，∴9067.522.5DAN MBN ∠=︒-︒=︒=∠，在FBD 和NAD 中，FBD DAN BD ADBDF ADN ∠=∠⎧⎪=⎨⎪∠=∠⎩， ∴()FBD NAD ASA ≅，∴DF DN =，故①正确；在AFB △和CNA 中，4522.5BAF C AB ACABF CAN ∠=∠=︒⎧⎪=⎨⎪∠=∠=︒⎩， ∴()AFB CNA ASA ≅，∴AF CN =，∵AF AE =，∴AE CN =，故④正确；在ABM 和NBM 中，90ABM NBM BM BMAMB NMB ∠=∠⎧⎪=⎨⎪∠=∠=︒⎩，∴()ABM NBM ASA ≅，∴AM MN =，在Rt ADN △中，AM DM MN ==，∴22.5DAN ADM ABM ∠=∠=︒=∠，∴22.522.545DMN DAN ADM ∠=∠+∠=︒+︒=︒，∴DM 平分BMN ∠，故③正确；∵4522.567.5DNA C CAN ∠=∠+∠=︒+︒=︒，∴1804567.567.5MDN DNM ∠=︒-︒-︒=︒=∠，∴DM MN =，∴DMN 是等腰三角形，故②正确．故选：D ．【点睛】 本题考查了全等三角形的性质与判断，三角形外角性质，三角形内角和定理，直角三角形斜边上中线的性质，等腰三角形的性质和判定，解题的关键是熟练掌握这些性质定理进行证明求解．4．C解析：C【分析】延长CD 到G ，使DG=BE ，连接AG ，易证ADG ABE △≌△所以AE=AG ，BAE=DAG ∠∠ ， 证AFG AEG △≌△，所以 GF=EF ，设BE=DG=x ，则EF=FG=x+2，在ECF Rt △中，利用勾股定理得222462x x 解得求出x ，最后求AGF S △问题即可求解．【详解】解：延长CD 到G ，使DG=BE ，连接AG ，在正方形ABCD 中，AB=AD ，90ADB B C ADC ∠=∠=∠=∠=︒ 90ADG B ∴∠=∠=︒，ADG ABE(SAS)∴△≌△，,AG AE BAE DAG ∴=∠=∠，45EAF ∠=︒ ，45DAF BAE ∴∠+∠=︒ ，GAF=45DAG DAF ∴∠∠+∠=︒，GAF=EAF ∴∠∠，又AF=AF ，AFG AEG ∴△≌△(SAS)，EF=FG ∴，设BE=DG=x ，则EC=6-x ，FC=4，EF=FG=x+2，在ECF Rt △中，222=FC CE EF +，()()22246=2x x ∴+-+，解得，x=3， GF=DG DF=2+3=5∴+，AEF AGF 11S =S =GF AD=56=1522∴⨯⨯△△， 故选：C ．【点睛】本题考查了正方形的性质，全等三角形的判定和性质，勾股定理，正确构造辅助线，证三角形全等是解决本题的关键.5．B 解析：B【分析】根据矩形的性质及正方形的判定进行分析即可．【详解】解：四边形ABCD 是矩形，AC BD ⊥，∴矩形ABCD 是正方形；四边形ABCD 是矩形，//AD BC ∴，DAC BCA ∴∠=∠，AC 平分BAD ∠，BAC DAC ∴∠=∠，BAC ACB ∴∠=∠，∴AB BC =，∴矩形ABCD 是正方形；ADB ABD ∠=∠，∴AB AD =，∴四边形ABCD 是矩形，∴矩形ABCD 是正方形；故选：B ．【点睛】本题考查矩形的判定，解题的关键是掌握正方形的判定方法．6．D解析：D【分析】根据邻边相等的平行四边形是菱形；根据所给条件可以证出邻边相等；根据有一个角是直角的平行四边形是矩形；根据对角线相等的平行四边形是矩形．【详解】解：A 、根据邻边相等的平行四边形是菱形可知：四边形ABCD 是平行四边形，当AB BC =时，它是菱形，故本选项不符合题意；B 、根据对角线互相垂直的平行四边形是菱形知：当AC BD ⊥时，四边形ABCD 是菱形，故本选项不符合题意；C 、根据有一个角是直角的平行四边形是矩形知：当90ABC ∠=时，四边形ABCD 是矩形，故本选项不符合题意；D 、根据对角线相等的平行四边形是矩形可知：当AC BD =时，它是矩形，不是正方形，故本选项符合题意；综上所述，符合题意是D 选项；故选：D ．【点睛】本题考查了对矩形的判定、菱形的判定，正方形的判定的应用，能正确运用判定定理进行判断是解此题的关键，难度适中．7．C解析：C【分析】由折叠结合矩形的性质先证明,BE DE =设,BE DE x == 则8,AE x =- 再利用勾股定理求解,x 从而可得BDE 的面积．【详解】 解： 长方形ABCD ，8,4,AD AB ==//,AD BC ∴,ADB CBD ∴∠=∠由对折可得：,CBD C BD '∠=∠,ADB C BD '∴∠=∠,BE DE ∴=设,BE DE x == 则8,AE x =-由222,BE AB AE =+ ()22248,x x ∴=+-1680,x ∴=5,x ∴= 5,DE BE ∴==115410.22BDE S DE AB ∴==⨯⨯= 故选：.C【点睛】本题考查的是矩形与折叠问题，勾股定理的应用，矩形的性质，掌握以上知识是解题的关键．8．A解析：A【分析】根据题意可得,CAB DBA ABC BAD ∠=∠∠=∠，再由直角三角形斜边的中线等于斜边的一半，可证CM DM AM BM ===，继而证明()AMC BMD SSS △≌△，解得1802AMC BMD CAM ∠=∠=︒-∠，最后根据三角形内角和180°定理，分别解得αβ、与CAM ∠的关系，整理即可解题．【详解】Rt Rt ABC BAD △≌△,CAB DBA ABC BAD ∴∠=∠∠=∠M 是AB 的中点，11,22CM AB DM AB ∴== CM DM AM BM ∴===∴∠CAM=∠MCA ，Rt Rt ABC BAD △≌△AC BD ∴=()AMC BMD SSS △≌△1802AMC BMD CAM ∴∠=∠=︒-∠CMD α∴=∠180AMC BMD =︒-∠-∠1802(1802)CAM =︒-⨯︒-∠4180CAM =∠-︒90ABC BAD CAM ∠=∠=︒-∠，AEB β=∠=180BAD ABC ︒-∠-∠180(90)(90)CAM CAM =︒-︒-∠-︒-∠2CAM =∠2180βα∴-=︒故选：A ．【点睛】本题考查全等三角形的判定与性质、直角三角形斜边中线的性质、等腰三角形的性质、三角形内角和180°等知识，是重要考点，难度较易，掌握相关知识是解题关键． 9．D解析：D【分析】只要证明DBE DCF ∆≅∆得出DEF ∆是等边三角形，因为BEF ∆的周长4BE BF EF BF CF EF BC EF EF =++=++=+=+，所以等边三角形DEF ∆的边长最小时，BEF ∆的周长最小，只要求出DEF ∆的边长最小值即可．【详解】解：连接BD ，菱形ABCD 中，60A ∠=︒，ADB ∴∆与CDB ∆是等边三角形，60DBE C ∴∠=∠=∠︒，BD DC =，60EDF ∠=︒，BDE CDF ∴∠=∠，在BDE ∆和CDF ∆中，DBE C BDE CDF BD CD ∠=∠⎧⎪∠=∠⎨⎪=⎩，DBE DCF ∴∆≅∆，DE DF ∴=，BDE CDF ∠=∠，BE CF =，60EDF BDC ∴∠=∠=︒，DEF ∴∆是等边三角形，BEF ∆的周长4BE BF EF BF CF EF BC EF EF =++=++=+=+，∴等边三角形DEF ∆的边长最小时，BEF ∆的周长最小，当DE AB ⊥时，DE最小=，BEF ∴∆的周长最小值为4+，故选：D ．【点睛】本题考查菱形的性质、全等三角形的判定和性质、等边三角形的判定和性质、最小值问题等知识，解题的关键是正确寻找全等三角形，利用全等三角形的性质解决问题，学会转化的思想解决问题，所以中考常考题型．10．A解析：A【分析】根据翻折的性质，可得当Q 与D 重合时，A 1B 最小，根据勾股定理，可得A 1C ，从而可得答案．【详解】解：由折叠可知：当Q 与D 重合时，A 1B 最小，A 1D=AD=10，由勾股定理，得：A 1221A D CD -=8，∴A 1B=10-8=2，故选A ．【点睛】本题考查了翻折变换，利用了翻折的性质得到当Q 与D 重合时，A 1B 最小是解题的关键． 11．B解析：B【分析】先由翻折的性质得到'AEN A EN ∠=∠，'BEM B EM ∠=∠，由图可得''''A EN B EM NEM A EB ∠+∠=∠+∠，然后根据180AEN NEM MEB ∠+∠+∠=︒，得到2''180NEM A EB ∠+∠=︒，进而可求出NEM ∠的度数．【详解】由翻折的性质可知：'AEN A EN ∠=∠，'BEM B EM ∠=∠，由图知：''''A EN B EM NEM A EB ∠+∠=∠+∠，又∵180AEN NEM MEB ∠+∠+∠=︒，∴''180A EN B EM NEM ∠+∠+∠=︒，∴2''180NEM A EB ∠+∠=︒，又∵''30A EB ∠=︒，∴75NEM ∠=︒．故选：B ．【点睛】本题主要考查的是翻折的性质，掌握翻折的性质是解题的关键．12．D解析：D【分析】首先设AG ＝x ，由矩形纸片ABCD 中，AB ＝4，AD ＝3，可求得BD 的长，又由折叠的性质，可求得A′B 的长，然后由勾股定理可得方程：x 2+22＝（4-x ）2，解此方程即可求得AG 的长，继而求得答案．【详解】解：设AG ＝x ，∵四边形ABCD 是矩形，∴∠A ＝90°，∵AB ＝4，AD ＝3，∴BD5，由折叠的性质可得：A′D ＝AD ＝3，A′G ＝AG ＝x ，∠DA′G ＝∠A ＝90°，∴∠BA′G ＝90°，BG ＝AB-AG ＝4-x ，A′B ＝BD-A′D ＝5-3＝2，∵在Rt △A′BG 中，A′G 2+A′B 2＝BG 2，∴x 2+22＝（4-x ）2，解得：x ＝32， ∴AG ＝32，∴在Rt △ADG 中，DG =． 故选：D ．【点睛】 此题考查了折叠的性质、矩形的性质以及勾股定理．此题难度适中，注意掌握折叠前后图形的对应关系，注意掌握数形结合思想与方程思想的应用．二、填空题13．3【分析】根据菱形的轴对称性可得AC 关于BD 对称当APE 三点共线时的值最小为AE 再根据三角形的面积即可得出答案【详解】解：∵四边形菱形∴AC 关于BD 对称∵点EC 在BD 的同侧∴当APE 三点共线时的值最解析：3【分析】根据菱形的轴对称性可得A 、C 关于BD 对称，当A 、P 、E 三点共线时，PE PC +的值最小为AE ，再根据三角形的面积即可得出答案．【详解】解：∵四边形ABCD 菱形，∴A 、C 关于BD 对称，∵点E ，C 在BD 的同侧，∴当A 、P 、E 三点共线时，PE PC +的值最小，且最小值为AE ；∵以AD 为斜边的Rt AED △的面积为3， 2DE =， ∴112322⨯=⨯=AE DE AE ， ∴AE=3， ∴PE PC +的最小值是3故答案为：3．【点睛】本题考查了菱形的性质、最短问题、面积法等知识，解题的关键是利用轴对称解决最值问题，是中考常考题型．14．10【分析】由菱形的性质和勾股定理求出CD ＝20证出平行四边形OCED 为矩形得OE ＝CD ＝10即可【详解】解：∵DEACCEBD ∴四边形OCED 为平行四边形∵四边形ABCD 是菱形∴AC ⊥BDOA ＝O解析：10【分析】由菱形的性质和勾股定理求出CD ＝20，证出平行四边形OCED 为矩形，得OE ＝CD ＝10即可．【详解】解：∵DE //AC ，CE //BD ，∴四边形OCED 为平行四边形，∵四边形ABCD 是菱形，∴AC ⊥BD ，OA ＝OC ＝12AC ＝6，OB ＝OD ＝12BD ＝8，∴∠DOC ＝90︒，CD＝10，∴平行四边形OCED 为矩形，∴OE ＝CD ＝10，故答案为：10．【点睛】本题考查了菱形的性质、矩形的判定与性质以及平行四边形判定与性质等知识；熟练掌握特殊四边形的判定与性质是解题的关键．15．2【分析】根据平行四边形的性质结合角平分线的定义可求解即可得利用等腰三角形的性质得到进而可得是的中位线根据三角形的中位线的性质可求解【详解】解：在平行四边形中∴∵平分∴∴∴∵∴∵是的中点∴是的中位线解析：2【分析】根据平行四边形的性质结合角平分线的定义可求解CBE BEC ∠=∠，即可得CB CE =，利用等腰三角形的性质得到BF EF =，进而可得GF 是ABE △的中位线，根据三角形的中位线的性质可求解．【详解】解：在平行四边形ABCD 中，//AB CD ，∴ABE BEC ∠=∠，∵BE 平分ABC ∠，∴ABE CBE ∠=∠，∴CBE BEC ∠=∠，∴CB CE =，∵CF BE ⊥，∴BF EF =，∵G 是AB 的中点，∴GF 是ABE △的中位线， ∴12GF AE =∵4AE =，∴2GF =； 故答案为：2．【点睛】本题主要考查了平行四边形的性质，等腰三角形的性质与判定，三角形中位线的性质，证明GF 是ABE △的中位线是解题的关键．16．【分析】根据正多边形的性质求解即可【详解】解：∵八边形是正八边形∴=∠HAB=×=故答案为：【点睛】本题主要考查多边形的内角和定理正多边形的性质掌握相关定理是解题的关键解析：67.5︒【分析】根据正多边形的性质求解即可【详解】解：∵八边形ABCDEFGH 是正八边形，∴EAB ∠=12∠HAB=12×()821808-⨯=67.5︒． 故答案为：67.5︒．【点睛】本题主要考查多边形的内角和定理，正多边形的性质，掌握相关定理是解题的关键． 17．【分析】根据翻折的性质可得∠GEH=∠1∠HEF=∠CEF 从而可求出∠DEH∠CEF的度数【详解】解：∵∠GEH=∠1∴∠GEH=∴∠DEH=+=∴∠HEF=∠CEF=×(180°-)=故答案为：【解析：2551'︒【分析】根据翻折的性质可得∠GEH=∠1，∠HEF=∠CEF，从而可求出∠DEH，∠CEF的度数．【详解】解：∵1649'∠=︒，∠GEH=∠1，∴∠GEH=649'︒，∴∠DEH =649'︒+649'︒=12818'︒，∴∠HEF=∠CEF=12×(180°-12818'︒)=2551'︒，故答案为：2551'︒．【点睛】本题考查了翻折变换的性质，熟练掌握折叠的性质找出相等的角是解题的关键．18．【分析】过点P作PG⊥CB交CB的延长线于点G过点Q作QF⊥CB运用AAS定理证明△QBF≌△BPG根据平行线的性质和角平分线的定义求得△AEC为等腰直角三角形利用勾股定理求得线段BC的长然后结合全解析：10【分析】过点P作PG⊥CB，交CB的延长线于点G，过点Q作QF⊥CB，运用AAS定理证明△QBF≌△BPG，根据平行线的性质和角平分线的定义求得△AEC为等腰直角三角形，利用勾股定理求得线段BC的长，然后结合全等三角形和矩形的性质求解．【详解】解：过点P作PG⊥CB，交CB的延长线于点G，过点Q作QF⊥CB∵BP BQ⊥，PG⊥CB∴∠1+∠2=90°，∠2+∠3=90°∴∠1=∠3∵QF⊥CB，BP BQ⊥∴∠QFB=∠PGB=90°又∵PBQ∆为等腰三角形∴QB=PB在△QBF和△BPG中1=3QFB PGB QB PB∠∠⎧⎪∠=∠⎨⎪=⎩∴△QBF≌△BPG∴PG=BF，BG=QF∵∠ACB=90°，CE平分ACB∠∴∠ACE=∠ECB=45°又∵AM∥CB，∴∠AEC=∠ECB=45°∴∠AEC=∠ACE=45°∴△AEC为等腰直角三角形∵AM∥BC，∠ACB=90°∴∠CAM+∠ACB=180°，即∠CAM=90°∴∠CAM=∠ACB=∠PGB=90°∴四边形ACGP为矩形，∴PG=AC=6，AP=CG在Rt△ABC中，BC=228-=AB AC∴CF=BC-BF=BC-PG=8-6=2∵QF⊥BC，∠ECB=45°∴△CQF是等腰直角三角形，即CF=QF=2∴AP=CG=BC+BG=BC+QF=8+2=10【点睛】本题考查矩形的判定和性质、全等三角形的判定和性质以及勾股定理，掌握相关性质定理正确推理论证是解题关键19．【分析】取AB的中点E则OE=1DE=利用三角形原理可确定最大值【详解】如图取AB的中点E连接OEDE∵OE是直角三角形ABO斜边上的中线AB=2∴OE=1在直角三角形DAE中根据勾股定理得DE==21【分析】取AB的中点E，则OE=1，2.【详解】如图，取AB的中点E，连接OE，DE，∵OE是直角三角形ABO斜边上的中线，AB=2，∴OE=1，在直角三角形DAE中，根据勾股定理，得22+2，DA AE∴当O，D，E三点共线时，DO最大，且最大值为2+1，故应该填21+.【点睛】本题考查了线段的最值，构造斜边上的中线，灵活运用三角形原理是解题的关键. 20．4【分析】根据30度所对的直角边等于斜边的一半求出AC=4利用矩形的性质得到BD=AC=4即可【详解】在矩形中∵四边形是矩形故答案为：4【点睛】此题考查矩形的性质直角三角形30度角的性质熟记各性质是解析：4【分析】根据30度所对的直角边等于斜边的一半求出AC=4，利用矩形的性质得到BD=AC=4即可．【详解】在矩形ABCD 中，90ABC ︒∠=，30,2ACB AB ︒∠==，2224AC AB ∴==⨯=，∵四边形ABCD 是矩形，4BD AC ∴==．故答案为：4．【点睛】此题考查矩形的性质，直角三角形30度角的性质，熟记各性质是解题的关键．三、解答题21．（1）见解析；（211【分析】（1）利用勾股定理的逆定理判定AC ⊥BC ；（2）在直角△BCE 中，利用勾股定理来求BE 的长度．【详解】证明：（1）∵在△ABC 中，AC ＝2，BC ＝2，AB ＝3∴AC 2＝4，BC 2＝8，AB 2＝12，∴AC 2+BC 2＝AB 2．∴∠ACB ＝90°；（2）由（1）知，∠ACB ＝90°，则∠BCE ＝90°．∵D 是AB 的中点，AB ＝23，CE ＝CD ，∴CE ＝CD ＝12AB ＝3． ∴在直角△BCE 中，由勾股定理得：BE ＝22BC EC +＝22(22)(3)+＝11．【点睛】本题主要考查了勾股定理，勾股定理的逆定理，直角三角形斜边上的中线．注意：勾股定理应用的前提条件是在直角三角形中．22．（1）证明见解析；（2）7【分析】（1）根据角平分线的性质可得DBC DBE ∠=∠，再根据已知条件BE BC =，BD BD =，即可证明；（2）根据（1）中结果，得2DE CD ==，90DEB C ∠=∠=︒，即可求得ABD △的面积．【详解】（1）∵BD 平分ABC ∠，∴DBC DBE ∠=∠，∴在BDC 和BDE 中，BD BD =，DBC DBE ∠=∠，BE BC =，∴BDC ≌BDE ；（2）∵BDC ≌BDE ，∴2DE CD ==，90DEB C ∠=∠=︒，∴1172722ABD S AB DE =⋅=⨯⨯=△． 【点睛】本题考查了角平分线的性质、全等三角形的证明和性质、三角形面积等知识，解题的关键是熟练掌握运用以上知识点．23．（1）见解析；（2）见解析【分析】（1）由四边形ABCD 是平行四边形，根据平行四边形的性质，可得AB ∥CD ，AB=CD ，又由点M 为边CD 的中点，点N 为边AB 的中点，即可得CM=AN ，继而可判定四边形ANCM是平行四边形，则可证得AM ∥CN ．（2）由AM ∥CN ，BH ⊥AM ，点N 为边AB 的中点，可证得BH ⊥CN ，ME 是△BAH 的中位线，则可得CN 是BH 的垂直平分线，继而证得△BCH 是等腰三角形．【详解】解：（1）证明：∵四边形ABCD 是平行四边形，∴AB ∥CD 且AB CD =．∵点M 、N 分别是边CD 、AB 的中点， ∴12CM CD =，1AN AB 2=． ∴CM AN =．又∵AB ∥CD ，∴四边形ANCM 是平行四边形∴AM ∥CN ．（2）设BH 与CN 交于点E ，∵AM ∥CN ，BH ⊥AM ，∴BH ⊥CN ，∵N 是AB 的中点，∴EN 是△BAH 的中位线，∴BE=EH ，∴CN 是BH 的垂直平分线，∴CH=CB ，∴△BCH 是等腰三角形．【点睛】此题考查了平行四边形的判定与性质、线段垂直平分线的性质以及等腰三角形的判定．此题难度适中，注意掌握数形结合思想的应用．24．（1）见解析；（2）GE=BE+GD ，理由见解析【分析】（1）由DF=BE ，四边形ABCD 为正方形可证△CEB ≌△CFD ，从而证出CE=CF ；（2）由（1）得，CE=CF ，∠BCE+∠ECD=∠DCF+∠ECD 即∠ECF=∠BCD=90°又∠GCE=45°所以可得∠GCE=∠GCF ，故可证得△ECG ≌△FCG ，即EG=FG=GD+DF ．又因为DF=BE ，所以可证出GE=BE+GD ．【详解】解：（1）证明：∵四边形ABCD 是正方形，∴BC=CD ，∠B=∠CDA ，∴∠B=∠CDF ，在△CBE 与△CDF 中，BC CD B CDF BE DF ⎧⎪∠∠⎨⎪⎩＝＝＝，∴△CBE ≌△CDF （SAS ），∴CE=CF ；（2）GE=BE+GD ，理由：由（1）得△CBE ≌△CDF ，∴∠BCE=∠DCF ，CE=CF ．∵∠GCE=45°，∴∠BCE+∠DCG=45°，∴∠GCF=∠DCF+∠DCG=45°，在△ECG 与△FCG 中，CE CF GCE GCF GC GC ⎧⎪∠∠⎨⎪⎩＝＝＝，∴△ECG ≌△FCG （SAS ），∴GE=GF ，∴GE=DF+GD=BE+GD ．【点睛】本题主要考查正方形的性质以及全等三角形的判定和性质，证两条线段相等往往转化为证明这两条线段所在三角形全等，在第二问中也考查了通过全等找出和GE 相等的线段，从而得出线段GE ，BE ，GD 之间的数量关系．25．（1）见解析；（2）菱形，理由见解析【分析】（1）因为M ，N 分别是AD ，BC 的中点，由矩形的性质可得DM=BN ，DM ∥BN ，利用平行四边形的判定定理可得结论；（2）由四边形DMBN 是平行四边形，求出BM=DN ，BM ∥DN ，求出三角形MPNQ 是平行四边形，根据直角三角形斜边上中线性质求出MQ=NQ ，根据菱形判定推出即可．【详解】解：（1）证明：∵四边形ABCD 是矩形，∴AD ∥BC ，AD=BC ，∵M 、N 分别AD 、BC 的中点，∴DM=BN ，∴四边形DMBN 是平行四边形；（2）四边形MPNQ 是菱形．∵四边形DMBN 是平行四边形，∴BM=DN ，BM ∥DN ，∵P 、Q 分别BM 、DN 的中点，∴MP=NQ ，MP ∥NQ ，∴四边形MPNC 是平行四边形，连接MN ，∵四边形ABCD 是矩形，∴AD ∥BC ，AD=BC ，∵M 、N 分别AD 、BC 的中点，∴DM=CN ，∴四边形DMNC 是矩形，∴∠DMN=∠C=90°，∵Q 是DN 中点，∴MQ=NQ ，∴四边形MPNQ 是菱形．【点睛】本题考查了平行四边形的性质和判定，菱形的判定，矩形的性质，综合运用各性质定理是解答此题的关键26．（1）3；（2）见解析；（3）60︒或15︒或37.5︒【分析】（1）根据含30°角的直角三角形的性质可得BC=2AB=4，BD=12AB=1，即可得出CD 的长；（2）在BD 上截取DF=EN ，可证出AEN ADF △≌△，由全等三角形的性质得AN=AF ，,EAN DAF ANE AFD ∠=∠∠=∠，可得出,MAN BAF ANM AFB ∠=∠∠=∠，则AMN ABF △≌△，可得12BF MN BC ==，即F 是BC 的中点，可得出AN=AF=FC=DF+CD=EN+CD ；（3）由题意可得AD=AE ，90EAD ∠=︒，45EDA AED ∠=∠=︒，分三种情况：①AM=MD ，②AM=AD ，③AD=MD ，根据等腰三角形的性质求出AMD ∠的度数，再根据三角形外角的性质即可求解．【详解】解：（1）∵90BAC ∠=︒，2,30AB C =∠=︒，∴BC=2AB=4，60B ∠=︒，∵AD BC ⊥∴90,30ADB BAD ∠=︒∠=︒，∴BD=12AB=1， ∴CD =BC-BD=4-1=3；（2）证明：如图2，在BD 上截取DF=EN ，∵把AD 绕点A 逆时针旋转90°，得到AE ，∴AD=AE ，90EAD ∠=︒，45EDA AED ∠=∠=︒，∵45ADB ∠=︒，∴45ADF AEN ∠=∠=︒，∴AEN ADF △≌△，∴AN=AF ，,EAN DAF ANE AFD ∠=∠∠=∠，∵90EAD ∠=︒，EAN DAF ∠=∠，∴90NAF ∠=︒，∵90BAC ∠=︒，ANE AFD ∠=∠，∴,MAN BAF ANM AFB ∠=∠∠=∠，∵AN=AF ，∴AMN ABF △≌△，∴12BF MN BC ==，即F 是BC 的中点， ∴AF=FC=DF+CD=EN+CD ，∵AN=AF ，∴AN EN CD =+；（3）解：由题意可得AD=AE ，90EAD ∠=︒， ∴45EDA AED ∠=∠=︒，分三种情况：①AM=MD 时，∵AM=MD ，∴45EDA MAD ∠=∠=︒，∴90AMD ∠=︒，∵30C ∠=︒，∴CDM AMD C ∠=∠-∠=60︒；②AM=AD 时，∵AM=AD ，∴45EDA AMD ∠=∠=︒，∵30C ∠=︒，∴CDM AMD C ∠=∠-∠=15︒；③AD=MD 时，∵AD=MD ，∴AMD MAD ∠=∠，∴45EDA ∠=︒， ∴1804567.52AMD MAD ︒-︒∠=∠==︒， ∵30C ∠=︒，∴CDM AMD C ∠=∠-∠=37.5︒．∴当ADM △为等腰三角形时，CDM ∠的度数为60︒或15︒或37.5︒．【点睛】本题主要考查了几何变换综合题，需要熟练掌握旋转的性质，直角三角形的性质，直角三角形斜边上中线的性质以及全等三角形的判定与性质，等腰三角形的性质，解题的关键是学会添加常用辅助线，正确寻找全等三角形解决问题．。