吉大附中2019-12期末试题
2019-2020学年吉林大学附中七年级(上)期末数学试卷(解析版)
2019-2020学年吉林大学附中七年级（上）期末数学试卷一、选择题1、20181-的相反数是（ ） A 、20181-B 、2018-C 、20181D 、2018 2、下列四个几何体中，主视图与左视图相同的几何体有（ ）A 、1个B 、2个C 、3个D 、4个3、下列合并同类项的结果正确的是（ ）A 、233a a a =+B 、2-3=a aC 、ab b a 33=+D 、2222-3-a a a =4、下列调查中，适合采用普查方法的是（ ）A 、对全市中学生使用“小影”情况的调查B 、对东风渠河水质量情况的调查C 、对旅客上飞机前的安检D 、对某类烟花爆竹燃放安全情况的调查5、如图所示，能用1,,∠∠∠O AOB 三种方法表示同一个角的图形是（ ）6、在数轴上到原点距离等于2的点所表示的数是（ ）A 、2±B 、2C 、-2D 、不能确定7、下列数中，不可能是某月相邻的三个日期之和的是（ ）A 、24B 、43C 、57D 、698、若整式b a b a m n 3212+化简的结果是单项式，则n m +的值是（ ）A 、2B 、3C 、4D 、5二、填空题9．（3分）计算：|﹣3|﹣2＝ ．10．（3分）如图是一个计算程序，若输入a 的值为﹣2，则输出的结果应为 ．11．（3分）已知∠α与∠β互余，且∠α＝35°18′，则∠β＝°′．12．（3分）如图，C岛在A岛的北偏东45°方向，在B岛的北偏西25°方向，则∠ACB ＝°．13．（3分）如图，将一副直角三角板叠在一起，使直角顶点重合于点O，则∠AOB+∠DOC ＝度．14．（3分）龙龙做事很认真，每次大扫除都会把桌椅排的很整齐!他先把每一列最前和最后的课桌摆好，然后再一次摆中间的课桌，一会儿一列课桌摆在一条线上整整齐齐的，这是因为．15．（3分）设a﹣3b＝5，则2（a﹣3b）2+3b﹣a﹣15的值是．16．（3分）如图，已知O是直线AB上一点，∠1＝20°，OD平分∠BOC，则∠2的度数是度．17．（3分）如图是一个正方体的平面展开图，正方体中相对的面上的数字或代数式互为相反数，则2x+3y的值为．18．（3分）在同一平面内，两条直线相交时最多有1个交点，三条直线相交时最多有3个交点，四条直线相交时最多有6个交点，…，那么十条直线相交时最多有个交点．三、计算题19．（1）﹣（+9）﹣12﹣（）（2）4﹣2×（﹣3）2+6÷（﹣）（3）化简：5（a2+5a）﹣（a2+7a）（4）先化简，再求值：2（a2b+ab2）﹣3（a2b﹣1）﹣2ab2﹣4，其中a＝2018，b＝．四、解答题20．小区规划一个长70m、宽30m的长方形草坪上修建三条同样宽的甬道，使其中两条与AB平行，另一条与BC平行，场地其余部分种草，甬道的宽度为xm．（1）用含x的代数式表示草坪的总面积S；（2）如果每一块草坪的面积都相等，且甬道的宽为1m，那么每块草坪的面积是多少平方米？（精确到0.1）21．用5个棱长为1的正方体组成如图所示的几何体．（1）该几何体的体积是立方单位，表面积是平方单位（包括底面积）；（2）请在方格纸中用实线画出它的三个视图．22．如图，直线AB、CD相交于点O，OE平分∠BOD（1）若∠AOC＝60°，求∠BOE的度数；（2）若OF平分∠AOD，试说明OE⊥OF．23．如图，已知AC⊥AE，BD⊥BF，∠1＝15°，∠2＝15°，AE与BF平行吗？为什么？24．如图a是长方形纸带（提示：AD∥BC），将纸带沿EF折叠成图b，再沿GF折叠成图c．（1）若∠DEF＝20°，则图b中∠EGB＝，∠CFG＝；（2）若∠DEF＝20°，则图c中∠EFC＝；（3）若∠DEF＝α，把图c中∠EFC用α表示为；（4）若继续按EF折叠成图d，按此操作，最后一次折叠后恰好完全盖住∠EFG，整个过程共折叠了9次，问图a中∠DEF的度数是．25．如图，从数轴上的原点开始，先向左移动2cm到达A点，再向左移动4cm到达B点，然后向右移动10cm到达C点．（1）用1个单位长度表示1cm，请你在题中所给的数轴上表示层A、B、C三点的位置；（2）把点C到点A的距离记为CA，则CA＝cm；（3）若点B以每秒3cm的速度向左移动，同时A、C点以每秒lcm、5cm的速度向右移动，设移动时间为t（t＞0）秒，试探究CA﹣AB的值是否会随着t的变化而改变？请说明理由．26．【问题原型】如图①，AB∥CD，点M在直线AB、CD之间，则∠M＝∠B+∠D，小明解决上述问题的过程如下：如图②，过点M作MN∥AB则∠B＝（）∵AB∥CD，（已知）MN∥AB（辅助线的做法）∴MN∥CD（）∴∠＝∠D（）∴∠B+∠D＝∠BMD请完成小明上面的过程．【问题迁移】如图③，AB∥CD，点M与直线CD分别在AB的两侧，猜想∠M、∠B、∠D之间有怎样的数量关系，并加以说明．【推广应用】（1）如图④，AB∥CD，点M在直线AB、CD之间，∠ABM的平分线与∠CDM的平分线交于点N，∠M＝96°，则∠N＝°；（2）如图⑤，AB∥CD，点M与直线CD分别在AB的两侧，∠ABM的平分线与∠CDM 的平分线交于点N，∠N＝25°，则∠M＝°；（3）如图⑥，AB∥CD，∠ABG的平分线与∠CDE的平分线交于点M，∠G＝78°，∠F＝64°，∠E＝64°，则∠M＝°．2019-2020学年吉林大学附中七年级（上）期末数学试卷参考答案与试题解析一、选择题1．【解答】解：A、﹣2＜﹣1，故A正确；B、﹣1＝﹣1，故B错误；C、﹣＞﹣1，故C错误；D、1＞﹣1，故D错误；故选：A．2．【解答】解：A、不是正方体展开图，故选项错误；B、有田字格，不是正方体展开图，故选项错误；C、不是正方体展开图，故选项错误；D、1﹣4﹣1型，是正方体展开图，故选项正确．故选：D．3．【解答】解：11700000用科学记数法表示为1.17×107，故选：B．4．【解答】解：（A）原式＝x2﹣2xy2，故A错误；（B）原式＝2a﹣3b，故B错误；（C）原式＝a2+a3，故C错误；故选：D．5．【解答】解：如图1，由M是AB的中点，N是BC的中点，得MB＝AB＝4cm，BN＝BC＝1cm，由线段的和差，得MN＝MB+BN＝4+1＝5cm；如图2，由M是AB的中点，N是BC的中点，得MB＝AB＝4cm，BN＝BC＝1cm，由线段的和差，得MN＝MB﹣BN＝4﹣1＝3cm；故选：B．6．【解答】解：如图，∵直线a∥b，∴∠3＝∠1＝60°．∵AC⊥AB，∴∠3+∠2＝90°，∴∠2＝90°﹣∠3＝90°﹣60°＝30°，故选：D．7．【解答】解：设小长方形卡片的长为a，宽为b，∴L上面的阴影＝2（n﹣a+m﹣a），L下面的阴影＝2（m﹣2b+n﹣2b），∴L总的阴影＝L上面的阴影+L下面的阴影＝2（n﹣a+m﹣a）+2（m﹣2b+n﹣2b）＝4m+4n﹣4（a+2b），又∵a+2b＝m，∴4m+4n﹣4（a+2b），＝4n．故选：B．8．【解答】解：a0＝0，a1＝﹣|a0+1|＝﹣|0+1|＝﹣1，a2＝﹣|a1+2|＝﹣|﹣1+2|＝﹣1，a3＝﹣|a2+3|═﹣|﹣1+3|＝﹣2，a4＝﹣|a3+4|═﹣|﹣2+4|＝﹣2，a5＝﹣|a4+4|＝﹣|﹣2+5|＝﹣3；a6＝﹣|a5+4|＝﹣|﹣3+6|＝﹣3；a7＝﹣|a6+7|＝﹣|﹣3+7|＝﹣4……由此可以看出，这列数是0，﹣1，﹣1，﹣2，﹣2，﹣3，﹣3，﹣4，﹣4，……2019÷2＝1009…1，故a2019＝﹣1009﹣1＝﹣1010故选：B．二、填空题9．【解答】解：|﹣3|﹣2＝3﹣2＝1．10．【解答】解：由图可得，当a＝﹣2时，（a2﹣2）×（﹣3）+4＝[（﹣2）2﹣2]×（﹣3）+4＝（4﹣2）×（﹣3）+4＝2×（﹣3）+4＝（﹣6）+4＝﹣2，故答案为：﹣2．11．【解答】解“∠β＝90°﹣∠α＝90°﹣35°18′＝54°42′．12．【解答】解：连接AB．∵C岛在A岛的北偏东45°方向，在B岛的北偏25°方向，∴∠CAB+∠ABC＝180°﹣（45°+25°）＝110°，∵三角形内角和是180°，∴∠ACB＝180°﹣（∠CAB+∠ABC）＝180°﹣110°＝70°．故答案为：70．13．【解答】解：如右图所示，∵∠AOD+∠COD＝90°，∠COD+∠BOC＝90°，∠BOD＝∠COD+∠BOC，∠AOD+∠BOD＝∠AOB，∴∠AOD+∠COD+∠COD+∠BOC＝180°，∴∠AOD+2∠COD+∠BOC＝180°，∴∠AOB+∠COD＝180°．故答案是180．14．【解答】解：根据题意，最前与最后的课桌看做两点，排成一条直线，所以应用的是直线的性质：两点确定一条直线．故答案为：两点确定一条直线．15．【解答】解：∵3b﹣a＝﹣5，∴2（a﹣3b）2+3b﹣a﹣15＝2×52﹣5﹣15＝30．16．【解答】解：如图，∵∠1＝20°，∠1+∠BOC＝180°，∴∠BOC＝160°．又∵OD平分∠BOC，∴∠2＝∠BOC＝80°；故填：80．17．【解答】解：正方体的表面展开图，相对的面之间一定相隔一个正方形．“5”与“2x﹣3”是相对面，“y”与“x”是相对面，“﹣2”与“2”是相对面，∵相对的面上的数字或代数式互为相反数，∴2x﹣3+5＝0，x+y＝0，解得x＝﹣1，y＝1，∴2x+3y＝﹣2+3＝1．故答案为：1．18．【解答】解：在同一平面内，两条直线相交时最多有1个交点，三条直线最多有3＝1+2个交点，四条直线最多有6＝1+2+3个交点，…，n条直线最多有1+2+3+4+…+（n﹣1）个交点，即1+2+3+4+…+（n﹣1）＝．当n＝10时，＝45故答案为：45三、计算题19．【解答】解：（1）原式＝﹣﹣21＝﹣21＝；（2）原式＝4﹣2×9﹣12＝4﹣18﹣12＝﹣14﹣12＝﹣26；（3）原式＝5a2+25a﹣a2﹣7a＝4a2﹣18a；（4）原式＝2a2b+2ab2﹣3a2b+3﹣2ab2﹣4＝﹣a2b﹣1，当a＝2018，b＝时，原式＝﹣20182×﹣1＝﹣2018﹣1＝﹣2019；四、解答题20．【解答】解：（1）S＝70×30﹣（70x+2×30x﹣2x2）＝2x2﹣130x+2100；（2）当x＝1时，S＝2×12﹣130×1+2100＝1972m2所以每一块草坪的面积为1972÷6＝328.6m2答：每一块草坪的面积是328.6m2．21．【解答】解：（1）几何体的体积：1×1×1×5＝5（立方单位），表面积：22（平方单位）；故答案为：5，22；（2）如图所示：22．【解答】解：（1）∵直线AB、CD相交于点O，∴∠BOD＝∠AOC＝60°，又∵OE平分∠BOD，∴∠BOE＝∠BOD＝30°；（2）∵OF平分∠AOD，∴∠DOF＝∠AOD，又∵OE平分∠BOD，∴∠DOE＝∠BOD，∴∠EOF＝∠DOF+∠DOE＝（∠AOD+∠BOD）＝×180°＝90°．∴OE⊥OF．23．【解答】解：AE∥BF．理由如下：因为AC⊥AE，BD⊥BF（已知），所以∠EAC＝∠FBD＝90°（垂直的定义）．因为∠1＝∠2（已知），所以∠EAC+∠1＝∠FBD+∠2（等式的性质），即∠EAB＝∠FBG，所以AE∥BF（同位角相等，两直线平行）．24．【解答】解：（1）∵长方形的对边是平行的，∴∠BFE＝∠DEF＝20°，∴∠EGB＝∠BFE+∠DEF＝40°，∴∠FGD＝∠EGB＝40°，∴∠CFG＝180°﹣∠FGD＝140°；故答案为：40°，140°；（2）∵长方形的对边是平行的，∴∠BFE＝∠DEF＝20°，∴图a、b中的∠CFE＝180°﹣∠BFE，以下每折叠一次，减少一个∠BFE，∴图c中的∠CFE度数是120°；故答案为：120°；（3）由（2）中的规律，可得∠CFE＝180°﹣3α．故答案为：180°﹣3α；（3）设图a中∠DEF的度数是x°，由（2）中的规律，可得180﹣10x＝0．解得：x＝18．故答案为：18°．25．【解答】解：（1）如图所示：（2）CA＝4﹣（﹣2）＝4+2＝6（cm）；故答案为：6．（3）CA﹣AB的值不会随着t的变化而变化，理由如下：根据题意得：CA＝（4+5t）﹣（﹣2+t）＝6+4t，AB＝（﹣2+t）﹣（﹣6﹣3t）＝4+4t，∴CA﹣AB＝（6+4t）﹣（4+4t）＝2，∴CA﹣AB的值不会随着t的变化而变化．26．【解答】解：【问题原型】如图①，过点M作MN∥AB，则∠B＝∠BMN（两直线平行，内错角相等）∵AB∥CD，（已知）∴MN∥AB（辅助线的做法）∴MN∥CD（平行于同一条直线的两直线平行）∴∠NMD＝∠D（两直线平行，内错角相等）∴∠B+∠D＝∠BMD，故答案为：∠BMN，两直线平行，内错角相等，平行于同一条直线的两直线平行，∠NMD，两直线平行，内错角相等，【问题迁移】过点M作MN∥AB，∴∠1＝∠B，∵AB∥CD，∴MN∥AB，∴∠NMD＝∠D，∵∠NMD＝∠1+∠BMD，∴∠BMD＝∠D﹣∠B；【推广应用】如图④，由如图①的结论可得，∠ABM+∠CDM＝∠M＝96°，∠N＝∠ABN+∠CDN，∵BN，DN分别平分∠ABM，∠CDM，∴∠ABN+∠CDN＝＝（∠ABM+∠CDM）＝48°，∴∠N＝48°；如图⑤，由如图②的结论可得，∠M＝∠CDM﹣∠ABM，∵BN，DN分别平分∠ABM，∠CDM，∴∠CDN﹣∠ABN＝∠CDM﹣∠ABM＝（∠CDM﹣∠ABM）＝M＝∠N＝25°，∴∠M＝50°；如图⑥，过G，F，E分别作GN∥AB，FH∥AB，EP∥AB，∵AB∥CD，∴AB∥GN∥FH∥EP∥CD，∴∠2＝∠GFH，∠3＝∠EFH，∴∠2+∠3＝∠GFE＝64°，∴∠1+∠4＝∠BGF+∠DEF﹣∠GFE＝78°，∵AB∥GN，EP∥CD，∴∠ABG＝∠1，∠CDE＝∠4，∴∠ABG+∠CDE＝78°，∵BM，DM分别平分∠ABG，∠CDE，∴∠ABM＝∠ABG，∠CDM＝∠CDE，由如图①中的结论可得∠M＝∠ABM+∠CDM＝（∠ABG+∠CDE）＝78°＝39°，故答案为：48，50，39．。
2019-2020学年吉林省长春市吉大中学高一物理期末试卷含解析
2019-2020学年吉林省长春市吉大中学高一物理期末试卷含解析一、选择题：本题共5小题，每小题3分，共计15分．每小题只有一个选项符合题意1. 某校高一的新同学分别乘两辆汽车去参加社会实践活动，两辆汽车在平直公路上运动，甲车内一同学看见乙车没有运动，而乙车内一同学看见路旁的树木向西移动．如果以地面为参考系，那么，上述观察说明（）A．甲、乙两车以相同的速度都向西运动B．乙车不动，甲车向东运动C．甲车向西运动，乙车向东运动D．甲、乙两车以相同的速度都向东运动参考答案：D【考点】参考系和坐标系．【分析】参考系是描述运动时，假设不动的物体．甲车内人看到乙没有动，则甲和乙的运动情况一样，乙车中的人看到路旁的树木向西运动，说明乙向东运动．【解答】解：因为甲车看乙车没有动，则甲和乙的运动情况一致，而乙车的人看到路旁的树木向西运动，说明乙车相对路旁的树木向东运动，则如果以大地为参考系则乙向东运动，因为甲车和乙车运动状态一致，故甲、乙两车以相同的速度向东运动．故D正确．故选：D．2. 如图所示，一物体恰能在一个斜面体上沿斜面匀速下滑，设此过程中斜面受到水平地面的摩擦力为f1。
若沿斜面向下方向用力向下推此物体，使物体加速下滑，设此过程中斜面受到地面的摩擦力为f2。
则（）A．f1为零，f2为零 B．f1为零，f2不为零C．f1不为零，f2为零 D．f1不为零，f2不为零参考答案：A3. 甲、乙两物体先后从同一地点出发，沿一条直线运动，它们的v-t图象如图所示，由图可知A．甲总是比乙运动快，且提前出发，所以乙追不上甲B．在t=20s之前，甲比乙运动快，t=20s之后乙比甲运动快，所以乙可以追上甲C．t=20s时，乙追上了甲D．由于乙在t=10s时才开始运动，所以t=10s时，甲在乙前面，它们之间距离为乙追上甲前最大参考答案：B4. 关于摩揀力，下列说法中正确的是（）A.物体所受正压力增大时，它所受的摩擦力一定增大B.物体受到摩擦力作用时，它一定受到弹力作用C.滑动摩擦力的方向，一定与物体的运动方向相反D.静止的物休不可能受到滑动摩擦力作用参考答案：B5. 如图所示，光滑水平面上，小球m在拉力F作用下作匀速圆周运动。
2018_2019学年吉林省长春市吉大实验中学七年级数学下学期期末检测卷解析版
2018_2019学年吉林省长春市吉大实验中学七年级数学下学期期末检测卷解析版一、选择题（本大题共12小题，每小题4分，共48分.在每个小题给出的A、B、C、C四个选项中，只有一项是符合题目要求的）1．下列方程中是一元一次方程的是（）A．4x﹣5=0 B．3x﹣2y=3 C．3x2﹣14=2 D．2．下列图形既是轴对称图形，又是中心对称图象的是（）A．B．C． D．3．如果仅用一种正多边形进行镶嵌，那么下列正多边形不能够将平面密铺的是（）A．正三角形 B．正四边形 C．正六边形 D．正八边形4．甲班有54人，乙班有48人，要使甲班人数是乙班人数的2倍，设从乙班调往甲班x人，可列方程（）A．54+x=2（48﹣x）B．48+x=2（54﹣x）C．54﹣x=2×48 D．48+x=2×545．若一个三角形的三个内角度数的比为2：3：4，则这个三角形是（）A．锐角三角形B．直角三角形C．钝角三角形D．等腰三角形6．关于x，y的二元一次方程组的解也是二元一次方程2x+3y=﹣6的解，则k的值是（）A．﹣ B．C．D．﹣7．将一副三角板如图放置，使点A在DE上，BC∥DE，则∠AFC的度数为（）（第7题图）A．45° B．50° C．60° D．75°8．如图，已知△ABC为直角三角形，∠C=90°，若沿图中虚线剪去∠C，则∠1+∠2=（）（第8题图）A．90° B．135°C．270°D．315°9．如图，∠A+∠B+∠C+∠D+∠E+∠F的度数为（）（第9题图）A．180°B．360°C．270°D．540°10．有甲，乙，丙三种商品，如果购甲3件，乙2件，丙1件共需315元钱，购甲1件，乙2件，丙3件共需285元钱，那么购甲，乙，丙三种商品各一件共需（）A．50 B．100 C．150 D．20011．如果关于x的不等式组无解，则a的取值范围是（）A．a＜2 B．a＞2 C．a≥2 D．a≤212．马小虎在计算一个多边形的内角和时，由于粗心少算了2个内角，其和等于830°，则该多边形的边数是（）A．7 B．8 C．7或8 D．无法确定二、填空题（本大题共4小题，每小题4分，共16分，请将最后答案直接填在题中横线上）13．已知x=﹣1是方程a（x+1）=2（x﹣a）的解，那么a= ．14．若（a﹣1）2+|b﹣2|=0，则以a、b为边长的等腰三角形的周长为．15．若不等式组的解集为﹣1＜x＜1，那么（a+1）（b﹣1）的值等于．16．如图，在△ABC中，∠A=m°，∠ABC和∠ACD的平分线交于点A1，得∠A1；∠A1BC和∠A1CD的平分线交于点A2，得∠A2；…∠A2015BC和∠A20l5CD的平分线交于点A2016，则∠A2016= ．（第16题图）三、解答题（本大题共6个小题，共56分，解答应写出必要的文字说明或演算步骤）17．（8分）解下列方程或不等式组，并把不等式的解集表示在数轴上．（1）（2）．18．（8分）顶点在网格交点的多边形叫做格点多边形，如图，在一个9×9的正方形网格中有一个格点△ABC．设网格中小正方形的边长为1个单位长度．（1）在网格中画出△ABC向上平移4个单位后得到的△A1B1C1；（2）在网格中画出△ABC绕点A逆时针旋转90°后得到的△AB2C2；（3）在（1）中△ABC向上平移过程中，求边AC所扫过区域的面积．（第18题图）19．（8分）一批货物要运往某地，货主准备租用汽车运输公司的甲、乙两种货车．已知过去两次租用这两种货车的情况如表：现租用该公司3辆甲种货车及5辆乙种货车一次刚好运完这批货，如果按每吨付运费30元计算．问：货主应付费多少元？20．（10分）如图所示，△ABC直角三角形，延长AB到D，使BD=BC，在BC上取BE=AB，连接DE．△ABC顺时针旋转后能与△EBD重合，那么：（1）旋转中心是哪一点？旋转角是多少度？（2）AC与DE的关系怎样？请说明理由．（第20题图）21．（10分）如图1，△ABC中，∠ABC与∠ACB的平分线交于点P，根据下列条件，求∠BPC的度数．（1）若∠A=50°，则∠BPC= ；（2）从上述计算中，我们能发现：∠BPC= （用∠A表示）；（3）如图2，若BP，CP分别是∠ABC与∠ACB的外角平分线，交于点P，则∠BPC= ．（用∠A表示），并说明理由．（第21题图）22．（12分）某房地产开发公司计划建A、B两种户型的经济适用住房共80套，该公司所筹资金不少于2090万元，但不超过2096万元，且所筹资金全部用于建房，两种户型的建房成本和售价如下表：（1）该公司对这两种户型住房有哪几种建房方案？（2）若该公司所建的两种户型住房可全部售出，则采取哪一种建房方案获得利润最大？（3）根据市场调查，每套A型住房的售价不会改变，每套B型住房的售价将会降低a万元（0＜a＜6），且所建的两种户型住房可全部售出，该公司又将如何建房获得利润最大？参考答案与试题解析一、1. A．【解答】解：A、4x﹣5=0，是一元一次方程，故此选项正确；B、3x﹣2y=3，是二元一次方程，故此选项错误；C、3x2﹣14=2，是一元二次方程，故此选项错误；D、﹣2=3是分式方程，故此选项错误．故选A．2．D．【解答】解：A、是轴对称图形，不是中心对称图形，故A错误； B、不是轴对称图形，是中心对称图形，故B错误； C、是轴对称图形，不是中心对称图形，故C错误； D、既是轴对称图形，又是中心对称图形，故D正确．故选D．3．D．【解答】解：A、正三角形的一个内角度数为180°﹣360°÷3=60°，是360°的约数，能镶嵌平面，不符合题意；B、正四边形的一个内角度数为180°﹣360°÷4=90°，是360°的约数，能镶嵌平面，不符合题意；C、正六边形的一个内角度数为180°﹣360°÷6=120°，是360°的约数，能镶嵌平面，不符合题意；D、正八边形的一个内角度数为180°﹣360°÷8=135°，不是360°的约数，不能镶嵌平面，符合题意；故选D．4．A．【解答】解：设从乙班调x人到甲班，则甲班人数为（54+x）人，乙班人数为：（48﹣x）人，由题意得：54+x=2（48﹣x）．故选A．5．A．【解答】解：∵三角形三个内角度数的比为2：3：4，∴三个内角分别是180°×=40°，180°×=60°，180°×=80°．所以该三角形是锐角三角形．故选A．6．A．【解答】解：解方程组得：x=7k，y=﹣2k，把x，y代入二元一次方程2x+3y=﹣6，得：2×7k+3×（﹣2k）=﹣6，解得：k=﹣，故选A．7. D．【解答】解：∵BC∥DE，△ABC为等腰直角三角形，∴∠FBC=∠EAB==45°.∵∠AFC是△AEF的外角，∴∠AFC=∠FAE+∠E=45°+30°=75°．故选D．8．C．【解答】解：∵∠C=90°，∴∠A+∠B=90°．∵∠A+∠B+∠1+∠2=360°，∴∠1+∠2=360°﹣90°=270°．故选C．9．B．【解答】解：如图延长AF交DC于G点，（第9题答图）由三角形的外角等于与它不相邻的两个内角的和，得∠1=∠E+∠F，∠2=∠1+∠D，由等量代换，得∠2=∠E+∠F+∠D，∠A+∠B+∠C+∠D+∠E+∠F=∠A+∠B+∠2+∠C=（4﹣2）×180°=360°．故选B．10．【解答】解：设购甲，乙，丙三种商品各一件需要x元、y元、z元．根据题意，得，两方程相加，得4x+4y+4z=600，x+y+z=150．则购甲，乙，丙三种商品各一件共需150元．11．D.【解答】解：∵不等式组无解，∴a+2≥3a﹣2，解得a≤2.故选D.12．C．【解答】解：设少加的2个内角和为x度，边数为n．则（n﹣2）×180=830+x，即（n﹣2）×180=4×180+110+x，因此x=70，n=7或x=250，n=8．故该多边形的边数是7或8．故选C．二、13．﹣1 【解答】解：根据题意将x=﹣1代入方程得：2（﹣1﹣a）=0，解得：a=﹣1．14．5．【解答】解：根据题意得，a﹣1=0，b﹣2=0，解得a=1，b=2，①若a=1是腰长，则底边为2，三角形的三边分别为1、1、2，∵1+1=2，∴不能组成三角形，②若a=2是腰长，则底边为1，三角形的三边分别为2、2、1，能组成三角形，周长=2+2+1=5．15．﹣6．【解答】解：解不等式组可得解集为2b+3＜x＜因为不等式组的解集为﹣1＜x＜1，所以2b+3=﹣1， =1，解得a=1，b=﹣2代入（a+1）（b﹣1）=2×（﹣3）=﹣6．16．【解答】解：∵A1B平分∠ABC，A1C平分∠ACD，∴∠A1BC=∠ABC，∠A1CA=∠ACD，∵∠A1CD=∠A1+∠A1BC，即∠ACD=∠A1+∠ABC，∴∠A1=（∠ACD﹣∠ABC），∵∠A+∠ABC=∠ACD，∴∠A=∠ACD﹣∠ABC，∴∠A1=∠A，∠A2=∠A1=∠A，…，以此类推可知∠A2015=∠A=（）°，故答案为：．三、17．【解答】解：（1）去分母得：3（x+2）﹣2（2x﹣1）=12，3x+6﹣4x+2=123x﹣4x=12﹣2﹣6﹣x=4x=﹣4；（2）∵解不等式①得：x＞﹣1，解不等式②得：x≤3，∴不等式组的解集为﹣1＜x≤3，在数轴上表示为：．18．【解答】解：（1）、（2）如图所示：（3）∵△ABC向上平移4个单位后得到的△A1B1C1，△ABC向上平移过程中，边AC所扫过区域是以4为边长，以2为高的平行四边形，∴边AC所扫过区域的面积=4×2=8．19.【解答】解：设甲种货车每辆车运x吨，乙种货车每辆车运y吨，根据题意得：，解得：，（3×4+5×2.5）×30=735（元），答：货主应付费735元．20．【解答】解：（1）∵BC=BD，BA=BE，∴BC和BD，BA和BE为对应边，∵△ABC旋转后能与△EBD重合，∴旋转中心为点B；∵∠ABC=90°，而△ABC旋转后能与△EBD重合，∴∠ABE等于旋转角，∴旋转角是90度；（2）AC=DE，AC⊥DE．理由如下：∵△ABC绕点B顺时针旋转90°后能与△EBD重合，∴DE=AC，DE与AC成90°的角，即AC⊥DE．21．115°；90°+∠A；90°﹣∠A【解答】解：（1）∵∠A=50°，∴∠ABC+∠ACB=180°﹣50°=130°，∵∠ABC与∠ACB的平分线交于点P，∴∠PBC=∠ABC，∠PCB=∠ACB，∴∠PBC+∠PCB=∠ABC+∠ACB=（∠ABC+∠ACB）=×130°=65°，∴∠BPC=180°﹣65°=115°，故答案为：115°；（2）∵∠ABC+∠ACB=180°﹣∠A由（1）得：∠PBC+∠PCB=（∠ABC+∠ACB）==90°﹣∠A∴∠BPC=180°﹣（∠PBC+∠PCB）=180°﹣（90°﹣∠A）=90°+∠A（3）∵BP，CP分别是∠ABC与∠ACB的外角平分线，∴∠PBC=∠DBC，∠PCB=∠BCE，∴∠PBC+∠PCB=（∠DBC+∠BCE），∵∠DBC+∠ABC+∠ACB+∠BCE=360°，∴∠DBC+∠BCE=360°﹣（∠ABC+∠ACB）=180°+∠A，∴∠PBC+∠PCB==90°+∠A，∴∠BPC=180°﹣（∠PBC+∠PCB）=180°﹣（90°+∠A）=90°﹣∠A，22．【解答】解：（1）设A种户型的住房建x套，则B种户型的住房建（80﹣x）套．根据题意，得，解得48≤x≤50．∵x取非负整数，∴x为48，49，50．∴有三种建房方案：（2）设该公司建房获得利润W万元．由题意知：W=5x+6（80﹣x）=480﹣x，∵k=﹣1，W随x的增大而减小，∴当x=48时，即A型住房建48套，B型住房建32套获得利润最大．（3）根据题意，得W=5x+（6﹣a）（80﹣x）=（a﹣1）x+480﹣80a．∴当0＜a＜l时，x=48，W最大，即A型住房建48套，B型住房建32套．当a=l时，a﹣1=0，三种建房方案获得利润相等．当1＜a＜6时，x=50，W最大，即A型住房建50套，B型住房建30套．。
2019-2020学年吉林大学附中八年级下学期期末数学试卷
2019-2020学年吉林大学附中八年级下学期期末数学试卷一、选择题（本大题共8小题，共24.0分）1.若定义：f(a,b)=(−a,b)，g(m,n)=(m,−n)，例如f(1,2)=(−1,2)、g(−4,−5)=(−4,5)，则g(f(4,−3))的值为()A. (4,−3)B. (−4,3)C. (4,3)D. (−4,−3)2.若关于x的一元二次方程mx2−4x+3=0有实数根，则m的取值范围是()A. m≤2B. m≠0C. m≤4且m≠0 D. m<233.如图，把一张长方形纸片ABCD沿EF折叠后，点A落在CD边上的点A′处，点B落在点B′处，若∠1=115°，则图中∠2的度数为()A. 40°B. 45°C. 50°D. 60°4.若△ABC相似△A′B′C′，面积比为1：2，则△ABC与△A′B′C′的相似比为()A. 1：√2B. 1：4C. 4：1D. √2：15.如图，图中的每个小方格都是边长为1的小正方形，每个小正方形的顶点称为格点．若△ABC与△A1B1C1是位似图形，且顶点都在格点上，则位似中心的坐标是()A. (0,9)B. (8,0)C. (9,0)D. (10,0)6.已知反比例函数y=k+3的图象位于第二、四象限，则k的取值范围为()xA. k>−3B. k≥−3C. k<−3D. k≤−37.数学课上，老师提出一个问题：如图①，在平面直角坐标系中，点A的坐标为(0,2)，点B是x轴正半轴上一动点，以AB为边作等腰直角三角形ABC，使∠BAC=90°，点C在第一象限，设点B的横坐标为x，设……为y，y与x之间的函数图象如图②所示．题中用“…”表示的缺失的条件应补为()A. 边AB的长B. △ABC的周长C. 点C的横坐标D. 点C的纵坐标8.在平面直角坐标系中，已知抛物线与直线的图象如图所示，则下列说法：①当0<x<2时，y1>y2；②y1随x的增大而增大的取值范围是x<2；③使得y2大于4的x值不存在；④若y1=2，则x=2−√2或x=1．其中正确的有()A. 1个B. 2个C. 3个D. 4个二、填空题（本大题共6小题，共18.0分）9.计算：(1)−1+2=______(2)8−(−8)=______(3)−16=______4×4=______(4)−1−12(5)(−2)3=______(6)13.8465≈______(精确到0.01)10.17、如图17，在△ABC中，AD⊥BC于点D，点E，F分别是AB，AC的中点，若AB=8，BC=7，AC=5，则△DEF的周长是______11.如图，在四边形ABCD中，AB=AD，∠BAD=∠BCD=90°，连接AC.若AC=8，则四边形ABCD的面积为______．12.三个形状大小相同的菱形按如图所示方式摆放，已知∠AOB=∠AOE=90°，菱形的较短对角线长为2cm.若点C落在AH的延长线上，则△ABE的周长为______cm．13.如图，在两个直角三角形中，∠ACB=∠ADC=90°，AC=6，AD=2，若△ABC与△ACD相似，AB=______．14.一次函数的图象与直线y=−3x+1平行，并且图象过点(−1,0)，则这个函数的表达式为______．三、解答题（本大题共10小题，共78.0分）15.解方程(1)(x+5)2=121；(2)2x2−2x−3=0．16.某数学兴趣小组对函数y=4的图象和性质进行探究，他们用描点法画此函数图象时，先列表x2+1如下(1)请补全此表；(2)根据表中数据，在如图坐标系中画出该函数的图象；(3)请写出此函数图象不同方面的三个性质；(4)若点(m,y1)，(2,y2)都在此函数图象上，且y1≤y2，求m的取值范围．x……______ ______ ______ ______ 01234……y……______ ______ ______ ______ 42452541717. 正方形网格中，小格的顶点叫做格点，每个小正方形的边长为1，小方按下列要求作图：①在正方形网格的三条不同实线上各取一个格点，使其中任意两点不在同一实线上；②连接三个格点，使之构成直角三角形，小方在图①中作出了Rt△ABC．(1)请你按照同样的要求，在右边的正方形网格中各画出一个直角三角形，并使二个网格中的直角三角形不全等．(2)图①中Rt△ABC的面积为______ ．18. 已知点A(3,0)、B(0,2)、C(−2,0)、D(0,−1)，在同一坐标系中描出A、B、C、D各点，并求出四边形ABCD的面积．19. 为了解本校九年级学生体育测试项目“400米跑”的训练情况，体育教师在2019年1−5月份期间，每月随机抽取部分学生进行测试，将测试成绩分为：A，B，C，D四个等级，并绘制如图两幅统计图根据统计图提供的信息解答下列问题：(1)______月份测试的学生人数最少，______月份测试的学生中男生、女生人数相等；(2)求扇形统计图中D等级人数占5月份测试人数的百分比；(3)若该校2019年5月份九年级在校学生有600名，请你估计出测试成绩是A等级的学生人数．20. 某服装店出售某品牌的棉衣，进价为100元/件，当售价为150元/件时，平均每天可卖30件；为了增加利润和减少库存，商店决定降价销售．经调査，每件每降价1元，则每天可多卖2件．(1)若每件降价20元，则平均每天可卖______件．(2)现要想平均每天获利2000元，且让顾客得到实惠，求每件棉衣应降价多少元？21. 一个水库的水位在某段时间内持续上涨，表格中记录了连续5小时内6个时间点的水位高度，其中x表示时间，y表示水位高度．x(小时)012345…y(米)3 3.3 3.6 3.9 4.2 4.5…(1)通过观察数据，请写出水位高度y与时间x的函数解析式(不需要写出定义域)；(2)据估计，这种上涨规律还会持续，并且当水位高度达到8米时，水库报警系统会自动发出警报．请预测再过多久系统会发出警报．22. 求证：平行四边形的各内角的平分线的交点是一个矩形的四个顶点．23. 如图，在平面直角坐标系xOy内，点A在直线y=3x上(点A在第一象限)，OA=2√10．(1)求点A的坐标；(2)过点A作AB⊥x轴，垂足为点B，如果点E和点A都在反比例函数y=−k(k≠0)图象上(点E在第一象限)，过点E作EF⊥y轴，垂足为点F，xS△AOB，求点E的坐标．如果S△AEF=13AB，点P在半圆弧AB上运动(不24. 如图，在⊙O上位于直径AB的异侧有定点C和动点P，AC=12与A、B两点重合)，过点C作直线PB的垂线CD交PB于D点．(1)如图1，求证：△PCD∽△ABC；(2)当点P运动到什么位置时，△PCD≌△ABC？请在图2中画出△PCD并说明理由；(3)如图3，当点P运动到CP⊥AB时，求∠BCD的度数．【答案与解析】1.答案：B解析：解：g(f(4,−3))=g(−4，−3)=(−4，3)，故选：B．根据f(a,b)=(−a,b)，g(m,n)=(m,−n)，可得答案．本题考查了点的坐标，利用f(a,b)=(−a,b)，g(m,n)=(m,−n)是解题关键．2.答案：C解析：解：因为方程是一元二次方程，所以m≠0，因为方程有实数根，所以△=16−12m≥0，所以m≤43且m≠0．所以m≤43故选：C．根据一元二次方程的定义和根的判别式，共同确定m的范围．本题考查了一元二次方程的定义和根的判别式．一元二次方程ax2+bx+c=0的根的判别式：△= b2−4ac．3.答案：A解析：解：∵∠1=115°，∴∠EFB′=∠1=115°，∠EFC=65°，∴∠CFB′=50°，又∵∠B=∠B′=90°，∴∠2=90°−∠CFB′=40°，故选：A．由邻补角概念和翻折变换性质得出∠EFB′=∠1=115°，∠EFC=65°，据此知∠CFB′=50°，结合∠B=∠B′=90°知∠2=90°−∠CFB′，从而得出答案．本题主要考查翻折变换的性质，解题的关键是掌握翻折变换的对应边、对应角相等的性质及直角三角形两锐角互余、对顶角相等的性质．4.答案：A解析：此题考查了相似三角形的性质．此题比较简单，注意熟记定理是解此题的关键．由△ABC相似△A′B′C′，面积比为1：2，根据相似三角形的面积比等于相似比的平方，即可求得答案．解：∵△ABC相似△A′B′C′，面积比为1：2，∴△ABC与△A′B′C′的相似比为1：√2．故选A．5.答案：C解析：本题考查直角坐标系中的位似变换.根据位似变换的性质确定位似中心即可．解：如图所示：点D即为所求，坐标为：(9,0)．故选：C．6.答案：C解析：解：根据题意得k+3<0，解得k<−3．故选：C．根据反比例函数的性质得k+3<0，然后解不等式即可．(k≠0)的图象是双曲线；当本题考查了反比例函数的性质，反比例函数的性质：反比例函数y=kxk>0，双曲线的两支分别位于第一、第三象限，在每一象限内y随x的增大而减小；当k<0，双曲线的两支分别位于第二、第四象限，在每一象限内y随x的增大而增大．7.答案：D解析：解：作AD//x轴，作CD⊥AD于点D，如右图所示，由已知可得，OB=x，OA=2，∠AOB=90°，∠BAC=90°，AB=AC，点C的纵坐标是y，∵AD//x轴，∴∠DAO+∠AOD=180°，∴∠DAO=90°，∴∠OAB+∠BAD=∠BAD+∠DAC=90°，∴∠OAB=∠DAC，在△OAB和△DAC中{∠AOB=∠ADC ∠OAB=∠DAC AB=AC，∴△OAB≌△DAC(AAS)，∴OB=CD，∴CD=x，∵点C到x轴的距离为y，点D到x轴的距离等于点A到x的距离2，∴y=x+2(x>0)．故选：D．根据题意作出合适的辅助线，可以先证明△ADC和△AOB的关系，即可建立y与x的函数关系，从而可以得到哪个选项是正确的．本题考查动点问题的函数图象，解题的关键是明确题意，建立相应的函数关系式，根据函数关系式判断出正确的函数图象．8.答案：A解析：解：由题意和图象可知：0<x≤2时，y1<y2，故①错误；由图象可知，y1随x的增大而增大，x为全体实数，故②错误；因为二次函数的最大值为4，使得y2大于4的x值不存在，故③正确；因为直线经过(0,0)(2,4)，所以直线解析式y1=2x，故y1=2时，x=1，故④错误．由上可得，③正确，①②④错误．故选：A．根据函数图象和题意，可以判断题目中①②③④的正确与否，从而解答本题，得到正确的选项．本题考查二次函数和一次函数的图象的相关知识，关键是会看函数的图象，能弄懂题意，能找出所求问题需要的条件．9.答案：1 16 −4−3−813.85解析：解：(1)−1+2=1；(2)8−(−8)=8+8=16；=−4；(3)−164(4)−1−1×4=−1−2=−3；2(5)(−2)3=−8；(6)13.8465≈13.85(精确到0.01)故答案为：1，16，−4，−3，−8，13.85．(1)根据有理数的加法可以解答本题；(2)根据有理数的减法可以解答本题；(3)根据有理数的除法可以解答本题；(4)根据有理数的乘法和减法可以解答本题；(5)根据有理数的乘方可以解答本题；(6)根据题目中的数据和近似数的方法可以解答本题．本题考查有理数的混合运算，解答本题的关键是明确有理数混合运算的计算方法．10.答案：解：首先根据E，F是△ABC的AB，AC两边的中点，可以得到EF是△ABC的中位线，则EF的长度是BC长度的一半，则;又因为AD⊥BC，则△ABD和△ACD都是直角三角形，则DE，DF分别是两个三角形斜边上的中线，则有;所以△DEF的周长为EF+DE+DF=．故答案为10．解析：本题主要考查三角形中位线定理和直角三角形斜边上中线的性质，三角形的中位线平行于第三条边并且等于第三条边的一半；直角三角形斜边上的中线等于斜边的一半，从而可以根据题目中AB，BC，AC的长度得到DE，EF，DF的长度进而求得△DEF的周长．11.答案：32解析：解：过A作AE⊥AC，交CD的延长线于E，如图所示：∵AE⊥AC，∴∠EAC=90°，∵∠DAB=90°，∴∠DAE=∠BAC，∵∠BAD=∠BCD=90°，∴∠ADC+∠B=180°，∵∠EDA+∠ADC=180°，∴∠EDA=∠B，∵AD=AB，在△ABC与△ADE中，{∠EAD=∠CAB AD=AB∠EDA=∠B，∴△ABC≌△ADE(ASA)，∴AC=AE=8，△ABC的面积=△ADE的面积，∴四边形ABCD的面积=△AEC的面积=12AC×AE=12×8×8=32，故答案为：32．过A作AE⊥AC，交CD的延长线于E，证明△ABC≌△ADE，得到AC=AE，△ABC与△ADE的面积相等，求出△AEC的面积即可解决问题．本题主要考查了全等三角形的判定及其性质、等腰直角三角形的性质等知识；解题的关键是作辅助线，构造全等三角形．12.答案：12+8√2解析：解：如图所示，连接IC，连接CH交OI于K，则A，H，C在同一直线上，CI=2，∵三个菱形全等，∴CO=HO，∠AOH=∠BOC，又∵∠AOB=∠AOH+∠BOH=90°，∴∠COH=∠BOC+∠BOH=90°，即△COH是等腰直角三角形，∴∠HCO=∠CHO=45°=∠HOG=∠COK，∴∠CKO=90°，即CK⊥IO，设CK=OK=x，则CO=IO=√2x，IK=√2x−x，∵Rt△CIK中，(√2x−x)2+x2=22，解得x2=2+√2，又∵S菱形BCOI =IO×CK=12IC×BO，∴√2x2=12×2×BO，∴BO=2√2+2，∴BE=2BO=4√2+4，AB=AE=√2BO=4+2√2，∴△ABE的周长=4√2+4+2(4+2√2)=12+8√2，故答案为：12+8√2．连接IC，连接CH交OI于K，则A，H，C在同一直线上，CI=2，根据△COH是等腰直角三角形，即可得到∠CKO=90°，即CK⊥IO，设CK=OK=x，则CO=IO=√2x，IK=√2x−x，根据勾股定理即可得出x2=2+√2，再根据S菱形BCOI=IO×CK=12IC×BO，即可得出BO=2√2+2，进而得到△ABE的周长．本题主要考查了菱形的性质，解题时注意：菱形的四条边都相等；菱形的两条对角线互相垂直，并且每一条对角线平分一组对角；菱形的面积等于两条对角线长的乘积的一半．13.答案：18或9√22解析：解：∵∠ACB=∠ADC=90°，AC=6，AD=2，∴CD=4√2，设AB=x，当AC：AD=AB：AC时，△ABC∽△ACD，∴6：2=AB：6，解得AB=18；当AB：AC=AC：CD时，△ABC∽△CAD，∴AB：6=6：4√2，，解得AB=9√22．故答案为：18或9√22应用两三角形相似的判定定理，列出比例式求解即可．此题考查了相似三角形的判定，解题时注意：①如果两个三角形的三组对应边的比相等，那么这两个三角形相似；②如果两个三角形的两条对应边的比相等，且夹角相等，那么这两个三角形相似；③如果两个三角形的两个对应角相等，那么这两个三角形相似．平行于三角形一边的直线截另两边或另两边的延长线所组成的三角形与原三角形相似．14.答案：y=−3x−3解析：根据所求一次函数解析式与y=−3x+1平行，设出所求一次函数解析式为y=−3x+b，把已知点坐标代入求出b的值，即可求出解析式．此题考查了待定系数法求一次函数解析式，熟练掌握待定系数法是解本题的关键．解：设所求一次函数解析式为y=−3x+b，把(−1,0)代入得：0=3+b，解得：b=−3，则一次函数解析式为y=−3x−3，故答案为：y=−3x−3．15.答案：解：(1)两边开方得：x+5=±11，x +5=11，x +5=−11， 解得：x 1=6，x 2=−16； (2)2x 2−2x −3=0，b 2−4ac =(−2)2−4×2×(−3)=28， x =2±√282×2， x 1=1+√72，x 2=1−√72．解析：(1)两边开方，即可得出两个一元一次方程，求出方程的解即可； (2)求出b 2−4ac 的值，再代入公式求出即可．本题考查了解一元二次方程的应用，能选择适当的方法解一元二次方程是解此题的关键．16.答案：(1)(1)如下表：x …… −4 −3 −2 −1 01 2 3 4 ……y……41725452 424525417(2)如图所示：(3)①函数值y >0，②当x >0时，y 随x 的增大而减小；当x <0时，y 随x 的增大而增大； ③图象的对称轴是y 轴；(4)由图象可知，若点(m,y 1)，(2,y 2)都在此函数图象上，且y 1≤y 2，m 的取值范围是x ≤−2或x ≥2． 解析：(1)把x =−1、−2、−3、−4分别代入y =4x 2+1中计算即可得到对应的函数值； (2)利用描点法画出函数图象； (3)结合图象写出三个性质即可；(4)根据图象即可求得．本题考查反比例函数的图象与性质、反比例函数图象上点的坐标特征，解题的关键是理解题意，灵活运用所学知识解决问题，属于中考常考题型．17.答案：5解析：解：(1)(答案不唯一)(4分)(2)√5×√20÷2=5.(7分)(1)利用网格，首先从网格中找出一个直角，可利用勾股定理，好可利用网格的对角线，比如从网格中找一个小正方形的对角线，再找一个2×2网格的对角线，两对角线所组成的角是直角，连接另两点即可．(2)利用勾股定理即可求出直角边的长，再利用面积公式可计算．本题主要考查了利用网格画三角形的画法，及勾股定理的应用．18.答案：解：如图所示：S ABCD=S△AOB+S△BOC+S△COD+S△AOD=12×(3×2+2×2+2×1+1×3)=152．所以，四边形ABCD的面积为152．解析：本题考查了坐标与图形的性质，属于基础题，做题时重点要掌握把不规则四边形的面积看做成几个三角形面积的和．已知A，B，C，D的坐标，在直角坐标系中画出四边形，再求四边形ABCD的面积．19.答案：解：(1)1；4=15%；(2)D等级人数占5月份测试人数的百分比是：1−25%−40%−72°360∘(3)根据题意得：600×25%=150(名)，答：测试成绩是A等级的学生人数有150名．解析：本题考查的是扇形统计图、折线统计图的综合运用以及用样本估计总体．读懂统计图，从不同的统计图中得到必要的信息是解决问题的关键．(1)根据折线统计图给出的数据直接得出答案；(2)用整体1减去A、B、C所占的百分比即可得出答案；(3)用总人数乘以测试成绩是A等级的学生人数所占的百分比即可．解：(1)根据折线统计图给出的数据可得：1月份测试的学生人数最少，4月份测试的学生中男生、女生人数相等；故答案为：1，4；(2)见答案；(3)见答案；20.答案：70解析：解：(1)30+20×2=70件，故答案为：70；(2)设每件棉衣降价x元，则日销售量是(30+2x)件依题意可得：(150−100−x)(30+2x)=2000解得x1=10，x2=25为了使顾客得到实惠，舍去x1=10答：每件棉衣降价25元．(1)在30件的基础上下降20个2件即可得到销售量；(2)根据等量关系为：每件商品的盈利×可卖出商品的件数=2000，把相关数值代入计算得到合适的解即可．此题主要考查了一元二次方程的应用；得到可卖出商品数量是解决本题的易错点；得到总盈利2000的等量关系是解决本题的关键．21.答案：解：(1)设y 与x 之间的函数解析式为y =kx +b ，{b =3k +b =3.3，得{k =0.3b =3， 即y 与x 之间的函数解析式为y =0.3x +3； (2)把y =8，代入y =0.3x +3，得 8=0.3x +3， 解得，x =503，503−5=353，答：再过353小时后系统会发出警报．解析：本题考查一次函数的应用，解答本题的关键是明确题意，利用一次函数的性质解答． (1)根据题意和表格中的数据可以求得y 与x 之间的函数解析式；(2)将y =8代入(1)中的函数解析式，求出x 的值，再用x 的值减去5即可解答本题．22.答案：已知：四边形ABCD 是平行四边形，AE 、BF 、CG 、DH 分别为四边形内角的平分线，AE 与BF 和DH 分别交于点L 、M ，CG 与BF 、DH 分别交于点O 、N ，求证：点L 、M 、N 、O 是矩形的四个顶点． 证明：∵四边形ABCD 是平行四边形， ∴∠DAB +∠ABC =180°， ∵AE 平分∠DAB ，BF 平分∠ABC ， ∴∠1+∠2=90°， ∴∠ALB =90°， 即∠MLO =90°，同理可知，∠LMN =90°，∠MNO =90°，∠NOL =90°， ∴四边形LMNO 是矩形，∴点L 、M 、N 、O 是矩形的四个顶点．解析：根据题意，画出图形，写出已知和求证，然后根据平行线的性质和矩形的判定，即可证明结论成立．本题考查平行四边形的性质，角平分线的性质、矩形的判定，解答本题的关键是明确题意，利用数形结合的思想解答．23.答案：解：(1)作AB ⊥x 轴，垂足为点B ．∴∠ABO =90°，∵点A 在直线y =3x 上(点A 在第一象限)， ∴设P(x,3x)，其中x >0， ∴BO =x ，AB =3x ， ∵BO 2+AB 2=OA 2， ∴x 2+(3x)2=(2√10)2， 解得：x =2 ∴A(2,6)；(2)∵点A 在反比例函数y =−kx (k ≠0)图象上， ∴−k =2×6=12， ∴反比例函数的解析式为y =12x ，∵点E 在反比例函数y =12x第一象限的图象上，∴设点E 的坐标为(n,12n )(n >0)， ∴EF =n ，OF =12n，∴S △AEF =12EF ⋅|6−12n|，∵S △AEF =13S △AOB ，S △AOB =12×12=6， ∴12n ⋅|6−12n |=13×6，解得n =83或43， ∴E(83,92)或(43,9)．解析：(1)根据点A 在直线y =3x 上(点A 在第一象限)，可设A(x,3x)，其中x >0，再根据勾股定理可得BO 2+AB 2=OA 2，即x 2+(3x)2=(2√10)2，解得x =2即可计算出A 点坐标；(2)根据待定系数法求得反比例函数的解析式，然后由点E 在反比例函数在第一象限的图象上，设出点E 的坐标为(n,12n )(n >0).利用三角形的面积公式利用含n 的代数式表示出S △AEF ，根据点A 在反比例函数图形上利用反比例函数系数k 的几何意义即可得出S △ABO 的值，结合题意给出的两三角形的面积间的关系即可得出关于n 的分式方程，解方程，即可得出n 值，从而得出点E 的坐标．本题考查了反比例函数图象上点的坐标特征、三角形的面积公式以及反比例函数系数k的几何意义，解题的关键是：(1)求出点A的坐标；(2)根据三角形的面积间的关系找出关于n的分式方程．本题属于中档题，难度不大．24.答案：(1)证明：∵AB是⊙O的直径，∴∠ACB=90°，∵PD⊥CD，∴∠D=90°，∴∠D=∠ACB，∵∠A与∠P是B^C对的圆周角，∴∠A=∠P，∴△PCD∽△ABC；(2)解：当PC是⊙O的直径时，△PCD≌△ABC，理由：∵AB，PC是⊙O的直径，∴∠PBC=∠ACB=90°，AB=PC，∵∠A=∠P∴△PCD≌△ABC；AB，(3)解：∵∠ACB=90°，AC=12∴∠ABC=30°，∵△PCD∽△ABC，∴∠PCD=∠ABC=30°，∵CP⊥AB，AB是⊙O的直径，∴ÂC=ÂP，∴∠ACP=∠ABC=30°，∴∠BCD=∠ACB−∠ACP−∠PCD=90°−30°−30°=30°．解析：(1)由AB是⊙O的直径，根据直径对的圆周角是直角，即可得∠ACB=90°，又由PD⊥CD，可得∠D=∠ACB，又由在同圆或等圆中，同弧或等弧所对的圆周角相等，即可得∠A=∠P，根据有两角对应相等的三角形相似，即可判定：△PCD∽△ABC；(2)由△PCD∽△ABC，可知当PC=AB时，△PCD≌△ABC，利用相似比等于1的相似三角形全等即可求得；AB，可求得∠ABC的度数，然后利用相似，即可得∠PCD的度数，又由垂(3)由∠ACB=90°，AC=12径定理，求得ÂC=ÂP，然后利用圆周角定理求得∠ACP的度数，继而求得答案．。
吉林省吉大附中2018-2019学年八年级(上)期末物理试卷解析版
吉林省吉大附中2018-2019学年八年级（上）期末物理试卷一、单选题（本大题共21小题，共42.0分）1.同学们上课时的教室里的空气质量大约是（）A. 300多毫克B. 300多克C. 300多千克D. 300多吨2.关于密度，下列说法中正确的是（）A. 把一块砖切成体积相等的两块后，每块砖的密度变为原来的一半B. 密度相同的两个物体其质量一定相同C. 铁的密度比水的密度大，表示铁的质量比水的质量大D. 密度不同的两个物体，它们的质量可能相同3.四个容积为500毫升的瓶子，分别装满海水、纯水、酒精和汽油，那么质量最多的（）（ρ海水＞ρ纯水＞ρ酒精＞ρ汽油）A. 海水B. 纯水C. 酒精D. 汽油4.如图，物体A与B叠放静止在水平桌面上，以下说法正确的是（）A. 物体B所受的重力和桌面对物体B的支持力是一对平衡力B. 物体B所受的重力和物体B对桌面的压力是一对相互作用力C. 桌面对物体B的支持力和物体B对桌面的压力是一对平衡力D. 物体A所受的支持力和A对B的压力是一对相互作用力5.平直公路上行驶的汽车，在关闭发动机后会慢慢地停下来，这是因为（）A. 汽车不受任何外力的作用B. 汽车惯性减小并最后消失C. 汽车受重力的作用D. 汽车受地面摩擦力的作用6.在下列自行车的零部件中，有利于增大摩擦的是（）A. 车轮制成圆形B. 轮胎表面制成凹凸花纹C. 车轮上装有滚动轴承D. 在车轴部分加润滑油7.甲、乙物体在某段时间内的路程时间图象如图，下列说法止确的是（）A. 甲受非平衡力作用，乙受平衡力作用B. 两物体都受非平衡力作用C. 甲受平衡力作用，乙受非平衡力作用D. 两物体都受平衡力作用8.已知g=9.8N/kg，关于5kg和49N的人小，下列说法正确的是（）A. 5kg=49NB. 5kg>49NC. .5kg<49ND. 不是同一物理量，无法比较9.如图，用钳子紧紧夹住没有顶帽的钉子同时用力拉钳子，可以把钉子从木头里拔出来，这里将钉子拔出来的力是（）A. 钳子夹钉子的力B. 钳子对钉子的摩擦力C. 钉子对钳子的摩擦力D. 钉子受到的重力10.如图所示，当人推墙时，人将向后退，对此现象的一些说法中正确的是（）A. 人能后退一段距离是因为仍然受到墙的作用力B. 人能后退一段距离是因为人具有惯性C. 人停下来后惯性就消失了D. 人对墙的力与墙对人的力是一对平衡力11.如图所示，小成的书桌上放着一本字典，字典的一部分悬空在桌面以外，小成发现后将字典水平推回桌面内。
2023-2024学年吉林省长春市吉大附中实验学校高一(下)期末数学试卷(含答案)
2023-2024学年吉林省长春市吉大附中实验学校高一（下）期末数学试卷一、单选题：本题共8小题，每小题5分，共40分。
在每小题给出的选项中，只有一项是符合题目要求的。
1.样本数据5，7，4，6，12，10，11，9的第70百分位数次为( )A. 7B. 9C. 9.5D. 102.已知向量a，b，其中|a=2，|b|=2，且(a−b)⊥a，则向量a与b的夹角是( )A. π4B. π6C. π2D. π33.从一批产品(既有正品也有次品)中随机抽取三件产品，设事件A=“三件产品全不是次品”，事件B=“三件产品全是次品”，事件C=“三件产品有次品，但不全是次品”，则下列结论中不正确的是( ) A. A与C互斥 B. B与C互斥C. A、B、C两两互斥D. A与B对立4.已知a，b是两条不同直线，α，β是两个不同平面，则( )A. a//α，a⊥b，则b⊥αB. a⊥α，a⊥b，则b//αC. a⊂α，b⊂α，a//β，b//β，则α//βD. a∩b=A，a//α，b//α，a//β，b//β，则α//β5.已知正四棱台ABCD−A1B1C1D1的上、下底面边长分别为1和2，且BB1⊥DD1，则该棱台的体积为( )A. 722B. 726C. 76D. 726.在△ABC中，角A，B，C的对边分别为a，b，c.已知三个向量m=(a,cos A2)，n=(b,cos B2)，p=(c,cos C2)共线，则△ABC的形状为( )A. 等边三角形B. 钝角三角形．C. 有一个角是π6的直角三角形 D. 等腰直角三角形7.一个电路如图所示，A ，B ，C ，D ，E ，F 为6个开关，其闭合的概率都是12，且是相互独立的，则灯亮的概率是( )A. 164 B. 5564C. 18 D. 1168.庑殿(图1)是中国古代传统建筑中的一种屋顶形式，多用于宫殿、坛庙、重要门楼等高级建筑上，庑殿的基本结构包括四个坡面，坡面相交处形成5根屋脊，故又称“四阿殿”或“五脊殿”.图2是根据庑殿顶构造的多面体模型，底面ABCD 是矩形，且四个侧面与底面的夹角均相等，则( )A. AB =BC +EFB. AB =BC2+EF C. AB =BC +EF2D. AB =2BC−EF二、多选题：本题共3小题，共18分。
2019学年吉林大学附中高二上学期期末英语试卷【含答案及解析】
2019学年吉林大学附中高二上学期期末英语试卷【含答案及解析】姓名___________ 班级____________ 分数__________一、阅读理解1. One rainy evening I went to fill up at the gas station. A pre-teen boy approached my car and asked me for money to help him and his mother stay in their hotel for an additional week. He stated that if they did not come up with $25 they would be evicted that same evening. Having worked in social services before and having doubt about this, I asked why his mother hadn’t applied for social services for assistance. The boy said that they needed to remain in their hotel for one more week until his grandmother, who lived out of town, could take them in. I gave the boy what I had — $5. He thanked me and continued to wander the parking lot asking for help. I got my gas and drove away.Some weeks ago, a boy asked me for money and I told him I didn’t have any though I did. Yet, I thought about it for a while and went looking for the boy to give him a dollar. But it seemed that he had disappeared into thin air. “This time,” I thought, “I’ll do it differently.” I went to my bank and got an additional $20, then I returned to the gas station. The boy was still there. I observed him shyly approaching strangers who walked past him without notice. I pulled up and waved at the boy to come over. I handed him the $20 bill. He reached through my car window and gave me a huge hug. His hug told me all I needed to know — that finally this kid could get out of the rain, the cold and the darkening skies and go inside where it was warm.1. The whole story is about _____.A. dirty tricks by poor teenage boysB. a car accident in a gas stationC. warm help in a cold rainy eveningD. loving gifts from a rich stranger2. The underlined word “evicted” in Paragraph 1 can be replaced by _____?A. starved to death___________B. driven out of the hotelC. thrown into prison________D. separated from each other3. From the story we know that the author _____.A. once worked in social servicesB. had came across the boy beforeC. borrowed money to help othersD. gave the boy $20 in total4. When the boy received the $20 bill, he was _____.A. thankful________B. astonished________C. doubtful________D. ashamed2. Dog FancyCover Price: $ 59.88________ Price: $ 12.00 ($ 1.00 / issue)________ You Save: $ 47.88 (80%)Issues: 12 issues / 12 monthsDetails:Dog Fancy is information driven and provides opportunity for reader interaction. Every issue includes a fold-out four-color poster. Your complete guide to help you better understand, care for and enjoy your dog.Dog for KidsCover Price: $ 23. 94 Price: $ 12.99 ($2.17 /issue)________ You Save: $ 10.95 (46%)Issues: 6 issues / 12 monthsDetails:Dogs for Kids offers interactive and educational activities, which is intended for children (ages 8 to 12) who love dogs and puppies. Each full-color issue has training tips, fun activities to do with dogs, games, puzzles and posters. Dogs for Kids has received the Maxwell Award for Special Interest Magazines from the Dog Writer’s of America for 2 years in a row.The BarkCover Price: $ 19.80________ Price: $ 15.00 ($ 2.50/issue)________ You Save: $ 4.80 (24%)Issues: 6 issues / 12 monthsDetails:The Bark magazine is designed to include everything relatedto dog culture. Each issue includes stories, essays, poetry, reviews, interviews and artwork related to the relationship between humans and dogs. The Bark is not a how-to-care-for-your-dog magazine. It’s a magazine about living with dogs, which is your magazine: touching, smart and simply wonderful.Dog WorldCover Price: $ 48.88________ Price: $ 15.00 ($1.25 /issue)________ You Save: $ 33.88 (69%)Details:Dog World is written for the dog enthusiast , including professionals in the pet industry. Articles entertain and educate readers about dog health —care, nutrition, appearance, training and behavior and the law. Dog World is a must–read for its devoted, loyal dog–loving readers.1. Who would be most interested in the above magazines?A. Wildlife protectors.B. Story book writers.C. Pet dog owners. _________D. City zoo managers.2. Which magazine saves most?A. Dog Fancy.B. Dogs for Kids.C. The Bark.D. Dog World.3. Which magazine might be the most popular with children?A. Dog Fancy.B. Dogs for Kids.C. The Bark.D. Dog World.4. The underlined word “ enthusiast ” in the last p art means _____.A. 主人________B. 兽医________C. 专家________D. 狂热者3. During Nelson Mandela’s 19 years in the prison on Robben Island, one particular commanding officer, Badenhorst, was the cruelest of them all:“A few days before Badenhorst’s leaving the prison, I was called to the main office. General Steyn was visiting the island and wanted to know if we had any complaints. Badenhorst was there as I went through a list of demands. When I had finished, Badenhorst spoke to me directly.He told me he would be leaving the island and added:‘I just want to wish you people good luck’. I do not know if I looked dumbfounded (目瞪口呆的), but I was amazed. He spoke these words like a human being and showed aside of himself we had never seen before. I thanked himfor his good wishes and wished him good luck too.I thought about this moment for a long time afterwards. Badenhorst had perhaps been the most cold – blooded andcruelest commanding officer we had had on Robben Island. But that day in the office, he had showed that there was another side to his nature, a side that had been hidden but still existed.It was obvious that all men, even the most seemingly cold - blooded, have a heart of kindness and that, if their hearts are touched, they are able to change. Actually, Badenhorst was not evil; his inhumanity (不人道) had been encouraged by an inhuman system. He behaved cruelly because he was rewardedfor cruel behavior.”1. When did the story happen?A. Before Badenhorst left the prison.B. Before Mandela gave demands.C. After General Steyn took over the prison.D. Just when Mandela was set free.2. How did Mandela feel at what Badenhorst said?A. Awkward.B. Surprised.C. Angry.D. Upset.3. Why did Badenhorst become the cruelest according to Mandela?A. He was born evil.B. He seemed cold-blooded.C. He was easily changed.D. His cruelty was rewarded.4. Which could be the best title of the passage?A. Hide oneself or express oneself?B. Hard to change or easy to change?C. Cruel by name or cruel by nature?D. To be a prisoner or to be a commander?4. On October 10, 2014, Malala, 17, was awarded the Nobel Peace Prize for struggling for the right of children to education. Malala is the youngestNobel winner in history.Malala Yousafzai has never been ordinary. When she was just 11, she started blogging (写博客) about the Taliban takeover of her hometown of Mingora, Pakistan. Taliban members follow an extreme belief of Islam and forbid girls to go to school. Classrooms were closed for several months. Malalaspoke out about her desire to go back to school. “All I want is an education,” she told one television broadcaster.Malala was later able to return to class. But shecontinued to blog and speak out about girls’ right to education. On October 9, 2012, the Taliban tried to silence her. A gunman boarded her school bus and shot her in the head. Malala survived and showed great courage and optimism during her long recovery. At that time she became a symbol of the struggle for girls’ rights all over the world.Nine months after she was shot, she gave a now - famous speech at the United Nations. “They thought that thebullets (子弹) would silence us. But they failed,” she said. “And then, out of that silence came thousands ofvoices. … Weakness, fe ar and hopelessness died. Strength, power, and courage were born.”Malala has also become an international symbol for peace. In 2011, she won Pakistan’s National Youth Peace Prize, which is now renamed the NationalMalala Peace Prize. Ma lala said the 2014 Nobel Prize was an “encouragement”to go forward to help kids. “I want to tell children all around the worldthat they should stand up for their rights,” she said. “This award is forall those children whose voices need to be heard.”1. All the statements about Malala are true EXCEPT that _____.A. she started blogging at the age of 11B. it took her a long time to recover from the injuryC. Taliban tried to silence her but failedD. she was born in1998 in Mingora, Pakistan.2. How many peace prizes have gone to Malala so far according to the passage?A.1.B. 2.C. 3.D. 4.3. When did Malala become a symbol for girls’ rights?A. When she began writing her blogs.B. Before Taliban wanted to kill her.C. During her long recovery after the shot.D. When she gave a speech in the UN.4. We can learn from the passage that Malala is _____.A. creative and outgoingB. strict and stubbornC. simple and warm-hearted_________D. brave and determined5. Should we say goodbye to chivalry (骑士精神) in the age of sex equality?Chivalry began as a response to the violence of theMiddle Ages. PierMassimo Forni, the founder of the Civility Institute, says chivalry “as a form of treatment inspiredby the sense that there was something special about women and that they deserve added respect.”Toda y “chivalry” is often used as a term for “gentlemanly” behavior, related to “fair sex”, honor,courage and loyalty.But we can hardly see chivalry nowadays with many women demanding to be treated equally in the workplace.According to a 2013 survey carried out by the BritishDaily Mail, only one in seven men will offer their seatto a woman on a bus or train; over three-quarters of men don’t offer to help carry a heavy bag or suitcase for women.In many cases, it’s not because these men are being insensitive, but on the contrary, they say they areunwilling to help women because they are worried aboutmaking them embarrassed.These men may worry too much. According to the same survey, only seven percent of women view acts like holding open doors as unpleasant.“Men seem confused by the modern ‘sex equality’ message”, psychologist and relationship expert Donna Dawson told theDaily Mail.“This message was meant for the workplace and was never meant to replace good manners. Men will always be the stronger sex physically, so it is natural for them to show consideration for women.”So, should the acts of chivalry be brought back? US writer Emily Smith says chivalry is what we should all long for. Many people are predicting the deathof chivalry, but chivalry is not dead yet. Slowly but surely, chivalry is making a come - back.1. The question at the very beginning of the passage is used to _____.A. express the author’s curiosityB. cause a heated discussionC. introduce a controversial topicD. solve a serious social problem2. Which is NOT part of “chivalry”?A. Violence.B. Loyalty.C. Courage.D. Honor.3. Some men are not willing to help women because _____.A. they are not sensitive enoughB. they misunderstood “sex equality”C. they are afraid of womenD. they had no good manners4. Emily Smith holds the view that _____.A. some massages can make men confusedB. men should show consideration for womenC. “sex equality” will never replace good mannersD. chivalry is quite good and sure to come back二、完形填空6. 完形填空阅读下面短文，从短文后各题所给的四个选项（A、B、C和D）中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。
2024届吉林省长春市吉大附中力旺实验学校数学九上期末统考试题含解析
2024届吉林省长春市吉大附中力旺实验学校数学九上期末统考试题注意事项：1． 答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。
2．选择题必须使用2B 铅笔填涂；非选择题必须使用0．5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。
3．请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。
4．保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀。
一、选择题（每题4分，共48分）1．如图，在矩形ABCD 中，AB=3，AD=4，若以点A 为圆心，以4为半径作⊙A ，则下列各点中在⊙A 外的是（ ）A ．点AB ．点BC ．点CD ．点D2．已知a 是方程x 2+3x ﹣1＝0的根，则代数式a 2+3a+2019的值是( )A ．2020B ．﹣2020C ．2021D ．﹣20213．如图，90AOD ∠=︒，OA OB BC CD ===，以下结论成立的是（ ）A ．OAB OCA △△∽B ．OAB ODA △△∽C ．BAC BDA ∽△△D ．以上结论都不对 4．下列事件中，是必然事件的是( )A ．经过有交通信号灯的路口，遇到红灯B ．明天太阳从西方升起C ．三角形内角和是180D ．购买一张彩票,中奖5．设A (﹣2，y 1)，B (1，y 2)，C (2，y 3)是抛物线y ＝﹣(x +1)2+m 上的三点，则y 1，y 2，y 3的大小关系为（ ）A ．y 3＞y 2＞y 1B ．y 1＞y 2＞y 3C ．y 1＞y 3＞y 2D ．y 2＞y 1＞y 36．如图，在△ABC 中，D 、E 分别在AB 、AC 上，且DE ∥BC ，AD ＝12DB ，若S △ADE ＝3，则S 四边形DBCE ＝( )A ．12B ．15C ．24D ．277．已知，二次函数y=ax 2+bx+c 的图象上部分点的横坐标x 与纵坐标y 的对应值如表格所示，那么它的图象与x 轴的另一个交点坐标是（ ）x… -1 0 1 3 … y … 0 3 4 3 …A ．（2，0）B ．（3，0）C ．（4，0）D ．（5，0） 8．小张同学制作了四张材质和外观完全一样的书签，每个书签上写着一本书的名称或一个作者姓名，分别是：《西游记》、施耐庵、《安徒生童话》、安徒生，从这四张书签中随机抽取两张，则抽到的书签正好是相对应的书名和作者姓名的概率是( )A ．12B ．13C ．14D ．169．如图，已知矩形OABC 的面积是200，它的对角线OB 与双曲线()0k y x x =>图象交于点D ，且:3:2OD DB =，则k 值是（ ）A ．9B ．18C ．36D ．7210．如图，将△ABC 绕点A 逆时针旋转一定角度，得到△ADE ，若∠CAE=65°，∠E=70°，且AD ⊥BC ，∠BAC 的度数为（ ）．A ．60 °B ．75°C ．85°D ．90°11．下列运算正确的是( )A ．2(2)-＝﹣2B ．(23)2＝6C ．235+=D ．236⨯=12．我们知道：过直线外一点有且只有一条直线和已知直线垂直，如图，已知直线l 和l 外一点A ，用直尺和圆规作图作直线AB ，使AB ⊥l 于点A ．下列四个作图中，作法错误的是（ ）A ．B ．C ．D ．二、填空题（每题4分，共24分）13．在一个不透明的袋子中有1个红球、2个绿球和3个白球，这些球除颜色外都相同，摇匀后从袋子中任意摸出一个球，摸出_______颜色的球的可能性最大. 14．如图，抛物线22y x =-+向右平移1个单位得到抛物线___________．15．若12,x x 是方程2210x x --=的两个根，则12122x x x x ++的值为________16．若a ，b 是一元二次方程22510x x -+=的两根,则11a b+=________. 17．长度等于2的弦所对的圆心角是90°，则该圆半径为_____．18．一种药品经过两次降价，药价从每盒80元下调至45元，平均每次降价的百分率是__．三、解答题（共78分）19．（8分）元旦期间，商场中原价为 100元的某种商品经过两次连续降价后以每件81元出售，设这种商品每次降价的百分率相同，求这个百分率．20．（8分）山西物产丰富，在历史传承与现代科技进步中，特色农林牧业、农产品加工业、传统手工业不断发展革新，富有地域特色和品牌的士特产品愈加丰富.根据市场调查，下面五种特产比较受人们的青睐：A 山西汾酒、B 山西老陈醋、C 晋中平遥牛肉、D 山西沁州黄小米、E 运城芮城麻片，某学校老师带领学生在集市上随机调查了部分市民对“我最喜爱的特产”进行投票，将票数进行统计.绘制了如图所示的条形统计图和扇形统计图(均不完整).请根据图中的信息解答下列问题.()1直接写出参与投票的人数，并补全条形统计图；()2若该集市上共有3200人，请估计该集市喜爱运城芮城麻片的人数；()3若要从这五种特产中随机抽取出两种特产，请用画树状图或列表的方法，求正好抽到山西汾酒和晋中平遥牛肉的概率.21．（8分）如图，已知AD•AC＝AB•AE．求证：△ADE∽△ABC．22．（10分）如图：△ABC与△DEF中，边BC，EF在同一条直线上，AB∥DE，AC∥DF，且BF＝CE，求证：AC＝DF．23．（10分）求的值.24．（10分）某农科所研究出一种新型的花生摘果设备，一期研发成本为每台6万元，该摘果机的销售量y(台)与售价x(万元/台)之间存在函数关系：24=-+．y x（1）设这种摘果机一期销售的利润为1W (万元)，问一期销售时，在抢占市场份额(提示：销量尽可能大)的前提下利润达到32万元，此时售价为多少？（2）由于环保局要求该机器必须增加除尘设备，科研所投入了7万元研究经费，使得环保达标且机器的研发成本每台降低了1万元，若科研所的销售战略保持不变，请问在二期销售中利润达到63万元时，该机器单台的售价为多少？25．（12分）如图，正方形网格中的每个小正方形的边长都是1，每个小正方形的顶点叫做格点．△ABC 的三个顶点A ，B ，C 都在格点上，将△ABC 绕点A 按顺时针方向旋转90°得到△AB′C′．（1）在正方形网格中，画出△AB′C′；（2）计算线段AB 在变换到AB′的过程中扫过区域的面积．26．某体育看台侧面的示意图如图所示，观众区AC 的坡度i 为1:2，顶端C 离水平地面AB 的高度为10m ，从顶棚的D 处看E 处的仰角1830'α=，竖直的立杆上C 、D 两点间的距离为4m ，E 处到观众区底端A 处的水平距离AF 为3m ．求：（1）观众区的水平宽度AB ；（2）顶棚的E 处离地面的高度EF ．（sin1830'0.32≈，tan1830'0.33≈，结果精确到0.1m ）参考答案一、选择题（每题4分，共48分）1、C【解题分析】试题分析：根据勾股定理求出AC的长，进而得出点B，C，D与⊙A的位置关系．解：连接AC，∵AB=3cm，AD=4cm，∴AC=5cm，∵AB=3＜4，AD=4=4，AC=5＞4，∴点B在⊙A内，点D在⊙A上，点C在⊙A外．故选C．考点：点与圆的位置关系．2、A【分析】根据一元二次方程的解的定义，将a代入已知方程，即可求得a2+3a的值，然后再代入求值即可. 【题目详解】解：根据题意，得a2+3a﹣1＝0，解得：a2+3a＝1，所以a2+3a+2019＝1+2019＝2020.故选：A.【题目点拨】此题考查的是一元二次方程的解，掌握一元二次方程解的定义是解决此题的关键3、C【分析】根据已知条件结合相似三角形的判定定理逐项分析即可．【题目详解】解：∵∠AOD=90°，设OA=OB=BC=CD=x∴2x，5，10x，OC=2x，OD=3x，BD=2x ,∴22ABBD=25222210BC ACAB DA====∴AB BC AC BD AB DA== ∴BAC BDA ∽△△．故答案为C ．【题目点拨】本题主要考查了相似三角形的判定，①如果两个三角形的三组对应边的比相等，那么这两个三角形相似；②如果两个三角形的两条对应边的比相等，且夹角相等，那么这两个三角形相似；③如果两个三角形的两个对应角相等，那么这两个三角形相似．4、C【分析】必然事件就是一定发生的事件，依据定义即可判断【题目详解】解：A ．经过有交通信号灯的路口，遇到红灯是随机事件;B ．明天太阳从西方升起是不可能事件;C ．任意画一个三角形,其内角和是180是必然事件;D ．购买一张彩票，中奖是随机事件;故选：C【题目点拨】本题考查的是必然事件，必然事件是一定发生的事件.5、B【分析】本题要比较y 1，y 2，y 3的大小，由于y 1，y 2，y 3是抛物线上三个点的纵坐标，所以可以根据二次函数的性质进行解答：先求出抛物线的对称轴，再由对称性得A 点关于对称轴的对称点A '的坐标，再根据抛物线开口向下，在对称轴右边，y 随x 的增大而减小，便可得出y 1，y 2，y 3的大小关系．【题目详解】∵抛物线y ＝﹣（x +1）2+m ，如图所示，∴对称轴为x ＝﹣1，∵A （﹣2，y 1），∴A点关于x＝﹣1的对称点A'（0，y1），∵a＝﹣1＜0，∴在x＝﹣1的右边y随x的增大而减小，∵A'（0，y1），B（1，y2），C（2，y3），0＜1＜2，∴y1＞y2＞y3，故选：B．【题目点拨】本题考查了二次函数图象上点的坐标的特征，解题的关键是能画出二次函数的大致图象，据图判断．6、C【分析】根据DE∥BC得到△ADE∽△ABC，再结合相似比是AD：AB＝1：3，因而面积的比是1：9，则可求出S△ABC，问题得解.【题目详解】解：∵DE∥BC，∴△ADE∽△ABC，∵AD：DB＝1：2，∴AD：AB＝1：3，∴S△ADE：S△ABC是1：9，∵S△ADE＝3，∴S△ABC＝3×9＝27，则S四边形DBCE＝S△ABC﹣S△ADE＝27﹣3＝24.故选：C.【题目点拨】本题考查的是相似三角形的判定与性质，熟知相似三角形面积的比等于相似比的平方是解答此题的关键．7、C【分析】根据（0，3）、（3，3）两点求得对称轴，再利用对称性解答即可．【题目详解】解：∵抛物线y=ax2+bx+c经过（0，3）、（3，3）两点，∴对称轴x=032=1.5；点（-1，0）关于对称轴对称点为（4，0），因此它的图象与x轴的另一个交点坐标是（4，0）．故选C．【题目点拨】本题考查抛物线与x轴的交点、二次函数图象上点的坐标特征，解题的关键是明确题意，利用二次函数的性质解答．8、D【解题分析】根据题意先画出树状图得出所有等情况数和到的书签正好是相对应的书名和作者姓名的情况数，再根据概率公式即可得出答案．【题目详解】解：根据题意画图如下：共有12种等情况数，抽到的书签正好是相对应的书名和作者姓名的有2种情况，则抽到的书签正好是相对应的书名和作者姓名的概率是212＝16；故选D．【题目点拨】此题考查的是用列表法或树状图法求概率．列表法可以不重复不遗漏的列出所有可能的结果，适合于两步完成的事件；树状图法适合两步或两步以上完成的事件；解题时要注意此题是放回实验还是不放回实验．用到的知识点为：概率＝所求情况数与总情况数之比．9、D【分析】过点D作DE∥AB交AO于点E，通过平行线分线段成比例求出,OE DE的长度，从而确定点D 的坐标，代入到解析式中得到k的值，最后利用矩形的面积即可得出答案.【题目详解】过点D作DE∥AB交AO于点E∵DE∥AB∴OE DE OD OA AB OB==∵:3:2 OD DB=∴35 OE DE OD OA AB OB===∴33,55 OE OA DE AB ==∴33(,)55D OA AB ∵点D 在()0k y x x =>上 ∴3355k OA AB = ∵200OA AB = ∴99200722525k OA AB ==⨯= 故选D【题目点拨】本题主要考查平行线分线段成比例及反比例函数，掌握平行线分线段成比例是解题的关键. 10、C【解题分析】试题分析：根据旋转的性质知，∠EAC=∠BAD=65°，∠C=∠E=70°． 如图，设AD ⊥BC 于点F ．则∠AFB=90°，∴在Rt △ABF 中，∠B=90°-∠BAD=25°，∴在△ABC 中，∠BAC=180°-∠B-∠C=180°-25°-70°=85°，即∠BAC 的度数为85°．故选C ．考点: 旋转的性质.11、D【解题分析】根据二次根式的性质以及二次根式加法，乘法及乘方运算法则计算即可．【题目详解】A 2(2)-＝2，故本选项错误；B ：32＝12，故本选项错误；C 23D ：根据二次根式乘法运算的法则知本选项正确，故选D ．【题目点拨】本题考查的是二次根式的性质及二次根式的相关运算法则，熟练掌握是解题的关键.12、C【分析】根据垂线的作法即可判断．【题目详解】观察作图过程可知：A ．作法正确，不符合题意；B ．作法正确，不符合题意；C ．作法错误，符号题意；D ．作法正确，不符合题意．故选：C ．【题目点拨】本题考查了作图-复杂作图、垂线，解决本题的关键是掌握作垂线的方法．二、填空题（每题4分，共24分）13、白【分析】根据可能性大小的求法，求出各个事件发生的可能性的大小，再按照大小顺序从小到大排列起来即可．【题目详解】根据题意，袋子中共6个球，其中有1个红球，2个绿球和3个白球，故将球摇匀，从中任取1球，①恰好取出红球的可能性为16， ②恰好取出绿球的可能性为 2163=， ③恰好取出白球的可能性为 3162=， 摸出白颜色的球的可能性最大．故答案是：白．【题目点拨】本题主要考查了可能性大小计算，即概率的计算方法，用到的知识点为：可能性等于所求情况数与总情况数之比，难度适中．14、()212y x =--+【分析】先确定抛物线22y x =-+的顶点坐标为（0，2），再利用点平移的规律得到点（0，2）平移后所得对应点的坐标为（1，2），然后根据顶点式可得平移后的抛物线的解析式．【题目详解】解：抛物线22y x =-+的顶点坐标为（0，2），把点（0，2）向右平移1个单位所得对应点的坐标为（1，2），∴平移后的抛物线的解析式是：2(1)2y x =--+；故答案为2(1)2y x =--+．【题目点拨】本题考查了二次函数图象与几何变换：由于抛物线平移后的形状不变，故a 不变，所以求平移后的抛物线解析式通常可利用两种方法：一是求出原抛物线上任意两点平移后的坐标，利用待定系数法求出解析式；二是只考虑平移后的顶点坐标，即可求出解析式．15、1【分析】先由根与系数的关系得出12122,1x x x x +==-，然后代入即可求解．【题目详解】∵12,x x 是方程2210x x --=的两个根12122,1x x x x ∴+==-∴原式=22(1)220+⨯-=-=故答案为：1．【题目点拨】本题主要考查一元二次方程根与系数的关系，掌握一元二次方程根与系数的关系是解题的关键．16、【分析】将11a b+通分变形为a b ab +，然后利用根与系数的关系即可求解.【题目详解】∵a 、b 是一元二次方程210x -+=的两根∴+=a b 1ab =∴11=++=a b a b ab故答案为：【题目点拨】 本题考查了一元二次方程的根与系数的关系，熟练掌握12b x x a +=-，12c x x a=是解题的关键. 17、1【分析】结合等腰三角形的性质，根据勾股定理求解即可．【题目详解】解：如图AB ＝，∠AOB ＝90°，且OA ＝OB ，在Rt OAB 中，根据勾股定理得222OA OB AB +=，即222272OA AB ===∴236OA =，0OA >6OA ∴=故答案为：1．【题目点拨】本题考查了等腰三角形的性质及勾股定理，在等腰直角三角形中灵活利用勾股定理求线段长度是解题的关键. 18、25%【分析】设每次降价的百分比为x ，根据前量80，后量45，列出方程280(1)45x ，解方程即可得到答案.【题目详解】设每次降价的百分比为x ， 280(1)45x ，解得：x 1=0.25=25%，x 2=1.75（不合题意舍去）故答案为：25%.【题目点拨】此题考查一元二次方程的实际应用，正确理解百分率问题，代入公式：前量（1±x ）2=后量，即可解答此类问题.三、解答题（共78分）19、10%【分析】此题可设每次降价的百分率为x ，第一次降价后价格变为100（1-x ），第二次在第一次降价后的基础上再降，变为100（x-1）2，从而列出方程，求出答案．【题目详解】解：设每次降价的百分率为x ，第二次降价后价格变为100（x-1）2元，根据题意得：100（x-1）2=81，即x-1=0.9，解之得x 1=1.9，x 2=0.1．因x=1.9不合题意，故舍去，所以x=0.1．即每次降价的百分率为0.1，即10%．答：这个百分率为10%．【题目点拨】此题考查了一元二次方程的应用，解答本题的关键在于分析降价后的价格，要注意降价的基础，另外还要注意解的取舍，难度一般．20、（1）50人，补图见解析；（2）320人；（3）1 10.【分析】⑴根据两个统计图形对比可以得到A占总数的40%共20人，得出总人数，再根据B的占比求出B的人数，最后总数减去ABCD的人数即可，在图上补全.⑵求出统计中C的占比比率，然后乘以总人数3200即可.⑶画出树状图，共有20种等可能的结果，正好抽到山西汾酒和晋中平通牛肉的结果有2种，根据概率公式求出即可.【题目详解】解：()1参与投票的人数为50人，补全的条形统计图如图所示，()2510%50=320010%320∴⨯=（人）∴估计该集市人群对运城芮城麻片比较喜爱的人数为320人()3根据题意画树状图如下共有20种等可能的结果，正好抽到山西汾酒和晋中平通牛肉的结果有2种，故其概率为212010 P==.【题目点拨】此题主要考查了条形统计图和扇形统计图及概率，熟练掌握知识是解题的关键.21、证明见解析.【分析】由AD•AC＝AE•AB，可得AD AEAB AC=,从而根据“两边对应成比例并且夹角相等的两个三角形相似”可证明结论成立.【题目详解】试题分析：证明：∵AD•AC＝AE•AB，∴ADAB＝AEAC在△ABC与△ADE 中∵ADAB＝AEAC，∠A＝∠A，∴△ABC∽△ADE22、见解析.【分析】先根据BF＝CE，得出BC＝EF，再利用平行线的性质可得出两组对应角相等，再加上BC＝EF，利用ASA即可证明△ABC≌△DEF，则结论可证.【题目详解】证明：∵AB∥DE，∴∠B＝∠E，∵AC∥DF∴∠ACB＝∠EFD，∵BF＝CE∴BC＝EF，且∠B＝∠E，∠ACB＝∠EFD，∴△ABC≌△DEF（ASA）∴AC＝DF【题目点拨】本题主要考查全等三角形的判定及性质，掌握全等三角形的判定方法是解题的关键.23、4【解题分析】先设t=x2+y2，则方程即可变形为t（t-1）-12=0，解方程即可求得t即x2+y2的值．【题目详解】设t=x2+y2，所以原式可变形为为t（t-1）-12=0，t2-t-12=0，（t-4）（t+3）=0，所以t=-3或t=4；因为x2+y2≥0，所以x2+y2=4.【题目点拨】此题考查换元法解一元二次方程，解题关键在于设t=x2+y2.24、（1）在抢占市场份额的前提下利润要达到32万元，此时售价为8万元/台；（2）要使二期利润达到63万元，销售价应该为10万元/台．【分析】（1）先根据等量关系式：总利润=（售价-成本）⨯销售量，列出函数关系式，再将132W=代入函数关系式得出方程求解即得；（2）先根据等量关系式：总利润=（售价-新成本）⨯销售量-7，列出函数关系式，再将263W =代入函数关系式得出方程求解即得．【题目详解】（1）根据题意列出函数关系式如下：21(6)(6)(24)(15)81W x y x x x =-⋅=--+=--+当132W =时，2(15)8132x --+=，解得18x =，222x =．∵要抢占市场份额∴8x =．答：在抢占市场份额的前提下利润要达到32万元，此时售价为8万元/台．（2）降低成本之后，每台的成本为5万元，每台利润为(5)x -万元，销售量24y x =-+．依据题意得22(5)(24)729127W x x x x =--+-=-+-，当263W =时，22912763x x -+-=，解得110x =，219x =．∵要继续保持扩大销售量的战略∴10x =答：要使二期利润达到63万元，销售价应该为10万元/台．【题目点拨】本题考查函数解析式及解一元二次方程，解题关键是正确找出等量关系式：总利润=（售价-成本）⨯销售量．25、（1）见解析；（2）254π． 【分析】（1）分别作出点B 、C 绕点A 按顺时针方向旋转90︒得到的对应点，再顺次连接可得；（2）根据扇形的面积公式列式计算可得．【题目详解】（1）解：如图所示：△AB′C′即为所求（2）解：∵AB= ，∴线段AB 在变换到AB′的过程中扫过区域的面积为：2905360π⨯=254π【题目点拨】本题主要考查作图以及旋转变换，解题的关键是根据旋转的性质作出变换后的对应点及扇形的面积公式．26、（1）20；（2）顶棚的E 处离地面的高度EF 约为21.6m ．【分析】（1）根据坡度的概念计算；（2）作CM EF ⊥于M ，DN EF ⊥于N ，根据正切的定义求出EN ，结合图形计算即可．【题目详解】（1）∵观众区AC 的坡度i 为1:2，顶端C 离水平地面AB 的高度为10m ，∴()220AB BC m ==，答：观众区的水平宽度AB 为20m ；（2）如图，作CM EF ⊥于M ，DN EF ⊥于N ，则四边形MFBC 、MCDN 为矩形，∴10MF BC ==，4MN CD ==，23DN MC BF ===，在Rt END ∆中，tan EN EDN DN∠=， 则tan 7.59EN DN EDN =⋅∠≈，∴()7.5941021.6EF EN MN MF m =++=++≈，答：顶棚的E 处离地面的高度EF 约为21.6m ．【题目点拨】本题考查解直角三角形的应用﹣仰角俯角问题、坡度坡角问题，掌握仰角俯角的概念、坡度的概念、熟记锐角三角函数的定义是解题的关键．。
吉林省长春市吉大附中力旺实验学校2025届化学九年级第一学期期末达标检测试题含解析
吉林省长春市吉大附中力旺实验学校2025届化学九年级第一学期期末达标检测试题注意事项：1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
2．回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。
回答非选择题时，将答案写在答题卡上，写在本试卷上无效。
3．考试结束后，将本试卷和答题卡一并交回。
一、单选题（本大题共10小题，共20分）1．图示中的“”和“”分别表示不同元素的原子。
在下列的图示中，有可能属于氧化物的是粒子图示选项 A B C DA．A B．B C．C D．D2．人若饮用了工业酒精勾兑的白酒，会导致甲醇中毒。
已知甲醇的分子结构如图所示，下列表述中不正确的是A．甲醇的相对分子质量为32B．甲醇是由3种元素组成的C．甲醇中碳元素的质量分效最大D．甲醇分子中碳氢氧原子个数比为1：4：13．物质的性质决定其用途，下列有关物质性质和用途的说法中不正确的是（）A．氧气有可燃性-------------可以做燃料B．氮气化学性质比较稳定-------------可充入食品包装袋中防腐C．活性炭具有吸附作用-------------可用于冰箱除臭D．干冰升华吸收热量-------------可用于人工降雨4．某纯净物X在空气中与氧气反应，反应的化学方程式为：X+3O2点燃2CO2+2H2O，推测X的化学式（）A．CH4B．C2H4C．C3H6D．C2H65．下列物质属于纯净物的是（）A．硬水B．洁净的空气C．石油D．干冰6．下列中草药煎制步骤中，属于过滤操作的是A．冷水浸泡B．加热煎制C．箅渣取液D．灌装保存A．A B．B C．C D．D7．实验室制取CO2有以下几个步骤：①按装置图连接好仪器②向长颈漏斗中加入稀盐酸③向锥形瓶内加入块状石灰石④检查装置的气密性⑤收集反应生成的气体。
以上操作的排列顺序正确的是（）A．①②③④⑤B．②①④③⑤C．①②④③⑤D．①④③②⑤8．以下是2019 年实验操作考查时小明完成“制取CO2”实验的部分操作示意图，其中错误的是（）A．检查气密性B．加入药品C．收集气体D．洗涤仪器9．下列各组物质中，带点的同种元素的化合价相同的是()A．C．l2、NaC．lB．N．H3、HN．O3C．M．nO2、KM．nO4D．C．O2、H2C．O310．溶液在稀释前后保持不变的是()A．溶质的质量分数B．溶质的质量C．溶液的质量D．溶剂的质量二、填空题（本大题共1小题，共4分）11．水是生命之源。
2019-2020学年吉林大学附中七年级下学期期末数学试卷 (含部分答案)
2019-2020学年吉林大学附中七年级第二学期期末数学试卷一.选择题（共10小题）.1．下列方程的解为x＝1的是（）A．3x+2＝2x+3B．x+1＝C．6＝5﹣x D．2x﹣1＝22．已知二元一次方程2x﹣3y＝4，用含x的代数式表示y，正确的是（）A．y＝B．y＝C．x＝D．x＝3．若不等式组的解集为﹣1≤x≤3，则用敷轴表示正确的是（）A．B．C．D．4．下列长度的三条线段能组成三角形的是（）A．2，2，6B．3，4，8C．4，6，10D．5，6，105．如图所示图案是中心对称图形的是（）A．B．C．D．6．如图是由4个相同的小正方形组成的网格图，其中∠1+∠2等于（）A．150°B．210°C．180°D．225°7．工人师健经常利用角尺平分一个任意角．如图所示，∠AOB是一个任意角，在边OA，OB上分别取OD＝OE，移动角尺，使角尺两边相同的刻度分别与D，E重合，这时过角尺顶点F的射线OF就是∠AOB的平分线．你认为工人师傅在此过程中用到的三角形全等的判定方法是（）A．SAS B．SA C．AAS D．SSS8．如图，△ABC中，DE是AC的垂直平分线，AE＝5cm．△ABD的周长为18cm，则△ABC的周长为（）A．23cm B．13cm C．28cm D．18cm9．等腰三角形一腰上的高与另一腰的夹角是45°，则这个三角形的底角为（）A．67°31′B．22°30′C．67°30′D．22°30′或67°30′10．某鞋店有甲、乙两款鞋各30双，甲鞋一双200元，乙鞋一双50元．该店促销的方式：买一双甲鞋，送一双乙鞋；只买乙鞋没有任何优惠．若打烊后得知，此两款鞋共卖得1800元，还剩甲鞋x双、乙鞋y双，则依题意可列出下列哪一个方程式？（）A．200（30﹣x）+50（30﹣y）＝1800B．200（30﹣x）+50（30﹣x﹣y）＝1800C．200（30﹣x）+50（60﹣x﹣y）＝1800D．200（30﹣x）+50[30﹣（30﹣x）﹣y]＝1800二.填空题（共10小题，共30分）11．一元一次方程﹣y＝﹣3的解为．12．已知是方程2kx﹣y＝1的解，则k的位为．13．若实数m，n满足|m﹣n﹣81|+（n﹣20）2＝0，则mn＝．14．0≤2x﹣1＜5的整数解是．15．如果不等式组无解，则a的取值范围是．16．多边形每增加一条边，它的内角和增加度．17．防控断冠肺炎疫情期间．某药店在市场抗病毒药品紧缺的情况下，将某药品提价后，使价格翻一番（即为原价的2倍），物价部门查处后，其价格降到比原价高10%．则该药品降的百分比是．18．如图，已知正五边形ABCDE，连结BE，AC交于点F，则∠AFE的大小为度．19．如图，在△BC中，∠B＝90°，AB＝2，点D在BC上，且AD＝DC．若将△ABC沿AD折叠，点B恰好落在AC上，则AC的长是．20．如图，此图是16块的共相同的小矩形砖块拼成了一个大矩形．若大矩形的一边长为75cm，那小矩形砖块的面积为cm2．三、解答题21．解下列方程（组）、不等式（组）．（1）2y+3＝11﹣6y（2）x﹣1＝x﹣3（3）（4）（5）≥（6）22．已知，如果点A，E，F，C在同一直线上，AD∥CE，∠1＝∠2，AE＝CF．求证：△ADF≌△CBE．23．某校计划购进A，B两种树木共100棵进行校园绿化，经市场调查：购买A种树木2棵．B种树木5棵共需600元；购买A种树木3棵，B种树木1棵共需380元．（1）直接写出A，B两种树苗的单价，A种每棵元；B种每棵元；（2）因布局需要，购买A种树木的数量不少于B种树木数量的3倍．实际付款总金额按市场价九折优惠，请设计一种购买树木的方案，使实际所花费用最省，并求出最省的费用．24．如图，在△ABC中，∠A＝120°，AB＝AC，D是BC边的中点，DE⊥AB，DF⊥AC，点E，F为垂足，求证：△DEF是等边三角形．25．如图，在△ABC中，∠ACB＝90°，AC＝BC，点E是∠ACB内部一点，连结CE，作AD⊥CE，BE⊥CE，垂足分别为点D，E．（1）求证：△BCE△CAD；（2）若BE＝5，DA＝12，则ED的长是．26．图1、图2均为4×4的正方形网格，每个小正方形的项点称为格点，线段AB、DE的端点均在格点上．（1）在图1中画出以AB为斜边的等腰直角△ABC，使点C在格点上；（2）在图2中正出以DE为斜边的直角△DEF，使点F在格点上且与△ABC不全等，再在DE上找到一点P，使得FP最短．（要求：用直尺画图，保留作图痕迹．不写作法．每题画出一个即可）．27．长春市开展综合治理活动中，需要将A，B，C三地的垃圾50立方米、40立方米、50立方米全部运往D，E两地进行处理，已知运往D地的数量比运往E地的数量的2倍少10立方米．（1）求运往D，E两地的数量各是多少立方米；（2）若A地运往D地m立方米（m为整数），B地运往D地30立方米，C地运往D 地的数量小于A地运往D地的数量2倍，其余全部运往E地，且C运往E地不超过12立方米，则A，C两地运往D，E两地有哪几种方案？28．如图，已知△ABC中，AB＝AC＝12cm，∠B＝∠C，BC＝8cm，点D为AB中点，点P的运动速度为2cm/s．（1）如果点P在线段BC上由点B向终点C运动，同时，点Q在线段CA上由点C向终点A运动，若点Q的运动速度与点P的运动速度相等．①经过2秒后，BP＝cm，CQ＝cm；②经过1秒后，△BPD与△CQP是否全等，请说明理由；③若点Q的运动速度与点P的运动速度不相等，当点Q的运动速度为多少时，能使△BPD与△CQP全等？（2）若点Q以③中的运动速度从点C出发，点P从点B同时出发，都沿△ABC三边逆（在时针方向运动，则经过秒后，点P与点Q第一次在△ABC的边上相遇．横线上直接写由答案，不必书写解题过程）参考答案一、选择题1．A；2．B；3．D；4．D；5．B；6．C；7．D；8．C；9．D；10．D；二.填空题（共10小题，共30分）11．6；12．2；13．2020；14．1和2；15．a≤1；16．180°；17．45%；18．72°；19．4；20．675；。
吉林省长春市吉大附中力旺实验校度第二学期七年级期末数学试题(无答案)
吉林省长春市吉大附中力旺实验校度第二学期七年级期末数学试题（无答案）长春吉大附中力旺实验中学2019-2019学年度下学期七年级数学学科期末考试测试题考试时间：100分钟一、选择题（本大题共8小题，每小题3分，共24分）1.方程2x −1=3的解是（ ）（A ）x ＝−1 （B ）x ＝12（C ）x ＝2 （D ）x ＝1 2.若x ＞y ，则下列不等式中不一定成立的是（ ）（A ）x +1>y +1 （B ）2x =3y （C ）x 2＞y 2（D ）x 2=y 2 3.在以下绿色食品、回收、节能、节水四个标志中，是轴对称图形的是（ ）（A ） （B ） （C ） （D ）4.如图，一扇窗户，用窗钩AB 可将其固定，这里所运用的几何原来是（ ）（A ）两点之间线段最短 （B ）三角形的稳定性（C ）两点确定一条直线 （D ）垂线段最短（第4题） （第5题）5.如图，△ACB ≌△A ′CB ′，∠A ′CB ＝30°，∠ACB ′＝110°，则∠ACA ′的度数是（ ）（A ）20° （B ）30° （C ）35° （D ）40°6.一件商品提价25%后，发现销路不好，欲恢复原价，则应降价（ ）（A ）40% （B ）25% （C ）20% （D ）15%7.将一张面值100元的人民币，兑换成10元或20元的零钱，兑换方案有（ ）（A ）6种 （B ）7种 （C ）8种 （D ）9种8.全等三角形又叫做合同三角形，平面内的合同三角形分为真合同三角形与镜面合同三角形，两个真合同三角形，都可以在平面内通过平移或旋转使它们重合；而两个镜面合同三角形要重合，则必须将其中的一个翻折，下列各组合同三角形中，是镜面合同三角形的是（ ）（A ） （B ） （C ） （D ）二、填空题（本大题共6小题，每小题3分，共18分）9.不等式3x +1<−2的解集是 ；10.已知x 、y 满足方程组{x +2y =52x +y =4,则x −y 的值是 ； 11.如图所示，在Rt △ABC 中，∠A ＝90°，小华用剪刀沿DE 剪去∠A ，得到一个四边形，则∠1＋∠2＝ °（第11题） （第13题） （第14题）12.设a 、b 、c 、d 为有理数，现规定一种新的运算|a b c d|=ad −bc ,则满足等式 |x 2x+1321|=1 的x 的值为 ；（2）如图（2），将图（1）中“AC⊥AB，BD⊥AB”改为“∠CAB＝∠DBA＝60°”，其他条件不变，点Q的运动速度为xcm/s，是否存在实数x，使得△ACP与△BPQ全等？若存在，求出相应的x、t的值；若不存在，请说明理由.24.（12分）如图，在△ABC中，BC＝8cm，AG∥BC，AG＝8cm，点F从点B出发，沿线段BC 以4cm/s的速度连续做往返运动，点E从点A出发沿线段AG以2cm/s的速度运动至点G，E、F 两点同时出发，当点E到达点G时，E、F两点同时停止运动，EF与AC交于点D，设点E的运动时间为t（秒）（1）分别写出当0＜t＜2和2＜t＜4时段BF的长度（用含t的代数式表示）（2）当BF＝AE时，求t的值；（3）当△ADE≌△CDF时，直接写出所有满足条件的t值.。
2019-2020学年吉林大学附属中学初中部高三英语上学期期末考试试卷及答案解析
2019-2020学年吉林大学附属中学初中部高三英语上学期期末考试试卷及答案解析第一部分阅读（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A、B、C、D四个选项中选出最佳选项AVienna Concerts 2021Every day, one to three dozen Vienna concerts are staged. You can use this checklist to find a fantastic Vienna concert that is worth its money.Vienna Chamber OrchestraThe Vienna Chamber Orchestra has existed for more than 70 years. The international reputation of the Vienna Chamber Orchestra is documented by worldwide tours. The length is 65 minutes.Date: 20th JuneLocation: Minoritenkirehe, Minoritenplatz 1, 1010 ViennaTickets: 30 Euros per adult and free admission for childrenVienna Philharmonic OrchestraIn 2021, famous conductor Gustavo Dudamel will lead the Vienna Philharmonic Orchestra. Expect an amazing show with top quality classical music and fireworks. The concert lasts one and a half hours. You have to arrive at least 20 minutes early to find a place to sit.Date: 4th and 5th OctoberLocation: Schonbrunn Palace, palace gardens, in front of Naptune fountain, Schonbrunner Schlossstrasse 47, 1130 Vienna.Tickets: 30 Euros（students, children and senior citizens will receive a 10% discount per ticket）Mozart Piano Sonatas（奏鸣曲）On Saturdays and Sundays, the St. Peter’s church opens its basement to a small group of Mozart fans. In simple but elegant surroundings, international pianists perform Mozart piano sonatas on a Steinway piano. The concerts start in the early evening and last 90 minutes.Date: throughout the yearLocation: St. Peter’s basement, Petersplatz 1, 1010 ViennaTickets: 29 Euros for adults and 16 Euros for children between 8 and 14（children below 8 can enterfor free.）Vivaldi: The Four SeasonsTo point out Vivaldi’s connection to Vienna, the Italian violinist lived in the city for some time, and eventually died there. Closer to where he was buried, the church St. Charles Borromeo regularly stages The Four Seasons, Vivaldi’s main work. The concerts start at 8:15 pm on weekends and last 60 minutes. People can arrive and enter anytime during the performance.Date: throughout the yearLocation: Church St. Charles Borromeo（Karlskirche）, Kreuzherrengase 1, 1040 ViennaTickets: 25 Euros for all ages（free cancellation 24 hours before the event）1.For a couple with their 10-year-old child, which is the cheapest?A.Mozart Piano Sonatas.B.Vienna Chamber Orchestra.C.Vivaldi: The Four Seasons.D.Vienna PhilharmonicOrchestra.2.What do the Vienna Philharmonic Orchestra and Mozart Piano Sonatas have in common?A.They last one and a half hours.B.They are held in closed surroundings.C.They offer a discount for students and the aged.D.They are suitable for people who prefer pop music.3.What can we know about the concert—The Four Seasons?A.It forbids people to enter after 8:15 pm.B.It describes Vivaldi’s stories related to Vienna.C.It allows you to return your ticket for free a day in advance.D.It was created by the Church St. Charles Borromeo to memorize Vivaldi.BA new look for technology, Solestrom’s new high-tech swimsuits promise to stand out all summer long. First in their new products is Solestrom’s new SmartSwimCMUV Smart Bikini featuring a smart UV meter.The bikini collects UV information through a smart fabric belt and reports the UV index to the wearer with 0.01 exactness. The electronic parts are neatly built into the removable belt, and can be worn even underwater. Next in the list is a lower cost cousin, the SmartSwimCMUV Index Detector Bikini, which has UV sensitive beads that change color1 with the level of UV intensity. The reading gives more of a range rather than an exact number, but for those who simply need to know if the UV is low, moderate or high, this bikini fits the bill.It is now available in Banana Split, more color1 s may become available later in the season. And finally, whatcould be better than a beach tote with built in energy source? No need to suffer dead batteries in your MP3, just plug them into your Solar Powered Beach Tote for on-the-go mobile charging. This beach tote combines fashion and functionality all in one, lightweight and roomy beach accessory. A built in solar panel charges fully most small electronics in only 2-3 hours of sunlight. Pauline Butler, Media Relations Manger at Solestrom states “the concept of blending fashion and technology is growing at amazing rate, and we are right on the leading edge. Our products are new, creative and meet the need of the young and environmentally conscious crowd.’’Solestrom’s SmartSwinirCMproducts retail from $98. 99- $189. 99，and can be found in their online store, Solestrom. com.4. What is the passage mainly about?A. Famous Solestrom and its Products.B. Fashionable and Functional Beach Tote.C. Smart swimsuits and Solar Powered Beach Tote.D. Where and How to Buy SmartSwirn and the Beach Tote.5. Why are UV sensitive beads used in the SmartSwirnCMUV Index Detector Bikini?A. To give an exact number.B. To know if the UV is low, moderate or high.C. To change color1 with the level of UV intensity.D. To improve the equality of the UV Index Detector Bikini.6. What can we know about Solar Powered Beach Tote?A. Its parts are fixed in the belt.B. It combines lightweight and functionality.C. It can tell the weaver the level of UV intensity.D. It saves people from worrying about dead batteries in their MP3.7. Who will prefer the new products mentioned in the text?A. The young people and the environmentalists.B. People who like to travel all over the world.C. People who love to buy goods online.D. People interested in the latest bag.CAs an eco-minimalist, Su Yige has maintained an environmentally friendly and sustainable lifestyle for the past three years while studying in Canada. She takes her own bag when she goes grocery shopping and uses second-hand items as often as possible. She avoids almost all paper-related products unless she has to use apublic toilet while away from home.Diligence and thrift are time-honored traditional Chinese virtues. Su's family is a good example of this, according to the native of Weihai, Shandong province. Although they have little formal “green” knowledge, her parents lead a very environmentally friendly life.For example, the family has used the same hair dryer for more than a decade, and Su remembers many of her mother's clothes from as far back as kindergarten. “As long as something can still be used, my mother will not replace it with a new item,” she said.“I frequently asked my father to bring the plastic bag back home after dumping our waste in the trash bin. He was unhappy, and argued that instead of making that request, I should go downstairs to dump the waste myself” she said. In another move, her father criticized her for doing too much shopping online. Eventually, they both made steps toward becoming better environmentalists. Her father brings the bag back for reuse and she has only bought two pieces of clothing online in the past six months.Back in Canada, Su is looking forward to finding a job related to sustainable development in China after she graduates as a computer science major in the summer.8. Which of the following best describes Su Yige?A. Conservative.B. Nostalgic.C. Economical.D. Productive.9. What can be found about Su's mother according to the third paragraph?A. She has a lot of formal green knowledge.B. She regards using the same items as a lifestyle.C. She always wears old clothes due to lack of money.D. She will not replace the old items until they are out of style.10. What can be inferred about Su and her father?A. Both of them like to criticize each other.B. Su's father is particular about her clothes.C. The relationship between them is very tense.D. They urge each other to become more environmentally friendly.11. What can we learn about the author soon after she graduates in Canada?A. She will stay there to look for a job.B. She will put effort into computer science.C. She will devote herself to her motherland's future.D. She will come back to China to stay with her parents.DNow most of the workers work from 9 am to 5 pm. However, according to the global Internet survey done by the UK Sleep Council, thesiesta（午睡）was the right idea all along. The UK Sleep Council called on the country'sbosses to end nine-to-five working in favor of more flexible hours. They believe what would really increase the workers' productivity is a nice afternoon nap, rather than those bonuses.Forty-one percent of the 12,000 people who responded to the council's survey said they were most productive in the morning, while 38 percent said theyhit their stridein the evening. "This means most of them cannot fully pay attention to what they do in the middle of the day," said sleep expert Dr. Chris Idzikowskii. "We must conclude from this survey that the traditional nine-to-five working day does not suit most workers." He suggested that allowing workers to follow their natural sleeping habits would actually benefit employers by allowing them to expand their working hours and be more productive.Fortunately, being a college lecturer, I don't have to go to work everyday. I only work three days a week, but during the three days I work really long hours and have no time for a little siesta. I'm usually so tired and sleepy in the afternoon, which really affects thevitality（活力）of my classes.I think Dr. Chris Idzikowskii's idea is worthwhile. When people have flexible working hours they could reach their highest productivity. On top of that, flexible working hours mean thatpeople don't have to work all at the same time. That way we could avoid traffic jams. Therefore, it's really killing two birds with one stone!12. What can improve the workers' productivity, according to the UK Sleep Council?A. More bonuses.B. The flexible working time.C. Working for long hours.D. Working in a relaxing way.13. What does the underlined part probably mean in Paragraph 2?A. Were most sleepy.B. Were most flexible.C. Worked at their own pace.D. Worked at their best.14. What did the UK Sleep Council's survey find?A. Few people are suitable to work at noon.B. People are more productive in the morning.C. Some people like to expand their working hours.D. More and more people prefer to work in the evening.15. Why does the author support Dr. Chris Idzikowskii's idea?A. It could solve most of the traffic problems.B. He finds Dr. Chris Idzikowskii respectable.C. He thinks the idea can benefit the society.D. It allows him to work for fewer hours.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2019-2020学年吉林大学附属中学高中部高三英语下学期期末试卷及答案解析
2019-2020学年吉林大学附属中学高中部高三英语下学期期末试卷及答案解析第一部分阅读（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A、B、C、D四个选项中选出最佳选项AWhile Jennifer was at home taking an online exam for her business law class, a monitor（监控器）a few hundred miles away was watching her every move.Using a web camera equipped in Jennifer'sLos Angelesapartment, the monitor inPhoenixtracked how frequently her eyes moved from the computer screen and listened for the secret sounds of a possible helper in the room. Her Internet access was locked remotely to prevent Internet searches, and her typing style was analyzed to make sure she was who she said she was: Did she enter her student number at the same speed as she had in the past？Or was she slowing down？In the battle against cheating, this is thecutting edgeand a key to encourage honesty in the booming field of online education. This technology gives trust to the entire system, to the institution and to online education in general. Only with solid measures against cheating, experts say, can Internet universities show that their exams and diplomas are valid — that students haven't searched the Internet to get the right answers.Although online classes have existed for more than a decade, the concern over cheating has become sharper in the last year with the growth of "open online courses". Private colleges, public universities and corporations are jumping into the online education field, spending millions of dollars to attract potential students, while also taking steps to help guarantee honesty at a distance.Aside from the web cameras, a number of other high-tech methods are becoming increasingly popular. Among them are programs that check students’ identities using personal information, such as the telephone numbers they once used.Other programs can produce unique exams by drawing on a large list of questions and can recognize possible cheaters by analyzing whether difficult test questions are answered at the same speed as easy ones. As in many university classes, term papers are scanned against some large Internet data banks for cheating.1. Why was Jennifer watched in an online exam?A. To correct her typing mistakes.B. To find her secrets in the room.C. To keep her from dishonest deeds.D. To prevent her from slowing down.2. What does the underlined expression "cutting edge" in Paragraph 3 probably mean?A. sharpening toolB. advanced techniqueC. effective ruleD. dividing line3. How can some programs find out possiblecheaters?A. By scanning the Internet test questions.B. By checking the question answering speed.C. By producing a large number of questions.D. By giving difficult test questions.BCoke was introduced by the Coca Cola company in 1886, making it a rather true andtested favorite of generations of people in over 200 countries. This list should give you some ideas on how to get more from your coke than usual.. Coca Cola is an excellent rust buster (除锈剂). If you have a bunch of small rusty objects, put them in coke overnight and give them a goodscrubin the morning. Coke helps to break down the rust, making cleaning much easier. Be sure to throw out the used coke when you are done with it or you might be taking a trip to the doctor.. Like the previous item, the citric acid (柠檬酸) in coke makes for an excellent window cleaner. This is especially useful for car windows. Pour a can of coke over the window and rub the window, then wipe it off with a wet cloth to remove any sugary matter from the sugar in the drink. As coke is fullof sugar, you should clean the sticky matter off the window glasses, or it will be not a cleaner but a dirt.. For those of you who live in areas where skunk (臭鼬) smells can be an issue from time to time, one can of coke added to water with detergent (清洁剂) really helps to break the smell down. If you have been sprayed, stand in the shower and cover yourself from head to toe with coke — wait for a few minutes, then wash yourself with a shower. Coke is an excellent hair treatment so you get two tips for the price of one with this item!. Pots can sometimes get black on the bottom. The black is almost impossible to remove; this is caused by over-cooking. To remove the black and renew your pot, pour in a can of coke (or as much as you need to cover the blackened area by an inch) and put it on the stove on a low heat. After an hour or so, wash the pot as normal.4. What does the underlined word “scrub”in Paragraph 2 probably mean?A. Start.B. Cleaning.C. Shake.D. Example.5. What is important while using coke to clean car windows?A. Use a dry cloth.B. Rub the window lightly.C. Don’t pour too much coke.D. Clean the sugary matter thoroughly.6. For which purpose does coke have to be mixed with other material?A. To get rid of the black on the pot.B. To breakdown the rust,C. To remove smells.D. To clean windows.7. What type of writing is this text?A. An advertisement.B. A review.C. A news report.D. A practical guide.CSurfing the Internet for fun will make you a better employee, according to an Australian study.The University of Melbourne study shows that people who use the Internet for their own reasons at work are about 9 percent more productive than those who do not. Study author Brent Coker said, “Surfing the Internet at times helps increase an employee's attention.”“People need to relax for a bit to get back their attention,” Coker said on the university's website. “Having a short break, such as a quick surfing of the Internet, helps the mind to rest itself, leading to a higher total Internet attention for a day's work, and as a result, increases productivity (生产效率),” he said.According to the study of 300 workers, 70 percent of people who use the Internet at work surf the Internet for their own reasons during office hours. Among the most popular surfing activities are searching for information about products, reading online news, playing online games and watching videos. “Firms spend a lot of money on software toblocktheir employees from watching videos, using social networking sites or shopping online,” said Coker. “That's not always a good idea.”However, Coker said the study looked at people who surfed the Internet in moderation (适度), or were on the Internet for less than 20 percent of their total time in the office. “Those who spend too much time surfing the Internet will have a lower productivity than those without.” he said.8. What does the University of Melbourne study mainlyshow?A. People who surf the Internet are good employees.B. Not everyone surfs the Internet for fun during office hours.C. The Internet is becoming more and more important in people's life.D. Surfing the Internet for fun at times during office hours increases productivity.9. Which of the following is NOT mentioned in the passage as one of the most popular surfing activities?A. Watching videos.B. Reading online news.C. Reading online novels.D. Playing online games.10. The underlined word “block” in Paragraph 4 means “________”.A. stopB. organizeC. protectD. separate11. What can we infer from the last paragraph?A. Those who never surf the Internet have the lowest productivity.B. Spending too much time surfing the Internet reduces productivity.C. Most people don't surf the Internet in moderation during office hours.D. People should spend as little time as possible surfing the Internet.DIn sportthe sexes are separate. Women and men do not run or swim in the same races. Women are less strong than men.That at least is what people say.Women are called the weaker sex, or, if men want to please them, the fair sex. But boys and girls are taught together at schools and universities. There are women who are famous Prime Ministers, scientists and writers. And women live longer than men. A European woman can expect to live until the age of 74, a man only until he is 68. Are women’s bodies really weaker?The fastest men can run a mile in under 4 minutes. The best women need 4.5 minutes. Women’s time is always slower than men’s, but some facts are a surprise. Some of the fastest women swimmers today are teenage girls. One of them swam 400 meters in 4 minutes 21.2 seconds when she was only 16. The first ‘Tartan’ in film was an Olympic swimmer, Johnny Weissmuller. His fastest 400 meters was 4 minutes 49.1 seconds, which is 37.9 seconds slower than a girl 50 years later! This does not mean that women are catching men up. Conditions are very different now and sport is much more serious. It is so serious that some women athletes are given hormoneinjections. At the Olympics a doctor has to check whether the women athletes are really women or not. It seems sad that sport has such problems. Life can be very complicated when there are two separate sexes!12. Women are called the weaker sex because _________.A. women do as much as menB. people think women are weaker than menC. sport is easier for men than for womenD. in sport the two sexes are always together13. Which of the following is true?A. Boys and girls study separately everywhere.B Women do not run or swim in races with men.C. Famous Prime Ministers are women.D. Men can expect to live longer than women in Europe.14. The underlined part “That at least is what people say” means people _________.A. say other things, tooB. don’t say this muchC. say this but may not think soD. only think this15. In this passage the author implies that _________.A. womenare weaker than men, but fasterB. women are slower than men, but strongerC. men are not always stronger and faster than womenD. men are faster and stronger than women第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2019-2020学年吉林大学附属中学高中部高三英语下学期期末考试试卷及答案解析
2019-2020学年吉林大学附属中学高中部高三英语下学期期末考试试卷及答案解析第一部分阅读（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A、B、C、D四个选项中选出最佳选项AEach year, theLas Vegasconsumer electronics show, or CES, presents the latest developments in many areas of technology. The newest products are designed to make our lives easier, fun and more productive.A car with legsOne of this year’s presentations was by South Korean carmaker Hyun-dai. The company introduced a small model of a “ walking car,” which is called Elevate. It has four movable legs that can raise the main part of the vehicle high off the ground. The electric-powered vehicle is designed to be used in search-and-rescue operations during emergencies or natural disasters.Changeable people moverGermany's Mercedes presented an experimental self-driving vehicle that it claims can revolutionize transportation for people and goods. The company says the vehicle, called Vision Urbanetic, will be able lo easily change bodies depending on its desired use. Mercedes says as a ride-sharing vehicle , the futuristic-looking car can seat 12 people.Fully electric HarleyAmerican manufacturer Harley-Davidson showed off its first fully electric motorcycle, called LiveWire. The company says the bike will be able to go 177 kilometers between charges. It can reach 96 kilometers per hour in under3.5 seconds. Although Harley is known for building powerful bikes with huge, loud motors, the LiveWire will be unusually quiet.Personal robotsOne of the new robots, called Temi, is really just a computer tablet on wheels. It is designed to be a personal electronic assistant. It moves around the home and performs commands when spoken to. It can link users to friends through voice or video, connect to video or place orders for food or goods.1. Which do you probably use to search for the injured in an earthquake?A. Elevate.B. Vision Urbanetic.C. LiveWire.D. Temi.2. What is the first fully electric motorcycle produced by Harley-Davidson?A. ElevateB. Hyun-daiC. LiveWire .D. Temi .3. Why are the four products designed?A. To ease traffic jam.B. To help us socialize.C. To improve our life.D. To protect the environment.BOlder adults with a better sense of smell may live longer than thosewho have a poor sense of smell, a new study suggests. The study was a project of researchers in theUnited Statesthat was ongoing for over 13 years. They asked nearly 2,300 men and women to identify 12 common smells. All the subjects were from 71 to 82 years of age. The researchers gave the adults scores, from 0 to as high as 12, based on how many smells they identified correctly.During the years of follow-up investigation, over 1,200 of the subjects died. When the study was launched, none of the adults were weak. They could walk a little under half a kilometer, climb 10 steps and independently complete daily activities. In the latest findings, the researchers noted that those with a weak nose were 30 percent more likely to die than people with a good sense of smell. The findings were reported last month in the scientific publication Annals of Internal Medicine.Honglei Chen, a doctor withMichiganStateUniversityinEast Lansing,Michigan, was the lead writer of a report on the study. He said the connection between a poor sense of smell and an increased risk of dying was limited to adults who first reported good-to-excellent health. This suggests that a poor sense of smell is an early and sensitive sign for worsening health before it is recognizable in medical tests. With a poor sense of smell, people are more likely to die of brain and heart diseases, but not of cancer or breathing disorders.The results also suggest that a poor sense of smell may be an early warning for poor health in older age that goesbeyond dementia or other neurodegenerative(神经变性的) diseases. These often signal the beginning of a weakening of the mind or body.4. What do you know about the study mentioned?A. The study involved researchers from the world.B. All the participants were of different ages.C. The study began to be performed about 13 years ago.D. 2 ,300 men and women were young and healthy.5. What was the situation like at the beginning of the study?A. More than 1,200 of the participants passed away.B. Many of the subjects were found with health problems.C. All the subjects were independent of others when walking.D. One third of the participants had a poor smell sense.6. What can be inferred from the last two paragraphs?A. People with a poor sense of smell have heart disease.B. You should be careful with your health if you smell poorly.C. People with a poor sense of smell won't suffer from cancer.D. Most of the elder people may have the dementia disease.7. Which is the best title for the passage?A. Strong Sense of Smell May Be Linked to Longer LifeB. Old People Tend to Have a Poor Sense of SmellC. A Number of Factors Result in Longer LifeD. Being Ill Means Losing the Sense of SmellCBe it from the mouths of foreigners who have lived here for a few years or from stories on travel websites, one of the most common qualities that people list about Shanghai is the infectious energy that courses through the city.For some, this energy is defined by the way of life—Shanghai is a city that never sleeps. In the day, the streets arc always bustling with people from all over the world. After all, the city has long been China’s most cosmopolitan city, having been the epicenter of trade and cultural exchange between Chinese and foreigners since the city was forced to open its door to the world in 1843 after the First Opium War (1840-42).Shanghai’s ubiquitous delivery people can be found on the roads even past midnight, rushing from point to point on their trusty electric scooters to satiate the hunger of night owls. Even before the break of dawn, pensioners can be found gathering in parks, ready to kick start their day with a tai chi session.For others, this energy is generated from the friction between the contrasts the city has. Indeed, it does not take long for one to realize that Shanghai's charmlies in it being a binary of old and new.Here, charming neoclassical architecture and art deco structures stand alongside modem buildings with shimmering glass and metal facades, rustic (质朴的)lane houses and shikumen buildings. Humble mom-and-pop shops that look stuck in time can often be found right next tohipdining venues or industrial-chic fashion stores selling designer apparel.One of the best places to get an overview of these surreal contrasts is none other than the tallest building in the city — the Shanghai Tower in Lujiazui. Measuring a dizzying 632 meters in height, this architectural marvel boasts having the world's highest observation deck within a building or structure. It also comes with the world's fastest elevators which would get you from the bottom to the top at 20.5 meters per second.On the other side of the Huangpu River is where you would find the Bund, which is home to magnificent neoclassical buildings. The Bund is to Shanghai what Times Square is to New York or what the Champs-61ysees is to Paris. A trip to Shanghai would not be complete without exploring this iconic waterfront promenade.Autumn is the best time to experience Shanghai on foot, not merely because the weather is conducive for walking, but because this is when the roads and sidewalks in many areas are blanketed with a layer of color1 ful fallen leaves.8. Why is the example of delivery man mentioned?A. To make a contrast with pensioners’ biological clock.B. To illustrate the vibrant energy of modern Shanghai.C. To highlight the diligence and consideration of delivery man.D. To feature the courier delivery service in full swing.9. Which of the following is TRUE about the contrast of Shanghai?A. The contrast mainly arises from the First Opium War.B. The design of the Shanghai Tower stands for a contrast.C. A marked contrast is shown in the use of building materials.D. The dishes served in mom-and-pop shops represent the outdated flavor.10. The underlined word “hip” in paragraph 5 is closest in meaning to________.A. photographicB. modestC. peculiarD. stylish11. Which of the following will be most probably discussed following the last paragraph?A. Stunning views of the Shanghai skyline.B. The best places to view the seasonal spectacle.C. The walking path thathugs the Huangpu River.D. Must-try dishes and food items typical of Shanghai.DThe United Nations Educational, Scientific and Cultural Organization (UNESCO) included on December 17, 2020 China's Tai Chi on the RepresentativeList of the Intangible（无形的）Cultural Heritage of Humanity. Thedecision was announced during the online meeting of the UNESCO Intergovernmental Committee for the Safeguarding of the Intangible Cultural Heritage held from December 14 to19 inKingston, capital ofJamaica.“Born in the mid-17th century in a small village named Chenjiagou located in Central China's Henan province, Tai Chi is not only a kind of traditional Wushu integrated with slow movements and deep breathing, but is also deeply rooted in many areas of Chinese culture, such as medicine and philosophy,”Zhu Xianghua says, who is the son of the famous Tai Chi master Zhu Tiancai.Although it has spread to more than 150 countries and regions, attracting more than 100 million people to practice, the idea that Tai Chi is for the elderly has stopped many young people practicing the ancient Wushu. They think of it as a slow exercise, which is specially made and better suited for their grandparents. Instead, many young people are turning to the Indian practice of yoga（瑜伽）to relieve stress, which was placed on the UNESCO's List in 2019.In order to promote Tai Chi, joint efforts have been made from individuals and the Chinese government in the last decades. Xi'an Jiaotong University requires students to learn Tai Chi. Wang Yunbing, a professor in the university's sports center, stressed that Tai Chi is not only good physical exercise-researchers from the American College of Rheumatology find that it can help manage several diseases but is also conned ted to ancient Chinese eivilization. Since 2014, the World Tai Chi Championships have been held every two years by the International Wushu Federation. It provides a platform for communication and learning between the Tai Chi masters and Tai Chi lovers around the globe. In January 2020, Tai Chi became an official event in the 2026 Dakar Youth Olympic Games.12. What does Zhu Xianghua say about Tai Chi in paragraph 2?A. It originated from fast Kung Fu action.B. It was born around the 1750s in a village.C. It is related to other cultural fields ofChina.D. It integrates Chinese medicine and western philosophy.13. Why do some young people choose to practice yoga instead of Tai Chi?A. They think it easier to practice yoga to keep fit.B. The elderly stop young people practicing Tai Chi.C. They consider Tai Chi is custom-built for old people.D. Yoga was included in the world culture earlier than Tai Chi.14. What is the main purpose of the last paragraph?A. To promote contemporary Chinese civilization.B. To show many efforts made to popularize Tai Chi.C. To stress the importance of Chinese Tai Chi masters.D. To advise people to practise Tai Chi to cure diseases.15.Which of the following is the best title for the passage?A. Tai Chi Steps on the UNESCO's List.B. Tai Chi is Competing against Yoga.C. Tai Chi Has Regained populate Globally.D. Opinions Greatly Differ on Tai Chi and Yoga.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。