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备战中考物理易错题专题训练-机械效率的计算练习题附答案解析

备战中考物理易错题专题训练-机械效率的计算练习题附答案解析

一、初中物理有用功额外功总功机械效率的计算问题1.如图所示,物体A在拉力的作用下沿水平面匀速运动了一段距离s,试比较拉力F1、F2及拉力所做的功W1、W2的大小(滑轮重、绳重及绳与滑轮之间的摩擦不计)。

下列判断正确的是A.F1=2F2W1=W2B.F1=12F2W1=12W2C.F1=4F2W1= W2D.F1=14F2W1=14W2【答案】C【解析】【详解】物体A在两种情况下的摩擦力f相等,上图滑轮是动滑轮,下图滑轮的轴固定不动,可以看做是特殊使用的定滑轮。

则:F1=2fF2=1 2 f故:F1=4F2根据功的公式可知:W1=F1×12s=2f×12s=fsW2=F2×2s=12f×2s=fs故:W1=W2,故选C。

2.小黄用图所示的滑轮组经过10s的时间,用150N的拉力将一个重270N的重物提高1m,求此过程:拉力F自由端拉出的距离是_____m;小黄所做的有用功是_______J;总功是_______J;拉力做功的功率是______W。

【答案】3 270 450 45 【解析】 【分析】 【详解】[1]由图可知,滑轮组的承重绳子根数n =3根,则拉力自由端拉出的距离s =nh =3×1m=3m[2]有用功W 有用=Gh =270N×1m=270J[3]总功W 总=Fs =150N×3m=450J[4]拉力做功的功率450J45W 10sW P t ===总3.如图所示,用滑轮组拉动重为200N 的物体在水平桌面上匀速直线运动。

已知F =20N ,滑轮组的机械效率为85%,则物体与桌面的之间的摩擦力大小为__________N 。

【答案】51 【解析】 【分析】 【详解】由图可知,由3段绳子通过动滑轮,则s F =3s 物,滑轮组的机械效率为85%,即η=W W 有总=F fs Fs 物 =3f F =320Nf=⨯85% 解得f =51N即物体与桌面的之间的摩擦力为51N 。

备战中考数学易错题专题复习-平行四边形练习题附详细答案

备战中考数学易错题专题复习-平行四边形练习题附详细答案

一、平行四边形真题与模拟题分类汇编(难题易错题)1.已知,在矩形ABCD中,AB=a,BC=b,动点M从点A出发沿边AD向点D运动.(1)如图1,当b=2a,点M运动到边AD的中点时,请证明∠BMC=90°;(2)如图2,当b>2a时,点M在运动的过程中,是否存在∠BMC=90°,若存在,请给与证明;若不存在,请说明理由;(3)如图3,当b<2a时,(2)中的结论是否仍然成立?请说明理由.【答案】(1)见解析;(2)存在,理由见解析;(3)不成立.理由如下见解析.【解析】试题分析:(1)由b=2a,点M是AD的中点,可得AB=AM=MD=DC=a,又由四边形ABCD 是矩形,即可求得∠AMB=∠DMC=45°,则可求得∠BMC=90°;(2)由∠BMC=90°,易证得△ABM∽△DMC,设AM=x,根据相似三角形的对应边成比例,即可得方程:x2﹣bx+a2=0,由b>2a,a>0,b>0,即可判定△>0,即可确定方程有两个不相等的实数根,且两根均大于零,符合题意;(3)由(2),当b<2a,a>0,b>0,判定方程x2﹣bx+a2=0的根的情况,即可求得答案.试题解析:(1)∵b=2a,点M是AD的中点,∴AB=AM=MD=DC=a,又∵在矩形ABCD中,∠A=∠D=90°,∴∠AMB=∠DMC=45°,∴∠BMC=90°.(2)存在,理由:若∠BMC=90°,则∠AMB+∠DMC=90°,又∵∠AMB+∠ABM=90°,∴∠ABM=∠DMC,又∵∠A=∠D=90°,∴△ABM∽△DMC,∴AM ABCD DM=,设AM=x,则x aa b x =-,整理得:x2﹣bx+a2=0,∵b>2a,a>0,b>0,∴△=b2﹣4a2>0,∴方程有两个不相等的实数根,且两根均大于零,符合题意,∴当b>2a时,存在∠BMC=90°,(3)不成立.理由:若∠BMC=90°,由(2)可知x2﹣bx+a2=0,∵b<2a,a>0,b>0,∴△=b2﹣4a2<0,∴方程没有实数根,∴当b<2a时,不存在∠BMC=90°,即(2)中的结论不成立.考点:1、相似三角形的判定与性质;2、根的判别式;3、矩形的性质2.操作:如图,边长为2的正方形ABCD,点P在射线BC上,将△ABP沿AP向右翻折,得到△AEP,DE所在直线与AP所在直线交于点F.探究:(1)如图1,当点P在线段BC上时,①若∠BAP=30°,求∠AFE的度数;②若点E 恰为线段DF的中点时,请通过运算说明点P会在线段BC的什么位置?并求出此时∠AFD 的度数.归纳:(2)若点P是线段BC上任意一点时(不与B,C重合),∠AFD的度数是否会发生变化?试证明你的结论;猜想:(3)如图2,若点P在BC边的延长线上时,∠AFD的度数是否会发生变化?试在图中画出图形,并直接写出结论.【答案】(1)①45°;②BC的中点,45°;(2)不会发生变化,证明参见解析;(3)不会发生变化,作图参见解析.【解析】试题分析:(1)当点P在线段BC上时,①由折叠得到一对角相等,再利用正方形性质求出∠DAE度数,在三角形AFD中,利用内角和定理求出所求角度数即可;②由E为DF中点,得到P为BC中点,如图1,连接BE交AF于点O,作EG∥AD,得EG∥BC,得到AF 垂直平分BE,进而得到三角形BOP与三角形EOG全等,利用全等三角形对应边相等得到BP=EG=1,得到P为BC中点,进而求出所求角度数即可;(2)若点P是线段BC上任意一点时(不与B,C重合),∠AFD的度数不会发生变化,作AG⊥DF于点G,如图1(a)所示,利用折叠的性质及三线合一性质,根据等式的性质求出∠1+∠2的度数,即为∠FAG度数,即可求出∠F度数;(3)作出相应图形,如图2所示,若点P在BC边的延长线上时,∠AFD的度数不会发生变化,理由为:作AG⊥DE于G,得∠DAG=∠EAG,设∠DAG=∠EAG=α,根据∠FAE为∠BAE一半求出所求角度数即可.试题解析:(1)①当点P在线段BC上时,∵∠EAP=∠BAP=30°,∴∠DAE=90°﹣30°×2=30°,在△ADE中,AD=AE,∠DAE=30°,∴∠ADE=∠AED=(180°﹣30°)÷2=75°,在△AFD中,∠FAD=30°+30°=60°,∠ADF=75°,∴∠AFE=180°﹣60°﹣75°=45°;②点E为DF 的中点时,P也为BC的中点,理由如下:如图1,连接BE交AF于点O,作EG∥AD,得EG∥BC,∵EG∥AD,DE=EF,∴EG=AD=1,∵AB=AE,∴点A在线段BE的垂直平分线上,同理可得点P在线段BE的垂直平分线上,∴AF垂直平分线段BE,∴OB=OE,∵GE∥BP,∴∠OBP=∠OEG,∠OPB=∠OGE,∴△BOP≌△EOG,∴BP=EG=1,即P为BC的中点,∴∠DAF=90°﹣∠BAF,∠ADF=45°+∠BAF,∴∠AFD=180°﹣∠DAF﹣∠ADF=45°;(2)∠AFD的度数不会发生变化,作AG⊥DF于点G,如图1(a)所示,在△ADE中,AD=AE,AG⊥DE,∵AG平分∠DAE,即∠2=∠DAG,且∠1=∠BAP,∴∠1+∠2=×90°=45°,即∠FAG=45°,则∠AFD=90°﹣45°=45°;(3)如图2所示,∠AFE的大小不会发生变化,∠AFE=45°,作AG⊥DE于G,得∠DAG=∠EAG,设∠DAG=∠EAG=α,∴∠BAE=90°+2α,∴∠FAE=∠BAE=45°+α,∴∠FAG=∠FAE﹣∠EAG=45°,在Rt△AFG中,∠AFE=90°﹣45°=45°.考点:1.正方形的性质;2.折叠性质;3.全等三角形的判定与性质.3.如图,在△ABC中,∠ACB=90°,∠CAB=30°,以线段AB为边向外作等边△ABD,点E 是线段AB的中点,连接CE并延长交线段AD于点F.(1)求证:四边形BCFD为平行四边形;(2)若AB=6,求平行四边形ADBC的面积.【答案】(1)见解析;(2)S平行四边形ADBC273【解析】【分析】(1)在Rt△ABC中,E为AB的中点,则CE=12AB,BE=12AB,得到∠BCE=∠EBC=60°.由△AEF≌△BEC,得∠AFE=∠BCE=60°.又∠D=60°,得∠AFE=∠D=60度.所以FC∥BD,又因为∠BAD=∠ABC=60°,所以AD∥BC,即FD//BC,则四边形BCFD是平行四边形.(2)在Rt△ABC中,求出BC,AC即可解决问题;【详解】解:(1)证明:在△ABC中,∠ACB=90°,∠CAB=30°,∴∠ABC=60°,在等边△ABD中,∠BAD=60°,∴∠BAD=∠ABC=60°,∵E为AB的中点,∴AE=BE,又∵∠AEF=∠BEC,∴△AEF≌△BEC,在△ABC中,∠ACB=90°,E为AB的中点,∴CE=12AB,BE=12AB,∴CE=AE,∴∠EAC=∠ECA=30°,∴∠BCE=∠EBC=60°,又∵△AEF≌△BEC,∴∠AFE=∠BCE=60°,又∵∠D=60°,∴∠AFE=∠D=60°,∴FC∥BD,又∵∠BAD=∠ABC=60°,∴AD∥BC,即FD∥BC,∴四边形BCFD是平行四边形;(2)解:在Rt△ABC中,∵∠BAC=30°,AB=6,∴BC=AF=3,AC=33∴S平行四边形BCFD=3×3393,S△ACF=12×3×3332,S平行四边形ADBC=32.【点睛】本题考查平行四边形的判定和性质、直角三角形斜边中线定理、等边三角形的性质、解直角三角形、勾股定理等知识,解题的关键是正确寻找全等三角形解决问题,属于中考常考题型.4.正方形ABCD,点E在边BC上,点F在对角线AC上,连AE.(1)如图1,连EF,若EF⊥AC,4AF=3AC,AB=4,求△AEF的周长;(2)如图2,若AF=AB,过点F作FG⊥AC交CD于G,点H在线段FG上(不与端点重合),连AH.若∠EAH=45°,求证:EC=HG+2FC.【答案】(1)25422)证明见解析【解析】【分析】(1)由正方形性质得出AB=BC=CD=AD=4,∠B=∠D=90°,∠ACB=∠ACD=∠BAC=∠ACD=45°,得出AC2AB=2,求出AF=2,CF=AC﹣AF2,求出△CEF 是等腰直角三角形,得出EF=CF2,CE2CF=2,在Rt△AEF中,由勾股定理求出AE,即可得出△AEF的周长;(2)延长GF交BC于M,连接AG,则△CGM和△CFG是等腰直角三角形,得出CM=CG,CG2CF,证出BM=DG,证明Rt△AFG≌Rt△ADG得出FG=DG,BM=FG,再证明△ABE≌△AFH,得出BE=FH,即可得出结论.【详解】(1)∵四边形ABCD是正方形,∴AB=BC=CD=AD=4,∠B=∠D=90°,∠ACB=∠ACD=∠BAC=∠ACD=45°,∴AC2AB=2,∵4AF=3AC=2,∴AF=2∴CF=AC﹣AF2∵EF⊥AC,∴△CEF是等腰直角三角形,∴EF=CF2CE2CF=2,在Rt△AEF中,由勾股定理得:AE2225+=AF EF=∴△AEF的周长=AE+EF+AF=252322542(2)证明:延长GF交BC于M,连接AG,如图2所示:则△CGM 和△CFG 是等腰直角三角形,∴CM =CG ,CG 2,∴BM =DG ,∵AF =AB ,∴AF =AD ,在Rt △AFG 和Rt △ADG 中,AG AG AF AD =⎧⎨=⎩, ∴Rt △AFG ≌Rt △ADG (HL ),∴FG =DG ,∴BM =FG ,∵∠BAC =∠EAH =45°,∴∠BAE =∠FAH ,∵FG ⊥AC ,∴∠AFH =90°,在△ABE 和△AFH 中,90B AFH AB AFBAE FAH ︒⎧∠=∠=⎪=⎨⎪∠=∠⎩, ∴△ABE ≌△AFH (ASA ),∴BE =FH ,∵BM =BE +EM ,FG =FH +HG ,∴EM =HG ,∵EC =EM +CM ,CM =CG 2CF ,∴EC =HG 2.【点睛】本题考查了正方形的性质、全等三角形的判定与性质、等腰直角三角形的判定与性质、勾股定理等知识;熟练掌握等腰直角三角形的判定与性质,证明三角形全等是解题的关键.5.问题探究(1)如图①,已知正方形ABCD 的边长为4.点M 和N 分别是边BC 、CD 上两点,且BM =CN ,连接AM 和BN ,交于点P .猜想AM 与BN 的位置关系,并证明你的结论.(2)如图②,已知正方形ABCD 的边长为4.点M 和N 分别从点B 、C 同时出发,以相同的速度沿BC、CD方向向终点C和D运动.连接AM和BN,交于点P,求△APB周长的最大值;问题解决(3)如图③,AC为边长为23的菱形ABCD的对角线,∠ABC=60°.点M和N分别从点B、C同时出发,以相同的速度沿BC、CA向终点C和A运动.连接AM和BN,交于点P.求△APB周长的最大值.【答案】(1)AM⊥BN,证明见解析;(2)△APB周长的最大值4+42;(3)△PAB的周长最大值=23+4.【解析】试题分析:根据全等三角形的判定SAS证明△ABM≌△BCN,即可证得AM⊥BN;(2)如图②,以AB为斜边向外作等腰直角△AEB,∠AEB=90°,作EF⊥PA于E,作EG⊥PB于G,连接EP,证明PA+PB=2EF,求出EF的最大值即可;(3)如图③,延长DA到K,使得AK=AB,则△ABK是等边三角形,连接PK,取PH=PB,证明PA+PB=PK,求出PK的最大值即可.试题解析:(1)结论:AM⊥BN.理由:如图①中,∵四边形ABCD是正方形,∴AB=BC,∠ABM=∠BCN=90°,∵BM=CN,∴△ABM≌△BCN,∴∠BAM=∠CBN,∵∠CBN+∠ABN=90°,∴∠ABN+∠BAM=90°,∴∠APB=90°,∴AM⊥BN.(2)如图②中,以AB为斜边向外作等腰直角三角形△AEB,∠AEB=90°,作EF⊥PA于E,作EG⊥PB于G,连接EP.∵∠EFP=∠FPG=∠G=90°,∴四边形EFPG是矩形,∴∠FEG=∠AEB=90°,∴∠AEF=∠BEG,∵EA=EB,∠EFA=∠G=90°,∴△AEF≌△BEG,∴EF=EG,AF=BG,∴四边形EFPG是正方形,∴PA+PB=PF+AF+PG﹣BG=2PF=2EF,∵EF≤AE,∴EF的最大值=AE=2,∴△APB周长的最大值=4+4.(3)如图③中,延长DA到K,使得AK=AB,则△ABK是等边三角形,连接PK,取PH=PB.∵AB=BC,∠ABM=∠BCN,BM=CN,∴△ABM≌△BCN,∴∠BAM=∠CBN,∴∠A PN=∠BAM+∠ABP=∠CBN+∠ABN=60°,∴∠APB=120°,∵∠AKB=60°,∴∠AKB+∠APB=180°,∴A、K、B、P四点共圆,∴∠BPH=∠KAB=60°,∵PH=PB,∴△PBH是等边三角形,∴∠KBA=∠HBP,BH=BP,∴∠KBH=∠ABP,∵BK=BA,∴△KBH≌△ABP,∴HK=AP,∴PA+PB=KH+PH=PK,∴PK的值最大时,△APB的周长最大,∴当PK是△ABK外接圆的直径时,PK的值最大,最大值为4,∴△PAB的周长最大值=2+4.6.(1)问题发现如图1,点E. F分别在正方形ABCD的边BC、CD上,∠EAF=45°,连接EF、则EF=BE+DF,试说明理由;(2)类比引申如图2,在四边形ABCD中,AB=AD,∠BAD=90°,点E. F分别在边BC、CD上,∠EAF=45°,若∠B,∠D都不是直角,则当∠B与∠D满足等量关系时,仍有EF=BE+DF;(3)联想拓展如图3,在△ABC中,∠BAC=90°,AB=AC,点D、E均在边BC上,且∠DAE=45°,猜想BD、DE、EC 满足的等量关系,并写出推理过程。

中考易错题

中考易错题

中考易错题可能会涉及许多不同的主题和知识点,但以下
是一些常见的中考易错题类型:
1. 单位换算:例如,将千米转换为米,或将磅转换为千
克等。

中考中经常会出现这种类型的题目,要求考生对不同
单位之间的换算关系有清晰的理解。

2. 计算错误:中考中经常会出现一些涉及基本运算的题目,例如加减乘除、平方、立方等。

考生在解题时可能会因
为粗心而犯错。

3. 概念混淆:中考中可能会要求考生对一些相似的概念
进行区分,例如相对运动和绝对运动、匀速直线运动和变速
直线运动等。

考生可能会因为对概念的理解不够深入而混淆
它们。

4. 物理问题中的单位换算和公式运用:中考中经常会出
现一些涉及物理问题的题目,要求考生对物理单位进行换算,或者运用不同的公式进行计算。

考生需要掌握基本的物理概
念和公式,并能够灵活运用它们。

5. 化学问题中的化学反应和化学式书写:中考中可能会
要求考生对一些常见的化学反应进行描述,或者书写一些基
本的化学式。

考生需要掌握基本的化学知识,并能够灵活运
用它们。

在备考中考时,建议考生多做一些历年真题和模拟题,找
出自己的薄弱环节并加以改进。

同时,要注重细节和计算准
确性,避免因为粗心而犯错。

精选备战中考数学易错题专题复习二次函数及详细答案

精选备战中考数学易错题专题复习二次函数及详细答案

一、二次函数 真题与模拟题分类汇编(难题易错题)1.如图,已知抛物线2(0)y ax bx c a =++≠的对称轴为直线1x =-,且抛物线与x 轴交于A 、B 两点,与y 轴交于C 点,其中(1,0)A ,(0,3)C .(1)若直线y mx n =+经过B 、C 两点,求直线BC 和抛物线的解析式;(2)在抛物线的对称轴1x =-上找一点M ,使点M 到点A 的距离与到点C 的距离之和最小,求出点M 的坐标;(3)设点P 为抛物线的对称轴1x =-上的一个动点,求使BPC ∆为直角三角形的点P 的坐标.【答案】(1)抛物线的解析式为223y x x =--+,直线的解析式为3y x .(2)(1,2)M -;(3)P 的坐标为(1,2)--或(1,4)-或317(+-或317()--. 【解析】分析:(1)先把点A ,C 的坐标分别代入抛物线解析式得到a 和b ,c 的关系式,再根据抛物线的对称轴方程可得a 和b 的关系,再联立得到方程组,解方程组,求出a ,b ,c 的值即可得到抛物线解析式;把B 、C 两点的坐标代入直线y=mx+n ,解方程组求出m 和n 的值即可得到直线解析式;(2)设直线BC 与对称轴x=-1的交点为M ,此时MA+MC 的值最小.把x=-1代入直线y=x+3得y 的值,即可求出点M 坐标;(3)设P (-1,t ),又因为B (-3,0),C (0,3),所以可得BC 2=18,PB 2=(-1+3)2+t 2=4+t 2,PC 2=(-1)2+(t-3)2=t 2-6t+10,再分三种情况分别讨论求出符合题意t 值即可求出点P 的坐标.详解:(1)依题意得:1203b a a b c c ⎧-=-⎪⎪++=⎨⎪=⎪⎩,解得:123a b c =-⎧⎪=-⎨⎪=⎩,∴抛物线的解析式为223y x x =--+.∵对称轴为1x =-,且抛物线经过()1,0A ,∴把()3,0B -、()0,3C 分别代入直线y mx n =+,得303m n n -+=⎧⎨=⎩,解之得:13m n =⎧⎨=⎩, ∴直线y mx n =+的解析式为3y x =+.(2)直线BC 与对称轴1x =-的交点为M ,则此时MA MC +的值最小,把1x =-代入直线3y x =+得2y =,∴()1,2M -.即当点M 到点A 的距离与到点C 的距离之和最小时M 的坐标为()1,2-. (注:本题只求M 坐标没说要求证明为何此时MA MC +的值最小,所以答案未证明MA MC +的值最小的原因).(3)设()1,P t -,又()3,0B -,()0,3C ,∴218BC =,()2222134PB t t =-++=+,()()222213610PC t t t =-+-=-+, ①若点B 为直角顶点,则222BC PB PC +=,即:22184610t t t ++=-+解得:2t =-,②若点C 为直角顶点,则222BC PC PB +=,即:22186104t t t +-+=+解得:4t =,③若点P 为直角顶点,则222PB PC BC +=,即:22461018t t t ++-+=解得: 1317t +=2317t -=. 综上所述P 的坐标为()1,2--或()1,4-或3171,2⎛+- ⎝⎭或3171,2⎛- ⎝⎭. 点睛:本题综合考查了二次函数的图象与性质、待定系数法求函数(二次函数和一次函数)的解析式、利用轴对称性质确定线段的最小长度、难度不是很大,是一道不错的中考压轴题.2.如图,已知直线y kx 6=-与抛物线2y ax bx c =++相交于A ,B 两点,且点A (1,-4)为抛物线的顶点,点B 在x 轴上。

中考 易错 选择100题 教

中考 易错 选择100题 教

中考 易错 选择100题1、在实数123.0,330tan ,60cos ,722,2121121112.0,,14.3,64,3,80032---- π中,无理数有( ) A 、3个 B 、4个 C 、5个 D 、6个2、下列运算正确的是( )A 、x 2 x 3 =x 6B 、x 2+x 2=2x 4C 、(-2x)2 =4x 2D 、(-2x)2 (-3x )3=6x 53、算式22222222+++可化为( ) A 、42 B 、28 C 、82 D 、1624、“世界银行全球扶贫大会”于2004年5月26日在上海开幕.从会上获知,我国国民生产总值达到11.69万亿元,人民生活总体上达到小康水平,其中11.69万亿用科学记数法表示应为( )A 、11.69³1410B 、1410169.1⨯C 、 1310169.1⨯D 、14101169.0⨯5、不等式2)2(2-≤-x x 的非负整数解的个数为( ) A 、1 B 、2 C 、3D 、4 6、不等式组⎩⎨⎧-≤-->x x x 28132的最小整数解是( ) A 、-1 B 、0 C 、2 D 、3 7、为适应国民经济持续协调的发展,自2004年4月18日起,全国铁路第五次提速,提速后,火车由天津到上海的时间缩短了7.42小时,若天津到上海的路程为1326千米,提速前火车的平均速度为x 千米/小时,提速后火车的平均速度为y 千米/时,则x 、y 应满足的关系式是( )A 、x – y = 42.71326B 、 y – x = 42.71326 C 、y x 13261326-= 7.42 D 、x y 13261326-= 7.42 8、一个自然数的算术平方根为a ,则与它相邻的下一个自然数的算术平方根为( )A 、1+aB 、 1+aC 、12+aD 、1+a9、设B A ,都是关于x 的5次多项式,则下列说法正确的是( )A 、B A +是关于x 的5次多项式 B 、 B A -是关于x 的4次多项式C 、 AB 是关于x 的10次多项式D 、BA 是与x 无关的常数 10、实数a,b 在数轴对应的点A 、B 表示如图,化简a a a b 244-++-||的结果为( )A 、22a b --B 、22+-b aC 、2-bD 、2+b11、某商品降价20%后出售,一段时间后恢复原价,则应在售价的基础上提高的百分数是 ( )A 、20%B 、25%C 、30%D 、35%12、某种出租车的收费标准是:起步价7元(即行驶距离不超过3km 都需付7元车费),超过3km 以后,每增加,加收2.4元(不足1km 按1km 计),某人乘这种车从甲地到乙地共支付车费19元,那么,他行程的最大值是( )A 、11 kmB 、8 kmC 、7 kmD 、5km13、在高速公路上,一辆长4米,速度为110千米/小时的轿车准备超越一辆长12米,速度为100千米/小时的卡车,则轿车从开始追及到超越卡车,需要花费的时间约是( )A 、1.6秒B 、4.32秒C 、5.76秒D 、345.6秒14、如果关于x 的一元二次方程0962=+-x kx 有两个不相等的实数根,那么k 的取值范围是( )A 、1<kB 、0≠kC 、1<k 且0≠kD 、1>k15、若a 2+ma +18在整数范围内可分解为两个一次因式的乘积,则整数m 不可能是( )A 、 ±9B 、±11C 、±12D 、±1916、在实数范围内把8422--x x 分解因式为( )A BA 、)1)(3(2+-x xB 、)51)(51(--+-x xC 、)51)(51(2--+-x xD 、)51)(51(2++-+x x17、用换元法解方程xx x x +=++2221时,若设x 2+x=y, 则原方程可化为( ) A 、y 2+y+2=0 B 、y 2-y -2=0 C 、y 2-y+2=0 D 、y 2+y -2=018、某商品经过两次降价,由每件100元降至81元,则平均每次降价的百分率为( )A 、8.5%B 、9%C 、9.5%D 、10%19、一列火车因事在途中耽误了5分钟,恢复行驶后速度增加5千米/时,这样行了30千米就将耽误的时间补了回来,若设原来的速度为x 千米/时,则所列方程为( ) A 、30305560x x --= B 、30530560x x +-= C 、30305560x x -+= D 、303055x x -+= 20、已知关于x 的方程02=+-m mx x 的两根的平方和是3,则m 的值是( )A 、1-B 、1C 、3D 、1-或321、如果关于x 的一元二次方程0)1(222=+--m x m x 的两个实数根为βα,,则βα+的取值范围是( )A 、1≥+βαB 、1≤+βαC 、21≥+βα D 、21≤+βα 22、已知数轴上的点A 到原点的距离为2,那么在数轴上到A 点的距离是3的点所表示的数有( ) A 、1个 B 、 2个 C 、 3个 D 、4个23、已知)0(1,≥+==a a y a x ,则y 和x 的关系是( ) A 、x y = B 、1+=x y C 、2x y = D 、)0(12≥+=x x y24、点A (2 ,-1)关于y 轴的对称点B 在( )A 、一象限B 、二象限C 、三象限D 、第四象限25、点P(x+1,x -1)不可能在( )A 、第一象限B 、第二象限C 、第三象限D 、第四象限26、已知函数式32+-=x y ,当自变量增加1时,函数值( )A 、增加1B 、减少1C 、增加2D 、减少227、在平面直角坐标系内,A、B、C三点的坐标为(0,0) 、(4,0)、(3,2),以A、B、C三点为顶点画平行四边形,则第四个顶点不可能在( )A、第一象限 B、第二象限 C、第三象限 D、第四象限28、已知一元二次方程02=++c bx ax 有两个异号根,且负根的绝对值较大,则),(bc ab M 在( )A 、第一象限B 、第二象限C 、第三象限D 、第四象限29、“龟兔赛跑”讲述了这样的故事:领先的兔子看着缓缓爬行的乌龟,骄傲起来,睡了一觉。

备战中考数学反比例函数(大题培优 易错 难题)及答案解析

备战中考数学反比例函数(大题培优 易错 难题)及答案解析

一、反比例函数真题与模拟题分类汇编(难题易错题)1.如图,反比例函数y= 的图象与一次函数y= x的图象交于点A、B,点B的横坐标是4.点P是第一象限内反比例函数图象上的动点,且在直线AB的上方.(1)若点P的坐标是(1,4),直接写出k的值和△PAB的面积;(2)设直线PA、PB与x轴分别交于点M、N,求证:△PMN是等腰三角形;(3)设点Q是反比例函数图象上位于P、B之间的动点(与点P、B不重合),连接AQ、BQ,比较∠PAQ与∠PBQ的大小,并说明理由.【答案】(1)解:k=4,S△PAB=15.提示:过点A作AR⊥y轴于R,过点P作PS⊥y轴于S,连接PO,设AP与y轴交于点C,如图1,把x=4代入y= x,得到点B的坐标为(4,1),把点B(4,1)代入y= ,得k=4.解方程组,得到点A的坐标为(﹣4,﹣1),则点A与点B关于原点对称,∴OA=OB,∴S△AOP=S△BOP,∴S△PAB=2S△AOP.设直线AP的解析式为y=mx+n,把点A(﹣4,﹣1)、P(1,4)代入y=mx+n,求得直线AP的解析式为y=x+3,则点C的坐标(0,3),OC=3,∴S△AOP=S△AOC+S△POC= OC•AR+ OC•PS= ×3×4+ ×3×1= ,∴S△PAB=2S△AOP=15;(2)解:过点P作PH⊥x轴于H,如图2.B(4,1),则反比例函数解析式为y= ,设P(m,),直线PA的方程为y=ax+b,直线PB的方程为y=px+q,联立,解得直线PA的方程为y= x+ ﹣1,联立,解得直线PB的方程为y=﹣ x+ +1,∴M(m﹣4,0),N(m+4,0),∴H(m,0),∴MH=m﹣(m﹣4)=4,NH=m+4﹣m=4,∴MH=NH,∴PH垂直平分MN,∴PM=PN,∴△PMN是等腰三角形;(3)解:∠PAQ=∠PBQ.理由如下:过点Q作QT⊥x轴于T,设AQ交x轴于D,QB的延长线交x轴于E,如图3.可设点Q为(c,),直线AQ的解析式为y=px+q,则有,解得:,∴直线AQ的解析式为y= x+ ﹣1.当y=0时, x+ ﹣1=0,解得:x=c﹣4,∴D(c﹣4,0).同理可得E(c+4,0),∴DT=c﹣(c﹣4)=4,ET=c+4﹣c=4,∴DT=ET,∴QT垂直平分DE,∴QD=QE,∴∠QDE=∠QED.∵∠MDA=∠QDE,∴∠MDA=∠QED.∵PM=PN,∴∠PMN=∠PNM.∵∠PAQ=∠PMN﹣∠MDA,∠PBQ=∠NBE=∠PNM﹣∠QED,∴∠PAQ=∠PBQ.【解析】【分析】(1)过点A作AR⊥y轴于R,过点P作PS⊥y轴于S,连接PO,设AP 与y轴交于点C,如图1,可根据条件先求出点B的坐标,然后把点B的坐标代入反比例函数的解析式,即可求出k,然后求出直线AB与反比例函数的交点A的坐标,从而得到OA=OB,由此可得S△PAB=2S△AOP,要求△PAB的面积,只需求△PAO的面积,只需用割补法就可解决问题;(2)过点P作PH⊥x轴于H,如图2.可用待定系数法求出直线PB的解析式,从而得到点N的坐标,同理可得到点M的坐标,进而得到MH=NH,根据垂直平分线的性质可得PM=PN,即△PMN是等腰三角形;(3)过点Q作QT⊥x轴于T,设AQ交x轴于D,QB的延长线交x轴于E,如图3.可设点Q为(c,),运用待定系数法求出直线AQ的解析式,即可得到点D的坐标为(c﹣4,0),同理可得E(c+4,0),从而得到DT=ET,根据垂直平分线的性质可得QD=QE,则有∠QDE=∠QED.然后根据对顶角相等及三角形外角的性质,就可得到∠PAQ=∠PBQ.2.如图,已知抛物线y=﹣x2+9的顶点为A,曲线DE是双曲线y= (3≤x≤12)的一部分,记作G1,且D(3,m)、E(12,m﹣3),将抛物线y=﹣x2+9水平向右移动a个单位,得到抛物线G2.(1)求双曲线的解析式;(2)设抛物线y=﹣x2+9与x轴的交点为B、C,且B在C的左侧,则线段BD的长为________;(3)点(6,n)为G1与G2的交点坐标,求a的值.(4)解:在移动过程中,若G1与G2有两个交点,设G2的对称轴分别交线段DE和G1于M、N两点,若MN<,直接写出a的取值范围.【答案】(1)把D(3,m)、E(12,m﹣3)代入y= 得,解得,所以双曲线的解析式为y= ;(2)2(3)解:把(6,n)代入y= 得6n=12,解得n=2,即交点坐标为(6,2),抛物线G2的解析式为y=﹣(x﹣a)2+9,把(6,2)代入y=﹣(x﹣a)2+9得﹣(6﹣a)2+9=2,解得a=6± ,即a的值为6± ;(4)抛物线G2的解析式为y=﹣(x﹣a)2+9,把D(3,4)代入y=﹣(x﹣a)2+9得﹣(3﹣a)2+9=4,解得a=3﹣或a=3+ ;把E(12,1)代入y=﹣(x﹣a)2+9得﹣(12﹣a)2+9=1,解得a=12﹣2 或a=12+2;∵G1与G2有两个交点,∴3+ ≤a≤12﹣2 ,设直线DE的解析式为y=px+q,把D(3,4),E(12,1)代入得,解得,∴直线DE的解析式为y=﹣ x+5,∵G2的对称轴分别交线段DE和G1于M、N两点,∴M(a,﹣ a+5),N(a,),∵MN<,∴﹣ a+5﹣<,整理得a2﹣13a+36>0,即(a﹣4)(a﹣9)>0,∴a<4或a>9,∴a的取值范围为9<a≤12﹣2 .【解析】【解答】解:(2)当y=0时,﹣x2+9=0,解得x1=﹣3,x2=3,则B(﹣3,0),而D(3,4),所以BE= =2 .故答案为2 ;【分析】(1)把D(3,m)、E(12,m﹣3)代入y= 得关于k、m的方程组,然后解方程组求出m、k,即可得到反比例函数解析式和D、E点坐标;(2)先解方程﹣x2+9=0得到B(﹣3,0),而D(3,4),然后利用两点间的距离公式计算DE的长;(3)先利用反比例函数图象上点的坐标特征确定交点坐标为(6,2),然后把(6,2)代入y=﹣(x ﹣a)2+9得a的值;(4)分别把D点和E点坐标代入y=﹣(x﹣a)2+9得a的值,则利用图象和G1与G2有两个交点可得到3+ ≤a≤12﹣2 ,再利用待定系数法求出直线DE的解析式为y=﹣ x+5,则M(a,﹣ a+5),N(a,),于是利用MN<得到﹣ a+5﹣<,然后解此不等式得到a<4或a>9,最后确定满足条件的a的取值范围.3.已知一次函数y=kx+b与反比例函数y= 交于A(﹣1,2),B(2,n),与y轴交于C 点.(1)求反比例函数和一次函数解析式;(2)如图1,若将y=kx+b向下平移,使平移后的直线与y轴交于F点,与双曲线交于D,E两点,若S△ABD=3,求D,E的坐标.(3)如图2,P为直线y=2上的一个动点,过点P作PQ∥y轴交直线AB于Q,交双曲线于R,若QR=2QP,求P点坐标.【答案】(1)解:点A(﹣1,2)在反比例函数y= 的图象上,∴m=(﹣1)×2=﹣2,∴反比例函数的表达式为y=﹣,∵点B(2,n)也在反比例函数的y=﹣图象上,∴n=﹣1,即B(2,﹣1)把点A(﹣1,2),点B(2,﹣1)代入一次函数y=kx+b中,得,解得:k=﹣1,b=1,∴一次函数的表达式为y=﹣x+1,答:反比例函数的表达式是y=﹣,一次函数的表达式是y=﹣x+1;(2)解:如图1,连接AF,BF,∵DE∥AB,∴S△ABF=S△ABD=3(同底等高的两三角形面积相等),∵直线AB的解析式为y=﹣x+1,∴C(0,1),设点F(0,m),∴AF=1﹣m,∴S△ABF=S△ACF+S△BCF= CF×|x A|+ CF×|x B|= (1﹣m)×(1+2)=3,∴m=﹣1,∴F(0,﹣1),∵直线DE的解析式为y=﹣x+1,且DE∥AB,∴直线DE的解析式为y=﹣x﹣1①.∵反比例函数的表达式为y=﹣②,联立①②解得,或∴D(﹣2,1),E(1,﹣2);(3)解:如图2由(1)知,直线AB的解析式为y=﹣x﹣1,双曲线的解析式为y=﹣,设点P(p,2),∴Q(p,﹣p﹣1),R(p,﹣),PQ=|2+p+1|,QR=|﹣p﹣1+ |,∵QR=2QP,∴|﹣p﹣1+ |=2|2+p+1|,解得,p= 或p= ,∴P(,2)或(,2)或(,2)或(,2).【解析】【分析】(1)把A的坐标代入反比例函数的解析式可求得m的值,从而可得到反比例函数的解析式;把点A和点B的坐标代入一次函数的解析式可求得一次函数的解析式;(2)依据同底等高的两个三角形的面积相等可得到S△ABF=S△ABD=3,再利用三角形的面积公式可求得点F的坐标,即可得出直线DE的解析式,即可求出交点坐标;(3)设点P(p,2),则Q(p,﹣p﹣1),R(p,﹣),然后可表示出PQ与QR的长度,最后依据QR=2QP,可得到关于p的方程,从而可求得p的值,从而可得到点P的坐标.4.如图,Rt△ABO的顶点A是双曲线y= 与直线y=﹣x﹣(k+1)在第二象限的交点.AB⊥x轴于B,且S△ABO= .(1)求这两个函数的解析式;(2)求直线与双曲线的两个交点A、C的坐标和△AOC的面积.【答案】(1)解:设A点坐标为(x,y),且x<0,y>0,则S△ABO= •|BO|•|BA|= •(﹣x)•y= ,∴xy=﹣3,又∵y= ,即xy=k,∴k=﹣3.∴所求的两个函数的解析式分别为y=﹣,y=﹣x+2;(2)解:由y=﹣x+2,令x=0,得y=2.∴直线y=﹣x+2与y轴的交点D的坐标为(0,2),A、C两点坐标满足∴交点A为(﹣1,3),C为(3,﹣1),∴S△AOC=S△ODA+S△ODC= OD•(|x1|+|x2|)= ×2×(3+1)=4.【解析】【分析】两解析式的k一样,根据面积计算双曲线中的k较易,由公式=2S△ABO,可求出k;(2)求交点就求两解析式联立的方程组的解,可分割△AOC为S△ODA+S△ODC,即可求出.5.如图,在平面直角坐标系xOy中,一次函数y=kx+b(k≠0)的图象与反比例函数的图象交于二四象限内的A、B 两点,与x轴交于C点,点B的坐标为(6,n),线段OA=5,E为x轴负半轴上一点,且sin∠AOE=.(1)求该反比例函数和一次函数的解析式;(2)求△AOC的面积;(3)直接写出一次函数值大于反比例函数值时自变量x的取值范围.【答案】(1)解:作AD⊥x轴于D,如图,在Rt△OAD中,∵sin∠AOD= = ,∴AD= OA=4,∴OD= =3,∴A(﹣3,4),把A(﹣3,4)代入y= 得m=﹣4×3=﹣12,所以反比例函数解析式为y=﹣;把B(6,n)代入y=﹣得6n=﹣12,解得n=﹣2,把A(﹣3,4)、B(6,﹣2)分别代入y=kx+b得,解得,所以一次函数解析式为y=﹣x+2(2)解:当y=0时,﹣x+2=0,解得x=3,则C(3,0),所以S△AOC= ×4×3=6(3)解:当x<﹣3或0<x<6时,一次函数的值大于反比例函数的值【解析】【分析】(1)作AD⊥x轴于D,如图,先利用解直角三角形确定A(﹣3,4),再把A点坐标代入y= 可求得m=﹣12,则可得到反比例函数解析式;接着把B(6,n)代入反比例函数解析式求出n,然后把A和B点坐标分别代入y=kx+b得到关于a、b的方程组,再解方程组求出a和b的值,从而可确定一次函数解析式;(2)先确定C点坐标,然后根据三角形面积公式求解;(3)观察函数图象,找出一次函数图象在反比例函数图象上方所对应的自变量的范围即可.6.如图,已知矩形OABC中,OA=3,AB=4,双曲线y= (k>0)与矩形两边AB、BC分别交于D、E,且BD=2AD(1)求k的值和点E的坐标;(2)点P是线段OC上的一个动点,是否存在点P,使∠APE=90°?若存在,求出此时点P 的坐标,若不存在,请说明理由.【答案】(1)解:∵AB=4,BD=2AD,∴AB=AD+BD=AD+2AD=3AD=4,∴AD= ,又∵OA=3,∴D(,3),∵点D在双曲线y= 上,∴k= ×3=4;∵四边形OABC为矩形,∴AB=OC=4,∴点E的横坐标为4.把x=4代入y= 中,得y=1,∴E(4,1);(2)解:(2)假设存在要求的点P坐标为(m,0),OP=m,CP=4﹣m.∵∠APE=90°,∴∠APO+∠EPC=90°,又∵∠APO+∠OAP=90°,∴∠EPC=∠OAP,又∵∠AOP=∠PCE=90°,∴△AOP∽△PCE,∴,∴,解得:m=1或m=3,∴存在要求的点P,坐标为(1,0)或(3,0).【解析】【分析】(1)由矩形OABC中,AB=4,BD=2AD,可得3AD=4,即可求得AD的长,然后求得点D的坐标,即可求得k的值,继而求得点E的坐标;(2)首先假设存在要求的点P坐标为(m,0),OP=m,CP=4﹣m,由∠APE=90°,易证得△AOP∽△PCE,然后由相似三角形的对应边成比例,求得m的值,继而求得此时点P的坐标.7.【阅读理解】我们知道,当a>0且b>0时,(﹣)2≥0,所以a﹣2 +≥0,从而a+b≥2 (当a=b时取等号),【获得结论】设函数y=x+ (a>0,x>0),由上述结论可知:当x= 即x= 时,函数y有最小值为2(1)【直接应用】若y1=x(x>0)与y2= (x>0),则当x=________时,y1+y2取得最小值为________.(2)【变形应用】若y1=x+1(x>﹣1)与y2=(x+1)2+4(x>﹣1),则的最小值是________(3)【探索应用】在平面直角坐标系中,点A(﹣3,0),点B(0,﹣2),点P是函数y= 在第一象限内图象上的一个动点,过P点作PC⊥x轴于点C,PD⊥y轴于点D,设点P的横坐标为x,四边形ABCD的面积为S①求S与x之间的函数关系式;②求S的最小值,判断取得最小值时的四边形ABCD的形状,并说明理由.【答案】(1)1;2(2)4(3)解:①设P(x,),则C(x,0),D(0,),∴AC=x+3,BD= +2,∴S= AC•BD= (x+3)( +2)=6+x+ ;②∵x>0,∴x+ ≥2 =6,∴当x= 时,即x=3时,x+ 有最小值6,∴此时S=6+x+ 有最小值12,∵x=3,∴P(3,2),C(3,0),D(0,2),∴A、C关于x轴对称,D、B关于y轴对称,即四边形ABCD的对角线互相垂直平分,∴四边形ABCD为菱形.【解析】【解答】解:(1)∵x>0,∴y1+y2=x+ ≥2 =2,∴当x= 时,即x=1时,y1+y2有最小值2,故答案为:1;2;(2)∵x>﹣1,∴x+1>0,∴ = =(x+1)+ ≥2 =4,∴当x+1= 时,即x=1时,有最小值4,故答案为:4;【分析】(1)直接由结论可求得其取得最小值,及其对应的x的值;(2)可把x+1看成一个整体,再利用结论可求得答案;(3)①可设P(x,),则可表示出C、D的坐标,从而可表示出AC和BD,再利用面积公式可表示出四边形ABCD的面积,从而可得到S 与x的函数关系式;②再利用结论可求得其最得最小值时对应的x的值,则可得到P、C、D的坐标,可判断A、C关于x轴对称,B、D关于y轴对称,可判断四边形ABCD为菱形.8.已知二次函数的图象经过三点(1,0),(-3,0),(0,).(1)求该二次函数的解析式;(2)若反比例函数图像与二次函数的图像在第一象限内交于点 , 落在两个相邻的正整数之间,请写出这两个相邻的正整数;(3)若反比例函数的图像与二次函数的图像在第一象限内的交点为A,点A的横坐标为满足,试求实数的取值范围。

精选备战中考物理易错题专题复习热学问题求解方法及详细答案

精选备战中考物理易错题专题复习热学问题求解方法及详细答案

一、初中物理热学问题求解方法1.水是人类生存环境的重要组成部分。

水的三种状态分别是冰、水和水蒸气。

以下关于水的说法错误..的是()A.相同质量0℃水的体积大于0℃冰的体积B.相同质量0℃水的内能大于0℃冰的内能C.水蒸气很容易被压缩,说明气体分子之间的距离很远,几乎没有作用力D.今年12月11日我县第一次出现霜林尽染的美景,说明气温已经低于0℃【答案】A【解析】【详解】A.根据mVρ=和ρρ>水冰得质量相同的0℃水的体积小于0℃冰的体积,故A错误,符合题意;B.0℃水放热凝固成相同质量的0℃冰,所以相同质量0℃水的内能大于0℃冰的内能,故B正确,不符合题意;C.水蒸气很容易被压缩,说明气体分子之间的距离很远,几乎没有作用力,故C正确,不符合题意;D.霜是水蒸气遇冷凝华而成的,在标准大气压下水的凝固点是0℃,而霜的形成需要的温度更低,所以霜的形成,说明气温已经低于0℃,故D正确,不符合题意。

2.戴眼镜的人从室外进入温暖的室内,镜片上会出现“水雾”,下列现象中的物态变化与“水雾”的形成相同的是()A.饮料中的冰块逐渐变小B.北方冬天植物上的雾淞C.蒸锅上方生成的“白气”D.寒冬,室外冰冻的衣服逐渐变干【答案】C【解析】【分析】【详解】戴眼镜的人从室外进入温暖的室内,镜片上会出现“水雾”,这是眼镜温度较低,而室内水蒸气温度较高,水蒸气接触到眼镜时,会放出热量降温,液化成小水珠,附在眼镜上。

A.饮料中的冰块逐渐变小,这是冰块吸热熔化成水,A项不合题意;B.雾淞是由于空气中的水蒸气凝华形成的固态小冰晶,B项不合题意;C.蒸锅上方生成的“白气”,这是水蒸气液化形成的小水珠,选项C符合题意;D.寒冬,室外冰冻的衣服逐渐变干,这是衣服上的固态冰升华成水蒸气,D项不合题意。

故选C。

3.假设我们手里现有一支刻度均匀,但读数不准的温度计,标准大气压下,在冰水混合物中的示数为4℃,在沸水中的示数为96℃,用此温度计测得某液体的温度是27℃,则所测液体的实际温度应该是( ) A .24℃ B .25℃C .26℃D .27℃【答案】B 【解析】 【详解】由题意可知,不准的温度计上一个小格表示的实际温度为:10025=96-423℃℃℃;用此温度计测得液体的温度是27℃,则这种液体的实际温度为:()272523425t =⨯-=℃℃℃。

中考易错题系列知识易错题解析

中考易错题系列知识易错题解析

中考易错题系列知识易错题解析在中考中,有一些知识点经常出现在易错题中,考生们需要特别注意。

本文将对几个常见的易错题进行解析,帮助考生们掌握相关知识点,提高答题准确性。

1. 数学题:简单方程求解题目:求方程2x + 3 = 7的解。

解析:这是一个简单的一元一次方程。

我们将方程转化为x的形式,即2x = 7 - 3,化简得2x = 4,再除以2得到x = 2。

因此,方程的解为x = 2。

2. 语文题:近义词辨析题目:下列词语中哪个与“喜爱”意思最接近?A. 痛恨B. 厌恶C. 喜欢D. 讨厌解析:根据题目要求,我们需要选择与“喜爱”意思最接近的词语。

痛恨、厌恶和讨厌与“喜爱”相反,而“喜欢”与“喜爱”在意思上非常相近。

因此,选项C“喜欢”是正确答案。

3. 物理题:简单机械概念运用题目:在以下几种行星中,哪种行星表面的重力最大?A. 地球B. 月亮C. 火星D. 金星解析:根据牛顿第二定律,物体所受重力的大小与物体的质量有关。

而行星的质量与其体积相关,体积越大,质量越大。

在给定的选项中,地球是体积最大的行星,因此具有最大的质量,所以地球的表面重力最大。

因此,选项A“地球”是正确答案。

4. 历史题:历史事件排序题目:请将以下历史事件按发生先后顺序排列:①五四运动②辛亥革命③五一运动④九一八事变解析:辛亥革命发生在1911年,五四运动发生在1919年,九一八事变发生在1931年,五一运动发生在1920年。

根据事件发生的时间顺序,正确的排序是②辛亥革命、③五一运动、①五四运动、④九一八事变。

5. 地理题:地理要素概念理解题目:下列地理要素中,与水有关的是:A. 沙漠B. 森林C. 河流D. 高山解析:题目要求选择与水有关的地理要素。

沙漠、森林和高山与水关系不大,而河流是水的重要组成部分。

因此,选项C“河流”是正确答案。

通过以上对几个常见易错题的解析,我们可以发现,只要我们对知识点掌握准确,理解清晰,就能轻松解答这些题目。

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2010备战中考易错选择题精选(来自学生错题)1. Some students were afraid ____in class because they thought their classmates might laugh atthem.A of speakB to speakC speakD to speaking2. I found ____ difficult to learn English grammar.A itB thatC it isD that is3. He decided ____school late again.A to comeB don‘t comeC come not toD not to come to4. She needs a partner ______A to practice English withB practicing EnglishC to practicing English withD practice English with5.Stop chatting .I have ____ to tell you.A anything importantB something importantC important anythingD important something6. It‘s good that _____have their own ideas about life as well as about being coo l.A the youngB youthC the young manD young7.My grandfather ___ me stories when I was young .A was used to tellB is used to tellingC used to tellD used to telling8. When I was a student , I was used to _____ at six .A get upB getting upC gets upD geting up9. It is ____ of a problem to be poor than to be dishonest.A moreB littleC lessD much10. My brother is ___to carry the heavy box by himself .A old enoughB enough oldC enough strongD strong enough11. I must get my homework ____,A doneB doesC doD did12. People are not allowed ____ in the cinema , but they will allow ____in the rest room.A to smoke, smokeB smoking , to smokeC to smoke , smokingD smoking ,smoke13.The music sounds _____A wellB nicelyC goodD beautifully14. _____ to improve our English?A What do you think we should doB Do you think what do we shouldC What do you think should weD Do you think what should we do15. His bike is broken .It needs _____soon.A be repairB to mendC to be repairedD being mend16. Three more men ____to do the work every day .A were neededB needC are needingD are needed17. He is against ______ computer games.A playingB playsC playD to play18.He was too hungry , so he ate ____in the evening.A plenty ofB a lot ofC manyD a lot19.I don‘t know _____.A what to do itB how to doC what to doD to do what20.I don‘t know if I _____anyone at the party this evening.If I _____anyone , I will get nervous.A will know, won‘t knowB will know ,don‘t knowB know, won‘t know D know , don‘t know21.Tom is afraid to speak in ______public.A theB aC anD /22. The professor always has good solutions_____others‘ problems.A ofB toC withD about23. If you take my ______, please don‘t tell _____about it.A advice ,anyB advices, someC advices, someoneD advice , anyone24.They are hardly ever tired ,______they?A areB aren‘tC willD won‘t25.I‘ll have a test ______ writing next week.A atB ofC onD in26.If you have any ideas ______, please return them to him.A whose gloves are theseB whose gloves is thisC whose gloves these areD whose gloves this is27._____ has been found out ____ oil food is bad for our healthA That , thatB That ,whatC It , whatD It , that28 I prefer music that_____ great lyrics.A haveB hasC there isD there are29. I only eat food that tastes _______.A wellB nicely Cgood D deliciously30 The Greeen family would like to_______for about three weeks.A leave homeB go outC come to ChinaD be away31. I hope ____have a happy year in our class.A you toB or youC to youD you32. The two men walked ______ the forest and got to a small house.A acrossB throughC crossingD over33.The girl _____ her mother . I know her mother likes reading,too.A takes afterB looks afterC similarD takes care34. Don‘t put off ____ to see the doctor when you are ill.A goB to goC goingD gone35.He spent every Sunday morning _____ in an old pe ople‘s home.A to workB workingC workedD works36.He ___ to read , so he always puts his ___ to good use by working in the after- school care center at his elementary school.A love ,lovesB loves ,loveC loving,lovingD loves ,loves37.The sudden rain made ______for the singers to put on performcesA that possibleB that impossibleC it possibleD it impossible38.____ ill, I can‘t go to school today.A Because ofB AsC BeingD With39. This watch ______China .A was made inB was made byC was made fromD was made of40. ____ our football team won .A By the endB In the endC At the end ofD Final41.The headmaster announced that there would ____ an English speech contest next month.A haveB hasC to haveD be42. Did you go to the movie with Lucy? No , I _____A didn‘t inviteB wasn‘t invitedC hadn‘t invitedD wasn‘t inviting43. –Excuse me, could you tell me ______? ---Of courseA when had the train left the stationB where is the nearest the hospitalC if it will be windy tomorrowD how much did the car cost44. Must I do my homework ? --- No you _____.A mustn‘tB can‘tC needn‘tD won‘t45. ---I don‘t know ______next. – You could ask your teacher for help.A how to doB what to doC . why to doD when to do46. Tom asked his friend ______.A not to be so angryB that knowledge is power.C when did he come backD where was he born47.I find ___ a little difficult to remember the English words.A thatB itC thisD them48 What are you nervous_____, Jenny.?A inB atC onD about49.We should ____ that.A thinking ofB thought ofC have thought ofD have thinking of50. Don‘t get _____when you listen to the old.A boredB boringC tiringD excited51. I don‘t like the people who always keep me ______.A waitB waitingC to waitD waited52.—Do you like loud music ? --- I am often ______ want to leave by it.A madeB made toC makingD making to53.The pen doesn‘t work .I need to buy a new one to write_____A with Bin C on D /54.—You want to improve your spoken English. Why ____an English languageclub?----Good idea.A don‘t joinB not joinC not to joinD not you join55.If you have some trouble ____the railway station ,please ask the police for help .A findingB finding outC looking for Ddiscovering56.—I don‘t know ______I should do with so many eggs. –You can sell them.A howB whyC whatD when57.There used _____an old church here, but now we can see a park here.A to haveB wasC to beD had58.Everyone is _____to find that the little boy can play the piano so well. He is only 5 years old.A interestedB surprisedC excitedD frustrated59. My calculator is ________more expensive than yours.A fairlyB veryC quiteD much60.I‘d like to go there by bike ______by c ar.A. not B instead C than D rather than61. At last , Mr Li ______a good idea , everyone felt happy.A thoughtB thought ofC came up withD thought about62.---Why hasn‘t Tom come here? ----He ____ill at home.A maybeB may beC wasD can‘t be63.-- ____does the book ____? ----Linda . She bought it this morning.A Whose , beB How much, costC Whose , belong toD Who , belong to64. The girl is too shy , she ____some time with her friends.A doesn‘t need spendingB needn‘t spendC needs to spendD needed spending65. I learn English by watching English – language videos______.A sometimesB sometimeC some timeD some times66. Just now I saw some young children _____together on the playground .A are playingB playingC to playD have played67. –The boy can hardly speak Chinese, _______? –No, He‘s been in China for only a few weeks.A can heB can‘t heC does heD doesn‘t he68.It‘s ver y impolite ___you ____in line.A of ,to cutB for , cutC of , cutD for ,to cut69. My life ____a lot in the last few years .A changeB has changedC changedD changes70.At that time, I was only ____11-year-old boy, I was a ‗problem child‖.A aB an Cthe D /71. My friend Jenny has moved to ____city , I miss her oftenA . otherB anotherC othersD the others72.This guitar might ___Alice. She plays the guitar.A beB hasC comes fromD belong to73.—Do you prefer grapes ____bananas?----I prefer grapes ______bananas.A to, orB or ,toC than ,toD or , than74. Why can‘t we ______to have more time to relax?A. are allowed B to allow C be allowed D allow75.Nobody except Lily and Linda ____the man in a white T-shirt.A knowB is knowingC have knownD knows76.She ______speak in class because she thought her classmates would laugh at her.A was afraid ofB is afraid toC was afraid toD is not afraid of77. I have ____the English club for three terms.A joinedB been inC taken part inD become a member of78.You ____to the meeting this afternoon if you have something important to do .A needn‘t to comeB don‘t need to comeC needn‘t comingD didn‘t need coming79. –May I go swimming now,Mum ?---No, you ____. You must finish your homework first.A mustn‘tB may notC couldn‘tD needn‘t80. The bridge in my hometown is about _______meters long.A two hundred ofB two hundreds ofC two hundredD two hundreds81. If he _____his father , he‘d spend more time studying English.A isB wasC wereD will be82 Thanks to the _____English course , I can live in the USA easily.A six-monthsB six- months‘C six –monthD six months83.The fish smells so _____. ---Thanks . Mum cooks fish very ______.A good, goodB well,goodC well,wellD good ,well84.What ______you most? ---Basketball does . I like it best.A interestB interestsC interestingD interested85.How I miss you !I ____you to come here to see me.( which is wrong)A hopeB expectC likeD want86.---Do you know when the calculator _______? ---Yes , in 1876.A inventedB inventingC was inventingD was invented87.Did you notice him ______out of the house ?A to leaveB leaveC leftD leaves88.When your homework ______, you can watch TV.A is finishedB finishesC finishedD is finishing89. At last the man ______a woman who was two years older than him.A married withB got marriedC marriedD got married with90.As soon as the bell for break rang, the boys _____to the playground.A ran intoB ran out ofC ran afterD ran out91.We should only obey all the school rules ,_______?A don‘tB aren‘tC can‘tD shouldn‘t92.It‘s good for you not to eat ______that‘s been cooked in oil.A anythingB somethingC everythingD nothingst night I listened to a CD______Heart Strings.A which callsB that calledC calledD calls94.Let‘s try to be__ honest person.A aB anC the D/95. I think you will look more beautiful if you wear shoes _____adjustable heals.A haveB hasC withD there are96. Sometimes ,when it‘s rainy, I go to school ______my father‘s car.A inB onC byD from97.I was _____ because I didn‘t go to bed until 3o‘clock a.m last night.A embarrassedB amazedC excitedD exhausted98.Yesterday I received a card that ____ ―Happy New Year‖ .A saysB tellsC speaksD writes99.Can you tell me ____ you can come to my birthday party on Friday or not.?A thatB ifC whenD whether100. ―Help _____to some chicken.‖ Mrs Smith said to us as soon as the chicken was served.A yourselfB youC yourselves Dyours101.There are many trees on_____sides of the road. They were planted several years ago.A eachB bothC eitherD every102.Though it was late , ______he went on with his work.A butB andC soD /103. Every summer we will have a _____holiday after the exam.A two monthB two-monthC two-monthsD two months104.Can you tell me ____you can come to my birthday party on Friday or not?A thatB ifC whenD whether105. This room is big enough for all of us ______.A liveB living inC to live inD to live106.All the workers were made ______some extra hours last month.A. workB. to work C worked D working107.Is this _____that you saw in the street yesterday?A oneB the manC thatD he108.You can talk with anyone ______you think is .friendly.A whoB whomC whichD the one109. All _____I want ______a room somewhere.A that ,isB what, isC what ,areD that are110. Susan is a girl _____bike was borrowed by me yesterday.A whoseB whoC whomD that111.Is this the coat you ____last Sunday.?A boughtB have bought itC bought itD had bought112.Look! The man who is ____the bus stop is my English teacher.A waiting forB waiting onC waiting atD waiting up113.My father prefers ______to staying at home. He loves playing sports.A to play footballB to travelC playing footballD traveling114. My brother told me there was a good movie ______TV the next week.A onB on theC inD about115.The children find that they have no paper_______.A to writeB to write with Cto write on D write on116. Why _____home tomorrow? I miss my parents.A not goB not goingC not to goD didn‘t go117.The TV set is too loud . Would you please _____?A turn down itB turn it downC to turn down itD to turn it down118.It‘s cold outside . You‘d better _____your coat.A to put onB putting onC puts onD put on119. The toy you bought in the USA ______in China.A madeB makesC was makingD was made120.Our sports meeting has been _____till next Monday because of the bad weather .A put onB put offC put upD put down121.I‘m not sure if it_____tomorrow. If it ______, we won‘t climb the South Hill.A will snow, snowsB will snow,will snowC snows , snowsD snows ,will snow 122. –Would you like to visit Shantou City with me this summer vacation?---No, I ______it before. Besides , it‘s hot and humid in summer.A visitB visitedC will visit Dhave visited123. The teacher asked me _____I had finished my homework and I said ―Yes‖.A whatB ifC thatD /124.I used to prefer ______to______.A swimming/runningB swim /runC swimming/runD swim/running125.---Could you tell me if it ____today,please?---Yes. The radio says there will ____a heavy rain later today.A will rain/haveB will rain / beC rains/haveD rains /be126. I ___the Human food though I‘ve been in Changsha for more than one year.A didn‘t use toB used toC don‘t get used toD gets used to127.We shouldn‘t eat or drin k_______walking down the street.A whileB untilC beforeD after128.Neither of my hands is empty . There is abook in one and there is a long ruler in ____.A otherB the otherC anotherD others129.The machine doesn‘t work ______it says in the advertisement.A as quickly asB as good asC as well asD as carefully as130.Ten years has passed _____I started to work in this school.A since Bbefore C when D until131.The cinema is next to the park. Walk _____the park and you can get there .A throughB pastC acrossD out132.Spending time with friends ____ very important to us.A isB areC hasD have133. They arrived ____ Paris ____ a winter evening.A at/inB to/onC in /onD in/at134. I prefer ____ rather than ______.A to be a teacher/ be a bossB to be a teacher/ to be a bossC being a teacher/ being a bossD be a teacher / be a boss135.______the help of my classmates ,I‘ve improved my English.A ByB WithC UnderD For136.Have you checked your licence ______?A alsoB tooC eitherD neither137.You must keep your eyes _____, touch it.A closeB closedC closingD to close138. My hair is too long . I‘ll hav e it _______tomorrow.A cutB being cutC cuttingD to cut139.Bill said they would have ______holiday.A a two-monthB two monthsC a two-monthsD two month‘s 140.—Do you have enough books to read?---- No, I think we need ______books.A another twoB other twoC two anotherD two the other141.---Listen, Helen is singing in the next rom.----It ______be Helen. She has gone to Beijing.A mustn‘tB can‘tC may Dshould142.It is a good way to keep both teachers and students_______.A to happyB happyingC happyD happily143.Many students like reading the book Harry Potter_____by J.K. Rowling.A writtenB was writtenC wroteD was writing144.I think it‘s difficul t to go _____the forest alone.A acrossB throughC thoughD cross145.The artist hoped ______drawing the picture soon.A his son to finishB to finishC finishingD his son will finished146.I visited Hong Kong_____in 2000,and I‘d like to travel there again._____A one day/ a dayB one day/some dayC some day/one dayD some day/ some day 147. He is considering _____a primary school in that mountain village. You surely can‘t consider him ____a selfish man.A building/ to beB building/beingC to build/beingD to build/to be148.Mrs Brown will never forget the day ____she met Jane in the street.A thatB whenC whichD where149.I am a League member . I volunteer my time _____ others.A helpB to helpC helpingD helped150.What‘s the best way to _____life‘s big and small problems?A deal withB do with toC deal with toD dealing with151. He is used to____up early in the morning.A getB gettingC to getD got152. The abacus was inviented in _____century.A sixB the sixthC sixthD the six153.If the child ____, please telephone the police.A foundB is foundC was foundD has found154.—English is ____useful language, isn‘t it? ----Of course it is.A aB theC an D/155. –How does your mother go to work?--She usually goes to work ____her car, but sometimes on foot.A byB onC inD about156.The big bowl ____wine warm in the old days.A was used for keepingB is used by keepingC was used by keepingD is used to keep 157. ____people will take part in the meeting next week.A Hundreds ofB Two hundreds ofC Two hundred ofD Two hundreds158.What if ____tomorrow?A it rainsB it will rainC does itD will it rain159.I ______play the piano when I was a young boy .A wasn‘t used toB wasn‘t use toC didn‘t use toD didn‘t used to160. Now the traffic in our city is becoming ______.than before.A much heavierB more heavierC much heavilyD very heavier161. But none of the artists knew _____to make the King happy.A when to doB what to doC how to doD where to do162. When they got to the station ,the train ______for 20 minutes.A had leftB went awayC had been awayD had gone163---May I play soccer with Tom now, Mum?---When all the homework ______, you may go out to play.A finishB will finish Cis finished D will be finished164. The number of teachers in our school ___60 and a number of them ___male teachers.A is/areB are/isC are/are Dis/is165.Nick _____a job in a bank, but to our surprise, he didn‘t take it.A is offeredB was offeredC offeredD has offered166.____ is believed that Bell invented the first telephone in 1876.A ThisB ThatC itD One答案:1-5 BADAB 6-10 ADBCD 11-15ACCAC 16-20DADCB 21-25DBDAC 26-30 CDBCD 31-35 DBACB 36-40 BDCAB 41-45 DBCCB 46-50 ABDCA 51-55BBABA 56-60 CCBDD 61-65CBDCA 66-70 BAABB 71-75 BDBCD 76-80 CBBAC 81-85CCDBA 86-90DBACD 91-95 DACBC 96-100 ADADC 101-105BDBDC 106-110 BBAAA 111-1115 ACCAC116-120 ABDDB 121-125 ADBAB 126-130 CABCA131-135 CACAB 136-140 BBAAA 141-145 BCABB146-150 BABBA 151-155 BBBAC 156-160 AAACA161-166BCCABC。

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