九年级总复习综合测试题
九年级数学上册期末复习综合测试题(含答案)

(第4题)九年级数学上册期末复习综合测试题(含答案)一、选择题(本大题共6小题,每小题2分,共12分.) 1.一元二次方程 x 2=x 的根是( )A .x 1=0,x 2=1B .x 1=0,x 2=-1C .x 1=x 2=0D .x 1=x 2=12.一个不透明布袋中有2个红球,3个白球,这些球除颜色外无其他差别,摇匀后从中随机摸出一个小球,该小球是红色的概率为( )A .12B .23C .15D .253.若一组数据 2,3,4,5,x 的方差比另一组数据 5,6,7,8,9 的方差大,则 x 的值可能是( ) A .1B .4C .6D .84.如图,OA 、OB 是⊙O 的半径,C 是⊙O 上一点.若∠OAC =16°,∠OBC =54°,则 ∠AOB 的度数是( )A .70°B .72°C .74°D .76°5.若关于x 的一元二次方程ax 2+k =0的一个根为2,则二次函数y =a (x +1)2+k 与x 轴的交点坐标为( ) A .(-3,0)、(1,0) B .(-2,0)、(2,0) C .(-1,0)、(1,0)D .(-1,0)、(3,0)6.如图,在Rt △ABC ,∠ACB =90°,AC =4,BC =3,点D ,E 分别在AB ,AC 上,连接DE ,将△ADE 沿DE 翻折,使点A 的对应点F 落在BC 的延长线上,若FD 平分∠EFB ,则AD 的长为( ) A . 157B .207C .258D .259二、填空题(本大题共10小题,每小题2分,共20分.) 7(第12题)l 1 l 2l 3A BCEFD (第11题)8.若a b =43,则a -b b= .9.设x 1、x 2是方程x 2+mx -m +3=0的两个根,则x 1+x 2-x 1x 2= .10.把抛物线y =-x 2向左平移2个单位,然后向上平移3个单位,则平移后该抛物线相应的函数表达式为 .11.如图,l 1∥l 2∥l 3,若AD =1,BE =3,CF =6,则ABBC的值为 .12.如图,点A 、B 、C 在⊙O 上,⊙O 的半径为3,∠AOC =的长为 . 13.已知关于x 的函数y =x 2+2mx +1,若x >1时,y 随x 的增大而增大,则m 的取值范围是 .14.如图,弦AB 是⊙O 的内接正六边形的一边,弦AC 是⊙O 的内接正方形的一边,若 BC =2+23,则⊙O 的半径为 .15.如图,正方形ABCD 的边长是4,点E 在DC 上,点F 在AC 上,∠BFE =90°,若 CE =116.如图,在矩形ABCD 中,AB =2,AD =4,点E 、F 分别为AD 、CD 边上的点,且EF 的长为2,点G 为EF 的中点,点P 为BC 上一动点,则P A +PG 的最小值为 . 三、解答题(本大题共11小题,共88分.请在答题卡指定区域.......内作答,解答时应写出文字说明、证明过程或演算步骤)17.(8分)解方程:(1)x 2-4x -5=0; (2)x 2-4=2x (x -2).18.(8分)甲乙两人在相同条件下完成了5次射击训练,两人的成绩(单位:环)如下(1)甲射击成绩的中位数为 环,乙射击成绩的众数为 环;(2)计算两人射击成绩的方差;(3)根据训练成绩,你认为选派哪一名队员参赛更好,为什么?19.(8分)某校开展秋季运动会,需运动员代表进行发言,从甲、乙、丙、丁四名运动员中随机抽取.(1)若随机抽取1名,甲被抽中的概率为 ; (2)若随机抽取2名,求甲在其中的概率.20.(7分)如图,在△ABC 中,点D 、E 分别在AB 、AC 上,且∠BCE +∠BDE =180°. (1)求证:△ADE ∽△ACB ;(2)连接BE 、CD ,求证:△AEB ∽△ADC .21.(8分)如图是二次函数y =-x 2+bx +c 的图像. (1)求该二次函数的关系式及顶点坐标; (2)当y >0时 x 的取值范围是 ;(3)当m <x <m +4时,-5<y ≤4,则m 的值为 .22.(7分)在Rt △ABC ,∠BAC =90°,AB =AC ,D 、E、F 分别为BC 、AB 、AC 边上的点,且∠EDF =45°.(1)求证:△EBD ∽△DCF ;(2)当D 是BC 的中点时,连接EF ,若CF =5,DF =4,则EF 的长为 .23.(8分)某超市销售一种商品,成本为每千克50元.当每千克售价60元时,每天的销售量为60千克,经市场调查,当每千克售价增加1元,每天的销售量减少2千克. (1)为保证某天获得750元的销售利润,则该天的销售单价应定为多少? (2)当销售单价定为多少时,才能使当天的销售利润最大?最大利润是多少?24.(8分)如图,AB 为⊙O 的直径,弦CD ⊥AB 于点P ,连接BC ,过点D 作DE ⊥CD ,交⊙O 于点E ,连接AE ,F 是DE 延长线上一点,且∠BCD =∠F AE . (1)求证:AF 是⊙O 的切线;(2)若AF =2,EF =1,求⊙O 的半径.25.(8分)已知二次函数y =(x -2)(x -m )(m 为常数). (1)求证:不论m 为何值,该函数的图像与x 轴总有公共点;(2)若M (-1,0), N (3,0),该函数图像与线段MN 只有1个公共点,直接写出 m 的取值范围;(3)若点A (-1,a ),B (1,b ),C (3,c )在该函数的图像上,当abc <0时,结合函数图像,直接写出m 的取值范围.26.(8分)如图,四边形ABCD 内接于⊙O ,AB =AC ,BD ⊥AC ,垂足为E . (1)求证:∠BAC =2∠DAC ; (2)若AB =10,CD =5,求BC 的长.27.(10分)定义:圆心在三角形的一边上,与另一边相切,且经过三角形一个顶点(非切点)的圆,称为这个三角形圆心所在边上的“伴随圆”.(1) 如图①,在△ABC 中,∠C =90°,AB =5,AC =3,则BC 边上的伴随圆的半径为 . (2)如图②,△ABC 中,AB =AC =5,BC =6,直接写出它的所有伴随圆的半径. (3)如图③,△ABC 中,∠ACB =90°,点E 在边AB 上,AE =2BE ,D 为AC 的中点,且∠CED =90°.①求证:△CED 的外接圆是△ABC 的AC 边上的伴随圆; ②DE的值为 .参考答案说明:本评分标准每题给出了一种或几种解法供参考,如果考生的解法与本解答不同,参照本评分标准的精神给分.一、选择题(本大题共6小题,每小题2分,共12分)二、填空题(本大题共10小题,每小题2分,共20分)7.9 8.13 9.-3 10.y =-(x +2)2+3 11.2312.2π 13.m ≥-1 14. 2 2 15.322 16.4 2 -1三、解答题(本大题共11小题,共88分) 17.(8分)(1)解:x 2-4x -5=0 x 2-4x +4=5+4(x -2)2=9 ········································································································ 1分x -2=±3 ········································································································ 2分 ∴ x 1=5,x 2=-1. ··························································································· 4分 (2)解:x 2-4=2x (x -2) x 2-4=2x 2-4xx 2-4x +4=0 ··································································································· 5分 (x -2)2=0 ········································································································ 6分 ∴ x 1=x 2=2. ··································································································· 8分 18.(8分)(1)7;8 ········································································································ 2分 (2)s 2甲=(7-8)2+(7-8) 2+(10-8)2+(9-8)2+(7-8)25=1.6环2. ······························ 4分s 2乙=(8-8)2+(8-8) 2+ (7-8)2+(8-8)2+(9-8)25=0.4环2. ······································ 6分(3)选择乙.因为甲乙两人平均数相同均为8,说明两人实力相当,但s 2乙<s 2甲,乙的成绩更加稳定,所以选乙. ······················································································· 8分19.(8分)(1)14. ·········································································································· 2分(2)解:随机抽取两名运动员,共有6种等可能性结果:(甲,乙)、(甲,丙)、(甲,丁)、(乙,丙)、(乙,丁)、(丙,丁).其中满足“有甲运动员”(记为事件A )的结果只有3种,所以P (A )=12. ·································································································· 8分20.(7分)(1)证明:∵ ∠BCE +∠BDE =180°, ∠EDA +∠BDE =180°,∴ ∠EDA =∠BCE . ·························································································· 1分 又 ∠A =∠A , ································································································· 2分 ∴ △ADE ∽△ACB . ·························································································· 3分 (2)∵ △ADE ∽△ACB , ∴ AD AC =AE AB, ·········································· 4分 ∴AD AE =ACAB, ······································· 5分 又 ∠A =∠A , ········································ 6分 ∴ △AEB ∽△ADC . ································· 7分21.(8分)(1)将(0,3)、 (3,0)代入,得⎩⎨⎧3=c ,0=-9+3b +c································································································· 1分解得⎩⎨⎧c =3,b =2····································································································· 2分∴ y =-x 2+2x +3 ····························································································· 3分 ∴ 顶点坐标为(1,4) ························································································ 4分 (2)-1<x <3. ······························································································ 6分 (3)-2或0 ···································································································· 8分 22.(7分)(1)解:∵∠BAC =90°,AB =AC ,∴ ∠B =∠C =45°. ··························································································· 1分 ∴ 在△BDE 中,∠BED +∠BDE =180°-∠B =135°, ∵ ∠EDF =45°,∴ ∠BDE +∠CDF =135°,∴ ∠BED =∠CDF . ·························································································· 3分 ∵ ∠B =∠C ,∴ △EBD ∽△DCF . ·························································································· 5分 (2 ········································································································ 7分23.(8分)(1)解:设每千克的销售价增加x 元,根据题意,得(60+x -50) (60-2x )=750 ··················································································· 2分 ∴ x 1=5,x 2=15. ····························································································· 3分 60+5=65或60+15=75 ···················································································· 4分 答:销售单价为65或75元时获得利润750元. (2)解:每千克的销售价增加x 元,利润为w 元.w =(60+x -50) (60-2x ) ···················································································· 6分 =-2(x -10)2+800 ···························································································· 7分 ∵ a =-2<0,∴ 当x =10时,w 有最大值800. ········································································ 8分 60+10=70答:当销售单价为70元时获得最大利润,为800元. 24.(8分) (1)连接BD .∵ AB 为⊙O 的直径,CD ⊥AB ,∴ ⌒BC = ⌒BD , ························································· 1分 ∴ ∠BDC =∠BCD .∵ 四边形ABDE 为⊙O 的内接四边形,∴ ∠BDE +∠BAE =180°,即∠BDC +∠CDF +∠BAE ····· 2分∵ DE ⊥CD , ∴ ∠CDF =90°, ∴ ∠BDC +∠BAE =90°.∵ ∠BCD =∠F AE , ·························································································· 3分 ∴ ∠BAE +∠F AE =90°,即∠F AB =90°, ∴ AF ⊥AB . 又 点A 在⊙O 上,∴ AF 与⊙O 相切. ·························································································· 4分 (2)过点O 作OG ⊥DF 垂足为G . ∵ ∠F AB =∠D =∠APD =90°, ∴ 四边形APDF 是矩形, ∴ ∠F =90°.∵ ∠F AB =∠F =∠OGF =90°, ∴ 四边形AOGF 是矩形,∴ AF =OG ,AO =GF . ···················································· 5分 设OE =OA =r ,则GE =r -1.在Rt △OGE 中,由勾股定理得OG 2+GE 2=OE 2, ···················································· 6分 即4+(r -1)2=r 2, ···························································································· 7分 解得r =5 2 . ····································································································· 8分25.(8分)(1)令y =0,即(x -2)(x -m )=0 ········································································· 1分 ∴ x 1=2,x 2=m . ····························································································· 2分 当m =2时,x 1=x 2,方程有两个相等的实数根; 当m ≠2时,x 1≠x 2,方程有两个不等的实数根. ∴ 不论m 为何值,方程总有实数根;∴ 不论m 为何值,该函数的图像与x 轴总有公共点. ·············································· 3分 (2)m =2或m >3或m <-1. ··········································································· 6分 (3)-1<m <1或m >3. ·················································································· 8分 26.(8分)。
浙江省中考英语总复习九年级阶段综合测试题(新版)外研版

2019届浙江省中考英语(外研)总复习阶段综合测试题(范围:九年级上、下册时间:120分钟分值:120分)第一部分听力部分一、听力(共15小题;满分25分)第一节:听小对话,从A、B、C三个选项中选出正确的选项,回答问题。
(共5小题;每小题1分,满分5分)1. What's the weather like today?A.Rainy.B.Cloudy.C.Sunny.2. When will the store close today?A.At 7:30.B.At 8:30.C.At 9:00.3. Who thinks the Maths test is easy?A.Tina.B.Rick.C.Anna.4. How does Cindy feel about her prize?A.Surprised.B.Nervous.C.Satisfied.5. What is Betty looking for?A.A handbag.B.A purse.C.A key.第二节:听长对话,从A、B、C三个选项中选出正确的选项,回答问题。
(共5小题;每小题2分,满分10分) 听下面一段对话,回答第6-7小题。
6. What food does Daisy like?A.Chicken.B.Fish.C.Eggs. 7. What are the speakers going to do?A.Cook dinner.B.Go shopping.C.Order dishes.听下面一段对话,回答第8-10小题。
8. Why is Dave sad?A.He stayed up too late.B.He thinks his team lost.C.He couldn't watch the game.9. What did Dave have last night?A.Some ice cream.B.Coke.C.A pizza.10. What's Nancy's suggestion to Dave?A.Eating something.B.Going online.C.Watching the game.第三节:听下面一段独白,从A、B、C三个选项中选出正确的选项,回答问题。
人教版九年级数学期末考试综合复习测试题(含答案)

人教版九年级数学期末考试综合复习测试题(含答案)一.选择题(共10小题,每小题3分,共30分)1.计算,3(2)a -结果正确的是( )A .32a -B .36a -C .38a -D .38a2.据教育部统计,2022年高校毕业生约1076万人,用科学记数法表示1076万为( )A .4107610⨯B .61.07610⨯C .71.07610⨯D .80.107610⨯3.下列汽车标志中,是中心对称图形的是( ) A . B . C . D .4.如图所示,直线//EF GH ,射线AC 分别交直线EF 、GH 于点B 和点C ,AD EF ⊥于点D ,如果20A ∠=︒,则(ACH ∠= )A .160︒B .110︒C .100︒D .70︒5.如图,已知ABC ADE ∆≅∆,若70E ∠=︒,30D ∠=︒,则BAC ∠的度数是( )A .70︒B .80︒C .40︒D .30︒6.方程2210x x --=实数根的情况为( )A .有两个不相等的实数根B .有两个相等的实数根C .没有实数根D .不能确定7.在平面直角坐标系中,若点(1,)A a b -+与点(,3)B a b -关于原点对称,则点(,)C a b 在( )A .第一象限B .第二象限C .第三象限D .第四象限8.如图,小正方形的边长均为1,则下列图中的三角形(阴影部分)与ABC ∆相似的是( )A .B .C .D .9.已知正比例函数11(0)y k x k =≠的图象与反比例函数22(0)k y k x =≠的图象交于A ,B 两点,其中点A 在第二象限,横坐标为2-,另一交点B 的纵坐标为1-,则12(k k ⋅= )A .4B .4-C .1-D .110.已知(3,2)A --,(1,2)B -,抛物线2(0)y ax bx c a =++>顶点在线段AB 上运动,形状保持不变,与x 轴交于C ,D 两点(C 在D 的右侧),下列结论:①2c -;②当0x >时,一定有y 随x 的增大而增大;③若点D 横坐标的最小值为5-,则点C 横坐标的最大值为3;④当四边形ABCD 为平行四边形时,12a =. 其中正确的是( )A .①③B .②③C .①④D .①③④二.填空题(共5小题,每小题3分,共15分)11.因式分解:22416x y -= . 12.若2|2|(3)0x y -++=,则2()x y += .13.已知m ,()n m n ≠是一元二次方程220230x x +-=的两个实数根,则代数式22m m n ++的值为 .14.如图,A ,B ,C ,D 是O 上的四点,且点B 是AC 的中点,BD 交OC 于点E ,60OED ∠=︒,35OCD ∠=︒,那么AOC ∠的度数是 .15.如图,E 为正方形ABCD 内一点,5AD =,4AE =,将ADE ∆绕点A 顺时针旋转90︒到ABE ∆',则边DE 所扫过的区域(图中阴影部分)的面积为 .题14图 题15图三.解答题(一)(共3小题,每小题8分,共24分)16.(1)计算:0111(2021)()2cos45221π--++-︒+; (2)先化简,再求值:23210(1)19x x x x --⋅---,其中x 是1、2、3中的一个合适的数.17.如图,DE AB ⊥于E ,DF AC ⊥于F ,若BD CD =,BE CF =.求证:(1)AD 平分BAC ∠;(2)2AC AB BE =+.18.今年,我市某学校举办了为贫困生捐赠书包活动.该学校用2000元在某商店购进一批学生书包,随后发现书包数量不够,于是又购进第二批同样的书包,所购数量是第一批的3倍,每个书包比第一批购买时贵了4元,结果第二批用了6300元.(1)该学校第一批购进的学生书包每个多少元?(2)如果该商店第一批、第二批学生书包每个的进价分别是68元、70元,售给该学校的这些学生书包,该商店盈利多少元?四.解答题(二)(共3小题,每小题9分,共27分)19.某银行柜台在储户人数较多时常开放1、2、3、4号窗口办理日常业务,一般是先到取号机拿号,按顾客“先到达,先服务“的方式服务(1)求某储户在3号窗口办业务的概率是(2)储户乙取号时发现储户甲已办理完业务准备离开(储户甲、乙先后到达银行取号办理业务),请用树状图或列表法求储户甲、乙两人在同一柜台办理业务的概率.20.如图,在平行四边形ABCD 中,BD AB ⊥,延长AB 至点E ,使BE AB =,连接EC .(1)求证:四边形BECD 是矩形.(2)连接AC ,若3AD =,2CD =,求AC 的长.21.Rt ABO ∆的顶点A 是双曲线k y x =与直线(1)y x k =--+在第二象限的交点,AB 垂直x 轴于点B 且32ABO S ∆=. (1)求这两个函数解析式;(2)求AOC ∆的面积;(3)根据图象直接写出不等式(1)k x k x >-+的解集.五.解答题(三)(共2小题,每小题12分,共24分)22.如图,AB 是⊙O 的直径,C 、D 是⊙O 上两点,连接CD ,C 是的中点,过点C 作AD 的垂线,垂足是E .连接AC 交BD 于点F .(1)求证:CE 是⊙O 的切线;(2)求证:△CDF ∽△CAD ;(3)若DF =2,CD =,求AC 值.23.如图,在平面直角坐标系中,抛物线21y ax bx =++交y 轴于点A ,交x 轴正半轴于点(4,0)B ,交直线AD 于点5(3,)2D ,过点D 作DC x ⊥轴于点C . (1)求抛物线的解析式;(2)点P 为x 轴正半轴上一动点,过点P 作PN x ⊥轴交直线AD 于点M ,交抛物线于点N ;若点P 在线段OC 上(不与O 、C 重合),连接CM ,求PCM ∆面积的最大值。
九年级数学第一学期期末考试综合复习测试题(含答案)

九年级数学第一学期期末考试综合复习测试题(含答案)一.选择题(共10小题,每小题3分,共30分) 1.2022的相反数是( )A .2022B .2022-C .12022D .2022± 2.若代数式3125m x y -与822m nx y +-是同类项,则( )A .73m =,83n =-B .3m =,4n =C .73m =,4n =- D .3m =,4n =-3.下列四组线段中,能组成直角三角形的是( ) A .1a =,3b =,3c = B .2a =,3b =,4c = C .2a =,4b =,5c =D .3a =,4b =,5c = 4.如图所示,直线//a b ,231∠=︒,28A ∠=︒,则1(∠= )A .61︒B .60︒C .59︒D .58︒5.下列关于事件发生可能性的表述,正确的是( )A .“在地面向上抛石子后落在地上”是随机事件B .掷两枚硬币,朝上面是一正面一反面的概率为13C .在同批次10000件产品中抽取100件发现有5件次品,则这批产品中大约有500件左右的次品D .彩票的中奖率为10%,则买100张彩票必有10张中奖6.某校10名学生参加课外实践活动的时间分别为:3,3,6,4,3,7,5,7,4,9(单位:小时),这组数据的众数和中位数分别为( ) A .9和7 B .3和3 C .3和4.5 D .3和5 7.一个正多边形的每一个内角都是150︒,则它的边数为( ) A .6 B .9 C .12 D .158.若不等式组841x x x m +<-⎧⎨>⎩的解集是3x >,则m 的取值范围是( )A .3m <B .3mC .3m >D .3m9.已知关于x 的一元二次方程22(21)0x m x m --+=有实数根,则m 的取值范围是( ) A .14m 且0m ≠ B .14m C .14m < D .14m >10.如图1,一个扇形纸片的圆心角为90︒,半径为6.如图2,将这张扇形纸片折叠,使点A 与点O 恰好重合,折痕为CD ,图中阴影为重合部分,则阴影部分的面积为( )A .9632π-B .693π-C .91232π-D .94π二.填空题(共5小题,每小题3分,共15分) 11.将数据2022万用科学记数法表示为 .12.已知当3x =时,代数式35ax bx +-的值为20,则当3x =-时,代数式35ax bx +-的值是 .13.将抛物线229y x x =-+-向左平移2个单位,再向上平移1个单位后,得到的抛物线的解析式为 .14.已知ABC ∆中,点O 是ABC ∆的外心,140BOC ∠=︒,那么BAC ∠的度数为 .15.如图,在正方形ABCD 中,顶点(5,0)A -,(5,10)C ,点F 是BC 的中点,CD 与y 轴交于点E ,AF 与BE 交于点G ,将正方形ABCD 绕点O 顺时针旋转,每次旋转90︒,则第2023次旋转结束时,点G 的坐标为 .三.解答题(一)(共3小题,每小题8分,共24分) 16.计算(1)2()(2)x y x y x +--;(2)2219(1)244a a a a --÷--+.17.如图,90ACB ∠=︒,AC AD =.(1)过点D 作AB 的垂线DE 交BC 与点E ,连接AE .(尺规作图,并保留作图痕迹) (2)如果8BD =,10BE =,求BC 的长.18.如图,在四边形ABCD 中,AC 与BD 交于点O ,BE AC ⊥,DF AC ⊥,垂足分别为点E ,F ,且BE DF =,ABD BDC ∠=∠.求证:四边形ABCD 是平行四边形.四.解答题(二)(共3小题,每小题9分,共27分) 19.阳光中学为了丰富学生的课余生活,计划购买围棋和中国象棋供棋类兴趣小组活动使用,若购买3副围棋和5副中国象棋需要98元;若购买1副围棋和2副中国象棋需要36元.(1)求每副围棋和每副中国象棋各多少元;(2)阳光中学决定购买围棋和中国象棋共40副,总费用不超过538元,且围棋的副数不低于象棋的副数,问阳光中学有几种购买方案;(3)请求出最省钱的方案需要多少钱?20.我市某中学举行“中国梦⋅我的梦”的演讲比赛,赛后整理参赛学生的成绩,将学生的成绩分为A,B,C,D四个等级,并将结果绘制成如图所示的条形统计图和扇形统计图,但均不完整,请你根据统计图解答下列问题.(1)参加比赛的学生人数共有名,在扇形统计图中,表示“D等级”的扇形的圆心角为度,图中m的值为;(2)补全条形统计图;(3)组委会决定从本次比赛中获得A等级的学生中,选出两名去参加市中学生演讲比赛,已知A等级中男生只有1名,请用画树状图或列表的方法求出所选学生恰是一男一女的概率.21.22.某网店专售一款新型钢笔,其成本为20元/支,销售中发现,该商品每天的销售量y与销售单价x(元/支)之间存在如下关系:10400y x=-+,自武汉爆发了“新型冠状病毒”疫情该网店店主决定从每天获得的利润中抽出200元捐赠给武汉,同时又让顾客得到实惠,当销售单价定位多少元时,捐款后每天剩余利润为550元?五.解答题(三)(共2小题,每小题12分,共24分)22.如图,以点O为圆心,AB长为直径作圆,在O上取一点C,延长AB至点D,连接DC,过点A作O的切线交DC的延长线于点E,且DCB DAC∠=∠.(1)求证:CD是O的切线;(2)若6AD=,2:3BC CA=,求AE的长.23.如图,在平面直角坐标系中,直线33y x =--与x 轴交于点A ,与y 轴交于点C .抛物线2y x bx c =++经过A 、C 两点,且与x 轴交于另一点B (点B 在点A 右侧). (1)求抛物线的解析式;(2)若点M 是线段BC 上一动点,过点M 的直线ED 平行y 轴交x 轴于点D ,交抛物线于点E ,求ME 长的最大值及此时点M 的坐标; (3)在(2)的条件下:当ME 取得最大值时,在x 轴上是否存在这样的点P ,使得以点M 、点B 、点P 为顶点的三角形是等腰三角形?若存在,请直接写出所有点P 的坐标;若不存在,请说明理由.答案一.选择题1. B .2. D .3. D .4. C .5. C .6. C .7. C .8. B .9. B .10. C . 二.填空题11. 72.02210⨯.12. 30-.13. 228y x x =---.14. 70︒或110︒.15. (4,3)-. 三.解答题16.解:(1)2()(2)x y x y x +--22222x xy y xy x =++-- 2y =;(2)2219(1)244a a a a --÷--+ 23(3)(3)2(2)a a a a a ---+=÷-- 23(2)2(3)(3)a a a a a --=⋅---+ 23a a -=--. 17.解:(1)如图所示即为所求作的图形. (2)ED 垂直AB , 90ADE EDB ∴∠=∠=︒,在Rt BDE ∆中,22221086DE BE BD =-=-=, 在Rt ADE ∆和Rt ACE ∆中, AC ADAE AE =⎧⎨=⎩, Rt ADE Rt ACE(HL)∴∆≅∆, 6EC ED ∴==, 16BC BE EC ∴=+=.18.证明:ABD BDC ∠=∠, //AB CD ∴.BAE DCF ∴∠=∠.在ABE ∆与CDF ∆中, 90BAE DCF AEB CFD BE DF ∠=∠⎧⎪∠=∠=︒⎨⎪=⎩. ()ABE CDF AAS ∴∆≅∆. AB CD ∴=.∴四边形ABCD 是平行四边形.19.解:(1)设每副围棋x 元,每副中国象棋y 元,根据题意得:3598236x y x y +=⎧⎨+=⎩,∴1610x y =⎧⎨=⎩,∴每副围棋16元,每副中国象棋10元;(2)设购买围棋z 副,则购买象棋(40)z -副, 根据题意得:1610(40)538m m +-,40m z -,2023m ∴,m 可以取20、21、22、23则有:方案一:购买围棋20副,购买中国象棋20副方案二:购买围棋21副,购买中国象棋19副方案:购买围棋22副,购买中国象棋18副方案四:购买围棋23副,购买中国象棋17副由4种方案;(3)由上一问可知共有四种方案:方案一:购买围棋20副,购买中国象棋20副;方案二:购买围棋21副,购买中国象棋19副;方案三:购买围棋22副,购买中国象棋18副;方案四:购买围棋23副,购买中国象棋17副;方案一需要20162010520x x +=; 方案二需要21161910526x x +=; 方案三需要22161810532x x +=; 方案四需要23161710538x x +=; 所以最省钱是方案一,需要520元.20.(1)解:根据题意得:总人数为:315%20÷=(人), 表示“D 等级”的扇形的圆心角为43607220⨯︒=︒;C等级所占的百分比为8100%40% 20⨯=,所以40m=,故答案为:20,72,40.(2)解:等级B的人数为20(384)5-++=(人),补全统计图,如图所示:(3)解:根据题意,列出表格,如下:男女1女2男女1、男女2、男女1男、女1女2、女1女2男、女2女1、女2共有6种等可能结果,其中恰是一男一女的有4种,所以恰是一男一女的概率为42 63 =.21.解:由题意可得(20)(10400)200550x x--+-=解得125x=,235x=因为要让顾客得到实惠,所以25x=答:当销售单价定为25元时,捐款后每天剩余利润为550元.22.(1)证明:连接OC,OE,如图,AB为直径,90ACB∴∠=︒,即190BCO∠+∠=︒,又DCB CAD∠=∠,1CAD∠=∠,1DCB∴∠=∠,90DCB BCO ∴∠+∠=︒,即90DCO ∠=︒, CD ∴是O 的切线;(2)解:EC ,EA 为O 的切线, EC EA ∴=,AE AD ⊥, OC OA =, OE AC ∴⊥,90BAC EAC ∴∠+∠=︒,90AEO EAC ∠+∠=︒, BAC AEO ∴∠=∠, tan tan BAC AEO ∴∠=∠,∴23BC AO AC AE ==, Rt DCO Rt DAE ∆∆∽,∴23CD OC OA DA AE AE ===, 2643CD ∴=⨯=, 在Rt DAE ∆中,设AE x =,222(4)6x x ∴+=+, 解得52x =. 即AE 的长为52.23.解:(1)直线33y x =--与x 轴、y 轴分别交于点A 、C , (1,0)A ∴-,(0,3)C -抛物线2y x bx c =++经过点(1,0)A -,(0,3)C -, ∴103b c c -+=⎧⎨=-⎩,解得23b c =-⎧⎨=-⎩,∴抛物线的解析式为223y x x =--.(2)设(E x ,223)(03)x x x --<<,则(,3)M x x -, 222393(23)3()24ME x x x x x x ∴=----=-+=--+,∴当32x =时,94ME =最大,此时3(2M ,3)2-. (3)存在.如图3,由(2)得,当ME 最大时,则3(2D ,0),3(2M ,3)2-,32DO DB DM ∴===; 90BDM ∠=︒,223332()()222OM BM ∴==+=. 点1P 、2P 、3P 、4P 在x 轴上, 当点1P 与原点O 重合时,则1322PM BM ==,1(0,0)P ; 当2322BP BM ==时,则232632322OP -=-=, 2632(2P -∴,0); 当点3P 与点D 重合时,则3332P M P B ==,33(2P ,0); 当4322BP BM ==时,则432632322OP +=+=, 4632(2P +∴,0). 综上所述,1(0,0)P ,2632(2P -,0),33(2P ,0),4632(2P +,0).。
九年级化学上册期末复习综合测试卷含参考答案

九年级化学上册期末复习综合测试卷含参考答案相对原子质量:H:1 C:12 N:14 O:16 S:32 Cl:35.5 Ca:40一、选择题(本题包括15小题,每小题1分,共15分。
每小题只有一个选项符合题意)1.空气的成分中体积分数大约为21%的是A.氮气B.氧气C.二氧化碳D.稀有气体2.水是生命的源泉,是人类宝贵的资源。
它有时能幻作朵朵白云,有时能化为绵绵细雨。
下列过程中,你认为水分子发生了变化的是A.水蒸气遇冷凝结成水B.水通电变成氢气和氧气C.蔗糖和水混合后得到糖水D.过滤净化黄泥水3.下列物质中,不属于溶液的是A.啤酒B.矿泉水C.葡萄糖注射液 D.液氧4.古人曾有赞美菊花的诗句“冲天香阵透长安”。
浓郁的花香遍布长安的原因是A.分子的质量很小B.分子间有间隔C.分子在不断运动D.分子由原子构成5.下列实验操作错误的是A.熄灭酒精灯B.检查装置的气密性 C.取用粉末状药品D.给液体加热6.决定元素种类的是A.质子数B.中子数C.电子数D.最外层电子数7.下列变化中,属于物理变化的是A.米饭变馊B.火药爆炸C.湿衣服晾干D.铁锅生锈8.某全麦饼干部分营养成分的含量如下表所示,表中的“铁、镁、锌、钙”是指营养成分铁镁锌钙含量(mg/100g) 4.4—5 90—100 3—4 280—300 A.分子B.原子C.元素D.离子9.减少污染,净化空气,“还我一片蓝天”,已成为世界各国人民的共同心声。
下列气体会造成空气污染的是A.二氧化硫B.二氧化碳C.氧气D.氮气10.对溶液的基本特征叙述正确的是A.溶液是均一、稳定、无色透明的液体B.凡是均一、稳定、透明的液体都是溶液C.一杯调好的蔗糖水,喝第一口特甜,越喝越不甜,说明蔗糖的质量分数越小D.当条件不变时,溶液长时间放置,溶质也不会从溶液中分离出来11.下列变化属于化合反应的是A.食盐和水混合后得到食盐水B.氢气在氧气中燃烧生成水C.水蒸气遇冷凝结成水D.水通电生成氢气和氧气12.1911年著名物理学家卢瑟福为探索原子的内部结构进行了实验。
期末复习综合测试卷(二)+++++2022-2023学年部编版语文九年级下册+

部编版九年级语文下册期末总复习综合性检测试卷(二)一、积累与运用。
(20分)1.下列加点字的注音完全正确的一项是()A.国殇.(shāng)伫.立(chù)诡谲.(jué)波澜.(lán)B.睥.睨(bì)稽.首(qǐ)行.头(xíng)污秽.(huì)C.踌躇.(chú)囫.囵(hú)童谣.(yáo)鞭挞.(tà)D.瘦削.(xuē)咀嚼.(jué)羡.慕(xiàn)弄.堂(nòng)2.下列词语书写完全正确的一项是()(3分)A.掬躬收揽犀利骂骂咧咧B.雷霆幌子侦辑咬牙跺脚C.怯懦忌讳拾掇摄手摄脚D.捣蛋凄惨竹匾喃喃自语3.下列各句中加点的成语运用不正确的一项是()(3分)A.母亲在家庭里极能任劳任怨....。
她性格和蔼,没有打骂过我们,也没有同任何人吵过架。
B.父亲老实厚道低三下四....累了一辈子,没人说过他有地位,父亲也从没觉得自己有地位。
C.但这是没有办法的,只得裹一条毯子,横着心躺下去。
因为实在太疲倦,一会儿就酣然..入梦了...。
D.假如一个男人跟朋友和熟人见面时彬彬有礼....,可是在家里对妻子儿女动不动就大发雷霆——那就可以肯定他不是一个有教养的人。
4.下列句子没有语病的一项是()(3分)A.是否注重用非语言沟通与孩子交流,才能让孩子培养更加优秀的语言能力。
B.那种不顾生态环境,片面强调经济效益,无疑是杀鸡取卵,到头来只能是得不偿失。
C.风油精的主要成分是由薄荷脑、樟脑桉油、丁香酚、水杨酸甲酯等配制而成的。
D.在各方重点扶持下,我们中国传统戏剧这颗璀璨明珠终会再焕光彩。
5.综合性学习材料:每年在湖北龙感湖自然保护区越冬的天鹅超过了6万只,为了让天鹅安心栖息,管理站划出300亩稻田,不予收割,为鸟留食。
但前不久发生的一件事,让管理站开始对天鹅“不近人情”:一只受伤的小天鹅在经过两周的救治后,放回水城时却趴在岸边一动不动。
(试题4)新人教版九年级总复习综合测试以及答案

A B C D 人教版九年级上期末复习检测试题一、选择题1、方程x (x-1)=2的两根为( )A .x 1=0,x 2=1B .x 1=0,x 2=-1C .x 1=1,x 2=2D .x 1= -1,x 2=22.下列计算正确的是( ) A.2·3=6 B. 2+3=6 C. 8=32 D. 4÷2=23.在平面内,将一个图形绕一个定点沿某个方向转动一个角度,这样的图形运动称为旋转.下列图案中,不能由一个圆形通过旋转而构成的是( )4.下列图形中,中心对称图形是( )5.根据下列表格的对应值:x3.23 3.24 3.25 3.26 ax 2+bx +c-0.06-0.020.030.09判断方程a x 2+bx+c=0(a ≠0,a 、b 、c 为常数)一个解x 的范围是 ( )A.3<x <3.23;B.3.23<x <3.24;C.3.24<x <3.25;D.3.25<x <3.26 6.一个均匀的立方体六个面上分别标有1,2,3,4,5,6,下图是这个立方体表面的展开图,抛掷这个立方体,则朝上一面上的数恰好等于朝下一面上的数的12的概率是( )A. 16 B. 13 ; C.12 D.237.如图,PA 、PB 分别切圆O 于A 、B 两点,C 为劣弧AB 上一点,∠APB=30°,则∠ACB=( )A .60°B .75°C .105°D .120°BAC PO8.甲、乙两位同学对代数式a ba b-+ (a>0,b>0),分别作了如下变形:甲:()()()()a b a b a b a b a b a b a b ---==-++-乙:()()a b a b a b a b a b a b--+==-++关于这两种变形过程的说法正确的是( )A .甲、乙都正确B .甲、乙都不正确C .只有甲正确D .只有乙正确 9.在半径为50cm 的圆形铁皮上剪去一块扇形铁皮,•用剩余部分制作成一个底面直径为80cm ,母线长为50cm 的圆锥形烟囱帽,则剪去的扇形的圆心角度数为( )A .228°B .144°C .72°D .36°10.将进货单价为70元的某种商品按零售价100元/个售出时每天能卖出20个,若这种商品的零售价在一定范围内每降价1元,其日销售量就增加1元,其日销售量就增加1个,为了获得最大利润,则应降价( )A .5元B .10元C .15元D .20元二、填空题11.在抛掷一枚普通正六面体骰子的过程中,出现点数为2的概率是 。
初中九年级英语 中考复习 综合模拟测试(五)

中考复习·综合模拟测试(五)一、基础知识(共 25 分)Ⅰ .在下列各句的空白处填入一个适当的词,使句子意思完整、语法正确。
(5 分)1.Changchun City is a very beautiful city. Most of people in love with it.2. My sister got up late yesterday because her alarm clock didn't go .3.I can't go to the movie with you.I have to take good of my little brother4. Jane was at me last night because I took her book away without telling her5.It is getting dark in the room.I can't see,please turn on the lights.Ⅱ . 用括号内所给单词的适当形式填空。
(5 分)6.June the (one) is a great day for children around the world.7. More and more (foreign) are going to China to travel.8.My aunt is a wonderful writer, she has (write) some great articles9. Everyone in our class is interested in Chinese (tradition) culture10. Kids often spend an hour with their parents (happy) during visiting the zoo.Ⅲ . 单项选择。
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九年级总复习综合测试题(十)一。
选择题。
i。
词语释义()1.The old man does morning exercises every day to keep fit.A.beautifulB.efficientC.dependentD.healthy()st week Tom hurt his leg, so he walked with the aid of the stick.A.aimB.colorC.woodD.help()3.When he says “ I won’t skate. I will play football instead.”, he means “ I will play football________ skating.”A.even ifB.instead ofC.as ifD.because of()4.When Ms Green says Tom is good at English, she means Tom______English.A.is good forB.is popular withC.does well inD.does harm to()5.Lily is quite afraid of mice. When she saw a mouse in the kitchen, she had her heart in her mouth.A.felt nervousB.got annoyedC.let her downD.made mistakesIi。
选择填空从下面每小题的A.B.C.D四个选项中选出最佳选项。
()6.How do your parents go to work every day?My father goes to work by______car, but my mother takes______bus.A.a; aB.a; /C.the; /D./; a()7.What______of noodles do you want to order?I’d like a bowl of noodles______beef.A.kind; withB.group; haveC.kind; andD.group; with()8.______did you choose black at last?________it matched my trousers pretty well.A.what; forB.when; whetherC.why; becauseD.how; if()9.The box is too heavy.Can you lend me a _______?Sorry. You can ask Steve. He is______to carry it.A.leg; strong enoughB.hand; strong enoughC.leg; enough strongD.hand; enough strong()10. How far is ______from your classroom to your dormitory?It is only___________.A.that; five minutes’walkB.it; five minutes’walkC.that; five minute’s walkD.it; five minute’s walk()11. How many English songs have you leamed?I _______twelve English songs ________last week.A.have learned;sinceB.have learned;forC.had learned;forD.had leaned;since()12.What did your brother_______you to do with the old clothes?He______ donating them to the people in need.A.suggest; advisedB.advise; suggestedC.suggest; suggestedD.advise; advise()13.What did the teacher say just now?He asked_______everyone_______here today.A./; isB.if; isC./; wasD.if; was()14.________the students________the teacher like the film.You mean it is a popular film?A.both; andB.not only; but alsoC.either; orD.neither; nor()15.Need I take some food?NO, you________.But I can’t go with you, I ________take care of my younger sister.A.can not; mustB.mustn’t; mustC.shouldn’t; have toD.needn’t; have to()16.Mr Huang, do you know________?I just know she_________on Huang hai Street two years ago, but I don’t know where she lives now.A.what Mrs Sun is; will liveB. what Mrs Sun lives; livedC. what Mrs Sun; will liveD.where does Mrs Sun live; lived()17. I don’t know________about the machine. Can you tell me?Wait a moment. I will tell you_______to start it.A.what to do; howB.what to do; whatC.how to do; whatD. how to do;how()18.Jim is ________than any other boy in our class.You are right. He is________of all the boys in our class.A.the tallest; the tallestB.taller; the tallestC.the tallest; tallerD.taller; taller()19.The girl cried loudly________her parents’attention.But the parents paid no attention to her. They just let her_______there.A.to attract; criesB.attracting; cryC.attracting; to cry()20. My family_____to Xiamen for our holiday next week.________.A.will go; I can’t believe itB.went; That’s very kind of youC.will go; Have a good tripD.went; Welcome to my homeII.完形填空。
阅读下面短文,从短文后每小题所给的A、B、C、D四个选项中选出最佳选项。
There is only one day left for the science camp. At school, we talk of nothing else. I like 21 of the camp part the swimming pool, the hikes and the games. The part that I don’t like is the staying-overnight-for-six-night’s part. I have 22 been away from home during the night.My sister 23 that the staying-overnight-for-six-night’s part is bad. I asked 24 she did during the last science camp. “ I cried,” she said. “I cried every night.”I dislike the idea of crying even one night. What will the others say? The kids in my class, 25 Mark Medford, are good at making nick-names(绰号)。
What if I had some terrible 26 ? The school wouldn’t let me go. But when I told Mrs Fontaine about the disease, she said, “You’re going to the science camp.”My sleeping bag and suitcase are on the bus. My dad and mom wave good-bye. I stand in line next to my best friend Pete. When I 27 from waving sadly to Mom and Dad, I 28 that Pete has a little tear in his eyes. He’s not the only one. When I look around, I see that there is a tiny tear ready to fa ll from Musty Bones’ right eye, and even Mark Medford looks 29Maybe the science camp is not as bad as a terrible disease. Even if it is, at least I’m not 30 .( ) 21. A. none B. anyC. someD. all( ) 22. A. always B. neverC. everD. yet( ) 23. A. agrees B. failsC. guessesD. keeps( ) 24. A. when B. whyC. whereD. what( ) 25. A. carefully B. probablyC. especiallyD. exactly( ) 26. A. speed B. powerC. stormD. disease( ) 27. A. turn back B. turn onC. turn downD. turn up( ) 28. A. allow B. noticeC. causeD. develop( ) 29. A. excited B. happyC. sadD. bored( ) 30. A. brave B. patientC. spareD. aloneIII.阅读理解( 35分)i. 阅读下列短文,从下面每小题的A、B、C、D共25小题,每小题1分)AIn Britain, children can have a part-time job when they are 13. Lots of teenagers work in the evenings or at weekends as shop assistants, or in restaurants and fast food places. Others deliver newspapers before they go to school in the morning. Girls often find work as babysitters. In one school near London, 60% of students said that they had part-time jobs. But why do they work? Most say that they want to buy new clothes and CDs. They don’t need money for their families.But part-time jobs are often hard, and not very exciting. Most part-time jobs don't get much money - perhaps two or three pounds an hour, if they're lucky. Of course, there are positive things for teenagers who do part-time jobs. They get important work experience and learn many things about the world. But the biggest problem is that students who work in the evening in a supermarket or a restaurant feel tired at school the next morning; you can’t study well when you are tired.( ) 31. When can children have a part-time job in Britain?A. When they are 13.B. When they are 16.C. When they graduate from university.D. When they graduate from high school.( ) 32. Why do most of the students in one school near London do part-time jobs?A. Because they want to buy new clothes.B. Because they want to buy CDs.C. Because they need money for their families.D. Both A and B.( ) 33. What does the underlined word “positive” mean in Chinese?A.消极的B.积极的C.放纵的D.奢侈的( ) 34. What's the biggest problem of doing part-time jobs for the students?A. It’s not good for their study.B. It is bad for their health.C. It makes them want to leave school.D. It allows them to spend a lot of money.( ) 35. What's the passage mainly about?A. Part-time jobs and teenagers in Britain.B. Part-time jobs and making money in Britain.C. Work experience and finding a part-time job.D. Making money to help your family.BThink of using your nose to pick up food, take a shower, and greet your friends. An elephant’s nose can do all these and more.An elephant’s long nose is called a trunk. Just like you, elephants breathe and smell with their noses. But elephants also use their trunks the way you use your arms and hands. Elephants reach up high and get leaves at the top of a tree, and they can even pick up pennies(便士) by using their trunks.Trunks become handy(灵活的) when elephants care for their babies. A mother helps the youngster up with her trunk. And just as you learned to hold a fork and spoon with your fingers, elephant babies must learn how to use their trunks. By the time elephants are a week old, they can pick up sticks with their trunks and carry them. Athree-month-old elephant can pick up some grass with its trunk. When a young elephantis first learning to feed itself, it sticks its trunk into its mother’s mouth and pulls out a little of her meal for a taste.How do elephants drink? They get water with their trunks, and then squirt it into their mouths. When a young elephant tries to shoot water from its trunk to its mouth, most of the water splashes on the elephant. By the time an elephant is six months old, its aim is better. All the water squirts into its mouth without splashing.( ) 36. What can an elephant’s nose do?A. Breathe.B. Pick up food.C. Greet friends.D. All of the above.( ) 37. When can baby elephants pick up some grass with their trunks?A. By the time they are a week old.B. By the time they are three months old.C. When they are like their mothers.D. When they are three years old.( ) 38. How does a mother elephant help her young baby try different food at first?A. By showing it how to raise its trunk for food.B. By letting it take food from her mouth.C. By helping it fill its mouth with food.D. By making it put food in her trunk.( ) 39. What does the un derlined word “squ i rt” mean in Chinese?A.请求B.递给C.喷射D.挑选( ) 40. When getting a drink, why does a young elephant splash most of the water on itself?A. Its aim is poor.B. It is playing.C. Its trunk is too long.D. It is saying hello.CSarah knew that it must be close to dinnertime. The sky was getting dark and she was very hungry.“I’d better go home now, Yvette,” Sarah said.“I want to ask my mom if you can stay for dinner,” Yvette said.“Okay,” Sarah said.Yvette called her mother, who was in the kitchen. “Hey, M om, what are we having for dinner? c an Sarah stay?”Yvette’s mom called back,“We are having spaghetti, salad, and garlic bread. And, yes, Sarah can stay.”“Thanks, Mom!” Yvette said.“Your mom makes great spaghetti. But I need to call my parents and ask them if I can have dinner with you,” Sarah said.Sarah started to dial her telephone number, but then she stopped. "I remember that my parents aren’t home. They went out shopping, so my sister Berta is taking care of me tonight," she told Yvette.“Well, ask Berta. Do you think she will mind?” Yvette said.“No, I don't think so,” Sarah said.The phone rang three times and then Sarah’s sixteen-year-old sister, Berta, answered. Sarah told Berta that Yvette had invited her to have dinner with her family.“You can if you want to. Only, I’m making pancakes. I know how much you like them,” Berta said.Sarah did love pancakes, but she loved spaghetti, too! Berta had just learned how to cook, and she had decided to make pancakes especially for Sarah. It was so nice of Berta! Sarah did not want to make Berta unhappy. She decided to go home for dinner.( ) 41. When did the story happen?A. In the morning.B. At noon.C. In the evening.D. In the early afternoon.( ) 42. Where was Yvette's mother when they were talking?A. In the kitchen.B. At Berta's home.C. In a shopping mall.D. In a school.( ) 43. How old was Berta?A. 10 years old.B. 16 years old.C. 8 years old.D. 20 years old.( ) 44. What is the main idea of this story?A. Two sisters decide to help their parents.B. A girl learns to get along with her sister.C. Two sisters decide to take care of themselves.D. A girl appreciates(感激) her sister doing something special for her. ( ) 45. Why does Sarah decide to eat dinner at home?A. She does not like spaghetti.B. She wants to please her parents.C. She thinks Berta is a good cook.D. She does not want to hurt Berta’s feeling s.A. Beach Camp:B. Camp James.C. Ballona Beach Summer Camp LLC.D. B and C.( ) 47. What can't we know about Beach Camp?A. The price.B. What kind it is.C. How long it lasts.D. The age of the campers.( ) 48. The Smiths are very busy this summer, so they have no time to look after their 4-year-old son. Which camp could the boy probably take part in?A. Beach Camp.B. Camp James.C. Ballona Beach Summer Camp LLC.D. We don’t knowEOn a cold winter morning, an old man sat against a wall at Sydney’s Circular Quay Station. I regarded him as a man who had no home or job.On my way home that afternoon, I saw the same man in the same place. He was sitting there, with his head almost on the ground. Two doctors were beside him. This time I stopped. He wasn’t a homeless man at all. He was old ce rtainly, but he wore a nice suit and was clean. I felt sorry. How difficult it was for that sick, old man to stay in the coldness for the whole day. He needed help. No one stopped. No one cared.A different season and I again came across an old man half lying on the ground. The morning heat made people uncomfortable. I just looked at him. However, the memory of the old Winter Man came back to me. I walked back to the man on the ground. He was dressed in smart clothes. I asked if he was OK. He told me he was sick and it might be agood idea to send him to hospital. I did --- it was a few minutes away.After that, he said to me, “Nobody stopped. Thank you.” I felt sadness for the Winter Man. I had not walked past another person in need: I was amazed that it had been so easy to be helpful.( ) 51. The first old man sat on the ground for_______.A. an hourB. two hoursC. half of the dayD. a whole day( ) 52. The underlined words “A different season” may refer to“________” according to the passage.A. winterB. summerC. autumnD. spring( ) 53. What did the writer probably think of the first old man?A. He might be waiting for somebody.B. He was having a rest there.C. He might be a beggar (乞丐).D. He missed his flight.( ) 54. How did the second man feel when the writer sent him to hospital?A. Surprised.B. Thankful.C. Amazed.D. Sad.( ) 55. What is the best title for the passage?A. A convenient station.B. Kindness of strangers.C. Helping others is helping yourself.D. How cold the world was!ii. 选择下列词汇完成下面对话。