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1、2011江苏南京中考数学及答案南京市2011年初中毕业生学业考试 数 学 数学注意事项: 1( 本试卷共6页，全卷满分120分，考试时间为120分钟，考生答题全部答在答题卡上，答在本试卷上无效( 2( 请认真核对监考教师在答题卡上所有粘贴条形码的姓名、考试证号是否与本人相符合，再将自己的姓名、准考证号用0.5毫米的黑色墨水签字笔填写在答题卡及本试卷上( 3( 答选择题必须用2B铅笔将答题卡上对应的答案标号涂黑(如需要改动，请用橡皮擦干净后，再选涂其他答案，答非选择题必须0.5毫米黑色墨水签字笔写在答题卡上指定位置，在其他位置答题一律无效( 4( 作图必须用2B铅笔作答，并请加黑加粗，描写清楚(
2、 一、选择题(本大题共6小题，每小题2分，共12分，在每小题所给出的四个选项中，恰有一项是符合题目要求的，请将正确的选项的字母代号填涂在答题卡相应位置上) (91(2011江苏南京，1，2分)的值等于 3A(3 B(,3 C(?3 D( 【答案】A 2(2011江苏南京，2，2分)下列运算正确的是 235 23632238A(a，a=a B(aa=a C(a?a=a D(a)=a 【答案】C 3(2011江苏南京，3，2分)在第六次全国人口普查中，南京市常住人口约为800万人，其中65岁及以上人口占9.2%(则该市65岁及以上人口用科学记数法表示约为 64 5 6 A(0.73610人 B(7
3、.3610人 C(7.3610人 D(7.3610人 【答案】C 4(2011江苏南京，4，2分)为了解某初中学校学生的视力情况，需要抽取部分学生进行调查，下列抽取学生的方法最合适的是 A(随机抽取该校一个班级的学生 B(随机抽取该校一个年级的学生 C(随机抽取该校一部分男生 D(分别从该校初一、初二、初三年级中各班随机抽取10%的学生 【答案】D 5(2011江苏南京，5，2分)如图是一个三棱柱，下列图形中，能通过折叠围成一个三棱柱的是 A( B( (第5题) C( D( 【答案】B items a,. archives, and seal, and fixed assets, and bo
4、oks, and phone, and health, and office supplies led with, and company property insurance,), supervision, and check, and Implementation the implementation of the corporate administrative system; 2.3 file and archive management: responsible for the collection of internal and external documents, number
5、ing, routing, reminders, responsible for internal documents to print, copy, fax sending and receiving, letters, newspaper and magazine subscriptions sent, responsible for contracts, information, documents, books, certificates, archiving and management, responsible for company registration, change of
6、 registration formalities; 2.4 the Conference Management: responsible for the internal organization of the meeting, make meeting records, to reminders, the meeting decided to deal with and implement, on behalf of the company to attend the meeting, is responsible for important meetings and planning,
7、or assist in the Organizations external public relations activities; 2.5 material management: responsible for the fixed assets and the purchase of office 6(2011江苏南京，6，2分)如图，在平面直角坐标系中，?P的圆心是(2，a)(a,2)，半径为2，函数y=x的图象被?P的弦AB的长为，则a的值是 23A( B( C( D( 232323，222，y y=x P B A O x (第6题) 【答案】B 二、填空题(本大题共10小题，每小
8、题2分，共20分，不需要写出解答过程，请把答案直接填写在答题卡相应位置上) 7(2011江苏南京，7，2分),2的相反数是_( 【答案】2 8(2011江苏南京，8，2分)如图，过正五边形ABCDE的顶点A作直线l?CD，则?1=_( A l 1 B E C D (第8题) 【答案】36 9(2011江苏南京，9，2分)计算=_( (21)(22)，,2【答案】 ，2分)等腰梯形的腰长为5?，它的周长是22?，则它的中位线10(2011江苏南京，10长为_?( 【答案】6 11(2011江苏南京，11，2分)如图，以O为圆心，任意长为半径画弧，与射线OM交于点A，再以A为圆心，AO长为半径画弧
9、，两弧交于点B，画射线OB，则cos?AOB的值等于_( ic relations activities; 2.5 material management: responsible for the fixed assets and the purchase of officel publhe company to attend the meeting, is responsible for important meetings and planning, or assist in the Organizations externaganization of the meeting, make
10、meeting records, to reminders, the meeting decided to deal with and implement, on behalf of tnal ornsible for company registration, change of registration formalities; 2.4 the Conference Management: responsible for the intere subscriptions sent, responsible for contracts, information, documents, boo
11、ks, certificates, archiving and management, respoagazing, routing, reminders, responsible for internal documents to print, copy, fax sending and receiving, letters, newspaper and mstrative system; 2.3 file and archive management: responsible for the collection of internal and external documents, num
12、berinproperty insurance,), supervision, and check, and Implementation the implementation of the corporate adminiitems a,. archives, and seal, and fixed assets, and books, and phone, and health, and office supplies led with, and company 2 B O A M (第11题) 1【答案】 212(2011江苏南京，12，2分)如图，菱形ABCD的连长是2?，E是AB中点
13、，且DE?AB，2则菱形ABCD的面积为_?( D A C E B (第12题) 23【答案】 13(2011江苏南京，13，2分)如图，海边有两座灯塔A、B，暗礁分布在经过A、B两点的弓形(弓形的弧是?O的一部分)区域内，?AOB=80?，为了避免触礁，轮船P与A、B的张角?APB的最大值为_?( P O A B (第13题) 【答案】40 14(2011江苏南京，14，2分)如图，E、F分别是正方形ABCD的边BC、CD上的点，BE=CF，连接AE、BF，将?ABE绕正方形的中心按逆时针方向转到?BCF，旋转角为a(0?,a,180?)，则?a=_( A D F B C E (第14题)
14、material management: responsible for the fixed assets and the purchase of office is responsible for important meetings and planning, or assist in the Organizations external public relations activities; 2.5ting, ake meeting records, to reminders, the meeting decided to deal with and implement, on beh
15、alf of the company to attend the meehange of registration formalities; 2.4 the Conference Management: responsible for the internal organization of the meeting, mon, cible for contracts, information, documents, books, certificates, archiving and management, responsible for company registratifor inter
16、nal documents to print, copy, fax sending and receiving, letters, newspaper and magazine subscriptions sent, respons nsibled archive management: responsible for the collection of internal and external documents, numbering, routing, reminders, responsurance,), supervision, and check, and Implementati
17、on the implementation of the corporate administrative system; 2.3 file anproperty iitems a,. archives, and seal, and fixed assets, and books, and phone, and health, and office supplies led with, and company 3 【答案】90 21115(2011江苏南京，15，2分)设函数与的图象的交战坐标为(a，b)，则y,yx,1xab的值为_( 1【答案】 ,216(2011江苏南京，16，2分)甲、
18、乙、丙、丁四位同学围成一圈依序循环报数，规定: ?甲、乙、丙、丁首次报出的数依次为1、2、3、4，接着甲报5、乙报6按此规律，后一位同学报出的数比前一位同学报出的数大1，当报到的数是50时，报数结束; ?若报出的数为3的倍数，则报该数的同学需拍手一次，在此过程中，甲同学需要拍手的次数为_( 【答案】4 三、解答题(本大题共12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) 523，x?,17(2011江苏南京，17，6分)解不等式组，并写出不等式组的整数解( xx，1,32,【答案】解: x,1解不等式?得: x,2解不等式?得: ,12x所以，不等式组的
19、解集是( ,1不等式组的整数解是，0，1( ab1(),18(2011江苏南京，18，6分)计算 22ababba,，,ab1【答案】解:(,) 22ababba,，,，aabb, ,()()()()ababababba，,，,，bba, ()()ababb，,1, ab，219(2011江苏南京，19，6分)解方程x,4x，1=0 2xx,41【答案】解法一:移项，得( 2xx,，,，4414配方，得， ic relations activities; 2.5 material management: responsible for the fixed assets and the purc
20、hase of officel publhe company to attend the meeting, is responsible for important meetings and planning, or assist in the Organizations externaganization of the meeting, make meeting records, to reminders, the meeting decided to deal with and implement, on behalf of tnal ornsible for company regist
21、ration, change of registration formalities; 2.4 the Conference Management: responsible for the intere subscriptions sent, responsible for contracts, information, documents, books, certificates, archiving and management, respoagazing, routing, reminders, responsible for internal documents to print, c
22、opy, fax sending and receiving, letters, newspaper and mstrative system; 2.3 file and archive management: responsible for the collection of internal and external documents, numberinproperty insurance,), supervision, and check, and Implementation the implementation of the corporate adminiitems a,. ar
23、chives, and seal, and fixed assets, and books, and phone, and health, and office supplies led with, and company 4 2 (2)3x,由此可得 x,23， x,，23x,2312解法二: abc,1,4,1.22， bac,，,4(4)411120412, x,23.2，( x,，23x,231220(2011江苏南京，20，7分)某校部分男生分3组进行引体向上训练，对训练前后的成绩进行统计分析，相应数据的统计图如下( 训练后第二组男生引体 训练前后各组平均成绩统计图 向上增加个数分布
24、统计图 12 11 平均成绩(个) 训练前 10 9 9 个数没有变化 8 50% 6 训练后 6 5 10% 20% 4 3 20% 增加5个 增加8个 2 增加6个 0 第一组 第二组 第三组 组别 ? ? (第20题) ?求训练后第一组平均成绩比训练前增长的百分数; ?小明在分析了图表后，声称他发现了一个错误:“训练后第二组男生引体向上个数没有变化的人数占该组人数的50%，所以第二组的平均数不可能提高3个这么多(”你同意小明的观点吗,请说明理由; ?你认为哪一组的训练效果最好,请提出一个解释来支持你的观点( 53,，100%【答案】解:?训练后第一组平均成绩比训练前增长的百分数是?67%
25、( 3?不同意小明的观点，因为第二组的平均成绩增加810%+620%+520%+050%=3(个)( (3)本题答案不唯一，我认为第一组训练效果最好，因为训练后第一组平均成绩比训练前增长的百分数最大( 21(2011江苏南京，21，7分)如图，将?ABCD的边DC延长到点E，使CE=DC，连接AE，交BC于点F( ?求证:?ABF?ECF ?若?AFC=2?D，连接AC、BE(求证:四边形ABEC是矩形( material management: responsible for the fixed assets and the purchase of office is responsible
26、 for important meetings and planning, or assist in the Organizations external public relations activities; 2.5ting, ake meeting records, to reminders, the meeting decided to deal with and implement, on behalf of the company to attend the meehange of registration formalities; 2.4 the Conference Manag
27、ement: responsible for the internal organization of the meeting, mon, cible for contracts, information, documents, books, certificates, archiving and management, responsible for company registratifor internal documents to print, copy, fax sending and receiving, letters, newspaper and magazine subscr
28、iptions sent, respons nsibled archive management: responsible for the collection of internal and external documents, numbering, routing, reminders, responsurance,), supervision, and check, and Implementation the implementation of the corporate administrative system; 2.3 file anproperty iitems a,. ar
29、chives, and seal, and fixed assets, and books, and phone, and health, and office supplies led with, and company 5 A D B C F E (第21题) 【答案】证明:?四边形ABCD是平行四边形，?AB?CD,AB=CD(?ABF=?ECF. ?EC=DC, ?AB=EC( 在?ABF和?ECF中，?ABF=?ECF，?AFB=?EFC，AB=EC， ?ABF?ECF( (2)解法一:?AB=EC ，AB?EC，?四边形ABEC是平行四边形(?AF=EF， BF=CF( ?四边形A
30、BCD是平行四边形，?ABC=?D，又?AFC=2?D，?AFC=2?ABC( ?AFC=?ABF+?BAF，?ABF=?BAF(?FA=FB( ?FA=FE=FB=FC, ?AE=BC(?口ABEC是矩形( 解法二:?AB=EC ，AB?EC，?四边形ABEC是平行四边形( ?四边形ABCD是平行四边形，?AD?BC，?D=?BCE( 又?AFC=2?D，?AFC=2?BCE， ?AFC=?FCE+?FEC，?FCE=?FEC(?D=?FEC(?AE=AD( 又?CE=DC，?AC?DE(即?ACE=90?( ?口ABEC是矩形( 22(2011江苏南京，22，7分)小颖和小亮上山游玩，小颖
31、乘会缆车，小亮步行，两人相约在山顶的缆车终点会合(已知小亮行走到缆车终点的路程是缆车到山顶的线路长的2倍，小颖在小亮出发后50 min才乘上缆车，缆车的平均速度为180 m/min(设小亮出发x min后行走的路程为y m(图中的折线表示小亮在整个行走过程中y与x的函数关系( ?小亮行走的总路程是_?，他途中休息了_min( ?当50?x?80时，求y与x的函数关系式; ?当小颖到达缆车终点为时，小亮离缆车终点的路程是多少, y/m 3000 1950 O 30 50 x/min 80 (第22题) 【答案】解:?3600，20( 5080,x?当时，设y与x的函数关系式为ykxb,，( x,
32、50x,80根据题意，当y,1950y,3600时，;当，( ic relations activities; 2.5 material management: responsible for the fixed assets and the purchase of officel publhe company to attend the meeting, is responsible for important meetings and planning, or assist in the Organizations externaganization of the meeting, mak
33、e meeting records, to reminders, the meeting decided to deal with and implement, on behalf of tnal ornsible for company registration, change of registration formalities; 2.4 the Conference Management: responsible for the intere subscriptions sent, responsible for contracts, information, documents, b
34、ooks, certificates, archiving and management, respoagazing, routing, reminders, responsible for internal documents to print, copy, fax sending and receiving, letters, newspaper and mstrative system; 2.3 file and archive management: responsible for the collection of internal and external documents, n
35、umberinproperty insurance,), supervision, and check, and Implementation the implementation of the corporate adminiitems a,. archives, and seal, and fixed assets, and books, and phone, and health, and office supplies led with, and company 6 所以，与的函数关系式为( yxyx,55800?缆车到山顶的路线长为3600?2=1800()， mmin()( 缆车到
36、达终点所需时间为1800?180,0min小颖到达缆车终点时，小亮行走的时间为10，50,60()( x,60把代入，得y=5560800=2500( yx,55800所以，当小颖到达缆车终点时，小亮离缆车终点的路程是3600-2500=1100()( m23(2011江苏南京，23，7分)从3名男生和2名女生中随机抽取2014年南京青奥会志愿者(求下列事件的概率: ?抽取1名，恰好是女生; ?抽取2名，恰好是1名男生和1名女生( 2:?抽取1名，恰好是女生的概率是( 【答案】解5?分别用男1、男2、男3、女1、女2表示这五位同学，从中任意抽取2名，所有可能出现的结果有:(男1，男2)，(男1
37、，男3)，(男1，女1)，(男1，女2)，(男2，男3)，(男2，女1)，(男2，女2)，(男3，女1)，(男3，女2)，(女1，女2)，共10种，它们出现的可能性相同，所有结果中，满足抽取2名，恰好是1名男生和1名女生(记为事件A)63,的结果共6种，所以P(A)=( 105224(2011江苏南京，24，7分)(7分)已知函数y=mx,6x，1(m是常数)( ?求证:不论m为何值，该函数的图象都经过y轴上的一个定点; ?若该函数的图象与x轴只有一个交点，求m的值( 【答案】解:?当x=0时，( y,12y所以不论为何值，函数的图象经过轴上的一个定点(0，1)( mymxx,，61m,0?当
38、时，函数的图象与轴只有一个交点; xyx,，612m,0?当时，若函数的图象与x轴只有一个交点，则方程ymxx,，6122m,9mxx,，,610有两个相等的实数根，所以，( (6)40,m2xm综上，若函数的图象与轴只有一个交点，则的值为0或9( ymxx,，6125(2011江苏南京，25，7分)如图，某数学课外活动小组测量电视塔AB的高度，他们借助一个高度为30m的建筑物CD进行测量，在点C处塔顶B的仰角为45?，在点E处测得B的仰角为37?(B、D、E三点在一条直线上)(求电视塔的高度h( (参考数据:sin37?0.60，cos37?0.80，tan37?0.75) material
39、 management: responsible for the fixed assets and the purchase of office is responsible for important meetings and planning, or assist in the Organizations external public relations activities; 2.5ting, ake meeting records, to reminders, the meeting decided to deal with and implement, on behalf of t
40、he company to attend the meehange of registration formalities; 2.4 the Conference Management: responsible for the internal organization of the meeting, mon, cible for contracts, information, documents, books, certificates, archiving and management, responsible for company registratifor internal docu
41、ments to print, copy, fax sending and receiving, letters, newspaper and magazine subscriptions sent, respons nsibled archive management: responsible for the collection of internal and external documents, numbering, routing, reminders, responsurance,), supervision, and check, and Implementation the i
42、mplementation of the corporate administrative system; 2.3 file anproperty iitems a,. archives, and seal, and fixed assets, and books, and phone, and health, and office supplies led with, and company 7 B D h ? 4537 ?E C A (第25题) DCRtECD,tan，DEC【答案】解:在中，,( ECDC30?EC,?()( ,40mtan，DEC0.75RtBAC,BACA,在中，?
43、BCA,45?，? hBARtBAE,tan，BEAh,120在中，,(?,0.75(?()( mEAh，40答:电视塔高度约为120( m26(2011江苏南京，26，8分)如图，在Rt?ABC中，?ACB=90?，AC=6?，BC=8?，P为BC的中点(动点Q从点P出发，沿射线PC方向以2?/s的速度运动，以P为圆心，PQ长为半径作圆(设点Q运动的时间为t s( ?P的位置关系，并说明理由; ?当t=1.2时，判断直线AB与?已知?O为?ABC的外接圆，若?P与?O相切，求t的值( A O P B C Q (第26题) AB【答案】解:?直线与?P相切( 如图，过点P作PD?AB, 垂足为
44、D( 在Rt?ABC中，?ACB,90?，?AC=6cm，BC=8cm， 22ABACBCcm,，,10?(?P为BC的中点，?PB=4cm( ?PDB,?ACB,90?，?PBD,?ABC(?PBD?ABC( PDPBPD4,?,即，?PD =2.4(cm) ( ACAB610ic relations activities; 2.5 material management: responsible for the fixed assets and the purchase of officel publhe company to attend the meeting, is responsi
45、ble for important meetings and planning, or assist in the Organizations externaganization of the meeting, make meeting records, to reminders, the meeting decided to deal with and implement, on behalf of tnal ornsible for company registration, change of registration formalities; 2.4 the Conference Ma
46、nagement: responsible for the intere subscriptions sent, responsible for contracts, information, documents, books, certificates, archiving and management, respoagazing, routing, reminders, responsible for internal documents to print, copy, fax sending and receiving, letters, newspaper and mstrative
47、system; 2.3 file and archive management: responsible for the collection of internal and external documents, numberinproperty insurance,), supervision, and check, and Implementation the implementation of the corporate adminiitems a,. archives, and seal, and fixed assets, and books, and phone, and health, and office supplies led with, and company 8 t,1.2当时，(cm) PQt,22.4?，即圆心到直线的距离等于?P的半径( PABPDPQ,?直线与?P相切( AB1? ?ACB,90?，?AB为?ABC的外切圆的直径(?( OBABcm,521连接OP(?P为BC的中点，?( OPACcm,32?点P在?O内部，?P与?O只能内切( 523,t253t,?或