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1、2011年安徽数学中考试题及答案2011安徽省中中考数学试题 一、选择题(本大题共10小题，每小题4分，满分40分) 1(,2、0、2、,3这四个数中最大的是【 】 A(2 B(0 C(,2 D(,3 2(我省2010年末森林面积为3804.2千公顷，用科学记数法表示3804.2千正确的是【 】 (3467 B(380.4210 C(3.804210 D(3.804210 A(3804.2103(下图是五个相同的小正方体搭成的几何体，其左视图是【 】 A( B( C( D( 4(设a,19,1，a在两个相邻整数之间，则这两个整数是【 】 A(1和2 B(2和3 C(3和4 D(4和5 5(从正
2、五边形的五个顶点中，任取四个顶点连成四边形，对于事件M:“这个四边形是等腰梯形”，下列推断正确的是【 】 A A(事件M是不可能事件 B(事件M是必然事件 12C(事件M发生的概率为 D(事件M发生的概率为 5 5 E F 6(如图，D是?ABC内一点，BD?CD，AD,6，BD,4，CD,3， D F、G、H分别是AB、AC、CD、BD的中点，则四边形EFGH E、H G 的周长是【 】 B C A(7 B(9 C(10 D(11 A 7(如图，?O的半径为1，A、B、C是圆周上的三点，?BAC,36?， 则劣弧BC的长是【 】 O 2413,A( B( C( D( C 5555B 8(一元
3、二次方程x(x,2),2,x的根是【 】 A(,1 B(2 C(1和2 D(,1和2 P A D 229(如图，在四边形ABCD中，?BAD,?ADC,90?，AB,AD,， C 32CD,，点P在四边形ABCD的边上(若点P到BD的距离为， 2B 则点P的个数为【 】 D A(1 B(2 C(3 D(4 N 10(如图，点P是菱形ABCD的对角线AC上的一个动点，过点A C P P垂直于AC的直线交菱形ABCD的边于M、N两点(设ACM ,2，BD,1，AP,x，?AMN的面积为y，则y关于x的函B 数图象大致形状是【 】 y y y y x x x x O 1 2 O 1 2 O 1 2
4、O 1 2 A( B( C( D( 二、填空题(本大题共4小题，每小题5分，满分20分) 2b，2ab，b, ( 11(因式分解:an12(根据里氏震级的定义，地震所释放出的相对能量E与震级n的关系为:E,10，那么9级地震所释放出的相对能量是7级地震所释放出的相对能量的倍数是 ( 13(如图，?O的两条弦AB、CD互相垂直，垂足为E，且AB,CD， A CE,1，DE,3，则?O的半径是 ( ,14(定义运算ab,a(1,b)，下面给出了关于这种运算的四个结论: O ,?2(,2),6 ?ab,ba C D E B ,?若a，b,0，则(aa)，(bb),2ab ?若ab,0，则a,0( 其
5、中正确结论的序号是 (填上你认为所有正确结论的序号)( 三、(本大题共2小题，每小题8分，满分16分) 12,15(先化简，再求值:，其中x,2( 2x,1x,116(江南生态食品加工厂收购了一批质量为10000kg的某种山货，根据市场需求对其进行粗加工和精加工处理，已知精加的这种山货质量比粗加工的质量的3倍还多2000kg，求粗加工的这种山货的质量( 四、(本大题共2小题，每小题8分，满分16分) 17(如图，在边长为1个单位长度的小正方形组成的网格中，按要求画出?ABC和?111ABC: 222(1)将?ABC先向右平移4个单位，再向上平移1个单位，得到?ABC; 111(2)以图中的点O
6、为位似中心，将?ABC作位似变换且放大到原来的两倍，得到?111ABC( 222C B A O 18(在平面直角坐标系中，一蚂蚁从原点O出发，按向上、向右、向下、向右的方向依次不断移动，每次移动1个单位，其行走路线如下图所示( y A A A AAA12569101 O A A A A A A x 34781112(1)填写下列各点的坐标:A( ， )、A( ， )、48A( ， ); 12(2)写出点A的坐标(n是正整数); 4n(3)指出蚂蚁从点A到点A的移动方向( 100101五、(本大题共2小题，每小题10分，满分20分) 19(如图，某高速公路建设中需要确定隧道AB的长度(已知在离地
7、面1500m高度C处的vibration pound used flat type and insert type phase combined vibration pound, specific for first with insert type vibrators vibration pound, requirements steep, fast plug slow pulled, plug points uniform, special strengthening on steel anchorage end of vibration pound, then with flat vib
8、rators vibration pound, before and after two times overlap sewing many Yu 100mm, improve concrete of dense degrees and surface can wipe sex. 7.4 vibration pound end Hou began steel drum rolling, rolling General not less than three again, first again and second again of rolling direction vertical, th
9、ird again direction with first again, guarantee concrete surface flat, rolling Hou, immediately with wood wipe child wipe flat a again, stay surface received water Hou, people stepped on has minor footprints Shi (settlement 5-10MM), began second again wipe pressure, with of with double plastic sheet
10、ing cover, sprinkler conservation, sprinkler conservation many Yu 7d. 8 concrete strength is not the same as note 8.1 during the different strength grade concrete pouring of concrete mix transport by car, listing number, clearly marked and signs indicating the grade of concrete, after delivery, led
11、by full-time staff to the appropriate placement of parts in case of mistake. 8.2 strengthening communications links, concrete pouring process, the front and rear, floor and ground radio link issues timely processing. 8.3 After pouring the concrete to meet the design requirements of time, cleaned aga
12、in, and watering than the concrete components with parts labeled a level concrete and Expander. 1.6 masonry construction engineering masonry with aerated concrete blocks and standard clay bricks. 1 material-for entry at the request of blocks and Clay tile product certificate, and product performance
13、 test report. -When aerated concrete masonry, its age should not exceed 28D. -Transportation, loading and unloading in the process throwing and dumping isC D 飞机上，测量人员测得正前方A、B两点处的俯角分别为60?和45?(求隧道AB的长(345? 60? ?1.73)( 1500m 【解】 O A B 20(一次学科测验，学生得分均为整数，满分为10分，成绩达到6分以上(包括6分)为合格，成绩达到9分为优秀(这次测验甲、乙两组学生成绩分
14、布的条形统计图如下: 学生数/人 甲 乙 5 4 3 2 1 成绩/分 0 1 2 3 4 5 6 7 8 9 10 (1)请补充完成下面的成绩统计分析表: 平均分 方差 中位数 合格率 优秀率 甲组 6.9 2.4 91.7% 16.7% 乙组 1.3 83.3% 8.3% (2)甲组学生说他们的合格率、优秀率均高于乙组，所以他们的成绩好于乙组(但乙组学生不同意甲组学生的说法，认为他们组的成绩要好于甲组(请你给出三条支持乙组学生观点的理由( 六、(本题满分12分) k 221(如图，函数y,kx，b的图象与函数y,(x,0)的图象交于点A(2，1)、B，与y112xy 轴交于点C(0，3)(
15、 C (1)求函数y的表达式和点B的坐标; 1B (2)观察图象，比较当x,0时y与y的大小( 12A 【解】 x O 七、(本题满分12分) ,22(在?ABC中，?ACB,90?，?ABC,30?，将?ABC绕顶点C顺时针旋转，旋转角为(0?,180?)，得到?ABC( 11A A A A1 A1A 1E , ,P D C C C B B B B1B 1B 1图1 图2 图3 时，设AB与BC相交于点D(证明:?ACD是等边三角形; (1)如图1，当AB?CB1111(2)如图2，连接AA、BB，设?ACA和?BCB的面积分别为S、S(求证:S?S11111212,1?3; ,(3)如图3
16、，设AC的中点为E，AB的中点为P，AC,a，连接EP(当, ?11时，EP的长度最大，最大值为 ( 八、(本题满分14分) 23(如图，正方形ABCD的四个顶点分别在四条平行线l、l、l、l上，这四条直线中相邻1234两条之间的距离依次为h、h、h(h,0，h,0，h,0)( A 123123l 1(1)求证:h,h; 12 h1B 22l (2)设正方形ABCD的面积为S，求证:S,(h，h)，h; 2121h 2l 3 3 D h (3)若h，h,1，当h变化时，说明正方形ABCD的面积S随h的变化情况( 312112l 4C 2011年安徽省初中毕业学业考试数学参考答案 110 ACA
17、CB DBDBC 2511. ; 12. 100; 13. 14. ?. ，ba，1x，1,2x,11115. 原式=. ,1(x，1)(x,1)(x，1)(x,1)x，1,2，116. 设粗加工的该种山货质量为xkg，根据题意，得 x+(3x+2000)=10000. 解得 x=2000. 答:粗加工的该种山货质量为2000kg. 17. 如下图 C2 BC2 1 C Avibration pound used flat type and insert type phase combined vibration pound, specific for first with insert ty
18、pe vibrators vi2 bration pound, requirements steep, fast plug slow pulled, plug points uniform, special strengthening on steel anchorage end of vibration pound, then with flat vibrators vibration pound, before and after two times overlap sewing many Yu 100mm, improve concrete of dense degrees and su
19、rface can wipe sex. 7.4 vibration pound end Hou began steel drum rolling, rolling General not less than three again, first again and second again of rolling direction vertical, third again direction with first again, guarantee concrete surface flat, rolling Hou, immediately with wood wipe child wipe
20、 flat a again, stay surface received water Hou, people stepped on has minor footprints Shi (settlement 5-10MM), began second again wipe pressure, with of with double plastic sheeting cover, sprinkler conservation, sprinkler conservation many Yu 7d. 8 concrete strength is not the same as note 8.1 dur
21、ing the different strength grade concrete pouring of concrete mix transport by car, listing number, clearly marked and signs indicating the grade of concrete, after delivery, led by full-time staff to the appropriate placement of parts in case of mistake. 8.2 strengthening communications links, conc
22、rete pouring process, the front and rear, floor and ground radio link issues timely processing. 8.3 After pouring the concrete to meet the design requirements of time, cleaned again, and watering than the concrete components with parts labeled a level concrete and Expander. 1.6 masonry construction
23、engineering masonry with aerated concrete blocks and standard clay bricks. 1 material-for entry at the request of blocks and Clay tile product certificate, and product performance test report. -When aerated concrete masonry, its age should not exceed 28D. -Transportation, loading and unloading in th
24、e process throwing and dumping isB1 B A1 ? A O 18(?A(0,1) A(1,0) A(6,0) 1312?A(2n,0) n?向上 3,19. 简答:?OA， ,1500，tan30,1500，,50033OB=OC=1500， 1500,5003,1500,865,635 ?AB=(m). 答:隧道AB的长约为635m. 20. (1)甲组:中位数 7; 乙组:平均数7， 中位数7 (2)(答案不唯一) ?因为乙组学生的平均成绩高于甲组学生的平均成绩，所以乙组学生的成绩好于甲组; ?因为甲乙两组学生成绩的平均分相差不大，而乙组学生的方差低于甲组
25、学生的方差，说明乙组学生成绩的波动性比甲组小，所以乙组学生的成绩好于甲组; ?因为乙组学生成绩的最低分高于甲组学生的最低分，所以乙组学生的成绩好于甲组。 k,1,2k，b,1,1121. (1)由题意，得 解得 ? y,x，3,1bb,3.,3.,kk222,y1,y 又A点在函数上，所以 ，解得 所以 k,2222xx24、初步学会应用加减法解决生活中简单问题，感受数学在日常生活中的作用,感受加减法与日常生活的密切联系,同时获得一些初步的数学活动经验，发展解决问题和运用数学进行思考的能力。y,x，3,x,2,x,1,21解方程组 得 ,2,y,1.y,2.y,2,1,x,所以点B的坐标为(1
26、, 2) 3、学习并掌握100以内加减法(包括不进位、不退位与进位、退位)计算方法，并能正确计算;能根据具体问题，估计运算的结果;初步学会应用加减法解决生活中简单问题，感受加减法与日常生活的密切联系。(2)当0,x,1或x,2时，y,y; 12（1）圆周角：:顶点在圆上,并且两边都与圆相交的角,叫做圆周角.当1,x,2时，y,y; 12当x=1或x=2时，y=y. 12,AC,DC，ACD,6022.(1)易求得, , 因此得证. 同心圆：圆心相同，半径不等的两个圆叫做同心圆。,ACA,BCB1:3(2)易证得?,且相似比为，得证. 115.75.13加与减（二）2 P61-63 数学好玩2
27、P64-673a(3)120?， 2当a0时，抛物线开口向上，并且向上方无限伸展。当a0时，抛物线开口向下，并且向下方无限伸展。23.(1)过A点作AF?l分别交l、l于点E、F，过C点作CH?l分别交l、l于点H、G，323223证?ABE?CDG即可. 2. 图像性质：(2)易证?ABE?BCH?CDG?DAF,且两直角边长分别为h、h+h,四边形EFGH是边长112为h的正方形， 2122222所以. ，S,4，hh，h，h,2h，2hh，h,(h，h)，h112211221212顶点坐标：（，）3(3)由题意，得 所以 h,1,h212235,22S,h，1,h，h,h,h，1,111
28、1124, 2524,h,，,1455,三三角函数的计算h，0,12,又 解得0,h, 1,33h1,，01,2,2?当0,h,时，S随h的增大而减小; 115点在圆内 dr;24 当h=时，S取得最小值; 15522当,h,时，S随h的增大而增大. 1153vibration pound used flat type and insert type phase combined vibration pound, specific for first with insert type vibrators vibration pound, requirements steep, fast plu
29、g slow pulled, plug points uniform, special strengthening on steel anchorage end of vibration pound, then with flat vibrators vibration pound, before and after two times overlap sewing many Yu 100mm, improve concrete of dense degrees and surface can wipe sex. 7.4 vibration pound end Hou began steel
30、drum rolling, rolling General not less than three again, first again and second again of rolling direction vertical, third again direction with first again, guarantee concrete surface flat, rolling Hou, immediately with wood wipe child wipe flat a again, stay surface received water Hou, people stepp
31、ed on has minor footprints Shi (settlement 5-10MM), began second again wipe pressure, with of with double plastic sheeting cover, sprinkler conservation, sprinkler conservation many Yu 7d. 8 concrete strength is not the same as note 8.1 during the different strength grade concrete pouring of concret
32、e mix transport by car, listing number, clearly marked and signs indicating the grade of concrete, after delivery, led by full-time staff to the appropriate placement of parts in case of mistake. 8.2 strengthening communications links, concrete pouring process, the front and rear, floor and ground r
33、adio link issues timely processing. 8.3 After pouring the concrete to meet the design requirements of time, cleaned again, and watering than the concrete components with parts labeled a level concrete and Expander. 1.6 masonry construction engineering masonry with aerated concrete blocks and standard clay bricks. 1 material-for entry at the request of blocks and Clay tile product certificate, and product performance test report. -When aerated concrete masonry, its age should not exceed 28D. -Transportation, loading and unloading in the process throwing and dumping is