江蘇省南京市中考數(shù)學(xué)試卷

1、2011年江蘇省南京市中考數(shù)學(xué)試卷一、選擇題（本大題共6小題，每小題2分，共12分,在每小題所給出的四個(gè)選項(xiàng)中，恰有一項(xiàng)是符合題目要求的，請(qǐng)將正確選項(xiàng)前的字母代號(hào)填涂在答題卡相應(yīng)位置上）19的值等于（）a3b-3c3d32下列運(yùn)算正確的是（）aa2+a3=a5ba2a3=a6ca3+a2=ad（a2）3=a63在第六次全國(guó)人口普查中，南京市常住人口約為800萬(wàn)人，其中65歲及以上人口占9.2%，則該市65歲及以上人口用科學(xué)記數(shù)法表示約為（）a0.736106人b7.36104人c7.36105人d7.36106人4為了了解某初中學(xué)校學(xué)生的視力情況，需要抽取部分學(xué)生進(jìn)行調(diào)查下列抽取學(xué)生的方法最合

2、適的是（）a隨機(jī)抽取該校一個(gè)班級(jí)的學(xué)生b隨機(jī)抽取該校一個(gè)年級(jí)的學(xué)生c隨機(jī)抽取該校一部分男生d分別從該校初一、初二、初三年級(jí)中各隨機(jī)抽取10%的學(xué)生5如圖是一個(gè)三棱柱下列圖形中，能通過(guò)折疊圍成一個(gè)三棱柱的是（）abcd6如圖，在平面直角坐標(biāo)系中，p的圓心是（2，a）（a2），半徑為2，函數(shù)y=x的圖象被p截得的弦ab的長(zhǎng)為23，則a的值是（）a22b2+2c23d2+3二、填空題（本大題共10小題，每小題2分，共20分,不需寫(xiě)出解答過(guò)程，請(qǐng)把答案直接填寫(xiě)在答題卡相應(yīng)位置上）7-2的相反數(shù)是8如圖，過(guò)正五邊形abcde的頂點(diǎn)a作直線(xiàn)lcd，則1=9計(jì)算（2+1）（2-2）=10等腰梯形的腰長(zhǎng)為5c

3、m，它的周長(zhǎng)是22cm，則它的中位線(xiàn)長(zhǎng)為cm11如圖，以0為圓心，任意長(zhǎng)為半徑畫(huà)弧，與射線(xiàn)om交于點(diǎn)a，再以a為圓心，ao長(zhǎng)為半徑畫(huà)弧，兩弧交于點(diǎn)b，畫(huà)射線(xiàn)ob，則cosaob的值等于12如圖，菱形abcd的邊長(zhǎng)是2cm，e是ab的中點(diǎn)，且de丄ab，則菱形abcd的面積為cm213如圖，海邊立有兩座燈塔a、b，暗礁分布在經(jīng)過(guò)a、b兩點(diǎn)的弓形（弓形的弧是o的一部分）區(qū)域內(nèi)，aob=80為了避免觸礁，輪船p與a、b的張角apb的最大值為14如圖，e、f分別是正方形abcd的邊bc、cd上的點(diǎn)，be=cf，連接ae、bf將abe繞正方形的中心按逆時(shí)針?lè)较蛐D(zhuǎn)到bcf，旋轉(zhuǎn)角為（0180），則=15

4、設(shè)函數(shù)y=2x與y=x-1的圖象的交點(diǎn)坐標(biāo)為（a，b），則1a-1b的值為16甲、乙、丙、丁四位同學(xué)圍成一圈依序循環(huán)報(bào)數(shù)，規(guī)定：甲、乙、丙、丁首次報(bào)出的數(shù)依次為1、2、3、4，接著甲報(bào)5，乙報(bào)6按此規(guī)律，后一位同學(xué)報(bào)出的數(shù)比前一位同學(xué)報(bào)出的數(shù)大1當(dāng)報(bào)到的數(shù)是50時(shí)，報(bào)數(shù)結(jié)束；若報(bào)出的數(shù)為3的倍數(shù)，則報(bào)該數(shù)的同學(xué)需拍手一次在此過(guò)程中，甲同學(xué)需拍手的次數(shù)為三、解答題（本大題共12小題，共88分，請(qǐng)?jiān)诖痤}卡指定區(qū)域內(nèi)作答，解答時(shí)應(yīng)寫(xiě)出文字說(shuō)明、證明過(guò)程或演算步驟）17解不等式組5+2x3x+13x2，并寫(xiě)出不等式組的整數(shù)解18計(jì)算（aa2b2-1a+b）bba19解方程：x2-4x-1=020某校部

5、分男生分3組進(jìn)行引體向上訓(xùn)練對(duì)訓(xùn)練前后的成績(jī)進(jìn)行統(tǒng)計(jì)分析，相應(yīng)數(shù)據(jù)的統(tǒng)計(jì)圖如下（1）求訓(xùn)練后第一組平均成績(jī)比訓(xùn)練前增長(zhǎng)的百分?jǐn)?shù)；（2）小明在分析了圖表后，聲稱(chēng)他發(fā)現(xiàn)了一個(gè)錯(cuò)誤：“訓(xùn)練后第二組男生引體向上個(gè)數(shù)沒(méi)有變化的人數(shù)占該組人數(shù)的50%，所以第二組的平均成績(jī)不可能提高3個(gè)這么多”你同意小明的觀(guān)點(diǎn)嗎？請(qǐng)說(shuō)明理由；（3）你認(rèn)為哪一組的訓(xùn)練效果最好？請(qǐng)?zhí)峁┮粋€(gè)解釋來(lái)支持你的觀(guān)點(diǎn)21如圖，將abcd的邊dc延長(zhǎng)到點(diǎn)e，使ce=dc，連接ae，交bc于點(diǎn)f（1）求證：abfecf；（2）若afc=2d，連接ac、be，求證：四邊形abec是矩形22小穎和小亮上山游玩，小穎乘坐纜車(chē)，小亮步行，兩人相約在

6、山頂?shù)睦|車(chē)終點(diǎn)會(huì)合已知小亮行走到纜車(chē)終點(diǎn)的路程是纜車(chē)到山頂?shù)木€(xiàn)路長(zhǎng)的2倍小穎在小亮出發(fā)后50min才乘上纜車(chē)，纜車(chē)的平均速度為180m/min設(shè)小亮出發(fā)xmin后行走的路程為ym，圖中的折線(xiàn)表示小亮在整個(gè)行走過(guò)程中y與x的函數(shù)關(guān)系（1）小亮行走的總路程是m，他途中休息了min；（2）當(dāng)50x80時(shí)，求y與x的函數(shù)關(guān)系式；當(dāng)小穎到達(dá)纜車(chē)終點(diǎn)時(shí)，小亮離纜車(chē)終點(diǎn)的路程是多少？23從3名男生和2名女生中隨機(jī)抽取2014年南京青奧會(huì)志愿者求下列事件的概率：（1）抽取1名，恰好是女生；（2）抽取2名，恰好是1名男生和1名女生24已知函數(shù)y=mx2-6x+1（m是常數(shù)）（1）求證：不論m為何值，該函數(shù)的圖象

7、都經(jīng)過(guò)y軸上的一個(gè)定點(diǎn)；（2）若該函數(shù)的圖象與x軸只有一個(gè)交點(diǎn)，求m的值25如圖，某數(shù)學(xué)課外活動(dòng)小組測(cè)量電視塔ab的高度他們借助一個(gè)高度為30m的建筑物cd進(jìn)行測(cè)量，在點(diǎn)c處測(cè)得塔頂b的仰角為45，在點(diǎn)e處測(cè)得b的仰角為37（b、d、e三點(diǎn)在一條直線(xiàn)上）求電視塔的高度h（參考數(shù)據(jù)：sin370.60，cos370.80，tan370.75）26如圖，在rtabc中，acb=90，ac=6cm，bc=8cmp為bc的中點(diǎn)，動(dòng)點(diǎn)q從點(diǎn)p出發(fā)，沿射線(xiàn)pc方向以2cm/s的速度運(yùn)動(dòng)，以p為圓心，pq長(zhǎng)為半徑作圓設(shè)點(diǎn)q運(yùn)動(dòng)的時(shí)間為t s（1）當(dāng)t=1.2時(shí)，判斷直線(xiàn)ab與p的位置關(guān)系，并說(shuō)明理由；（2）

8、已知o為abc的外接圓若p與o相切，求t的值27如圖，p為abc內(nèi)一點(diǎn)，連接pa、pb、pc，在pab、pbc和pac中，如果存在一個(gè)三角形與abc相似，那么就稱(chēng)p為abc的自相似點(diǎn)（1）如圖，已知rtabc中，acb=90，abca，cd是ab上的中線(xiàn)，過(guò)點(diǎn)b作be丄cd，垂足為e試說(shuō)明e是abc的自相似點(diǎn)；（2）在abc中，abc如圖，利用尺規(guī)作出abc的自相似點(diǎn)p（寫(xiě)出作法并保留作圖痕跡）；若abc的內(nèi)心p是該三角形的自相似點(diǎn)，求該三角形三個(gè)內(nèi)角的度數(shù)28【問(wèn)題情境】已知矩形的面積為a（a為常數(shù)，a0），當(dāng)該矩形的長(zhǎng)為多少時(shí)，它的周長(zhǎng)最??？最小值是多少？【數(shù)學(xué)模型】設(shè)該矩形的長(zhǎng)為x，周長(zhǎng)

9、為y，則y與x的函數(shù)關(guān)系式為y=2（x+ax）（x0）【探索研究】（1）我們可以借鑒以前研究函數(shù)的經(jīng)驗(yàn)，先探索函數(shù)y=x+1x（x0）的圖象和性質(zhì)填寫(xiě)下表，畫(huà)出函數(shù)的圖象；x1413121234y觀(guān)察圖象，寫(xiě)出該函數(shù)兩條不同類(lèi)型的性質(zhì)；在求二次函數(shù)y=ax2+bx+c（a0）的最大（小）值時(shí)，除了通過(guò)觀(guān)察圖象，還可以通過(guò)配方得到請(qǐng)你通過(guò)配方求函數(shù)y=x+1x（x0）的最小值【解決問(wèn)題】（2）用上述方法解決“問(wèn)題情境”中的問(wèn)題，直接寫(xiě)出答案 tgz7r4i30ka1dkaghn3xtkknbycudxqa7fhyi2chhi92tgkqcwa3ptgshls50clmtwn60eo8wgqv7x

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