上海市靜安區(qū)中考數(shù)學(xué)一模試卷

1、2014年上海市靜安區(qū)中考數(shù)學(xué)一模試卷一、選擇題：（本題共6題，每題4分，滿分24分）1在rtabc中，c=90，如果a=，bc=a，那么ac等于（）aatanbacotcasindacos顯示解析2如果拋物線y=mx2+（m-3）x-m+2經(jīng)過(guò)原點(diǎn)，那么m的值等于（）a0b1c2d3顯示解析3如圖，已知平行四邊形abcd中，向量bd在ba，bc方向上的分量分別是（）aab、bcbab、bccab、bcdab、bc顯示解析4拋物線y=-（x-2）2+1經(jīng)過(guò)平移后與拋物線y=-（x+1）2-2重合，那么平移的方法可以是（）a向左平移3個(gè)單位再向下平移3個(gè)單位b向左平移3個(gè)單位再向上平移3個(gè)單位c

2、向右平移3個(gè)單位再向下平移3個(gè)單位d向右平移3個(gè)單位再向上平移3個(gè)單位顯示解析5在abc，點(diǎn)d、e分別在邊ab、ac上，如果ad=1，bd=2，那么由下列條件能夠判定debc的是（）adebc12bdebc13caeac12daeac13顯示解析6如圖，已知ab、cd分別表示兩幢相距30米的大樓，小明在大樓底部點(diǎn)b處觀察，當(dāng)仰角增大到30度時(shí)，恰好能通過(guò)大樓cd的玻璃幕墻看到大樓ab的頂部點(diǎn)a的像，那么大樓ab的高度為（）a103米b203米c303米d60米顯示解析二、填空題：（本大題共12題，每題4分，滿分48分）7函數(shù)y=（x+5）（2-x）圖象的開(kāi)口方向是顯示解析8在rtabc中，c=

3、90，如果a=45，ab=12，那么bc=顯示解析9已知線段a=3cm，b=4cm，那么線段a、b的比例中項(xiàng)等于cm顯示解析10如果兩個(gè)相似三角形周長(zhǎng)的比是2：3，那么它們面積的比是顯示解析11如圖，在abc于ade中，abbcaeed，要使abc于ade相似，還需要添加一個(gè)條件，這個(gè)條件是顯示解析12已知點(diǎn)g是abc的重心，ab=ac=5，bc=8，那么ag=顯示解析13已知向量a與單位向量e方向相反，且|a|3，那么a=（用向量e的式子表示）顯示解析14如果在平面直角坐標(biāo)系xoy中，點(diǎn)p的坐標(biāo)為（3，4），射線op與x的正半軸所夾的角為，那么的余弦值等于顯示解析15已知一條斜坡的長(zhǎng)度為10

4、米，高為6米，那么坡角的度數(shù)約為（備用數(shù)據(jù)：tan31=cot590.6，sin37=cos530.6）顯示解析16如果二次函數(shù)y=x2+2kx+k-4圖象的對(duì)稱軸為x=3，那么k=顯示解析17如圖，小李推鉛球，如果鉛球運(yùn)行時(shí)離地面的高度y（米）關(guān)于水平距離x（米）的函數(shù)解析式y(tǒng)18x2+12x+32，那么鉛球運(yùn)動(dòng)過(guò)程中最高點(diǎn)離地面的距離為米顯示解析18如果將一個(gè)三角形繞著它一個(gè)角的頂點(diǎn)旋轉(zhuǎn)后使這個(gè)角的一邊與另一邊重疊，再將旋轉(zhuǎn)后的三角形相似縮放，使重疊的兩邊互相重合，我們稱這樣的圖形為三角形轉(zhuǎn)似，這個(gè)角的頂點(diǎn)稱為轉(zhuǎn)似中心，所得的三角形稱為原三角形的轉(zhuǎn)似三角形如圖，在abc中，ab=6，bc=

5、7，ac=5，a1b1c是abc以點(diǎn)c為轉(zhuǎn)似中心的其中一個(gè)轉(zhuǎn)似三角形，那么以點(diǎn)c為轉(zhuǎn)似中心的另一個(gè)轉(zhuǎn)似三角形a2b2c（點(diǎn)a2，b2分別與a、b對(duì)應(yīng)）的邊a2b2的長(zhǎng)為顯示解析三、解答題（本大題共7題，滿分78分）19如圖，已知在直角坐標(biāo)系中，點(diǎn)a在第二象限內(nèi)，點(diǎn)b和點(diǎn)c在x軸上，原點(diǎn)o為邊bc的中點(diǎn)，bc=4，ao=ab，tanaob=3，求圖象經(jīng)過(guò)a、b、c三點(diǎn)的二次函數(shù)解析式顯示解析20如圖，已知在abc中，點(diǎn)d、e分別在邊ab、ac上，debc，addb23，如果aba，bcb（1）求ea（用向量a，b的式子表示）（2）求作向量12ab（不要求寫(xiě)作法，但要指出所作圖表中表示結(jié)論的向量）

6、顯示解析21已知：如圖，在平行四邊形abcd中，e、f分別是邊bc，cd上的點(diǎn)，且efbd，ae、af分別交bd與點(diǎn)g和點(diǎn)h，bd=12，ef=8求：（1）dfab的值；（2）線段gh的長(zhǎng)顯示解析22如圖，已知某船向正東方向航行，在點(diǎn)a處測(cè)得某島c在其北偏東60方向上，前進(jìn)8海里處到達(dá)點(diǎn)b處，測(cè)得島c在其北偏東30方向上已知島c周圍6海里內(nèi)有一暗礁，問(wèn)：如果該船繼續(xù)向東航行，有無(wú)觸礁危險(xiǎn)？請(qǐng)說(shuō)明你的理由顯示解析23已知，如圖，在梯形abcd中，adbc，bcd=90，對(duì)角線ac、bd相交于點(diǎn)e，且acbd（1）求證：cd2=bcad；（2）點(diǎn)f是邊bc上一點(diǎn)，聯(lián)結(jié)af，與bd相交于點(diǎn)g，如果b

7、af=dbf，求證：ag2ad2bgbd顯示解析24已知在平面直角坐標(biāo)系xoy中，二次函數(shù)y=-2x2+bx+c的圖象經(jīng)過(guò)點(diǎn)a（-3，0）和點(diǎn)b（0，6）（1）求此二次函數(shù)的解析式；（2）將這個(gè)二次函數(shù)的圖象向右平移5個(gè)單位后的頂點(diǎn)設(shè)為c，直線bc與x軸相交于點(diǎn)d，求abd的正弦值；（3）在第（2）小題的條件下，聯(lián)結(jié)oc，試探究直線ab與oc的位置關(guān)系，并說(shuō)明理由顯示解析25如圖，已知在rtabc中，acb=90，ab=10，tana=43，點(diǎn)d是斜邊ab上的動(dòng)點(diǎn)，聯(lián)結(jié)cd，作decd，交射線cb于點(diǎn)e，設(shè)ad=x（1）當(dāng)點(diǎn)d是邊ab的中點(diǎn)時(shí)，求線段de的長(zhǎng)；（2）當(dāng)bed是等腰三角形時(shí)，求x

8、的值；（3）如果y=dedb，求y關(guān)于x的函數(shù)解析式，并寫(xiě)出它的定義域 tgz7r4i30ka1dkaghn3xtkknbycudxqa7fhyi2chhi92tgkqcwa3ptgshls50clmtwn60eo8wgqv7xav2ohum32wgeauwydiawgmer4i30ka1dkaghn3xtkknbycudxqa7fhyi2chhi92tgkqcwa3ptgz7r4i30ka1dkagtgk tgz7r4i30ka1dkaghn3xtkknbycudxqa7fhyi2chhi92tgkqcwa3ptgshls50clmtwn60eo8wgqv7xav2ohum32wgeauwy

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