江蘇省鹽城市東臺(tái)市第一教研片中考數(shù)學(xué)一模試卷

1、2014年江蘇省鹽城市東臺(tái)市第一教研片中考數(shù)學(xué)一模試卷一、選擇題（本題共8小題每小題3分，共24分在每小題所給出的四個(gè)選項(xiàng)中，只有一項(xiàng)符合題目要求，請(qǐng)將正確選項(xiàng)的字母代號(hào)填寫在題后的括號(hào)里）112的相反數(shù)為（）a2b-2c12d-12顯示解析2如果+30m表示向東走30m，那么向西走40m表示為（）a+40mb-40mc+30md-30m顯示解析3式子2x在實(shí)數(shù)范圍內(nèi)有意義，則x的取值范圍是（）ax2bx2cx2dx2顯示解析4數(shù)據(jù)5，7，5，8，6，13，5的中位數(shù)是（）a5b6c7d8顯示解析5下列計(jì)算中，正確的是（）a（a3b）2=a6b2baa4=a4ca6a2=a3d3a+2b=5a

2、b顯示解析6下列四個(gè)立體圖形中，主視圖為圓的是（）abcd顯示解析7如圖：已知abc中，abc=90，ab=bc，三角形的頂點(diǎn)分別在相互平行的三條直線l1、l2、l3上，且1=15，則2等于（）a15b35c30d25顯示解析8如圖：在abc中，acb=90，abc=30，ac=1，現(xiàn)將abc繞點(diǎn)c逆時(shí)針旋轉(zhuǎn)至efc，使點(diǎn)e恰巧落在ab上，連接bf，則bf的長度為（）a3b2c1d2顯示解析二、填空題（本題共有10小題，每小題3分，共30分不需要寫出解答過程，請(qǐng)將答案直接寫在題中的橫線上）94的平方根是顯示解析10分解因式：2x2-2=顯示解析11霧霾天氣是由于空氣中含有顆粒物過多造成的現(xiàn)測(cè)得

3、有一種顆粒物的直徑為0.0000025m，這個(gè)數(shù)據(jù)用科學(xué)記數(shù)法表示為m顯示解析12要使分式x+2x1的值為0，則x的值為顯示解析13寫出一個(gè)一次函數(shù)，使該函數(shù)的圖象不經(jīng)過第三象限：顯示解析14已知關(guān)于x的一元二次方程（m-1）x2+x+1=0有實(shí)數(shù)根，則m的取值范圍是顯示解析15如圖，abc內(nèi)接于o，acb=35，則oab=顯示解析16已知扇形的圓心角為120，弧長為10cm，則扇形的半徑為cm顯示解析17已知二次函數(shù)y=ax2+bx+c，經(jīng)過點(diǎn)（-1，m）和（3，m），則二次函數(shù)的對(duì)稱軸方程為顯示解析18如圖，已知菱形abcd，e、f分別為ab、bc的中點(diǎn)，epdc，垂足為p，連接pf，若a

4、=110，則fpc=顯示解析三、解答題（本題共10題，共96分，解答時(shí)應(yīng)寫出必要的文字說明、推理過程或演算步驟）19計(jì)算：（3-）0-（12）-1-（-1）2013+|-2|；解方程：3x12x+1顯示解析20化簡求值：x21x+2（1x+2-1），其中x取你喜歡的值顯示解析21已知：如圖，d是abc的邊ab上一點(diǎn)，cnab，dn交ac于點(diǎn)m，ma=mc求證：cd=an；若amd=2mcd，求證：四邊形adcn是矩形顯示解析22四張撲克牌的點(diǎn)數(shù)分別是2，3，4，8，將它們洗勻后背面朝上放在桌上（1）從中隨機(jī)抽取一張牌，求這張牌的點(diǎn)數(shù)偶數(shù)的概率；（2）從中隨機(jī)抽取一張牌，接著再抽取一張，求這兩張

5、牌的點(diǎn)數(shù)都是偶數(shù)的概率顯示解析23為迎接建黨90周年，某校組織了以“黨在我心中”為主題的電子小報(bào)制作比賽，評(píng)分結(jié)果只有60，70，80，90，100五種現(xiàn)從中隨機(jī)抽取部分作品，對(duì)其份數(shù)及成績進(jìn)行整理，制成如下兩幅不完整的統(tǒng)計(jì)圖根據(jù)以上信息，解答下列問題：（1）求本次抽取了多少份作品，并補(bǔ)全兩幅統(tǒng)計(jì)圖；（2）已知該校收到參賽作品共900份，請(qǐng)估計(jì)該校學(xué)生比賽成績達(dá)到90分以上（含90分）的作品有多少份？顯示解析24如圖，在rtabc中，c=90，abc的平分線交ac于點(diǎn)d，點(diǎn)o是ab上一點(diǎn)，o過b、d兩點(diǎn)，且分別交ab、bc于點(diǎn)e、f（1）求證：ac是o的切線；（2）已知ab=10，bc=6，求

6、o的半徑r顯示解析25如圖，為了測(cè)量某風(fēng)景區(qū)內(nèi)一座塔ab的高度，小明分別在塔的對(duì)面一樓房cd的樓底c，樓頂d處，測(cè)得塔頂a的仰角為45和30，已知樓高cd為10m，求塔的高度（結(jié)果精確到0.1m）（參考數(shù)據(jù)：21.41，31.73）顯示解析26某商場(chǎng)銷售甲、乙兩種品牌的智能手機(jī)，這兩種手機(jī)的進(jìn)價(jià)和售價(jià)如下表所示：甲乙進(jìn)價(jià)（元/部）40002500售價(jià)（元/部）43003000該商場(chǎng)計(jì)劃購進(jìn)兩種手機(jī)若干部，共需15.5萬元，預(yù)計(jì)全部銷售后可獲毛利潤共2.1萬元（毛利潤=（售價(jià)-進(jìn)價(jià)）銷售量）（1）該商場(chǎng)計(jì)劃購進(jìn)甲、乙兩種手機(jī)各多少部？（2）通過市場(chǎng)調(diào)研，該商場(chǎng)決定在原計(jì)劃的基礎(chǔ)上，減少甲種手機(jī)的

7、購進(jìn)數(shù)量，增加乙種手機(jī)的購進(jìn)數(shù)量已知乙種手機(jī)增加的數(shù)量是甲種手機(jī)減少的數(shù)量的2倍，而且用于購進(jìn)這兩種手機(jī)的總資金不超過16萬元，該商場(chǎng)怎樣進(jìn)貨，使全部銷售后獲得的毛利潤最大？并求出最大毛利潤vip顯示解析27如圖所示，已知a、b為直線l上兩點(diǎn)，點(diǎn)c為直線l上方一動(dòng)點(diǎn)，連接ac、bc，分別以ac、bc為邊向abc外作正方形cadf和正方形cbeg，過點(diǎn)d作dd1l于點(diǎn)d1，過點(diǎn)e作ee1l于點(diǎn)e1（1）如圖，當(dāng)點(diǎn)e恰好在直線l上時(shí)（此時(shí)e1與e重合），試說明dd1=ab；（2）在圖中，當(dāng)d、e兩點(diǎn)都在直線l的上方時(shí)，試探求三條線段dd1、ee1、ab之間的數(shù)量關(guān)系，并說明理由；（3）如圖，當(dāng)點(diǎn)e

8、在直線l的下方時(shí)，請(qǐng)直接寫出三條線段dd1、ee1、ab之間的數(shù)量關(guān)系（不需要證明）顯示解析28如圖，拋物線y=ax2-2ax+c（a0）交x軸于a、b兩點(diǎn)，a點(diǎn)坐標(biāo)為（3，0），與y軸交于點(diǎn)c（0，4），以oc、oa為邊作矩形oadc交拋物線于點(diǎn)g（1）求拋物線的解析式；（2）拋物線的對(duì)稱軸l在邊oa（不包括o、a兩點(diǎn)）上平行移動(dòng)，分別交x軸于點(diǎn)e，交cd于點(diǎn)f，交ac于點(diǎn)m，交拋物線于點(diǎn)p，若點(diǎn)m的橫坐標(biāo)為m，請(qǐng)用含m的代數(shù)式表示pm的長；（3）在（2）的條件下，連結(jié)pc，則在cd上方的拋物線部分是否存在這樣的點(diǎn)p，使得以p、c、f為頂點(diǎn)的三角形和aem相似？若存在，求出此時(shí)m的值，并直接

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