上海市學(xué)鼎教育中考數(shù)學(xué)一模試卷

1、2014年上海市學(xué)鼎教育中考數(shù)學(xué)一模試卷一、單項選擇題：（本大題共6題，每題4分，滿分24分）下列各題的四個選項中，有且只有一個選項是正確的，選擇正確項的代號并填涂在答題紙的相應(yīng)位置上1下列四個函數(shù)中，一定是二次函數(shù)的是（）ay1x2+xby=ax2+bx+ccy=x2-（x+7）2dy=（x+1）（2x-1）顯示解析2下列說法中不正確的是（）a如果m、n為實數(shù)，那么(m+n)ama+nab如果k=0或a0，那么ka0c長度為1的向量叫做單位向量d如果m為實數(shù)，那么m(a+b)ma+mb顯示解析3已知二次函數(shù)y=ax2+bx+c的圖象如圖所示，那么a，b，c的符號為（）aa0，b0，c0ba0

2、，b0，c0ca0，b0，c0da0，b0，c0顯示解析4如圖，能推得debc的條件是（）aad：ab=de：bcbad：db=de：bccad：db=ae：ecdae：ac=ad：db顯示解析5如圖，在rtabc中，cd是斜邊ab上的中線，已知cd=2，ac=3，則sinb的值是（）a23b32c34d43顯示解析6如圖，a、b、c、p、q、甲、乙、丙、丁都是方格紙中的格點，如果rpqabc，那么點r應(yīng)是甲、乙、丙、丁四點中的（）a甲b乙c丙d丁顯示解析二、填空題：（本大題共12題，每題4分，滿分48分）7已知拋物線的表達式是y=-2（x-1）2，那么它的頂點坐標(biāo)是顯示解析8如果二次函數(shù)y=

3、x2+2ax+3的對稱軸是直線x=1，那么a的值是顯示解析9在平面直角坐標(biāo)系中，如果把拋物線y=3x2+5向右平移4個單位，那么所得拋物線的表達式為顯示解析10實際距離為3000米的兩地，在比例尺為1：100000的地圖上的距離為厘米顯示解析11如果兩個相似三角形的面積比為1：2，那么它們的周長比為顯示解析12已知點m是線段ab的黃金分割點（ammb），如果am=512cm，那么ab=cm顯示解析13已知點g是abc的重心，ad是中線，如果ag=6，那么ad=顯示解析14已知一個二次函數(shù)的圖象具有以下特征：（1）經(jīng)過原點；（2）在直線x=1左側(cè)的部分，圖象下降，在直線x=1右側(cè)的部分，圖象上升

4、試寫出一個符合要求的二次函數(shù)解析式顯示解析15已知a、b是拋物線y=x2+2x-1上的兩點（a在b的左側(cè)），且ab與x軸平行，ab=4，則點a的坐標(biāo)為顯示解析16如圖，已知平行四邊形abcd，e是邊ab的中點，聯(lián)結(jié)ac、de交于點o記向量ab=a，ad=b，則向量oe=（用向量a、b表示）顯示解析17如圖，已知abc中，acb=90，d是邊ab的中點，ceab，垂足為點e，若sindce35，則cota=顯示解析18如圖，平面直角坐標(biāo)系中，已知矩形oabc，o為原點，點a、c分別在x軸、y軸上，點b的坐標(biāo)為（1，2），連接ob，將oab沿直線ob翻折，點a落在點d的位置則點d的坐標(biāo)為顯示解析三

5、、解答題：（本大題共7題，滿分78分）19計算：22+1(3.14)03cos45+(12)12顯示解析20如圖，已知兩個不平行的向量a、b先化簡，再求作：2（a+12b）-12（2a-4b）（不要求寫作法，但要指出圖中表示結(jié)論的向量）顯示解析21已知一個二次函數(shù)的圖象經(jīng)過a（0，1）、b（1，3）、c（-1，1）三點，求這個函數(shù)的解析式，并用配方法求出圖象的頂點坐標(biāo)顯示解析22某學(xué)校體育場看臺的側(cè)面如圖陰影部分所示，看臺有四級高度相等的小臺階，每級小臺階都為0.4米現(xiàn)要做一個不銹鋼的扶手ab及兩根與fg垂直且長均為l米的不銹鋼架桿ad和bc（桿子的底端分別為d，c），且dab=66（1）求點

6、d與點c的高度差dh的長度；（2）求所用不銹鋼材料的總長度l（即ad+ab+bc，結(jié)果精確到0.1米）（參考數(shù)據(jù)：sin660.91，cos660.41，tan662.25，cot660.45）顯示解析23如圖，在abc中，bac=90，ad是bc邊上的高，點e在線段dc上，egac，垂足分別為f，g求證：（1）egadcgcd；（2）fddg顯示解析24已知二次函數(shù)y=ax2+bx+c（a0）的圖象經(jīng)過點a（1，0），b（2，0），c（0，-2），直線x=m（m2）與x軸交于點d（1）求二次函數(shù)的解析式；（2）在直線x=m（m2）上有一點e（點e在第四象限），使得e、d、b為頂點的三角形與以

7、a、o、c為頂點的三角形相似，求e點坐標(biāo)（用含m的代數(shù)式表示）；（3）在（2）成立的條件下，拋物線上是否存在一點f，使得四邊形abef為平行四邊形？若存在，請求出m的值及四邊形abef的面積；若不存在，請說明理由顯示解析25如圖，在rtabc中，c=90，ac=3，ab=5點p從點c出發(fā)沿ca以每秒1個單位長的速度向點a勻速運動，到達點a后立刻以原來的速度沿ac返回；點q從點a出發(fā)沿ab以每秒1個單位長的速度向點b勻速運動伴隨著p、q的運動，de保持垂直平分pq，且交pq于點d，交折線qb-bc-cp于點e點p、q同時出發(fā)，當(dāng)點q到達點b時停止運動，點p也隨之停止設(shè)點p、q運動的時間是t秒（t

8、0）（1）當(dāng)t=2時，ap=，點q到ac的距離是；（2）在點p從c向a運動的過程中，求apq的面積s與t的函數(shù)關(guān)系式；（不必寫出t的取值范圍）（3）在點e從b向c運動的過程中，四邊形qbed能否成為直角梯形？若能，求t的值；若不能，請說明理由；（4）當(dāng)de經(jīng)過點c時，請直接寫出t的值3xtkknbycudxqa7fhyi2chhi92tgkqcwa3ptgz7r4i30ka1dkagtgkqcwa3p tgz7r4i30ka1dkaghn3xtkknbycudxqa7fhyi2chhi92tgkqcwa3ptgshls50clmtwn60eo8wgqv7xav2ohum32wgeauwydia

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