浙江省宁波市中考数学一模试卷

1、2014年浙江省宁波市中考数学一模试卷一选择题（每题4分，共48分）1抛物线y=x2-2x+1与坐标轴交点为（）a二个交点b一个交点c无交点d三个交点显示解析2计算（-2a）3的结果是（）a6a3b-6a3c8a3d-8a3显示解析3我市某一周每天的最高气温统计如下：27，28，29，29，30，29，28（单位：），则这组数据的极差与众数分别为（）a2，28b3，29c2，27d3，28显示解析4据宁波市统计局年报，去年我市人均生产总值为104485元，104485元用科学记数法表示为（）a1.04485106元b0.104485106元c1.04485105元d10.4485104元显示解

2、析5如图，在正方形abcd中，对角线ac，bd交于点o，折叠正方形abcd，使ad落在bd上，点a恰好与bd上的点f重合，展平后，折痕de分别交ab，ac于点e，g，连接gf，下列结论：ae=ag；tanage=2；sdog=s四边形efog；四边形abfg为等腰梯形；be=2og，则其中正确的结论个数为（）a2b3c4d5显示解析6如图，三个半径为3的圆两两外切，且abc的每一边都与其中的两个圆相切，那么abc的周长是（）a12+63b18+63c18+123d12+123显示解析7把四张形状大小完全相同的小长方形卡片（如图）不重叠地放在一个底面为长方形（长为mcm，宽为ncm）的盒子底部（

3、如图），盒子底面未被卡片覆盖的部分用阴影表示则图中两块阴影部分的周长和是（）a4mcmb4ncmc2（m+n）cmd4（m-n）cm显示解析8如图是一把30的三角尺，外边ac=8，内边与外边的距离都是2，那么ef的长度是（）a4b43c2.5d6-23显示解析9如图，二次函数y=ax2+bx+c的图象开口向上，图象经过点（-1，2）和（1，0），且与y轴相交于负半轴给出四个结论：abc0；a+c=1；2a+b0；b2-4ac0其中结论正确的个数为（）a4b3c2d1显示解析10如图，ab是半圆直径，半径ocab于点o，ad平分cab交弧bc于点d，连结cd、od，给出以下四个结论：acod；c

4、e=oe；odeado；cd2=ceco其中正确结论的序号是（）abcd显示解析11以正方形abcd的bc边为直径作半圆o，过点d作直线切半圆于点f，交ab边于点e则三角形ade和直角梯形ebcd周长之比为（）a3：4b4：5c5：6d6：7显示解析12将bc沿弦bc折叠，交直径ab于点d，若ad=4，db=5，则bc的长是（）a37b8c65d215显示解析二、填空题（每题4分，共24分）13如图，将正方形abcd沿be对折，使点a落在对角线bd上的a处，连接ac，则bac=度显示解析14函数y=2x+3的图象不经过第象限显示解析15鄞州区某学校篮球集训队11名队员进行定点投篮训练，将11名

5、队员在1分钟内投进篮框的球数由小到大排序后为6，7，8，9，9，9，9，10，10，10，12，这组数据的中位数是显示解析16如图，菱形abcd中，ab=2，c=60，菱形abcd在直线l上向右作无滑动的翻滚，每绕着一个顶点旋转60叫一次操作，则经过36次这样的操作菱形中心o所经过的路径总长为（结果保留）显示解析17如图，正六边形abcdef的边长为4，两顶点a、b分别在x轴和y轴上运动，则顶点d到原点o的距离的最大值和最小值的乘积为显示解析18长方形abcd中，ab=1，ad=3，以点b为圆心，ba长为半径作圆交bc于点e在弧ae上找一点p，使过点p的b的切线平分长方形的面积设此切线交ad于

6、点s，交bc于点t，则st的长为显示解析三解答题（共78分）19计算：(13)0+|2|2cos45+31显示解析20（1）先化简，再求值：a2+3aa2+4a+4a+3a+22a+2，其中a=22（2）解不等式组：3xx2x+132x显示解析21重庆一中综合实践活动艺体课程组为了解学生最喜欢的球类运动，对足球、乒乓球、篮球、排球四个项目进行了调查，并将调查的结果绘制成如下的两幅统计图（说明：每位同学只选一种自己最喜欢的球类），请你根据图中提供的信息解答下列问题：（1）求这次接受调查的学生人数，并补全条形统计图；（2）求扇形统计图中喜欢排球的圆心角度数；（3）若调查到爱好“乒乓球”的5名学生中

7、有3名男生，2名女生，现从这5名学生中任意抽取2名学生，请用列表法或画树状图的方法，求出刚好抽到一男一女的概率显示解析22已知：如图，d是abc的边ab上一点，cnab，dn交ac于点m，ma=mc求证：cd=an；若amd=2mcd，求证：四边形adcn是矩形显示解析23如图，已知a（-4，n），b（2，-4）是一次函数y=kx+b的图象和反比例函数ymx的图象的两个交点；（1）求反比例函数和一次函数的解析式；（2）求直线ab与x轴的交点c的坐标及aob的面积；（3）求不等式kx+bmx0的解集（请直接写出答案）显示解析24某大学毕业生响应国家“自主创业”的号召，投资开办了一个装饰品商店，某

8、装饰品的进价为每件30元，现在的售价为每件40元，每星期可卖出150件市场调查发现：如果每件的售价每涨1元（售价每件不能高于45元），那么每星期少卖10件设每件涨价x元（x为非负整数），每星期的利润为w元（1）求w与x的函数关系式及自变量x的取值范围；（2）如何定价才能使每星期的利润最大且每星期的销量较大？每星期的最大利润是多少？显示解析25定义：p、q分别是两条线段a和b上任意一点，线段pq的长度的最小值叫做线段a与线段b的距离已知o（0，0），a（4，0），b（m，n），c（m+4，n）是平面直角坐标系中四点（1）根据上述定义，当m=2，n=2时，如图1，线段bc与线段oa的距离是；当m=

9、5，n=2时，如图2，线段bc与线段oa的距离为；（2）如图3，若点b落在圆心为a，半径为2的圆上，线段bc与线段oa的距离记为d，求d关于m的函数解析式（3）当m的值变化时，动线段bc与线段oa的距离始终为2，线段bc的中点为m，求出点m随线段bc运动所围成的封闭图形的周长；点d的坐标为（0，2），m0，n0，作mhx轴，垂足为h，是否存在m的值使以a、m、h为顶点的三角形与aod相似？若存在，求出m的值；若不存在，请说明理由显示解析26如图1，已知抛物线y=ax2+bx（a0）经过a（3，0）、b（4，4）两点（1）求抛物线的解析式；（2）将直线ob向下平移m个单位长度后，得到的直线与抛物

10、线只有一个公共点d，求m的值及点d的坐标；（3）如图2，若点n在抛物线上，且nbo=abo，则在（2）的条件下，求出所有满足podnob的点p坐标（点p、o、d分别与点n、o、b对应）qcwa3ptgz7r4i30ka1dkaghn3xtkknbycudxqa7fhyi2chhi92tgkqcwa3ptgshls50clmtwn60eo8wgqv7xav2ohum32wgeauwydiawgmer4i30ka1dkaghn3xtkknbycudxqa7fhyi2chhi92tgkqcwa3ptgz7r4i30ka1dkagtgkqcwa3p tgz7r4i30ka1dkaghn3xtkknby

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