区原创试题命题竞赛初中数学学科中考试题
一、选择题（每题3分，共36分）
1、若![](https://wkrtcs.bdimg.com/rtcs/image?w=60&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"60","h":"39","dataType":"gif","c":"word/media/image1.png"})
，则=
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"13","h":"39","dataType":"gif","c":"word/media/image3.png"})
B. C. D.
2、世界最长的跨海大桥—舟山跨海大桥总造价为131.1亿元，131.1亿用科学计数法可表示为 元。
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=83&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"83","h":"21","dataType":"gif","c":"word/media/image7.png"})
B. C. D.
3、下列运算正确的是
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=91&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"91","h":"21","dataType":"gif","c":"word/media/image11.png"})
B. C. D..
4、圆锥的底面半径为3cm，母线为9![](https://wkrtcs.bdimg.com/rtcs/image?w=24&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"24","h":"15","dataType":"gif","c":"word/media/image15.png"})
，则圆锥的表面积为
A.36![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"13","h":"15","dataType":"gif","c":"word/media/image16.png"})
B.9 C.12 D.27
5、下列美丽的图案，既是轴对称图形又是中心对称图形的个数是
![](https://wkrtcs.bdimg.com/rtcs/image?w=402.66666666667&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"402.66666666667","h":"72","dataType":"gif","c":"word/media/image18.png"})
A.1个 B.2个 C.3个 D.4个
6、已知⊙O1和⊙O2的半径分别为1和4，如果两圆的位置关系为相交，那么圆心距O1O2的取值范围在数轴上表示正确的是
![](https://wkrtcs.bdimg.com/rtcs/image?w=492&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"492","h":"62.666666666667","dataType":"gif","c":"word/media/image19.png"})
7、在坡比为1：3的斜坡上有两棵树AC、BD，已知两树间的坡面距离AB=![](https://wkrtcs.bdimg.com/rtcs/image?w=40&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"40","h":"24","dataType":"gif","c":"word/media/image20.png"})
m，那么两树间的水平距离为
m
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=32&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"32","h":"24","dataType":"gif","c":"word/media/image21.png"})
B.12 C.4 D.
8、把一张长为60厘米，宽为40厘米的矩行纸张对折8次，所得的小矩形面积的大小约同
A.一元硬币 B.书包 C.单人课桌 D.火柴盒
9、已知关于![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"13","h":"15","dataType":"gif","c":"word/media/image23.png"})
的不等式组的整数解共有3个，则的取值范围是
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=45&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"45","h":"19","dataType":"gif","c":"word/media/image26.png"})
B. C. D.
10、如图，点E、F是以线段BC为公共弦的两条圆弧的中点，BC=6.点A、D分别为线段EF、BC上的动点.连结AB、AD，设BD=x，AB2－AD2=y，下列图像中，能表示y与x的函数关系的图象是
![](https://wkrtcs.bdimg.com/rtcs/image?w=498.66666666667&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"498.66666666667","h":"144","dataType":"gif","c":"word/media/image30.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=182.66666666667&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"182.66666666667","h":"122.66666666667","dataType":"gif","c":"word/media/image31.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=117&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"117","h":"104","dataType":"png","c":"word/media/image32.png","imgOriW":153,"imgOriH":136})
11、如图所示，在梯形![](https://wkrtcs.bdimg.com/rtcs/image?w=48&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"48","h":"19","dataType":"gif","c":"word/media/image33.png"})
中，，点是线段上一定点，且=8．动点从点出发沿的路线运动，运动到点停止．在点的运动过程中，使为等腰三角形的点有 个。
A.1 B.2 C. 3 D.4
12、![](https://wkrtcs.bdimg.com/rtcs/image?w=61&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"61","h":"19","dataType":"gif","c":"word/media/image43.png"})
的三个顶点A,B,C均在抛物线上，并且斜边平行于x轴。若斜边上的高为h,则
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=57&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"57","h":"19","dataType":"gif","c":"word/media/image45.png"})
B. C. D.
二、填空题（每题3分，共18分）
13、函数![](https://wkrtcs.bdimg.com/rtcs/image?w=77&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"77","h":"45","dataType":"gif","c":"word/media/image49.png"})
中自变量的取值范围是 。
14、方程![](https://wkrtcs.bdimg.com/rtcs/image?w=52&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"52","h":"21","dataType":"gif","c":"word/media/image50.png"})
的解为
![](https://wkrtcs.bdimg.com/rtcs/image?w=309&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"309","h":"62","dataType":"png","c":"word/media/image51.png","imgOriW":309,"imgOriH":62})
15、如图，在数轴上有两点A,B,在线段AB上任取一点P,则点P表示到2的点的距离不大于1的概率是 。
16、2011年3月11日，日本发生了里氏9.0级大地震。日本政府12号晚将核电站周边的避难半径扩大到20公里。在1:10000的地图上，避难半径应为 cm。
17、已知线段AB=2cm,P是AB的黄金分割点，则AP= cm。
18、已知：定点（5,4），动点P在函数![](https://wkrtcs.bdimg.com/rtcs/image?w=39&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"39","h":"17","dataType":"gif","c":"word/media/image52.png"})
的图像上运动，动点Q在轴上运动，则的周长的最小值为 。
三、解答题（第19-20题各6分，第21-24各8分，第25题10分，第26题12分，共66分）
![](https://wkrtcs.bdimg.com/rtcs/image?w=108&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"108","h":"124.8","dataType":"png","c":"word/media/image54.png","imgOriW":111,"imgOriH":137})
19、解方程：
20、已知反比例函数y＝![](https://wkrtcs.bdimg.com/rtcs/image?w=37&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"37","h":"37","dataType":"gif","c":"word/media/image56.png"})
(m为常数)的图象经过点A（－1，6）．
（1）求m的值；
（2）如图，过点A作直线AC与函数y＝的图象交于点B，与x轴交于点C，且AB＝2BC，求点C的坐标。
![](https://wkrtcs.bdimg.com/rtcs/image?w=224.2&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"224.2","h":"145.6","dataType":"png","c":"word/media/image57.png","imgOriW":385,"imgOriH":263})
21、为了了解初中生减负的实施情况，在我区几所学校中随机抽取了50名初三学生进行问卷调查，发现被调查的学生中，每天完成课外作业时间最长为120分钟，没有低于40分钟的，并将抽查结果绘制成一个不完整的频数分布直方图，如图所示：
（1）补全频数分布直方图，并指出众数、中位数分别在哪一组
（2）若我区共有1万名初三学生，请估计我区大约有多少名初三学
生每天完成课外作业时间在80分钟以上？
（3）教育行政部门规定初三学生的课外作业时间不得超过90分钟。
请估计我区初三学生课外作业时间的平均值有没有超过教育行政部
门规定的时间
![](https://wkrtcs.bdimg.com/rtcs/image?w=180&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"180","h":"145.6","dataType":"png","c":"word/media/image58.png","imgOriW":347,"imgOriH":219})
22、周末有六个学生分成甲、乙两组（每组三个人），分乘两辆出租车同时从学校出发去距学校60km的滨海博物馆参观，10分钟后到达距离学校12km处甲组的汽车出现故障，只好步行一段路。而正常行驶的另一辆车先把第乙组学生送到博物馆，再原路加速返回接甲组学生，同时甲组学生步行12km后停下休息10分钟恰好与返回接他们的汽车相遇，当甲组学生到达博物馆时，恰好已到原计划时间．设汽车载人和空载时的速度不变，学生步行速度不变，汽车离开学校的路程s（千米）与汽车行驶时间t（分钟）之间的函数关系如图，假设学生上下车时间忽略不计．
（1）正常行驶的一辆汽车第一次去博物馆时，求汽车离开学校的
路程s（千米）与汽车行驶时间t（分钟）之间的函数关系
(2) 求汽车在返回接甲组学生途中的速度；
(3)求 原计划从学校出发到达博物馆的时间。
![](https://wkrtcs.bdimg.com/rtcs/image?w=144&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"144","h":"136","dataType":"gif","c":"word/media/image59.png"})
23、如图所示，△ABC内接于⊙O，AB是⊙O的直径，点D
在⊙O 上，过点C的切线交AD的延长线于点E，且AE⊥CE，连接CD．
（1）求证：DC=BC；
（2）若AB=5，AC=4，求tan∠DCE的值．
24、如图![](https://wkrtcs.bdimg.com/rtcs/image?w=135&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"135","h":"21","dataType":"gif","c":"word/media/image60.png"})
,垂足分别为B,C,
（1）当AB=4，DC=1，BC=4时，在线段BC上是否存在点P,使![](https://wkrtcs.bdimg.com/rtcs/image?w=67&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"67","h":"17","dataType":"gif","c":"word/media/image61.png"})
？
![](https://wkrtcs.bdimg.com/rtcs/image?w=156&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"156","h":"93.6","dataType":"png","c":"word/media/image62.png","imgOriW":286,"imgOriH":173})
若存在，求线段BP的长；若不存在，请说明理由。
（2）设![](https://wkrtcs.bdimg.com/rtcs/image?w=155&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"155","h":"21","dataType":"gif","c":"word/media/image63.png"})
，那么当之间满足
什么关系时, 线段BC上存在点P,使
25、如图，在边长为![](https://wkrtcs.bdimg.com/rtcs/image?w=12&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"12","h":"19","dataType":"png","c":"word/media/image65_1.png","imgOriW":288,"imgOriH":448})
厘米的正方形ABCD内，贴上一个边长为厘米的正方形AEFG，正方形ABCD未被盖住的部分为多边形EBCDGF．动点P从点B出发，沿B→C→D方向以厘米／秒速度运动，到点D停止，连结PA，PE．设点P运动x秒后，△APE与多边形EBCDGF重叠部分的面积为y厘米2。
(1) 当x = 4时，求y的值；
(2) 当x = 11时，求y的值；
(3) 求y与x之间的函数关系式；
(4) 在给出的直角坐标系中画出![](https://wkrtcs.bdimg.com/rtcs/image?w=15&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"15","h":"17","dataType":"png","c":"word/media/image68_1.png","imgOriW":352,"imgOriH":416})
与之间的函数图象．
![](https://wkrtcs.bdimg.com/rtcs/image?w=541&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"541","h":"158","dataType":"png","c":"word/media/image70.png","imgOriW":541,"imgOriH":158})
26．如图，平面直角坐标系中有一直角梯形OMNH，点H的坐标为（－8，0），点N的坐标为（－6，－4）．
（1）画出直角梯形OMNH绕点O旋转180°的图形OABC，并写出顶点A，B，C的坐标（点M的对应点为A，
点N的对应点为B， 点H的对应点为C）；
（2）求出过A，B，C三点的抛物线的表达式；
（3）截取CE=OF=AG=t，且E，F，G分别在线段CO，OA，AB上，求四边形BEFG的面积S与t之间的函数关系式，并写出自变量t的取值范围；
![](https://wkrtcs.bdimg.com/rtcs/image?w=223.2&md5sum=1977463121fbafb6fceb414ade5a6125&sign=b72b86e911&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=104&ipr={"t":"img","w":"223.2","h":"197.6","dataType":"png","c":"word/media/image71_1.png","imgOriW":323,"imgOriH":260})
（4）在（3）的情况下，四边形BEFG是否存在邻边相等的情况，若存在，请直接写出此时t的值，并指出相等的邻边；若不存在，说明理由．
内部资料 仅供参考 |
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