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嗷呜喵呜
上传于：2024-04-22
2013学年普陀区九年级期终调研
数学试卷
（测试时间：100分钟，满分：150分）
考生注意：
1．本试卷含三个大题，共25题．答题时，考生务必按答题要求在答题纸规定的位置上作答，在草稿纸、本试卷上答题一律无效．
2．除第一、二大题外，其余各题如无特别说明，都必须在答题纸的相应位置上写出证明或计算的主要步骤．
3．本次测试可使用科学计算器．
一、选择题：（本大题共6题，每题4分，满分24分）
1．用放大镜将图形放大，应该属于（ ）
INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.001.png"．平移变换； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.002.png"．相似变换； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.003.png"．对称变换； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.004.png"．旋转变换．
2．在比例尺是1:38000的黄浦江交通游览图上，某隧道长约7INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.005.png"，它的实际长度约为（ ）
INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.001.png"．0.266INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.006.png"； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.002.png"．2.66INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.006.png"； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.003.png"．26.6INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.006.png"； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.004.png"．266INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.006.png".
3．在△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.007.png"中，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.008.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.009.png"，那么△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.007.png"是（ ）
INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.001.png"．钝角三角形； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.002.png"．直角三角形； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.003.png"．锐角三角形； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.004.png"．等腰三角形.
4．二次函数INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.010.png"的图像一定不经过（ ）
INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.001.png"．第一象限； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.002.png"．第二象限； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.003.png"．第三象限； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.004.png"．第四象限.
5．下列命题中，正确的是（ ）
INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.001.png"．如果一条直线截三角形两边的延长线所得的对应线段成比例，那么这条直线一定平行于三角形的第三边；
INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.002.png"．不同向量的单位向量的长度都相等，方向也都相同；
INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.003.png"．相似三角形的中线的比等于相似比；
INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.004.png"．一般来说，一条线段的黄金分割点有两个.
6．在INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.011.png"△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.012.png"中，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.013.png"90°，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.014.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.015.png"，那么下面各式正确的是（ ）
INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.001.png"．INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.016.png"； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.002.png"．INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.017.png"； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.003.png"．INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.018.png"； INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.004.png"．INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.019.png".
二、填空题：（本大题共12题，每题4分，满分48分）
7．如图，直线INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.021.png"∥INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.022.png"∥INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.023.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.024.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.025.png"，那么INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.026.png"的值是 ．
8．在一个陡坡上前进5米，水平高度升高了3米，则坡度INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.027.png" ．
9．抛物线INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.028.png"关于INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.029.png"轴对称的抛物线的解析式是 ．
10．请写出一个以直线INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.030.png"为对称轴，且在对称轴左侧部分是上升的抛物线的表达式可以是 ．
11．如果INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.031.png"、INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.032.png"是△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.012.png"的边INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.033.png"和INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.034.png"的中点，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.035.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.036.png"，那么INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.037.png" ．
12．如图，在边长为1的正方形网格中有点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.038.png"、INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.039.png"、INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.002.png"、INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.003.png"，则图中所形成的三角形中，相似的三角形是________．
13．若INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.041.png"为一锐角，且INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.042.png"60°，则INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.043.png" ．
14．已知INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.041.png"为一锐角，化简：INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.044.png" ．
15．如果直角三角形的斜边长为12，那么它的重心与外心之间的距离为 ．
16．已知二次函数的顶点坐标为INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.045.png"，并且经过平移后能与抛物线INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.046.png"重合，那么这个二次函数的解析式是 ．
17．若一个三角形的边长均满足方程INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.047.png"，则此三角形的周长为 ．
18．已知梯形INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.048.png"中，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.049.png"∥INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.050.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.051.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.052.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.053.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.054.png"是锐角，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.054.png"的正弦值为INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.055.png"，那么INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.056.png"的长为 ．
三、解答题：（本大题共7题，满分78分）
19．（本题满分10分）
计算：INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.057.png"．
20．（本题满分10分）
已知：如图，△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.012.png"中，点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.059.png"是INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.060.png"边上的一点，且INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.061.png":INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.062.png"2:1．
（1）设INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.063.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.064.png"，先化简，再求作：INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.065.png"；
（2）用INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.066.png"（INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.067.png"、INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.068.png"为实数）的形式表示INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.069.png"．
21．（本题满分10分）
如图，在△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.012.png"中，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.070.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.071.png"，点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.072.png"是△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.012.png"内一点，且INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.073.png"．
（1）求证：△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.075.png"∽△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.076.png"；
（2）试求INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.077.png"的值．
22．（本题满分10分）
如图，浦西对岸的高楼INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.079.png"，在INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.080.png"处测得楼顶INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.081.png"的仰角为30°，向高楼前进100米到达INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.082.png"处，在INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.082.png"处测得INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.083.png"的仰角为45°，求高楼INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.084.png"的高．
23．（本题满分12分，其中第（1）小题3分，第（2）小题5分，第（3）小题4分）
如图，已知INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.086.png"是△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.087.png"中INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.088.png"的角平分线，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.089.png"是INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.090.png"上的一点，且INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.091.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.092.png"，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.093.png"．
（1）求证：△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.094.png"∽△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.095.png"；
（2）求证：△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.096.png"∽△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.097.png"；
（3）求INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.098.png"的长．
24．（本题满分12分，其中第（1）小题3分，第（2）小题9分）
如图，抛物线INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.099.png"经过点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.100.png"，且与INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.101.png"轴交于点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.102.png"、点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.103.png"，若INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.104.png"．
（1）求此抛物线的解析式；
（2）若抛物线的顶点为INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.106.png"，点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.107.png"是线段INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.108.png"上一动点（不与点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.109.png"重合），INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.110.png"，射线INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.111.png"与线段INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.112.png"交于点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.113.png"，当△INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.114.png"为等腰三角形时，求点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.107.png"的坐标．
25．（本题满分14分，其中第（1）小题5分，第（2）小题7分，第（3）小题2分）
如图，在正方形INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.115.png"中，INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.116.png"，点INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.117.png"是边INCLUDEPICTURE "http://image.klxuexi.com/paper/20140104/122719609/122719609.118.png"上的任意一点，INCLUDEPICT