浙大附中自选模块测试卷 2010.3.19.doc

浙大附中自选模块测试卷
1 题号:03“数学史与不等式选讲”模块
证明:①已知,且,求证:
②已知且,求证:
2题号:03“数学史与不等式选讲”模块
(1).、为非负数,+=1,,求证:;
(2).已知实数满足, 试求的最值
3题号:04“矩阵与变换和坐标系与参数方程”模块
已知直线
(1)求直线l的参数方程;
(2)设直线l与圆相交于M、N两点,求|PM|·|PN|的值。
4题号:04“矩阵与变换和坐标系与参数方程”模块
已知曲线的参数方程为(为参数),曲线的极坐标方程为.
(1)将曲线的参数方程化为普通方程,将曲线的极坐标方程化为直角坐标方程;
(2)曲线,是否相交,若相交请求出公共弦的长,若不相交,请说明理由.
5题号:05 阅读下面的短文,并根据短文后的要求答题。
From good reading we can get pleasure, companionship, experience, and instruction. A good book may absorb our attention pletely that for the time being we forget our surroundings and even our It increases our contentment when we are cheerful, and lessens our troubles when we are sad. Whatever our main purpose in reading may be, our contact with good books should never fail to give us enjoyment and satisfaction.
    ___2____ Whether the characters are taken from real life or purely imaginary, they may e panions and friends. In the pages of books we can walk with the wise and the good of all lands and all times. The people we meet in books may delight us either because they resemble human friends whom we hold dear or because they present unfamiliar types whom we are glad to e as new acquaintances. ___3___ By turning the page we can dismiss them without any fear of hurting their feelings. When human friends desert us, good books are always ready to give us friendship, sympathy, and encouragement.
    ____4____. Few of us can travel far from home or have a wide range of experiences, but all of us can lead varied lives through the pages of books. Whether we wish to escape from the seemingly dull realities of everyday life or whether we long to visit some far-off place, a book will help us when nothing else can. To travel by book we need no bank account to pay our way; no train or airplane to transport us; no passport to enter the land of our hearts’ desire. Through books we may get the excitement of dangerous adventure without danger. We can climb noble mountains, brave the freeze of an