自选模块(二).docVIP

2012年普通高等学校招生全国统一考试（浙江） 自选模块试题(二) 编者：衢州二中 题号：03 科目：数学 “数学史与不等式选讲”模块（10分） 已知为正实数，且. （Ⅰ）证明：； （Ⅱ）求的最小值. 题号：04 科目：数学 “矩阵与变换和坐标系与参数方程”模块（10分） 已知直线的极坐标方程为，圆的参数方程为为参数. （Ⅰ）求圆上的点到直线的距离的最小值； （Ⅱ）若过点的直线与圆交于、两点，且，求直线的斜率. 题号：05号 科目：英语 阅读理解（分两节，共5题；每小题2分，共10分） 阅读下面短文，并根据短文后的要求答题。 I turned off the lights in my classroom and asked the students to close their eyes and , “Imagine you are at a beach on a sunny day.” With your mind’s eye, look around you. You see the waves lapping at the shore. To your left you see children in colorful swimsuits building sand castles, laughing and splashing in the water. To the right you see a boat dock painted blue. Several small boats are tied to the dock. You are living in the present, observing your surroundings and feeling the warmth of the sun on your skin. After spending some time sitting on the beach, you are becoming bored and hot, and you begin to think of the future. What do you want to do? How did you decide? Based on your past experience you know the water will be cool and refreshing, and plying in the waves will be fun, so you decide to go for a swim. Living in the present, you are making a plan for the future based on your knowledge of the past. 1 . It’s getting later now, and the sun is beginning to set over the water. It is time to think about going home. You recall that you arrived the beach on a boat and that you left the boat tied to the dock. You know how you will get home. 2 . As you can see, your decisions about the future are based on your knowledge of the past. Suddenly a spaceship falls from the sky knocking your unconscious. You awake with amnesia, remembering nothing of the past. You don’t know why you are on a beach, where home is now or how to get there. 3 . Relax. You will probably never be struck by a falling spaceship. You will learn what you need to know about beaches and swimming ad getting home from your own personal experience. But, how will you learn of important things that you cannot experience for y