江苏省苏州市 高三调研考试—(巩固部分).doc

江苏省苏州市2011届高三第一次调研考试巩固部分1-4已知函数的图像如图所示，则 。【解析】由图象知最小正周期（），故，又时，即，可得，所以，2。【答案】 .2-5连掷两次骰子分别得到点数，向量，若中与同向，与反向，则是钝角的概率是 .【解析】则是钝角，即向量夹角为锐角，,所以包含个基本事件，又共有 个基本事件，所以是钝角的概率是【答案】。3-6等边三角形中，在线段上，若，则实数的值是 【解析】设三角形的边长为1，则AP=。又，。【答案】.4-8已知，且为锐角，【解析】，.这里如果通过，就会出现或，需进一步确定结果。【答案】。5-14曲线在点处的切线与坐标轴所围三角形的面积为 .【解析】切线的斜率 切线的方程为 令，则；，.即切线与两坐标轴的交点分别是 曲线在点处的切线与坐标轴所围三角形的面积为. 【答案】.C1B1A1BADC6-16如图，在直三棱柱中，为中点.（）求证：；（）求证：平面平面；（）求三棱锥的体积.【解析】（）又由直三棱柱性质知平面 又平面.（）由，为中点，可知，即.又 平面 又平面,故平面平面 .（）解： .7-19设为数列的前项和，对任意的N，都有为常数，且（1）求证：数列是等比数列；（2）设数列的公比，数列满足 ，N，求数列的通项公式；（3）在满足（2）的条件下，求数列的前项和【解析】（1）当时，解得 当时，即为常数，且， 数列是首项为1，公比为的等比数列 （2）由（1）得，即是首项为，公差为1的等差数列，即（）（3）解：由（2）知，则所以，即， 则， 得， 故8-20已知函数，其中。（1）当时，求的值并判断函数的奇偶性； （2）当时，若函数的图像在处的切线经过坐标原点，求的值；（3）当时，求函数在上的最小值。【解析】（1） 时 ，所以，所以时非奇非偶函数.（2）时，所以, 所以在处的切线方程为,因为过原点，所以.（3）（）当时，上，所以在内单调递减，递增，所以.（） 当时，上，所以单调递增，.（）当时，当时，所以单调递增，,当时，因，所以在上单调递减，在上递增，所以若，则，当时而 时 ，所以，时，同样，因，所以,综上：时， 时, 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