20090514
平面ABC
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image165.gif)
又![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image167.gif)
又F为AB中点,
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image171.gif)
,
平面SOF,
平面SAB,
平面SAB
10分
18.解:![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image181.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image183.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image185.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image187.gif)
6分
(I)由
,
得对称轴方程
8分
(II)由已知条件得,![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image195.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image197.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image199.gif)
12分
19.解:设点
,点
共有16个:(0,0),(0,-1),(-1,0),(0,1),(1,0),
(0,2),(2,0),(-1,-1),(-1,1),(1,-1),(-1,2),(2,-1),(1,1),(1,2),
(2,1),(2,2)
3分
(I)
倾斜角为锐角,
,
则点P有(-1,1),(1,-1),(-1,2),(2,-1),
6分
(II)
直线不平行于x轴且不经过第一象限
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image213.gif)
即
10分
点P有(-1,-1),(-1,0),
概率
12分
20.解:(I)
,直线AF2的方程为![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image224.gif)
设![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image226.gif)
则有
,
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image230.gif)
6分
(II)假设存在点Q,使![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image133.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image235.gif)
8分
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image239.gif)
Q在以MN为直径的圆(除去M,N点)上,
圆心O(0,0),半径为![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image242.gif)
又
点Q在圆![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image245.gif)
圆O与圆
相离,
假设不成立
圆
上不存在符合题意的点Q。 12分
21.解:(I)![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image250.gif)
是等差数列
又![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image254.gif)
2分
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image258.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image260.gif)
5分
又![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image264.gif)
为首项,以
为公比的等比数列
6分
(II)![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image269.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image271.gif)
当![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image273.gif)
又
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image277.gif)
是单调递增数列
9分
(III)
时,![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image283.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image285.gif)
即![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image287.gif)
12分
22.解L![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image291.gif)
的值域为[0,1] 2分
设
的值域为A,
,
总存在![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image299.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image301.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image303.gif)
(1)当
时,
上单调递减,
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image309.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image311.gif)
5分
(2)当
时,
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image317.gif)
令![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image319.gif)
(舍去)
①当
时,列表如下:
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image066.gif)
0
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image326.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image328.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image330.gif)
3
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image332.gif)
-
0
+
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image112.gif)
0
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image334.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image336.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image337.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image339.gif)
若
,
则![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image345.gif)
9分
②当
时,
时,
函数
上单调递减
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image309.gif)
![](http://pic.1010jiajiao.com/pic4/docfiles/down/test/down/f97467a1b0ef7e99b9f5f62326e54556.zip/75233.files/image358.gif)
11分
综上,实数
的取值范围是
12分