甘肃省镇原县平泉中学2013-2014学年高二下学期期中考试数学（理）试题
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| 名称 | 甘肃省镇原县平泉中学2013-2014学年高二下学期期中考试数学（理）试题 |  | |
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| 科目 | 数学 | ||
| 更新时间 | 2014-05-07 11:36:29 | ||
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本资料来自于资源最齐全的２１世纪教育网www.21cnjy.com
甘肃省镇原县平泉中学2013-2014学年高二下学期期中考试数学（理）试题
第I卷（选择题）
一、选择题（本大题共12小题，每小题5分，共60分）
1．在复平面内与复数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 所对应的点关于虚轴对称的点为 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，则 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 对应的复数为（ ）
A． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｂ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 C． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｄ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4
2．已知 ( http: / / www.21cnjy.com )为自然对数的底数，设函数 ( http: / / www.21cnjy.com )，则( )
A． ( http: / / www.21cnjy.com )是 ( http: / / www.21cnjy.com )的极小值点 B． ( http: / / www.21cnjy.com )是 ( http: / / www.21cnjy.com )的极小值点
C． ( http: / / www.21cnjy.com )是 ( http: / / www.21cnjy.com )的极大值点 D． ( http: / / www.21cnjy.com )是 ( http: / / www.21cnjy.com )的极大值点
3．函数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 的单调增区间为（ ）
A. HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 B． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3
C. HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 D． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3
4．曲线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 在 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 处的切线平行于直线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，则 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 点的坐标为（ ）
A． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 B． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 C． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 和 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 D． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 和 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3
5．二项式 ( http: / / www.21cnjy.com )的展开式中 ( http: / / www.21cnjy.com )的系数是( )
A．84 B．-84 C．126 D．-12621世纪教育网版权所有
6．下面几种推理过程是演绎推理的是( )
(A)某校高三有8个班,1班有51人,2班有53人,3班有52人,由此推测各班人数都超过50人
(B)由三角形的性质,推测空间四面体的性质
(C)平行四边形的对角线互相平分,菱形是平行四边形,所以菱形的对角线互相平分
(D)在数列{an}中,a1=1,an= HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 QUOTE http://www.21cnjy.com/ ( http: / / www.21cnjy.com ) 错误！未找到引用源。 EMBED Equation.DSMT4 ,由此归纳出{an}的通项公式
7．曲线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 与 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 轴以及直线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 所围图形的面积为（ ）
Ａ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｂ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｃ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｄ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4
8．已知偶函数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 在区间 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 上满足 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，则满足 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的取值范围是
A． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 B． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4
C． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 D． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4
9．如果△A1B1C1的三个内角的余弦值分别等于△A2B2C2的三个内角的正弦值,那么( )
(A)△A1B1C1和△A2B2C2都是锐角三角形
(B)△A1B1C1和△A2B2C2都是钝角三角形
(C)△A1B1C1是钝角三角形,△A2B2C2是锐角三角形
(D)△A1B1C1是锐角三角形,△A2B2C2是钝角三角形
10．若函数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的导函数在区间 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 上的图像关于直线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 对称，则函数 ( http: / / www.21cnjy.com )在区间 ( http: / / www.21cnjy.com )上的图象可能是（ ）
( http: / / www.21cnjy.com )
A．①④ B．②④ C．②③ D．③④
11．我国第一艘航母“辽宁舰”在某次舰载 ( http: / / www.21cnjy.com )机起降飞行训练中，有5架舰载机准备着舰．如果甲乙2机必须相邻着舰，而丙丁不能相邻着舰，那么不同的着舰方法有（ ）种
A．12 B．18 C．24 D．48
12．已知f(x)= ( http: / / www.21cnjy.com )，在区间[0,2]上任取三个数 ( http: / / www.21cnjy.com ),均存在以 ( http: / / www.21cnjy.com ) 为边长的三角形，则 ( http: / / www.21cnjy.com )的取值范围是（ ）21cnjy.com
A. ( http: / / www.21cnjy.com ) B. ( http: / / www.21cnjy.com ) C. ( http: / / www.21cnjy.com ) D. ( http: / / www.21cnjy.com )
第II卷（非选择题）
二、填空题（本大题共4小题，每小题5分，共20分）
13．设 ( http: / / www.21cnjy.com )（i为虚数单位），则 ( http: / / www.21cnjy.com ) ．
14．在平面上，若两个正三角形的边长的比为 ( http: / / www.21cnjy.com )1∶2，则它们的面积比为1∶4，类似地，在空间内，若两个正四面体的棱长的比为1∶2，则它们的体积比为________．21教育网
15．已知函数f(x)＝lnx－ HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 (m∈R)在区间[1，e]上取得最小值4，则m＝________．
16．新华学校自实施素质教育以来，学生社团 ( http: / / www.21cnjy.com )得到迅猛发展．新华高一新生中的五名同学打算参加“春晖文学社”、“舞者轮滑俱乐部”、“篮球之家”、“围棋苑”四个社团．若每个社团至少有一名同学参加，每名同学至少参加一个社团且只能参加一个社团，且同学甲不参加“围棋苑”，则不同的参加方法的种数为________．2·1·c·n·j·y
三、解答题（本大题共6小题，共70分，要写出必要的过程和演算步骤，否则不得分）
17．（本小题10分）已知m∈R，设p：复数z1＝(m－1)＋(m＋3)i (i是虚数单位)在复平面内
对应的点在第二象限，q：复数z2＝1＋(m－2)i的模不超过 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ．
（1）当p为真命题时，求m的取值范围；
（2）若命题“p且q”为假命题，“p或q”为真命题，求m的取值范围．
18．（本小题12分）在(3－x)20(x∈R，x≠0)的展开式中，已知第2r项与第r＋1项(r≠1)的
二项式系数相等．
(1)求r的值；
(2)若该展开式的第r项的值与倒数第r项的值的 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 相等，求x的值．
19．（本小题12分）用一颗骰子连掷三次，投掷出的数字顺次排成一个三位数，此时：
(1)各位数字互不相同的三位数有多少个？
(2)可以排出多少个不同的数？
(3)恰好有两个相同数字的三位数共有多少个？
20．（本小题12分）已知数列{an}满足a1＝1，且4an＋1－anan＋1＋2an＝9(n∈N?)．
(1)求a2，a3，a4的值；
(2)由(1)猜想{an}的通项公式，并给出证明．
21．（本小题12分）已知函数错误！未找到引用源。（e为自然对数的底数）
（1）求 HYPERLINK "http://www.21cnjy.com" EMBED Equation.KSEE3 SKIPIF 1 < 0 \* MERGEFORMAT 错误！未找到引用源。的最小值；
（2）若对于任意的 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 ，不等式错误！未找到引用源。恒成立，求实数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 的取值范围.
22．（本小题12分）已知函数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 （ HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 、 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 为常数），在 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 时取得极值．
（1）求实数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的取值范围；
（2）当 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 时，关于 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的方程 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 有两个不相等的实数根，求实数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的取值范围；
（3）数列 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 满足 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 （ HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 且 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ）， HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，数列 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的前 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 项和为 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，
求证： HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 （ HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 , HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 是自然对数的底）．
高二（理科）数学期中考试答案卷
一.选择题(共60分)
题号 1 2 3 4 5 6 7 8 9 10 11 12
答案
二、填空题(共20分)
13. ______________； 14. ______________；15. ______________；16. ______________；
三、解答题(共70分)
17.
18.
19.
20.
21.22.（做在背面）
( http: / / www.21cnjy.com )18．
解：(1)由题意知C202r-1＝C202r，
即2r－1＝r或2r－1＝20－r，解得r＝7或r＝1(舍去)．
(2)Tr＝C202r-1·321－r·(－x)r－1，
当r＝7时，T7＝C206·314·x6，
倒数第7项，即T15＝C2014·36·x14，
( http: / / www.21cnjy.com )
(2)猜想an＝ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/14/9efdcc57-cc56-4e21-9939-ad862f698a37/paper.files/image052.png" \* MERGEFORMATINET .证明：①当n＝1时，猜想成立．
②设当n＝k时(k∈N*)时，猜想成立，即ak＝ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/14/9efdcc57-cc56-4e21-9939-ad862f698a37/paper.files/image055.png" \* MERGEFORMATINET ，
则当n＝k＋1时，有ak＋1＝2－ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/14/9efdcc57-cc56-4e21-9939-ad862f698a37/paper.files/image056.png" \* MERGEFORMATINET ＝2－ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/14/9efdcc57-cc56-4e21-9939-ad862f698a37/paper.files/image057.png" \* MERGEFORMATINET ，所以当n＝k＋1时猜想也成立．
综合①②，猜想对任何n∈N*都成立．21·cn·jy·com
( http: / / www.21cnjy.com )
当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image218.png" \* MERGEFORMATINET 时，上述不等式显然成立，故只需考虑 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image223.png" \* MERGEFORMATINET 的情况.
将 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image222.png" \* MERGEFORMATINET 变形为 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image208.png" \* MERGEFORMATINET .
令 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image209.png" \* MERGEFORMATINET ，则 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image210.png" \* MERGEFORMATINET 的导函数 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image224.png" \* MERGEFORMATINET ，
令 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image225.png" \* MERGEFORMATINET ，解得 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image226.png" \* MERGEFORMATINET ；令 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image227.png" \* MERGEFORMATINET ，解得 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image228.png" \* MERGEFORMATINET .
从而 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image210.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image229.png" \* MERGEFORMATINET 内单调递减，在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image230.png" \* MERGEFORMATINET 内单调递增.
所以，当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image017.png" \* MERGEFORMATINET 时， HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image210.png" \* MERGEFORMATINET 取得最小值 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image211.png" \* MERGEFORMATINET ，
从而实数 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image106.png" \* MERGEFORMATINET 的取值范围是 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image207.png" \* MERGEFORMATINET . 12分
www.21-cn-jy.com
22．（1） HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 且 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ；（2） HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ；
（1） HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image366.png" \* MERGEFORMATINET ∵ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image030.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image334.png" \* MERGEFORMATINET 有定义 ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image347.png" \* MERGEFORMATINET
∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image334.png" \* MERGEFORMATINET 是方程 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image349.png" \* MERGEFORMATINET 的根，且不是重根
∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image367.png" \* MERGEFORMATINET 且 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image368.png" \* MERGEFORMATINET 又 ∵ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image347.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image343.png" \* MERGEFORMATINET 且 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image344.png" \* MERGEFORMATINET 4分
（2） HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image335.png" \* MERGEFORMATINET 时 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image352.png" \* MERGEFORMATINET 即方程 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image369.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image370.png" \* MERGEFORMATINET 上有两个不等实根
即方程 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image371.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image372.png" \* MERGEFORMATINET 上有两个不等实根
令 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image353.png" \* MERGEFORMATINET HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image354.png" \* MERGEFORMATINET
HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image373.png" \* MERGEFORMATINET HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image354.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image355.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image374.png" \* MERGEFORMATINET 上单调递减，在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image375.png" \* MERGEFORMATINET 上单调递增 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image376.png" \* MERGEFORMATINET 当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image377.png" \* MERGEFORMATINET 时， HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image378.png" \* MERGEFORMATINET 且当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image379.png" \* MERGEFORMATINET 时， HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image378.png" \* MERGEFORMATINET
∴当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image345.png" \* MERGEFORMATINET 时，方程 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image336.png" \* MERGEFORMATINET 有两个不相等的实数根 8分
（3） HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image337.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image358.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image359.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image380.png" \* MERGEFORMATINET
∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image360.png" \* MERGEFORMATINET 10分
由（2）知 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image362.png" \* MERGEFORMATINET
代 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image363.png" \* MERGEFORMATINET 得 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image381.png" \* MERGEFORMATINET 即 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image364.png" \* MERGEFORMATINET
∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image382.png" \* MERGEFORMATINET
HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image383.png" \* MERGEFORMATINET
HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image364.png" \* MERGEFORMATINET
累加得
HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image385.png" \* MERGEFORMATINET
即 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image357.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image386.png" \* MERGEFORMATINET 得证 12分．
21世纪教育网 -- 中国最大型、最专业的中小学教育资源门户网站。 版权所有@21世纪教育网
甘肃省镇原县平泉中学2013-2014学年高二下学期期中考试数学（理）试题
第I卷（选择题）
一、选择题（本大题共12小题，每小题5分，共60分）
1．在复平面内与复数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 所对应的点关于虚轴对称的点为 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，则 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 对应的复数为（ ）
A． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｂ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 C． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｄ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4
2．已知 ( http: / / www.21cnjy.com )为自然对数的底数，设函数 ( http: / / www.21cnjy.com )，则( )
A． ( http: / / www.21cnjy.com )是 ( http: / / www.21cnjy.com )的极小值点 B． ( http: / / www.21cnjy.com )是 ( http: / / www.21cnjy.com )的极小值点
C． ( http: / / www.21cnjy.com )是 ( http: / / www.21cnjy.com )的极大值点 D． ( http: / / www.21cnjy.com )是 ( http: / / www.21cnjy.com )的极大值点
3．函数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 的单调增区间为（ ）
A. HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 B． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3
C. HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 D． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3
4．曲线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 在 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 处的切线平行于直线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，则 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 点的坐标为（ ）
A． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 B． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 C． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 和 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 D． HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 和 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3
5．二项式 ( http: / / www.21cnjy.com )的展开式中 ( http: / / www.21cnjy.com )的系数是( )
A．84 B．-84 C．126 D．-12621世纪教育网版权所有
6．下面几种推理过程是演绎推理的是( )
(A)某校高三有8个班,1班有51人,2班有53人,3班有52人,由此推测各班人数都超过50人
(B)由三角形的性质,推测空间四面体的性质
(C)平行四边形的对角线互相平分,菱形是平行四边形,所以菱形的对角线互相平分
(D)在数列{an}中,a1=1,an= HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 QUOTE http://www.21cnjy.com/ ( http: / / www.21cnjy.com ) 错误！未找到引用源。 EMBED Equation.DSMT4 ,由此归纳出{an}的通项公式
7．曲线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 与 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 轴以及直线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 所围图形的面积为（ ）
Ａ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｂ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｃ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 Ｄ． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4
8．已知偶函数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 在区间 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 上满足 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，则满足 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的取值范围是
A． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 B． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4
C． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 D． HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4
9．如果△A1B1C1的三个内角的余弦值分别等于△A2B2C2的三个内角的正弦值,那么( )
(A)△A1B1C1和△A2B2C2都是锐角三角形
(B)△A1B1C1和△A2B2C2都是钝角三角形
(C)△A1B1C1是钝角三角形,△A2B2C2是锐角三角形
(D)△A1B1C1是锐角三角形,△A2B2C2是钝角三角形
10．若函数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的导函数在区间 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 上的图像关于直线 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 对称，则函数 ( http: / / www.21cnjy.com )在区间 ( http: / / www.21cnjy.com )上的图象可能是（ ）
( http: / / www.21cnjy.com )
A．①④ B．②④ C．②③ D．③④
11．我国第一艘航母“辽宁舰”在某次舰载 ( http: / / www.21cnjy.com )机起降飞行训练中，有5架舰载机准备着舰．如果甲乙2机必须相邻着舰，而丙丁不能相邻着舰，那么不同的着舰方法有（ ）种
A．12 B．18 C．24 D．48
12．已知f(x)= ( http: / / www.21cnjy.com )，在区间[0,2]上任取三个数 ( http: / / www.21cnjy.com ),均存在以 ( http: / / www.21cnjy.com ) 为边长的三角形，则 ( http: / / www.21cnjy.com )的取值范围是（ ）21cnjy.com
A. ( http: / / www.21cnjy.com ) B. ( http: / / www.21cnjy.com ) C. ( http: / / www.21cnjy.com ) D. ( http: / / www.21cnjy.com )
第II卷（非选择题）
二、填空题（本大题共4小题，每小题5分，共20分）
13．设 ( http: / / www.21cnjy.com )（i为虚数单位），则 ( http: / / www.21cnjy.com ) ．
14．在平面上，若两个正三角形的边长的比为 ( http: / / www.21cnjy.com )1∶2，则它们的面积比为1∶4，类似地，在空间内，若两个正四面体的棱长的比为1∶2，则它们的体积比为________．21教育网
15．已知函数f(x)＝lnx－ HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 (m∈R)在区间[1，e]上取得最小值4，则m＝________．
16．新华学校自实施素质教育以来，学生社团 ( http: / / www.21cnjy.com )得到迅猛发展．新华高一新生中的五名同学打算参加“春晖文学社”、“舞者轮滑俱乐部”、“篮球之家”、“围棋苑”四个社团．若每个社团至少有一名同学参加，每名同学至少参加一个社团且只能参加一个社团，且同学甲不参加“围棋苑”，则不同的参加方法的种数为________．2·1·c·n·j·y
三、解答题（本大题共6小题，共70分，要写出必要的过程和演算步骤，否则不得分）
17．（本小题10分）已知m∈R，设p：复数z1＝(m－1)＋(m＋3)i (i是虚数单位)在复平面内
对应的点在第二象限，q：复数z2＝1＋(m－2)i的模不超过 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ．
（1）当p为真命题时，求m的取值范围；
（2）若命题“p且q”为假命题，“p或q”为真命题，求m的取值范围．
18．（本小题12分）在(3－x)20(x∈R，x≠0)的展开式中，已知第2r项与第r＋1项(r≠1)的
二项式系数相等．
(1)求r的值；
(2)若该展开式的第r项的值与倒数第r项的值的 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 相等，求x的值．
19．（本小题12分）用一颗骰子连掷三次，投掷出的数字顺次排成一个三位数，此时：
(1)各位数字互不相同的三位数有多少个？
(2)可以排出多少个不同的数？
(3)恰好有两个相同数字的三位数共有多少个？
20．（本小题12分）已知数列{an}满足a1＝1，且4an＋1－anan＋1＋2an＝9(n∈N?)．
(1)求a2，a3，a4的值；
(2)由(1)猜想{an}的通项公式，并给出证明．
21．（本小题12分）已知函数错误！未找到引用源。（e为自然对数的底数）
（1）求 HYPERLINK "http://www.21cnjy.com" EMBED Equation.KSEE3 SKIPIF 1 < 0 \* MERGEFORMAT 错误！未找到引用源。的最小值；
（2）若对于任意的 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 ，不等式错误！未找到引用源。恒成立，求实数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.3 的取值范围.
22．（本小题12分）已知函数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 （ HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 、 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 为常数），在 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 时取得极值．
（1）求实数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的取值范围；
（2）当 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 时，关于 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的方程 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 有两个不相等的实数根，求实数 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的取值范围；
（3）数列 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 满足 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 （ HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 且 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ）， HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，数列 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 的前 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 项和为 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ，
求证： HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 （ HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 , HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 是自然对数的底）．
高二（理科）数学期中考试答案卷
一.选择题(共60分)
题号 1 2 3 4 5 6 7 8 9 10 11 12
答案
二、填空题(共20分)
13. ______________； 14. ______________；15. ______________；16. ______________；
三、解答题(共70分)
17.
18.
19.
20.
21.22.（做在背面）
( http: / / www.21cnjy.com )18．
解：(1)由题意知C202r-1＝C202r，
即2r－1＝r或2r－1＝20－r，解得r＝7或r＝1(舍去)．
(2)Tr＝C202r-1·321－r·(－x)r－1，
当r＝7时，T7＝C206·314·x6，
倒数第7项，即T15＝C2014·36·x14，
( http: / / www.21cnjy.com )
(2)猜想an＝ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/14/9efdcc57-cc56-4e21-9939-ad862f698a37/paper.files/image052.png" \* MERGEFORMATINET .证明：①当n＝1时，猜想成立．
②设当n＝k时(k∈N*)时，猜想成立，即ak＝ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/14/9efdcc57-cc56-4e21-9939-ad862f698a37/paper.files/image055.png" \* MERGEFORMATINET ，
则当n＝k＋1时，有ak＋1＝2－ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/14/9efdcc57-cc56-4e21-9939-ad862f698a37/paper.files/image056.png" \* MERGEFORMATINET ＝2－ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/14/9efdcc57-cc56-4e21-9939-ad862f698a37/paper.files/image057.png" \* MERGEFORMATINET ，所以当n＝k＋1时猜想也成立．
综合①②，猜想对任何n∈N*都成立．21·cn·jy·com
( http: / / www.21cnjy.com )
当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image218.png" \* MERGEFORMATINET 时，上述不等式显然成立，故只需考虑 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image223.png" \* MERGEFORMATINET 的情况.
将 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image222.png" \* MERGEFORMATINET 变形为 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image208.png" \* MERGEFORMATINET .
令 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image209.png" \* MERGEFORMATINET ，则 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image210.png" \* MERGEFORMATINET 的导函数 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image224.png" \* MERGEFORMATINET ，
令 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image225.png" \* MERGEFORMATINET ，解得 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image226.png" \* MERGEFORMATINET ；令 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image227.png" \* MERGEFORMATINET ，解得 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image228.png" \* MERGEFORMATINET .
从而 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image210.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image229.png" \* MERGEFORMATINET 内单调递减，在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image230.png" \* MERGEFORMATINET 内单调递增.
所以，当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image017.png" \* MERGEFORMATINET 时， HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image210.png" \* MERGEFORMATINET 取得最小值 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image211.png" \* MERGEFORMATINET ，
从而实数 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image106.png" \* MERGEFORMATINET 的取值范围是 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/17/2f64cab6-86b4-4ae8-b9b6-718039a1990d/paper.files/image207.png" \* MERGEFORMATINET . 12分
www.21-cn-jy.com
22．（1） HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 且 HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ；（2） HYPERLINK "http://www.21cnjy.com" EMBED Equation.DSMT4 ；
（1） HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image366.png" \* MERGEFORMATINET ∵ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image030.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image334.png" \* MERGEFORMATINET 有定义 ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image347.png" \* MERGEFORMATINET
∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image334.png" \* MERGEFORMATINET 是方程 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image349.png" \* MERGEFORMATINET 的根，且不是重根
∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image367.png" \* MERGEFORMATINET 且 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image368.png" \* MERGEFORMATINET 又 ∵ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image347.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image343.png" \* MERGEFORMATINET 且 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image344.png" \* MERGEFORMATINET 4分
（2） HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image335.png" \* MERGEFORMATINET 时 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image352.png" \* MERGEFORMATINET 即方程 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image369.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image370.png" \* MERGEFORMATINET 上有两个不等实根
即方程 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image371.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image372.png" \* MERGEFORMATINET 上有两个不等实根
令 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image353.png" \* MERGEFORMATINET HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image354.png" \* MERGEFORMATINET
HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image373.png" \* MERGEFORMATINET HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image354.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image355.png" \* MERGEFORMATINET 在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image374.png" \* MERGEFORMATINET 上单调递减，在 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image375.png" \* MERGEFORMATINET 上单调递增 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image376.png" \* MERGEFORMATINET 当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image377.png" \* MERGEFORMATINET 时， HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image378.png" \* MERGEFORMATINET 且当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image379.png" \* MERGEFORMATINET 时， HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image378.png" \* MERGEFORMATINET
∴当 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image345.png" \* MERGEFORMATINET 时，方程 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image336.png" \* MERGEFORMATINET 有两个不相等的实数根 8分
（3） HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image337.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image358.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image359.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image380.png" \* MERGEFORMATINET
∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image360.png" \* MERGEFORMATINET 10分
由（2）知 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image362.png" \* MERGEFORMATINET
代 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image363.png" \* MERGEFORMATINET 得 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image381.png" \* MERGEFORMATINET 即 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image364.png" \* MERGEFORMATINET
∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image382.png" \* MERGEFORMATINET
HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image383.png" \* MERGEFORMATINET
HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image364.png" \* MERGEFORMATINET
累加得
HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image385.png" \* MERGEFORMATINET
即 HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image357.png" \* MERGEFORMATINET ∴ HYPERLINK "http://www.21cnjy.com" INCLUDEPICTURE "http://static.zujuan.com/Upload/2014-04/16/e3587c95-7c3a-4d5b-a339-7533fa156819/paper.files/image386.png" \* MERGEFORMATINET 得证 12分．
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