2016年南昌市高考数学模拟试题（理科）

南昌市2016届高三上学期摸底测试数学(理)试题及答案

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024459660.jpg">

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500102.jpg">

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500918.jpg">

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500544.jpg">

 

南昌市2016届高三上学期摸底测试数学(理)试题及答案

一、选择题：本大题共12小题，每小题5分，共60分．

题号	1	2	3	4	5	6	7	8	9	10	11	12
答案	C	C	D	A	B	A	B	A	C	D	B	B

二、填空题：本大题共4小题，每小题5分，共20分．

13．高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500741.png">      14．高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500441.png">      15．高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500701.png">      16． 高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500609.png">

三、解答题：本大题共6个题，共70分．

17．解: （Ⅰ）依题意得，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500392.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500626.png">，

解得高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500435.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500379.png">. ……………6分

（Ⅱ）高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500726.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500469.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500408.png">，

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500337.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500713.png">……………10分

所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500907.png">的分布列为

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500721.png">	1	2	3	4	5
高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500186.png">	0.2	0.4	0.2	0.1	0.1

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500985.png">的数学期望为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024500650.png">.……………12分

18．解：（Ⅰ）由题意：高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501262.png">

∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501194.png">即高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501913.png"> ……………3分

∵高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501758.png">

∴ 高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501100.png">

∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501941.png">即高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501520.png">   ……………6分

（Ⅱ）由（1）知：高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501285.png">

∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501971.png">……………8分

∵高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501180.png">为锐角三角形． 

∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501288.png">  高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501889.png">

∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501625.png"> 又高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501929.png">

∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501330.png"> ∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501326.png"> ……………………10分

∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501539.png"> ……………………………12分

19．解：(Ⅰ)证明：由题意高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501623.png">

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501852.png">注意到高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501875.png">,所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501903.png">,

所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501578.png">,所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501344.png">,………………3分

又高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501312.png">侧面高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501815.png">，

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501957.png"> 又高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501219.png">与高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501537.png">交于点高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024501144.png">，所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502205.png">,

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502188.png">又因为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502306.png">,所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502299.png">.……………6分

(Ⅱ) 解：如图，分别以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502101.png">所在的直线为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502965.png">轴，

以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502300.png">为原点，建立空间直角坐标系高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502943.png">

则高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502485.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502485.png">，

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502914.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502565.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502674.png">，

又因为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502804.png">，

所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502190.png">      …………8分

所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502604.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502135.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502417.png">

设平面高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502143.png">的法向量为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502659.png">，

则根据高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502269.png">可得高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502918.png">是平面高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502562.png">的一个法向量,

设直线高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502748.png">与平面高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024502262.png">所成角为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503775.png">，则高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503564.png">高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503220.png">………………12分

20．解：（Ⅰ）高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503894.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503102.png">，∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503265.png">                ………1分

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503100.png">，    

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503191.png">                                          ………3分

∴高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503472.png">的方程为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503300.png">．                           ………5分

（Ⅱ）联立高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503193.png">得高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503437.png">，联立高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503500.png">得高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503136.png">，  ………7分

从而高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503822.png">，

点高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503886.png">到直线高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503951.png">的距离高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503388.png">，进而高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503560.png">………9分

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503756.png">令高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503479.png">，

有高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503164.png">，  ………11分

当高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503791.png">，时高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503796.png">，

即当过原点直线为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503208.png">时，△高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503451.png">面积取得最小值高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024503966.png">．………12分

21．解（Ⅰ）定义域为R，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504126.png">   ……………2分

当高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504914.png">时， 高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504715.png">时，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504289.png">；高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504689.png">时，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504280.png">

当高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504409.png">时， 高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504584.png">时，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504282.png">；高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504575.png">时，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504584.png">  ……………4分

所以当高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504374.png">时,高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504947.png">的增区间是高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504785.png">，减区间是高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504467.png">

当高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504384.png">时,高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504285.png">的减区间是高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504504.png">，增区间是高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504207.png"> ……………6分

（Ⅱ）高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504172.png">时，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504455.png">，由高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504495.png">得：高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504632.png">

设高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024504212.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505874.png">，   ……………8分

所以当高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505697.png">时，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505903.png">；当高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505671.png">时，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505805.png">，

所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505355.png">在高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505637.png">上递增， 在高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505831.png">上递减，      ……………10分

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505269.png">   

所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505352.png">的取值范围是高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505121.png">     ……………12分

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505858.png">22．解：（I）连接高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505532.png">，因为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505431.png">，所以 高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505442.png">

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505715.png">为半圆的切线   高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505906.png">，

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505927.png"> 高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505989.png">高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505853.png">

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505712.png">平分高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505457.png">…………………………5分

（Ⅱ）连接高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505238.png">，

由高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505898.png">知高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505861.png">

所以高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505345.png">四点共圆

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505970.png">， 

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505317.png">，

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505740.png">    ……………10分

23．解（Ⅰ）将高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505602.png"> 代入高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024505429.png"> ，得高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024506615.png">的参数方程为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024506300.png">

∴曲线高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024506332.png">的普通方程为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024506286.png">．       ………5分

（Ⅱ）设高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024506105.png">，高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024506588.png">，又高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507824.png">，且高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507837.png">中点为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507757.png">

所以有：高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507177.png">

又点高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507858.png">在曲线高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507615.png">上，

∴代入高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507610.png">的普通方程高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507289.png">得高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507958.png">

∴动点高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507325.png">的轨迹方程为高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507196.png">．              ………10分

24．（Ⅰ）由高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507886.png">得高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507315.png">  ……………5分

（Ⅱ）高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507950.png">     

而高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507598.png">

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507672.png"> ……………8分

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507188.png">   

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507496.png">   高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507533.png">

高三上学期摸底测试数学（理）试题及答案 src="/static/wddqxz/img/default/default.png" data-src="https://oss.zyxzdq.com/dyfwdq/img/img.liexue.cn/uploadfile/2015/0828/20150828024507433.png">                                        …………………10分

 

2016年南昌市高考数学模拟试题（理科）.doc

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