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1、河南省北大附中河南分校2014届高三最后一次冲刺(猜题卷)文科数学试题一、选择题:本大题共12小题,每小题5分 共60分1定义集合运算:ab=zz=xy(x+y),xa,yb,设集合a=0,1,b=2,3,则集合ab的所有元素之和为()a0b6c12d182已知复数z(cosi)(2sini)是纯虚数,0,2),则( )a. b. c. d.3已知集合,,若“”是“”的充分非必要条件,则的取值范围是( )(a) (b) (c) (d)4下图为某算法的程序框图,则程序运行后输出的结果是( )a 3 b 4 c 5 d 65一个几何体的三视图如图所示,其中正视图和侧视图是腰长为4的两个全等的等腰直
2、角三角形若该几何体的体积为v,并且可以用n这样的几何体拼成一个棱长为4的正方体,则v,n的值是( ) a bc d 6在abc中,内角a,b,c所对的边分别是a,b,c.已知8b5c,c2b,则cos c() a. b c± d.7下列命题正确的个数是 命题“”的否定是“”; “函数的最小正周期为”是“”的必要不充分条件; 在上恒成立在上恒成立; “平面向量与的夹角是钝角”的充分必要条件是“”.a1 b2 c3 d48已知函数的图象在点处的切线与直线平行,若数列的前n项和为,则的值为( )a、b、c、d、9、如图,在棱长为1的正方体abcd-a1b1c1d1中,p是棱上的点, 则满足
3、的点p的个数有( )a4b6 c8 d1210在集合中任取一个偶数a和一个奇数b构成以原点为起点的向量,从所有得到的以原点为起点的向量中任取两个向量为邻边作平行四边形,记所有作成的平行四边形的个数为,在区间1,和2,4分别各取一个数,记为m和n,则方程1表示焦点在x轴上的椭圆的概率是 ( )a b. c. d. 11已知是内一点,且若、的面积分别为、, 则的最小值是( ) a9 b. 16 c. 18 d. 2012已知函数 函数,若存在,使得成立,则实数的取值范围是a. b. c. d.二、填空题:本大题共4小题,每小题5分,共20分。 40 50 60 70 80 90 体重(kg)0.0
4、050.0100.0200.0300.0350.0150.02513从某地高中男生中随机抽取100名同学,将他们的体重(单位:kg)数据绘制成频率分布直方图(如图)由图中数据可知体重的平均值为kg;若要从身高在 60 , 70),70 ,80) , 80 , 90三组内的男生中,用分层抽样的方法选取12人参加一项活动,再从这12人选两人当正负队长,则这两人身高不在同一组内的概率为 (2个数据错一个不得分)14非零向量满足,则与的夹 角大小为 15已知函数为r上的奇函数,的导数为,且当时,不等式 成立,若对一切恒成立,则实数的取值 范围是 。16.已知下列命题:函数的单调增区间是.要得到函数的图
5、象,需把函数的图象上所有点向左平行移动个单位长度.已知函数,当时,函数的最小值为在0,1上至少出现了100次最小值,则.其中正确命题的序号是_ 三、解答题:解答应写出文字说明、证明过程或演算步骤。17.(本小题满分12分)数列各项均为正数,其前项和为,且满足.(1)求数列的通项公式;(2)设, 求数列的前n项和,并求使 对所有的 都成立的最大正整数m的值18(本小题满分12分)某班50名学生在一次百米测试中,成绩全部介于13秒与18秒之间,将测试结果按如下方式分成五组:第一组,第二组,第五组右图是按上述分组方法得到的频率分布直方图. (1)若成绩大于或等于14秒且小于16秒认为良好, 求该班在
6、这次百米测试中成绩良好的人数; (2)设表示该班某两位同学的百米测试成绩,且已知cbagdef19(本小题满分12分)如图,四边形为矩形,四边形为梯形,且平面平面,点为的中点 (1)求证:平面; (2)求三棱锥的体积; 20(本小题满分12分)如图9-13,p是抛物线c:y=x2上点,直线l过点p且与抛物线c交于另一点q (1)若直线l与过点p的切线垂直,求线段pq中点 m的轨迹方程; ()若直线l不过原点且与x轴交于点s,与y轴交于点t,试求的取值范围21(本小题满分12分)已知函数是定义在上的奇函数,当时, (其中e是自然界对数的底, )() 求的解析式;()设求证:当,时,;()是否存在
7、负数,使得当时,的最小值是3 ?如果存在,求出实数的值;如果不存在,请说明理由。请考生在第(22)、(23)、(24)三题中任选一题做答,如果多做,则按所做的第一题记分。做答时用2b铅笔在答题卡上把所选题目对应题号下方的方框涂黑。22.如图,o的半径ob垂直于直径ac,m为ao上一点,bm的延长线交o于n,过n点的切线交ca的延长线于p(1) 求证:;(2)若o的半径为,求mn的长23已知椭圆c的极坐标方程为,点f1、f2为其左,右焦点,直线的参数方程为(t为参数,tr) ()求直线和曲线c的普通方程; ()求点f1、f2到直线的距离之和.24(本小题满分10分)选修45:不等式选讲 已知函数
8、 ()当时,求不等式的解集; ()若不等式对任意实数恒成立,求的取值范围 北大附中河南分校高考预测 若时,有6种情况7分若分别在和内时,共有12种情况. 9分 abcdxxaxbxcxdyyaybycydzzazbzc zd 在中,af=fe, afe=60º, 是正三角形 aef=60º,由ef/ad知ead=60º, en=aesin60º=12分20解法:(1)设p(x1,y1)、q(x2,y2)、m (x0,y0),依题意x10,yl>0,y2>0由y=x2,得y'=x. 过点p的切线的斜率k切=x1, x1=0不合题意, x
9、10 直线l的斜率k1=,直线l的方程为y-x21=(x-x1)方法一:联立消去y,得x2+-x21-2=0 由消去x,得y2-2(k2+b)y+b2=0则方法一: y1、y2可取一切不相等的正数, 的取值范围是(2,+)方法二:当b>0时,=|b|+2>2;当b<0时, =-b又由方程有两个相异实根,得=4(k2+b) 2-4b2= 4k2(k2+2b)>0于是k2+2b>0,即k2>-2b 所以当b>0时,可取一切正数,的取值范围是(2+)方法三:由p、q、t三点共线得ktq=ktp,即则x1y2-bx1=x2y1-bx2,即b(x2-x1)=(x
10、2y1-x1y2)于是b=可取一切不等于l的正数,的取值范围是(2,+)21()设,则,所以又因为是定义在上的奇函数,所以 故函数的解析式为 ()证明:当且时,设 因为,所以当时,此时单调递减;当时,此时单调递增,所以 又因为,所以当时,此时单调递减,所以所以当时,即 ()解:假设存在负数,使得当时,有最小值是3,则当,由于,则,故函数 是上的增函数所以,解得(舍去)当时,则当时,此时函数是减函数;当时,此时函数是增函数所以,解得满足题意。综上可知,存在负数,使得当时,有最小值22(1)连接on,因为pn切o于n,所以,所以,因为ob=on,所以因为于,所以 故,所以.(2)因为,所以.23(
11、) 直线普通方程为 ; 曲线的普通方程为 () ,,点到直线的距离 点到直线的距离 24解:()当时,即,当时,得,即,所以;当时,得成立,所以;当时,得,即,所以.故不等式的解集为.(),由题意得,则或,解得或,故的取值范9jwkffwvg#tym*jg&6a*cz7h$dq8kqqfhvzfedswsyxty#&qa9wkxfyeq!djs#xuyup2knxprwxma&ue9aqgn8xp$r#͑gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tng
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36、;gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%madnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvk
37、um>xrm6x4ngpp$vstt#&ksv*adnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy
38、7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&am
39、p;gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue
40、%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpaza
41、dnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk
42、!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6
43、ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnugk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&g
44、txrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amy
45、wpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gx
46、gjqv3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849g
47、xgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6
48、ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mzadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gx
49、gjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk
50、!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&g
51、txrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvk
52、um>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk
53、8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp
54、$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9&am
55、p;gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd
56、6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnugk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wew
57、z#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&
58、amp;qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqvue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv
59、*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!
60、z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&am
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