2017年全国高中数学联赛A卷试题和答案(word精校版).pdf
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2017年全国高中数学联赛A卷试题和答案(word精校版).pdf
word 2017 年全国高中数学联赛A卷一试一、填空题1.设)(xf是定义在R上的函数,对任意实数x有1)4()3(xfxf.又当70 x时,)9(log)(2xxf,则)100(f的值为 _.2.若实数yx,满足1cos22yx,则yxcos的取值范围是_.3.在平面直角坐标系xOy中,椭圆C的方程为1109:22yx,F为C的上焦点,A为C的右顶点,P是C上位于第一象限内的动点,则四边形OAPF的面积的最大值为_.4.若一个三位数中任意两个相邻数码的差不超过1,则称其为“平稳数”.平稳数的个数是5.正三棱锥ABCP中,1AB,2AP,过AB的平面将其体积平分,则棱PC与平面所成角的余弦值为_.6.在平面直角坐标系xOy中,点集1,0,1,),(yxyxK.在K中随机取出三个点,则这三点中存在两点之间距离为5的概率为 _.7.在ABC中,M是边BC的中点,N是线段BM的中点.若3A,ABC的面积为3,则ANAM的最小值为 _.8.设两个严格递增的正整数数列nnba,满足:20171010ba,对任意正整数n,有nnnaaa12,nnbb21,则11ba的所有可能值为_.二、解答题9.设mk,为实数,不等式12mkxx对所有bax,成立.证明:22ab.10.设321,xxx是非负实数,满足1321xxx,求)53)(53(321321xxxxxx的最小值和最大值.word 11.设复数21,zz满足0)Re(1z,0)Re(2z,且2)Re()Re(2221zz(其中)Re(z表示复数z的实部).(1)求)Re(21zz的最小值;(2)求212122zzzz的最小值.2017 年全国高中数学联赛A卷二试一.如图,在ABC中,ACAB,I为ABC的内心,以A为圆心,AB为半径作圆1,以I为圆心,IB为半径作圆2,过点IB,的圆3与1,2分别交于点QP,(不同于点B).设IP与BQ交于点R.证明:CRBR二.设数列na定义为11a,,2,1,1nnanananaannnnn.求满足20173rar的正整数r的个数.三.将3333方格纸中每个小方格染三种颜色之一,使得每种颜色的小方格的个数相等.若相邻连个小方格的颜色不同,则称它们的公共边为“分隔边”.试求分隔边条数的最小值.四.设nm,均是大于1 的整数,nm,naaa,21是n个不超过m的互不相同的正整数,且naaa,21互 素.证 明:对 任 意 实 数x,均 存 在 一 个)1(nii,使 得文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1文档编码:CE7J4V3G9R7 HN2C5R5M9W2 ZY7S3M2N4B1word xmmxai)1(2,这里y表示实数y到与它最近的整数的距离.2017 年全国高中数学联赛A卷一试答案1.2.3.4.文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 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ZX5H6G5V1A1word 5.6.7.文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 HB4Y6Y1N2J5 ZX5H6G5V1A1文档编码:CK9N3F1M4N9 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