2015全国卷1数学试卷及答案(文科).pdf
2015年普通高等学校招生全国统一考试文科数学全国卷-1-绝密启封并使用完毕前一.选择题：本大题共12 小题，每题 5 分。1、已知集合32,6,8,10,12,14Ax xnnNB，则集合AB中的元素个数为A 5 B4 C 3 D2 2、已知点(0,1),(3,2)AB，向量(4,3)AC，则向量BCA(7,4)B(7,4)C(1,4)D(1,4)3、已知复数z满足(1)1zii，则zA2iB2i C2iD2i4、如果 3 个正数可作为一个直角三角形三条边的边长，则称这3 个数为一组勾股数，从1,2,3,4,5中任取 3 个不同的数，则这3 个数构成一组勾股数的概率为A310B15 C110D1205、已知椭圆E 的中心为坐标原点，离心率为12，E 的右焦点与抛物线2:8Cyx的焦点重合，,A B是 C 的准线与E 的两个交点，则ABA3B6 C9 D126、九章算术是我国古代内容极为丰富的数学名著，书中有如下问题：“今有委米依垣内角，下周八尺，高五尺，问”积及为米几何？”其意思为：“在屋内墙角处堆放米如图，米堆为一个圆锥的四分之一，米堆底部的弧长为8 尺，米堆的高为5 尺，米堆的体积和堆放的米各位多少？”已知 1 斛米的体积约为立方尺，圆周率约为3，估算出堆放的米有A14斛B22斛C36斛 D66斛7、已知na是公差为 1 的等差数列，nS为na的前n项和，假设844SS，则10aA172B192C10 D128、函数()cos()fxx的部分图像如下图，则()fx的单调递减区间为A13(,),44kkkZB13(2,2),44kkkZC13(,),44kkkZD13(2,2),44kkkZ9、执行右面的程序框图，如果输入的0.01t，则输出的nA5B6C10D12 2015年普通高等学校招生全国统一考试文科数学全国卷-2-10、已知函数1222,1()log(1),1xxf xxx，且()3f a，则(6)faA47 B54C34D1411、圆柱被一个平面截去一部分后与半球半径为r组成一个几何体，该几何体的三视图中的正视图和俯视图如下图，假设该几何体的外表积为1620，则r()A1B2C4D812、设函数()yf x的图像与2x ay的图像关于直线yx对称，且(2)(4)1ff，则a()（A）1B1 C2 D4第卷二、填空题：本大题共4 小题,每题 5 分13、数列na中112,2,nnnaaaS为na的前 n 项和，假设126nS，则n.14.已知函数31fxaxx的图像在点1,1f的处的切线过点2,7，则a.15.假设 x,y 满足约束条件20210220 xyxyxy,则 z=3x+y 的最大值为16.已知P是双曲线22:18yCx的右焦点，P 是 C 左支上一点，0,66A，当APF周长最小时，该三角形的面积为三、解答题17.本小题总分值12 分已知,a b c分别是ABC内角,A B C的对边，2sin2sinsinBAC.I假设ab，求cos;B文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6文档编码:CN6Q5S5D10V8 HM4U8T5T2X6 ZN1M9F9Z10N6 2015年普通高等学校招生全国统一考试文科数学全国卷-3-II假设90B，且2,a求ABC的面积.18.本小题总分值12 分如图四边形ABCD 为菱形，G 为 AC 与 BD 交点，BEABCD平面，I证明：平面AEC平面BED；II假设120ABC，,AEEC三棱锥EACD的体积为63，求该三棱锥的侧面积.19.本小题总分值12 分某公司为确定下一年度投入某种产品的宣传费，需了解年宣传费x单位：千元对年销售量单位：t和年利润z单位：千元的影响，对近8 年的宣传费ix，和年销售量1,2,3,8iy i的数据作了初步处理，得到下面的散点图及一些统计量的值.I根据散点图判断，yabx与ycdx，哪一个宜作为年销售量y 关于年宣传费x 的回归方程类型给出判断即可，不必说明理由；II根据 I的判断结果及表中数据，建立y 关于 x 的回归方程；III 已知这种产品的年利润z 与 x，y 的关系为0.2zyx，根据 II的结果答复以下问题：i当年宣传费90 x时，年销售量及年利润的预报值时多少？ii 当年宣传费x为何值时，年利润的预报值最大？附：对于一组数据u1 v1,u2 v2.un vn,其回归线 v=u 的斜率和截距的最文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 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ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3 2015年普通高等学校招生全国统一考试文科数学全国卷-4-小二乘估计分别为：20 本小题总分值12 分已知过点1,0A且斜率为k 的直线 l 与圆 C：22231xy交于 M，N 两点.I求 k 的取值范围；II12OMON，其中 O 为坐标原点，求MN.21.本小题总分值12 分设函数2lnxfxeax.I讨论fx的导函数fx的零点的个数；II证明：当0a时22lnfxaaa.请考生在22、23、24 题中任选一题作答,如果多做,则按所做的第一题计分,作答时请写清题号22.本小题总分值10 分选修4-1：几何证明选讲如图 AB 是圆 O 直径，AC 是圆 O 切线，BC 交圆 O 与点 E.I假设 D 为 AC 中点，求证：DE 是圆 O 切线；II假设3OACE，求ACB的大小.23.本小题总分值10 分选修4-4：坐标系与参数方程在直角坐标系xOy中，直线1:2Cx，圆222:121Cxy，以坐标原点为极点,x 轴正半轴为极轴建立极坐标系.I求12,C C的极坐标方程.II假设直线3C的极坐标方程为R4，设23,CC的交点为,M N，求2C MN的面积.24.本小题总分值10 分选修4-5：不等式证明选讲已知函数12,0fxxxa a.I当1a时求不等式1fx的解集；II假设fx图像与 x 轴围成的三角形面积大于6，求 a 的取值范围.文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 ZY3T3Q7A5D3文档编码:CK4W3K3U8X6 HE5F6P5E10X1 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