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    2019浙江高考数学试题及答案解析【word精校版】

    2019-06-13 11:56:50文/刘美娟

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    2019年普通高等学校招生全国统一考试(浙江卷)

    数学

    选择题部分(共40分)

     

    一、选择题:本大题共10小题,每小题4分,共40分。在每小题给出的四个选项中,只有一项是符合题目要求的。

     

    1.已知全集U={-1,0,1,2,3},集合A={0,1,2},B={-1,0,1},则()∩B=

    A.{-1}

    B.{0,1}

    C.{-1,2,3}

    D.{-1,0,1,3}

     

    2.渐进线方程为x±y=0的双曲线的离心率是

    A.

    B.1

    C.

    D.2

     

    3.若实数x,y满足约束条件 则z=3x+2y的最大值是

    A.-1

    B.1

    C.10

    D.12

    4. 组暅是我国南北朝时代的伟大科学家,他提出的“幂势既同,则积不容异”称为祖暅原理,利用该原理可以得到柱体的体积公式,其中是柱体的底面积, 是柱体的高,若某柱体的三视图如图所示,则该柱体的体积是(?? ) 

     

    A. 158

    B. 162

    C. 182

    D. 32

    A. 充分不必要条件

    B. 必要不充分条件

    C. 充分必要条件

    D. 既不充分也不必要条件

     

    6.在同一直角坐标系中,函数,,(?>0且?≠0)的图像可能是(?? )

     

    A.

    B.

    C.

    D.

    7.设,随机变量的分布列是(? )

    则当在(0,1)内增大时

    A. 增大

    B. 减小

    C. 先增大后减小

    D. 先减小后增大

    9.已知,函数恰有三个零点

    则(??? )

    A.

    B.

    C.

    D.

    10.设,数列满足,, ,则 

    A.当时,

    B.当时,

    C.当时,

    D.当时,

     

    非选择题部分(共110分)

     

    二、填空题:本大题共7小题,多空题每题6分,单空题每题4分,共36分。

    11.复数z = (i为虚数单位),则||=?????????????

    12.已知圆C的圆心坐标是(0,m),半径长是r.若直线与圆相切与点A(-2,-1),则m=?????????? ? ,r= ?????????? ?

    13.在二项式的展开式中,常数项是 ?????????? ,系数为有理数的项的个数是

    ??????????

    14.在△ABC中,∠ABC=90°,AB=4,BC=3,点D在线段AC上,若∠BDC=45°则BD= ??????????  ,cos∠ABD= ??????????

    15.已知椭圆的左焦点为F,点P在椭圆上且在x轴的上方,若线段PF的中点在以原点O为圆心,|OF|为半径的圆上,则直线PF的斜率是 ??????????

    ABC-A柱子??????????????XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX?????XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX16.已知,函数,若存在,使得,则实数的最大值是?????

    三、解答题:本大题共5小题,共74分。解答应写出文字说明、证明过程或演算步骤。

    18.设函数

    (1)已知,函数是偶函数,求的值.

    (2)求函数的值域

     

    19.如图,已知三棱柱,平面⊥平面,E,F分别是AC,的中点.

    (1)证明:

    (2)求直线EF与平面所成角的余弦值

     

     

     

     

     

     

     

    20.设等差数列的前n项和为,数列满足:对每个成等比数列.

    (1)求数列的通项公式

    (2)记 ,证明: ABC-A柱子??????????????XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX?????XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

    21.(本题满分15分)过焦点F(1,0)的直线与抛物线交于A,B 两点,C 在抛物线,的重心P在x轴上,AC交x轴于点Q(点Q在点P的右侧)。

    (1)求抛物线方程及准线方程;

    (2)记,的面积分别为,,求的最小值及此时点P的坐标。

     

    22.已知实数,设函数

    (1)当时,求函数的单调区间

    (2)对任意 均有 ,求的取值范围

     

     

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