全一卷
1.已知集合
,集合
,则
_______ .
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2.若排列数
,则
________
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3.不等式
的解集为________
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4.已知球的体积为
,则该球主视图的面积等于________
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5.已知复数
满足
,则
_____________ .
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6.设双曲线
的焦点为
、
,
为该双曲线上的一点,若
,则
________
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7.如图,以长方体
的顶点
为坐标原点,过
的三条棱所在的直线为坐标轴,建立空间直角坐标系,若
的坐标为
,则
的坐标为________
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8.定义在
上的函数
的反函数为
,若
为奇函数,则
的解为________ .
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9.已知四个函数:①
;②
;③
;④
. 从中任选2个,则事件“所选2个函数的图像有且仅有一个公共点”的概率为________
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10.已知数列
和
,其中
,
,
的项是互不相等的正整数,若对于任意
,
的第
项等于
的第
项,则
________
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11.设
、
,且
,则
的最小值等于________
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12.如图,用35个单位正方形拼成一个矩形,点
、
、
、
以及四个标记为“”的点在正方形的顶点处,设集合
,点
,过
作直线
,使得不在
上的“”的点分布在
的两侧. 用
和
分别表示
一侧和另一侧的“”的点到
的距离之和. 若过
的直线
中有且只有一条满足
,则
中所有这样的
为________
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13.关于
、
的二元一次方程组
的系数行列式
为( )
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A.![]() | B.![]() | C.![]() | D.![]() |
14.在数列
中,
,
,则
( )
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A.等于![]() | B.等于0 | C.等于![]() | D.不存在 |
15.已知
、
、
为实常数,数列
的通项
,
,则“存在
,
使得
、
、
成等差数列”的一个必要条件是( )
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使得
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A.![]() | B.![]() | C.![]() | D.![]() |
16.在平面直角坐标系
中,已知椭圆
和
.
为
上的动
点,
为
上的动点,
是
的最大值. 记
在
上,
在
上,且
,则
中元素个数为( )
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点,
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A.2个 | B.4个 | C.8个 | D.无穷个 |
17.如图,直三棱柱
的底面为直角三角形,两直角边AB和AC的长分别为4和2,侧棱
的长为5.
(1)求三棱柱
的体积;
(2)设M是BC中点,求直线
与平面
所成角的大小.
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(1)求三棱柱
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(2)设M是BC中点,求直线
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18.已知函数
.
(1)求
的单调递增区间;
(2)设
为锐角三角形,角
所对边
,角
所对边
,若
,求
的面积.
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(1)求
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(2)设
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19.根据预测,某地第
个月共享单车的投放量和损失量分别为
和
(单位:辆),
其中
,
,第
个月底的共享单车的保有量是前
个月的
累计投放量与累计损失量的差.
(1)求该地区第4个月底的共享单车的保有量;
(2)已知该地共享单车停放点第
个月底的单车容纳量
(单位:辆). 设在某月底,共享单车保有量达到最大,问该保有量是否超出了此时停放点的单车容纳量?
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其中
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累计投放量与累计损失量的差.
(1)求该地区第4个月底的共享单车的保有量;
(2)已知该地共享单车停放点第
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20.在平面直角坐标系xOy中,已知椭圆
,
为
的上顶点,
为
上异于
上、下顶点的动点,
为x正半轴上的动点.
(1)若
在第一象限,且
,求
的坐标;
(2)设
,若以A、P、M为顶点的三角形是直角三角形,求M的横坐标;
(3)若
,直线AQ与
交于另一点C,且
,
,
求直线
的方程.
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上、下顶点的动点,
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(1)若
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(2)设
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(3)若
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求直线
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21.设定义在
上的函数
满足:对于任意的
、
,当
时,都有
.
(1)若
,求
的取值范围;
(2)若
为周期函数,证明:
是常值函数;
(3)设
恒大于零,
是定义在
上、恒大于零的周期函数,
是
的最大值.
函数
. 证明:“
是周期函数”的充要条件是“
是常值函数”.
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(1)若
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(2)若
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(3)设
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函数
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