全一卷
1.若
是单位向量,且
,则
__________ .
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2.函数
的值域为__________.
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3.4个函数
,
,
,
图象的交点数共有__________.
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4.若
,则
__________.
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5.已知
,
,
,则
__________.
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6.甲乙两人玩猜数字游戏,先由甲在心中任想一个数字,记为
,再由乙猜甲刚才所想的数字,把乙猜的数字记为
,且
。若
,则称甲乙“心有灵犀”。现任意找两人玩这个
游戏,则他们“心有灵犀”的概率为 。
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7.在
中,角
所对边分别为
,若
,则
__________.
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8.将10个数1,2,3,…,9,10按任意顺序排列在一个圆圈上,设其中连续相邻的3数之和为
,则
的最大值不小于__________.
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9.已知函数
(
)是偶函数,若
对一切实数
都成立,求实数
的取值范围.
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10.记
表示不超过实数
的最大整数,在数列
中,
,
(
),证明:
.
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11.如图,定直线与定
相离,
为
上任意一点,
为
的两条切线,
为两切点,
其垂足为点
,
交于点
,证明:
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12.有
(
)个整数:
,
,…,
,满足
,
,证明
能被4整除.
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