名校
解题方法
1 . 已知点
,则与向量AB同方向的单位向量为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b460f35525e7dbfe681dcbdc6bc1ab30.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 下列说法中正确的是( )
A.一组数据3,4,2,8,1,5,8,6,9,9,的第60百分位数为6 |
B.将一组数据中的每一个数据加上同一个正数后,方差变大 |
C.若甲、乙两组数据的相关系数分别为![]() ![]() |
D.在一个![]() ![]() ![]() |
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解题方法
3 . 已知数列
为各项不为零的等差数列,
为数列
的前
项和,
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7702425507306b9722fd26b35eb1f1cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
A.4 | B.8 | C.12 | D.16 |
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解题方法
4 . 已知圆
的圆心与抛物线
的焦点关于直线
对称,直线
与
相交于
两点,且
,则圆
的标准方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089243ad31b799d65b9e86ec2a116188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0907a673d52825cd7df84b400972d4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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5 . 已知集合
,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282e995abdf2a7a0be290f9538359968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f400a6e39af4b56edbfdbef4485a0d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8436bd688c9c4425bbf16ab3b55692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d19c887002cc13f351b14b929c02d1d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e12bd6146b3a1f9f9c7790936bf68f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/379063e86cd968fd34afe4e1ef69a828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eca07dc5ab2f0858b2134e29ccd074.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 已知函数
,关于该函数有下列四个说法:
(1)函数
的图象关于点
中心对称
(2)函数
的图象关于直线
对称
(3)函数
在区间
内有4个零点
(4)函数
在区间
上单调递增
以上四个说法中,正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32df380fd4eec992e81e40864eedd509.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358c8c0e7bc2f31f50d9aab6b2f84f5b.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b7442b37570f882b1b7bafbb2459bf.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28933f93d4952657848a1564f37bd6e5.png)
(4)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7ac80b964f5baf79f5faa7ac1e2983.png)
以上四个说法中,正确的个数为( )
A.1 | B.2 | C.3 | D.4 |
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2024高一·全国·专题练习
解题方法
8 . 甲、乙两人下围棋,若甲执黑子先下,则甲胜的概率为
;若乙执黑子先下,则乙胜的概率为
.假定每局之间相互独立且无平局,第二局由上一局负者先下,若甲、乙比赛两局,第一局甲执黑子先下,则甲、乙各胜一局的概率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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名校
9 . 如图,在三棱锥
中,
平面
,E,F分别为BC,PC的中点,且
.
;
(2)求直线EF与平面ABC所成角的正弦值;
(3)求
到平面AEF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a219cbad3454275ec748c3e00d535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)求直线EF与平面ABC所成角的正弦值;
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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名校
10 . 某公司为了解所经销商品的使用情况,随机问卷50名使用者,然后根据这50名的问卷评分数据,统计得到如图所示的频率分布直方图,其统计数据分组区间为
,
,
,
,
,
.
的值;
(2)估计这50名问卷评分数据的中位数、众数、平均数;
(3)从评分在
的问卷者中随机抽取2人,求此2人评分都在
的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fc138be9688253cbdeae2808eb74ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486c7705dbd7b7b9ec5dd17b4891088b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea146d8ec45e63ad14683fd31064de66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77699e3d1ddc6e698a640573a7ef787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d90faf85d1548242098a6fe3accd84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1a32a9f2b04fc931c6a0da0b7485e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)估计这50名问卷评分数据的中位数、众数、平均数;
(3)从评分在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4204a934372022fa08a7e739ab46a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486c7705dbd7b7b9ec5dd17b4891088b.png)
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