1 . 已知点P是双曲线C:
(
,
)上一点,
,
分别是C的左、右焦点,设
,若
的重心和内心的连线垂直于x轴,则
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa4ae8d7537feb98c7de50302705609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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解题方法
2 . 设函数
的定义域为R,
为奇函数,
为偶函数,当
时,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3d75d78903bd1fe1334b87a159deff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c79e24a717a8cf46aa75d3437a9e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51459b19f03662079f9b08d47375683c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bbec4f3caec14801bac08683d0f331.png)
A.![]() | B.![]() ![]() |
C.![]() ![]() | D.方程![]() |
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解题方法
3 . 如图,四边形ABCD内接于圆O,圆O的半径
,
,
.
的大小以及线段AB的长;
(2)求四边形ABCD面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e159fa38488741d395ea9cb03386b1ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09ea9254c90d1a9ce85df41dbcbeb97e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e142544a6d4e6851096afbd3cbad2fe2.png)
(2)求四边形ABCD面积的取值范围.
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解题方法
4 . 已知正方形ABCD的四个顶点都在椭圆上,且椭圆的两个焦点分别为边AD和BC的中点,则该椭圆的离心率为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 已知圆C:
,直线l:
,若l与圆C交于A,B两点,设坐标原点为O,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ca01d1c400707e011745ad16199da13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef6d00ddabcb1bb41fae534f5183ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df09bff72dab3e6555a0597b638a3bd0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 某射击运动员进行射击训练,已知其每次命中目标的概率均为
.
(1)若该运动员共射击6次,求其在恰好命中3次的条件下,第3次没有命中的概率;
(2)该运动员射击训练不超过n(
)次,当他命中两次时停止射击(射击n次后,若命中的次数不足两次也不再继续),设随机变量X为该运动员的射击次数,试写出随机变量X的分布列,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)若该运动员共射击6次,求其在恰好命中3次的条件下,第3次没有命中的概率;
(2)该运动员射击训练不超过n(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ab800bb4666f21dbe05ec239ca39ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f0d793fc77a1befa103b46f0d5307b.png)
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解题方法
7 . 已知函数
.
(1)当
时,请判断
的极值点的个数并说明理由;
(2)若
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ec761e879aa6a6a25ee87106270529.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79863748bbb4f280cdbfd58bb94b84dd.png)
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8 . 已知两条抛物线
,
.
(1)求
与
在第一象限的交点的坐标.
(2)已知点A,B,C都在曲线
上,直线AB和AC均与
相切.
(ⅰ)求证:直线BC也与
相切.
(ⅱ)设直线AB,AC,BC分别与曲线
相切于D,E,F三点,记
的面积为
,
的面积为
.试判断
是否为定值,若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1138c04fc3a0e1c217db0d432e4aff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知点A,B,C都在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(ⅰ)求证:直线BC也与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(ⅱ)设直线AB,AC,BC分别与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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9 . 在四棱锥P-ABCD中,
底面
,四边形
是矩形,且
,点
是棱
上的动点(包括端点),则满足
的
点有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b929269c53a44907dba8ee298a0a522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248ddfad39864ab0e183e01f82859e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.0个 | B.1个 | C.2个 | D.3个 |
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10 . 如图,在正方体
中,P为线段
的中点,Q为线段
上的动点(不包括端点),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.存在点Q,使得![]() | B.存在点Q,使得![]() ![]() |
C.三棱锥![]() | D.二面角![]() ![]() |
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