解题方法
1 . 已知抛物线:
,焦点为F,
为
上的一个动点,
是
在点A处的切线,点P在
上且与点A不重合.直线PF与Γ交于B、C两点,且
平分直线AB和直线AC的夹角.
(1)求
的方程(用
表示);
(2)若从点F发出的光线经过点A反射,证明:反射光线平行于x轴;
(3)若点A坐标为
,求点P坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32e577ae1f4449efbd64c1199efe7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23cb0c85ef0ac4d8722bba9fde0a851c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8750c7a9d012d136a878dc8f4233dfb7.png)
(2)若从点F发出的光线经过点A反射,证明:反射光线平行于x轴;
(3)若点A坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76678d7fed19144e94bb7c0bd6dba6d9.png)
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解题方法
2 . 在义乌,婺剧深受民众喜爱.某次婺剧表演结束后,老生、小生、花旦、正旦、老旦各一人排成一排合影留念,其中小生和老生不相邻且老旦不排在最右边的不同排法总数是( )
A.36 | B.48 | C.60 | D.72 |
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名校
解题方法
3 . 若正实数数列
满足
,则称
是一个对数凸数列;若实数列
满足
,则称
是一个凸数列.已知
是一个对数凸数列,
.
(1)证明:
;
(2)若
,证明:
;
(3)若
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c162242a938a5a12decf95e793a38bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb56942a7c324e61bf64f45182aac6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010baf415f792018ad9abd752e37b983.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7de869d778679e553d65c8feee7a0b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fae07f950aea5270e6b48fe2cedaaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e44bb3c3c56c02ae33d480b556fece.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e32b345649f33632c83903c6014dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac648580405ecaa29e91d45738a08af7.png)
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4 . 若函数
满足以下三个条件,则称
为
函数.①定义域为
;②对任意
,
;③对任意正整数
,
,当
时,有
.若给定
函数
某几个函数值,在满足条件①②③的情况下,可能的
如果有
种,分别为
,
,
,
.
等于
,
,
,
的最大值.这样得到的
称为
的最大生成函数.
(1)若
为
函数,且
是在给定条件
,
下的
的最大生成函数,求
和
的值;
(2)若
为
函数,且满足
,求数列
的前10项和;
(3)若
为
函数,且
是在给定条件
,
下的
的最大生成函数,求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f63c9be8167a50ac3996e007b124df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f133fb6340a11e7ba0240ac0e19339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2c8fda00e52527ee1472293c011eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b7acae2f2543b05e3c5677bd755b136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12877ebeba622c766be60b77efea9eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406957a919b3f16fb095aa9a8b7e2dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42bf9afee931791911f748fd84d45f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b754b86e63e02f3faeebff9c18c7460b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0749e3eddfb6056f19812d7fa713b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ddc3eab5cedbd4cba439126a8d2ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43172b8f2f645afeada31271d6f2dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a788e92a6e3e5e721096e78cc112adf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f196f6236188084f3b2c9f2b68c05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f196f6236188084f3b2c9f2b68c05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b17b16fdf70d2a885f5ab346afd18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ecae1c7e6e0dbb211105b27a0319c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830acb3d191d323e9ea6e710c7de0061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1135b03537fa6527c9ba3f639f64474c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31c3e1c4206e9bed7dd3c63d842080d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46069372b8f2a59194dad5978e18445.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7002fdc43f0d600cb517470ac65144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41678e5c9b510a2a4b798a0be444eb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc095001df2e68af03d6ed197a8d4372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab050e103632618580d0ec8728b584a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
5 . 在
的二项式展开式的所有项中,依次不放回地抽取两项,且每一项被取到的可能性相等.
(1)在第一次取到有理项的条件下,求第二次取到无理项的概率;
(2)记取到有理项的项数为随机变量X,求X的分布列及数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab49019e113af64c5bea07804526690.png)
(1)在第一次取到有理项的条件下,求第二次取到无理项的概率;
(2)记取到有理项的项数为随机变量X,求X的分布列及数学期望.
您最近一年使用:0次
2024-05-16更新
|
860次组卷
|
4卷引用:浙江省东阳市2024届高三5月模拟考试数学试题
浙江省东阳市2024届高三5月模拟考试数学试题四川省凉山州民族中学2023-2024学年高二下学期5月月考数学试题山东省泰安第一中学2023-2024学年高二下学期5月月考数学试题(已下线)专题04 条件概率与全概率公式(6类题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(江苏专用)
6 . 设p为素数,对任意的非负整数n,记
,
,其中
,如果非负整数n满足
能被p整除,则称n对p“协调”.
(1)分别判断194,195,196这三个数是否对3“协调”,并说明理由;
(2)判断并证明在
,
,
,…,
这
个数中,有多少个数对p“协调”;
(3)计算前
个对p“协调”的非负整数之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1538e59a0527883bb6ff5f5a5eb8e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0dd417ec70cf425efddea5f4c7ba7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ded2da98f74d955ff5dd8f9ac051968b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208ffeb1f7342c141f490e3185d11930.png)
(1)分别判断194,195,196这三个数是否对3“协调”,并说明理由;
(2)判断并证明在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366cfc0dec131eacf81cb194da71eb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60c0322d41827fa6dc18ee22de5e769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d950956eba112b45bb5b0a26393c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe9ad3cf2737677a9d3f1fb9fb2d2b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223ec16c7b0b7d25431d352d89215462.png)
(3)计算前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223ec16c7b0b7d25431d352d89215462.png)
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解题方法
7 . 金华市选拔2个管理型教师和4个教学型教师去新疆支教,把这6个老师分配到3个学校,要求每个学校安排2名教师,且管理型教师不安排在同一个学校,则不同的分配方案有( )
A.72种 | B.48种 | C.36种 | D.24种 |
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解题方法
8 . 为鼓励消费,某商场开展积分奖励活动,消费满100元的顾客可拋掷骰子两次,若两次点数之和等于7,则获得5个积分:若点数之和不等于7,则获得2个积分.
(1)记两次点数之和等于7为事件A,第一次点数是奇数为事件B,证明:事件A,B是独立事件;
(2)现有3位顾客参与了这个活动,求他们获得的积分之和X的分布列和期望.
(1)记两次点数之和等于7为事件A,第一次点数是奇数为事件B,证明:事件A,B是独立事件;
(2)现有3位顾客参与了这个活动,求他们获得的积分之和X的分布列和期望.
您最近一年使用:0次
2024-04-19更新
|
986次组卷
|
3卷引用:浙江省金华十校2024届高三4月模拟考试数学试卷
名校
9 . 设全集为
,定义域为
的函数
是关于x的函数“函数组”,当n取
中不同的数值时可以得到不同的函数.例如:定义域为
的函数
,当
时,有
若存在非空集合
满足当且仅当
时,函数
在
上存在零点,则称
是
上的“跳跃函数”.
(1)设
,若函数
是
上的“跳跃函数”,求集合
;
(2)设
,若不存在集合
使
为
上的“跳跃函数”,求所有满足条件的集合
的并集;
(3)设
,
为
上的“跳跃函数”,
.已知
,且对任意正整数n,均有
.
(i)证明:
;
(ii)求实数
的最大值,使得对于任意
,均有
的零点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2425552313d50a253bfb3cb4e9974ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5182856db60fa5cfda34c97b5748197a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02670179163cffe5070d209066b7aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d18ae300954e363c2637120f4f3ef82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45020afb5156159ad42add5537797ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05f8bcb38a5c47e2e8fe9889717fc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e77ed55488688257efc354fad8875c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c853fd24a33bd11fbf2d5dba50806d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00108abe0b3ee27e7549f6cc0d86c36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02670179163cffe5070d209066b7aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3946552f0f9f048a916879402e4d315a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47efc68941a3be03f5bebbabfbe388fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e94f0ab8e7418164e0c7481150e6b5.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d80a81e375bf3c3bdc3603ef7a2a37.png)
(ii)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05f8bcb38a5c47e2e8fe9889717fc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fbab6e1a7963d26e1265e1686cba40.png)
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10 . 在直角坐标系
中,圆Γ的圆心P在y轴上(
不与
重合),且与双曲线
的右支交于A,B两点.已知
.
(1)求Ω的离心率;
(2)若Ω的右焦点为
,且圆Γ过点F,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d37718920f48d43b0e3100fd251cd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c76dcc869ec710b956726d073fec3e7.png)
(1)求Ω的离心率;
(2)若Ω的右焦点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937b28e497387547778e7acedbb9aae5.png)
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