解题方法
1 . 一条光线从
射出与x轴相交于点
,经x轴反射,交y轴于R,则光线从P到R所走的路程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90da86e2098f65a0490ba55c671439e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f579b73ca01978ec68e716f993bc3766.png)
您最近一年使用:0次
2024-03-24更新
|
151次组卷
|
2卷引用:湖北省荆门市2023-2024学年高二上学期1月期末学业水平检测数学试题
2 . 在三棱锥
中,M是线段
的中点,
,
,
,
.
(1)证明:P在平面
内的射影O为
的垂心;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3735a467f788624fe63946e0da5b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fe75f967e8915c9124a5d4ac420a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c327b3e91d8bea53255d9308a952a276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827c7d9ca8f0e06a09bd37e930b3c3ee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/d44cbe49-473b-42e9-a1e4-0a171e6be968.png?resizew=156)
(1)证明:P在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
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解题方法
3 . 如图,在平面直角坐标系
中,点
,直线
,设圆C的半径为1,圆心在l上.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/5426adc8-1854-4d34-b385-3a24824b222a.png?resizew=147)
(1)若圆心C也在直线
上,过点A作圆C的切线,求切线的方程;
(2)若圆C上存在点M,使
,求圆心C的横坐标a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc878a5fd7b508cf817cbb65d3940547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db0a1cbf7b0ed76c443b953af8734d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/5426adc8-1854-4d34-b385-3a24824b222a.png?resizew=147)
(1)若圆心C也在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c1212804e6d784756d48083d166e8.png)
(2)若圆C上存在点M,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a464b0c729f294287d3d89119a585293.png)
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解题方法
4 . 已知椭圆
的离心率为
,
,
,
,
,设P为椭圆C上一点
的面积的最大值为
.
(1)求椭圆C的方程;
(2)当P在第三象限,直线
与y轴交于点M,直线
与x轴交于点N,求证:四边形
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9199b50dd0036be9b764c621d1d46f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87e24ea042ecf3f25150338e22b45b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374cdec65a41dc616f6f099551880d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
(1)求椭圆C的方程;
(2)当P在第三象限,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
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解题方法
5 . 甲、乙两人组成“上元队”参加猜灯谜比赛,每轮活动由甲、乙各猜一个灯谜,已知甲每轮猜对的概率为
,乙每轮猜对的概率为
.在每轮活动中,甲和乙猜对与否互不影响,各轮结果也互不影响.记事件
“甲第一轮猜对”,
“乙第一轮猜对”,
“甲第二轮猜对”,
“乙第二轮猜对”.
(1)求“上元队”在第一轮活动中仅猜对1个灯谜的概率;
(2)求“上元队”在两轮活动中,甲、乙猜对灯谜的个数相等且至少为1的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9fabbbe61a759e52ec975215e2e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a6d85799453899836bc34ad276ec80e.png)
(1)求“上元队”在第一轮活动中仅猜对1个灯谜的概率;
(2)求“上元队”在两轮活动中,甲、乙猜对灯谜的个数相等且至少为1的概率.
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6 . 设数列
的前n项和为
,
,则下列说法正确的是( )
![](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/e9ba984e922424ae65819c8a2bc27c64.png)
A.![]() |
B.当且仅当![]() ![]() |
C.![]() |
D.![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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7 . 已知平面
和平面
的夹角为
,
,已知A,B两点在棱上,直线
,
分别在这个二面角的两个半平面内,且都垂直于
.已知
,
,则
的长度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/b9557223-2fbf-4e9d-9b76-afdf84a76288.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b707f5ee4fbb2e637c65fbc6d8ed03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aabdde5c06a238f7623344f13755fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/b9557223-2fbf-4e9d-9b76-afdf84a76288.png?resizew=162)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
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8 . 已知数列
的首项
,且满足
.
(1)求证:数列
为等比数列;
(2)若
,求满足条件的最大整数n.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6545b8eca1c4223ed701a199a85683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7643e8b7aa32ebf299048417a94432dc.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2d452650bc21fc7ef50bf7ca7ebd4f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90021cb37adf08bdd61e96ac3d9cfc2.png)
您最近一年使用:0次
2024-02-28更新
|
1148次组卷
|
4卷引用:湖北省荆门市2023-2024学年高二上学期1月期末学业水平检测数学试题
湖北省荆门市2023-2024学年高二上学期1月期末学业水平检测数学试题(已下线)5.3.2 等比数列的前n项和(3知识点+8题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)四川省绵阳南山中学2024届高三下学期4月绵阳三诊热身考试文科数学试题四川省南充高中2023-2024学年高三下学期第十六次月考理科数学
解题方法
9 . 在流行病学中,基本传染数
是指在没有外力介入,同时所有人都没有免疫力的情况下,一个感染者平均传染的人数.
一般由疾病的感染周期、感染者与其他人的接触频率、每次接触过程中传染的概率决定,假设某种传染病的基本传染数
,平均感染周期为7天,那么感染人数由1(初始感染者)增加到3333大约需要的天数为( )(初始感染者传染
个人为第一轮传染,这
个人每人再传染
个人为第二轮传染……参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9b4a83b9aebebf29de0c4406ebf894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9b4a83b9aebebf29de0c4406ebf894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b17c923943b7c49d42ce4b36293f78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9b4a83b9aebebf29de0c4406ebf894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9b4a83b9aebebf29de0c4406ebf894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9b4a83b9aebebf29de0c4406ebf894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282724a3b2b45f1966a91389fdcedfcf.png)
A.42 | B.43 | C.35 | D.49 |
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10 . 在下列关于概率的命题中,正确的是( )
A.若事件![]() ![]() ![]() ![]() ![]() |
B.若三个事件![]() ![]() ![]() ![]() |
C.若事件![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若事件![]() ![]() ![]() ![]() |
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