解题方法
1 . 有以下6个函数:①
;②
;③
;④
;⑤
;⑥
.记事件
:从中任取1个函数是奇函数;事件
:从中任取1个函数是偶函数,事件
的对立事件分别为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0865bfbdbed6158be8f799af53eeb2e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c9320d009a17deba67f208c7d8be8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcaf2bf2e03dd6d33e03b69c5a318b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4508929da7db1adb7cc7a70e91be543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94281abc10cdc81b129f685b79b60bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53b03386ed265ae10a1b62f99f1bbb9.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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3卷引用:河南省濮阳市2024届高三第三次模拟考试数学试题
2 . 已知函数
的最小正周期为
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6321349608ca05d80eea5f3e7afffbd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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解题方法
3 . 已知椭圆
的左、右顶点分别为
,上、下顶点分别为
,记四边形
的内切圆为
,过
上一点
引圆
的两条切线(切线斜率均存在且不为0),分别交
于点
(异于
).
(1)求直线
与
的斜率之积的值;
(2)记
为坐标原点,试判断
三点是否共线,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654e60a0749ca2875a6aad49c3a0ee42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e5d91f4f631c580c155eba8c92bda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea2cde209f39851e2674877d30e3e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e733a15f50fdde9ac81ac1ce6e863f.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898d3e920ab55020c4fb064963a139cc.png)
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4 . 已知函数
.
(1)如果
,求曲线
在
处的切线方程;
(2)如果对于任意的
都有
且
,求实数
满足的条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94136a5fcb9f6d52342f1a572c3d5b54.png)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba0cdede7f0a093df20271a6d2ea53c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d02059613da3797ae406925b6ee5b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c3319647314c3b6d82958a909acd2a.png)
(2)如果对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17af43cc460a6a7010d51a0c9403d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 如图所示,在四棱锥
中,
,
,
,
为正三角形.
在平面
上的射影
为
的外心(外接圆的圆心);
(2)当二面角
为
时,求直线
与平面
所成角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08062a925efb07c38a229b8628e3b41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d399d731913a563e291b817831a0c678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231b861d6d1f1d0b9f52b041cb40eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745e0525a41fe2e2a7739c75a942290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
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解题方法
6 . 已知数列
的各项都为正数,且其前
项和
.
(1)证明:
是等差数列,并求
;
(2)如果
,求数列
的前
项和
.
![](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/28237e10ec7133ec600fbd57ed2ec664.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4565e9a0c413851da65f5c44c7ba82a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
7 . 多年统计数据表明如果甲、乙两位选手在决赛中相遇,甲每局比赛获胜的概率为
,乙每局比赛获胜的概率为
.本次世界大赛,这两位选手又在决赛中相遇.赛制为五局三胜制(最先获得三局胜利者获得冠军).
(1)现在比赛正在进行,而且乙暂时以
领先,求甲最终获得冠军的概率;
(2)若本次决赛最终甲以
的大比分获得冠军,求甲失分局序号之和
的分布列和数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)现在比赛正在进行,而且乙暂时以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124656394b0674aa1266ba4760bc602f.png)
(2)若本次决赛最终甲以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1dcdac71e394e495d069f64e1f1ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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解题方法
8 . 已知
,且
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0e9b3dcb25156d84ba8f8f02ae1771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e327ba789cbab8832344298ef9506781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
9 . 如图,在
中,角
所对的边分别为
,已知
,
的平分线
交边
于点
边上的高为
边上的高为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ada871ccdbd83b6ccbddbcd84521bc.png)
__________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7330af1eaa4fbb442ebc7b47be6b6d7a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0d44899ceb7b3137a82f2498c6d9b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78bea1b93dcf0514f157720793da1a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383d609af37a655a531e3e7441cd123e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa9e9cc8d1a0e6846523986552693cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d287c4df5c0cac5a4931edb43b01d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ada871ccdbd83b6ccbddbcd84521bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7330af1eaa4fbb442ebc7b47be6b6d7a.png)
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10 . 抛物线
的焦点坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba1762f7706a7fef3b2e346125c6f09.png)
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