解题方法
1 . 已知抛物线
,其准线方程为
.
(1)求抛物线
的方程;
(2)直线
与抛物线
交于不同的两点
,求以线段
为直径的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db0a1cbf7b0ed76c443b953af8734d0.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2 . 如图,在正四棱柱
中,
为棱
上的一个动点,给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/4d20d730-2c99-4233-9d32-582e23bf5b1b.png?resizew=119)
①
;
②三棱锥
的体积为定值;
③存在点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
平面
;
④存在点
,使得
平面
.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94b82dd1753348cf763d36f6941155c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/4d20d730-2c99-4233-9d32-582e23bf5b1b.png?resizew=119)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9c3f0236e1f9416d34c12272e8598b.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95944bab519692fe8551a7557ab58a09.png)
③存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c1acd7da8817385417e1dff25bfe25.png)
④存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c1acd7da8817385417e1dff25bfe25.png)
其中所有正确结论的序号是
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解题方法
3 . 如图,在四棱锥
中,
平面
,底面
为菱形,
分别为
的中点.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)若
,再从条件①、条件②这两个条件中选择一个作为已知.求二面角
的大小.
条件①:
;
条件②:
.
注:如果选择条件①和条件②分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.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/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac4ee9a98647379757a6f643fb73438.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/e8b24db6-9aad-4943-8f98-126bdf572477.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442ddcea3d1c0c8536c091e0969eee60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b8df87ef099eae61bb07018f2ab335.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c383691e8d740830a865b12d66f7633.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3672e603d06c9186edd20cfc662d8dc.png)
注:如果选择条件①和条件②分别解答,按第一个解答计分.
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4 . 方程
表示的曲线是__________ ,其标准方程是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266ed8002a339746965afc42d6ba1dec.png)
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5 .
为直线
上一点,过
总能作圆
的切线,则
的最小值( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8041c797b98b834c70dbf7d1d4346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 甲、乙两个篮球队在4次不同比赛中的得分情况如下:
(1)在4次比赛中,求甲队的平均得分;
(2)分别从甲、乙两队的4次比赛得分中各随机选取1次,求这2个比赛得分之差的绝对值为1的概率;
(3)甲,乙两队得分数据的方差分别记为
,
,试判断
与
的大小(结论不要求证明)
甲队 | 88 | 91 | 93 | 96 |
乙队 | 89 | 94 | 97 | 92 |
(2)分别从甲、乙两队的4次比赛得分中各随机选取1次,求这2个比赛得分之差的绝对值为1的概率;
(3)甲,乙两队得分数据的方差分别记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a669412290af652fc6eb84909b9b2310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a639d13faa2e8ba41e49cd18fe5c7292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a669412290af652fc6eb84909b9b2310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a639d13faa2e8ba41e49cd18fe5c7292.png)
您最近一年使用:0次
2024-01-29更新
|
229次组卷
|
2卷引用:北京市石景山区2023-2024学年高一上学期期末考试数学试卷
解题方法
7 . 已知直线
,直线
.若
,则实数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a9c615ba94fe65108b130cc4244243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547c5b2a5e407bdbf9d85e8438a93bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
A.![]() | B.![]() | C.![]() | D.3 |
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8 . 在空间直角坐标系
中,点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a46b72ddcd17a1675af204176f50442.png)
A.直线![]() ![]() ![]() | B.直线![]() ![]() |
C.直线![]() ![]() ![]() | D.直线![]() ![]() |
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解题方法
9 . 函数
的定义域为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9932b65ef88d78b17d5647ce9f594d5.png)
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解题方法
10 . 已知集合
,集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5626980859ceb75c05de5bc39a8df3dd.png)
(1)当
时,求
;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98235f2fdcbec42d7e17661b4bd020a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5626980859ceb75c05de5bc39a8df3dd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a758c6686891c3f08ccd4b63f540a9b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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