名校
1 . 已知
、
是异面直线,给出下列结论:
①一定存在平面
,使直线
平面
,直线
平面
;
②一定存在平面
,使直线
平面
,直线
平面
;
③一定存在无数个平面
,使直线
与平面
交于一个定点,且直线
平面
.
则所有正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
①一定存在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe623bd25476a860fa4c2a179b81464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
②一定存在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764b59b077bda19d131095b454942d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
③一定存在无数个平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
则所有正确结论的序号为( )
A.①② | B.② | C.②③ | D.③ |
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2 . 下列结论:
“直线l与平面
平行”是“直线l在平面
外”的充分不必要条件;
若p:
,
,则
:
,
;
命题“设a,
,若
,则
或
”为真命题;
“
”是“函数
在
上单调递增”的充要条件.
其中所有正确结论的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c512c047783c07da1d4f4455a4033ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876959b9f90f2379cf3d0927a8e31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bded4e08a5c75fd82f1868c9f4c5b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3719d2ca3c5877bafc18f58c1fdf4b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4690a619a829c621fb7cd1e98df13f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdf492b48e5da4602f2bde199deae4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bc9e7fe40882f2f79bcf8d87a7f031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67773252101fb3704fdac88b5f3f1bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bea9391c115618bb84a7aa3da8a242d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60dbdf0c087ab6be44595a5ca285acbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd594e99f82b7736c44e18b2721e607f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10baec9d907f3ccb3f64ad3de53a589d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74269cfb503e736149e1ac3165fcbafa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89e1ee3b8e2751f354aa5ab7135c75b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b3de9d6894829d7de515544cd6cd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8fe868d4152f599a9ae5a0dae150cb0.png)
其中所有正确结论的序号为
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3 . 历史上,许多人研究过圆锥的截口曲线.如图,在圆锥中,母线与旋转轴夹角为
,现有一截面与圆锥的一条母线垂直,与旋转轴的交点
到圆锥顶点
的距离为
,对于所得截口曲线给出如下命题:
①曲线形状为椭圆;
②点
为该曲线上任意两点最长距离的三等分点;
③该曲线上任意两点间的最长距离为
,最短距离为
;
④该曲线的离心率为
.其中正确命题的序号为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/8bbb22a4-8c3f-49fd-b3cf-cf5375c6fc4e.png?resizew=153)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
①曲线形状为椭圆;
②点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
③该曲线上任意两点间的最长距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b87ecc72d8130ea6b4fe0512837345b.png)
④该曲线的离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/8bbb22a4-8c3f-49fd-b3cf-cf5375c6fc4e.png?resizew=153)
A.①②④ | B.①②③④ | C.①②③ | D.①④ |
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4 . 下列关于直线
和平面
的四个命题中:
(1)若
,
,则
;(2)若
,
,
,则
;
(3)若
,
,
,则
;(4)若
,
,则
.
所有正确命题的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15bd315b801f71bc30b8d772098614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba83980a38c5e1fe4be841bc8a51d1d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048e833e0c0995d4cf039ed30ba38b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e13118bd6b2a419a18992b1877dbed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfefa5d15ec71994fa5aa91ea10d870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfefa5d15ec71994fa5aa91ea10d870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e29247633f040a72a8ea6b733a5e37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238f509e26564449419d6375a0894d45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048e833e0c0995d4cf039ed30ba38b56.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/687b2fd8d6280e26f623c73c68454d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c4e97ef0d612e8ecc334d838e53ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac84eb9ece2e7e8d12fb884ce206156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfefa5d15ec71994fa5aa91ea10d870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfefa5d15ec71994fa5aa91ea10d870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb083c827a7fffbff90916dea20570f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526985744fe472beef406c56b531ef85.png)
所有正确命题的序号为
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5 . 下列说法中所有正确命题的序号是__________ .
①“
”是“
”成立的充分非必要条件;
②
、
,则“
”是“
”的必要非充分条件;
③若一个命题的逆命题为真,则它的否命题一定为真;
④设等比数列
的前
项和为
,则“
”是“
”成立的充要条件.
①“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200849ce71f53c0321506e27de437b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0973815df3264c67f94eccde1c279ea.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5f0d374837655cc286d326305da36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc03d6198a94cfdf5ba108fd4ae668e2.png)
③若一个命题的逆命题为真,则它的否命题一定为真;
④设等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179513ce80436471efbe1d9b31735f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f00dae44d94b0499bd40de73772b4b.png)
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