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1 . 如图,圆锥
的底面圆半径为1,侧面积为
,一只蚂蚁要从
点沿圆锥侧面爬到
上的
点,且
,则此蚂蚁爬行的最短路径长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf1f865bafd4a820406d336d99f8091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dfd76585cf7eece74fdd50acefd1ada.png)
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292次组卷
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2卷引用:云南省曲靖市部分学校2023-2024学年高一下学期6月联考数学试题
2 . 把白菜、萝卜、西红柿、土豆及黄瓜五种不同的蔬菜放到三个不同的菜篮子中,每个菜篮子至少放一种且最多放两种蔬菜,则不同的放法种数为____________ (用数字作答).
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3 . 已知
的展开式中
项的系数为
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6df371dce7cd2d464270768d344fbf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1480672ec92c4698aac745b029ad8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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4 . “杨辉三角”揭示了二项式展开式中的组合数在三角形数表中的一种几何排列规律,如图所示,则在第10行中最大数为___________ .
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解题方法
5 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18ac2817c37f1e8ceaf0b2ad0719945.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c73c1ef3fc6763dbfb042719abaa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18ac2817c37f1e8ceaf0b2ad0719945.png)
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6 . 已知平面向量
的夹角为
,且
,
,则
在
方向上的投影向量为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b901cc29a51575d40f331c7b9b1e696f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29276b43a2950ed71f0f9629a35dfa74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2085ac9183250abd57ce2fccc477677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
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7 . 设集合
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1336d38741aab2255a35c26612bbd7cc.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a3d44c61aba49b2adfc31ec2655775a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcb16be70f3e091a71d9f0f21724c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1336d38741aab2255a35c26612bbd7cc.png)
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解题方法
8 . 在
中,
是
的中点,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7590a22611f3935d8e32eac956c2a4c1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7590a22611f3935d8e32eac956c2a4c1.png)
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解题方法
9 . 设
为常数,
是定义在
上的奇函数,当
时,
,若
对一切
成立,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead5b2a29f2459bbe384ee62ed998385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4392aee4827eea380055c2f3df1f7420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 过三点
的圆的标准方程是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd209afb481cfc83f2284ec87b53fb0.png)
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