1 . 已知函数
,则
的值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c36520e5715681c64bf7a4bd31a176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383acb6637f314601906b2b617c823bc.png)
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名校
2 . 冰雹猜想又称考拉兹猜想、角谷猜想、
想等,其描述为:任一正整数x,如果是奇数就乘以3再加1,如果是偶数就除以2,反复计算,最终都将会得到数字1如给出正整数5,则进行这种反复运算的过程为5→16→8→4→2→1,即按照这种运算规律进行5次运算后得到1.若从正整数6,7,8,9,10中任取2个数按照上述运算规律进行运算,则至少有1个数的运算次数为奇数的概率为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5307c068845c65410cb30291d62ec2.png)
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3 . 如图,2024年元宵节在浙江桐乡凤凰湖举行“放孔明灯”活动.为了测量孔明灯的高度,在地上测量了一根长为200米的基线
,在点
处测量这个孔明灯的仰角为
,在
处测量这个孔明灯的仰角为
,在基线
上靠近
的四等分点处有一点
,在
处测量这个孔明灯的仰角为
,则这个孔明灯的高度![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a548e8a2e2205f2faa87e25180a083.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ec007c9c7ce7e13af3ca8b84c64ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc0c3626d9b2c9cc92403e99e727912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c0b52fdca650c96f803556a514b08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a548e8a2e2205f2faa87e25180a083.png)
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解题方法
4 . 已知平面向量
,
,
不共线,且两两所成角相等,若
,
,
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7bf0d709033bd16591a75a514c21c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4acc71d9fbe05cb8cb98e0f6cf19a474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fac4f178f5c15ce56117b1bc855e8c.png)
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5 . 若复数
满足
(其中
是虚数单位),则复数
的共轭复数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9c3d509e77d6a7e4874302308c2aba.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb62a6a6742580ea5360209b79dbdae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9c3d509e77d6a7e4874302308c2aba.png)
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6 . 已知向量
夹角为
,若对任意
,恒有
,则函数
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e09f672bb45167707574ab02a812de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d967e63a1bf0e3c07a26b09c4ff008a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494e6f063695a49c44972a8544870446.png)
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7 . 已知
是钝角三角形,角
的对边依次是
,且
,则边
的取值范围是______ .
![](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/2293e25112b028c10edbf063146ecb3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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8 . 已知
的面积为4,下图是
的直观图,已知
,
轴,过
作
轴于
,则
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac39f40f5d82bfb09d9dc5036fd4c531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56fa5cea6f5d8e2a8a898822deb09e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2653bcab817704ebe955db23485fd34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cfad1ba71a78d8f415335cde2f8c52.png)
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9 . 将4个不同的小球放入3个不同的盒子,每个盒子非空,则不同的放法有 _______ 种.
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10 . 已知椭圆
的右焦点为F,过坐标原点O的直线l与椭圆C交于M,N两点,点M位于第一象限,直线MF与椭圆C交于另外一点A,且
,若
,
,则椭圆C的离心率为 ____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39e618d8e11bd21c0eafdd7cb2db642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599f8583d8aafc84c867f5416e5138fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab7dbee93af2c2aa7ca0e52abbbda47.png)
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