名校
解题方法
1 . 已知函数
,
,
.当
时,
的图象至少向右移动________ 个单位长度可以得到
的图象;若
使
对
恒成立,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2bb7354fb64b7bf5ae232a93747955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18012858f9d9bf65a117d28af01a4df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05a467ddaa138590b3b56615c2c42a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b46e325d705925a44b2f8b17a5fafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574d748e941b906f56315827fdab099e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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解题方法
2 . 如图,在棱长为4的正方体
中,
为棱
的中点,
,过点
的平面截该正方体所得的截面为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8cabbfce2c5459fa4e35d737c52ca41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b861c59576112ec3a816c73a23bba541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
A.不存在![]() ![]() ![]() |
B.当平面![]() ![]() ![]() |
C.线段![]() ![]() |
D.当![]() ![]() |
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名校
解题方法
3 . 如图所示,在边长为3的等边三角形
中,
,且点P在以
的中点O为圆心、
为半径的半圆上,若
,则下列说法正确的是____________ .
①
②
的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb03865bc5bbd5acdf68260d6a1454f6.png)
③
最大值为9 ④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de75a2e98f7c16a0be0ccbb8fd4b72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81889370d45239939a36de53c4445d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95d146bdcc8ac0a256c12696e9b9826.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc5c4b886a48affa3e6103f7e4c2bfd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb03865bc5bbd5acdf68260d6a1454f6.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ccdceb57c6df84b42b1b9032a636e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de75a2e98f7c16a0be0ccbb8fd4b72b.png)
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名校
解题方法
4 . 已知函数
,则方程
在区间
上的所有实根之和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d114a9b8c3264711e25db9515aec56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9c64ba837387d640de4b8e2191b1b5.png)
A.2 | B.4 | C.6 | D.8 |
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5 . 已知向量
,
,定义运算
,同时定义
.
(1)若
,求实数
的取值集合;
(2)已知
,求
;
(3)已知定义域为
的函数
满足
为奇函数,
为偶函数,且
时,
,是否存在实数
,使
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ec6dba44a83ae69146c26a2eec325c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66717aa3e7a771427c1d4433c77a5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4817c9821c3c5268e665a3ebcfe2e9cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153f8261059b286d175e53adb666d0bd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e993a236a70e4a094013a28c07079f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237b1a6f3e6ee0ef92b4aef7bffe58ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5285f8cfbab2baf73267d7649a58ac.png)
(3)已知定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91340ce6d32493c33527a32c2d448896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffde73ff7d3cd5125eb8d8a17a9f01c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994dcf841d356002fcebaed37497013c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de03de9f4bea859252f0158b32acf378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb0b435b3f1a00ee1df0d02384d6e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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名校
解题方法
6 . 高斯是德国著名数学家,近代数学奠基者之一,享有“数学王子”称号,他和阿基米德、牛顿并列为世界三大数学家,用其名字命名的“高斯函数”为:设
,用
表示不超过
的最大整数,则
称为高斯函数,例如
,
. 已知函数
,函数
,则下列4个命题中,其中正确结论的选项是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1dffa925101e9e19720ee7295133d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be209b4634a4169d727f9fac198acce3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bbc6c3245906550c7641ce0471ac202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c583c96c958b9653dd9b66f7dbd7079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9bcf0effd771e30ab3399d2fcd9fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bed8d403d5e4e232c8ac65ed87af5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259118296ced0cf932f15d08c3feee77.png)
A.函数 ![]() |
B.函数 ![]() ![]() |
C.函数 ![]() ![]() |
D.方程 ![]() |
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7 . 在等腰
中,
,若点M为
的垂心,且满足
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e4a2df58a236c20df5df0d29a466c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f23a8277574896dd8c46d744851b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d54d09ef825305de83671448a3dea21.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
8 . 在
中,
,
,点
是边
的中点,点
为线段
的中点,则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c974c20de0e31685d64e26522969e2f.png)
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9 . 已知函数
,
(1)若
,函数
在区间
上单调递增,求
的取值范围;
(2)若
,
,求函数
在
上的值域;
(3)若
,函数
在
内没有对称轴,求
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d58ebc68f8481976fdcbf3535c4527.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590e165e407098fcac9f871beb047dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a908cff3963ed5281930402c853b0b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcee772e6187ac31d7f8d69b0487000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d47dbed3333b180fce58a6d9e440f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d47dbed3333b180fce58a6d9e440f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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名校
解题方法
10 . 在
中,
,
,
.点
为
所在平面上一点,满足
(
、
且
).
(1)若
,用
,
表示
;
(2)若点
为
的外心,求
、
的值;
(3)若点
在
的角平分线上,当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d81d732204a3c2384a27606f858677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec7ea9a9bf46fe5dfe7bdb028289bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3276b5e12396fc4753eb3f8254f9fa68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d100f6eb4bfc0b0191c12d5ab35d0d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03698c9b972ce8c2a569195d00d0312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbaeae7045ad94158cdf5ae97073bc17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34bf00aeba15bce2cdee8ab487388dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ce17f8f08bc11bd78885c80223466c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21306b0138363c1cb99ee8c1ecc5a486.png)
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