名校
1 . 平面直角坐标系中
,设点
是线段
的
等分点,其中
.
时,试用
表示
;
(2)当
时,求
的值;
(3)当
时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c26ad9deaf1c845754137638bb4e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa963c9dbb012bb08c2fdf5e5e41034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c941130c5d1166ced3b09aa0c883b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c12f9c428675ab178fc31e01f4334ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349eef3a3e97e2718ed5e77f313a4292.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ea0392d4bd0374c8a2b12a355e4655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60f5e90b85f837727d1148b18b9a0db.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec5d76db9bd05547932966c9913dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554b87fd0258955a65d55b1daf41eac0.png)
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2 . 设
.
(1)当
时,用函数单调性的定义证明:函数
在区间
上是严格增函数.
(2)①根据a的不同取值,讨论函数
在区间
上零点的个数;
②若函数
在区间
(k为正整数)上恰有7个零点,求k的最小值及此时a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14696ba10834f2d6b8891bf80abd0c79.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301605e86e5a5e61a65c91cd3dd8b77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)①根据a的不同取值,讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d6a66a015ddd2a8076f35ed191927.png)
②若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7f465e11dcb6a1cf9b4cf111f7b249.png)
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3 . 已知函数
的部分图象如图所示.
的解析式与单调增区间;
(2)若将
的图象向右平移
个单位,再向上平移1个单位得到
的图象,写出
图象的对称中心的坐标,并求当
时,
的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6309e18f51f43800c0a16205c6a491b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31a8b7f6d3b664b2c9bae09c3a6f884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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解题方法
4 . 已知函数
在
时取得最大值,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f6d4796986a8943ced3b085f8b9394.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fae022680cd3df914cec0d2fb7a12af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19099ff9ce1b01be72e4535e600aeb63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f6d4796986a8943ced3b085f8b9394.png)
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名校
解题方法
5 . 设
为锐角,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10ac0e2a8707c0d8914949912c87369.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b22d6e7e4223111b9974e825ddf6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10ac0e2a8707c0d8914949912c87369.png)
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6 . 已知
,下列结论错误的个数是( )
①若
,且
的最小值为
,则
;②存在
,使得
的图像向右平移
个单位长度后得到的图像关于
轴对称;③若
在
上恰有7个零点,则
的取值范围是
;④若
在
上单调递增,则
的取值范围是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234d723094aea93152142d5a7b6bb80a.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4b8f430bc9c87dd4633b8aff127532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05a467ddaa138590b3b56615c2c42a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439963be2791e40927a406aa74c233d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bccd6a6e85bdf500218a3e75b31f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e8577af5e97ed7b25c42f23c826d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7afbd154d5f993012b880e4e0c7f9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d6d8f1ce4eb43c61849cea0b4d72d8.png)
A.1 | B.2 | C.3 | D.4 |
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解题方法
7 . 设
,若对任意的
,都存在
,使得
成立,则
可以是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae470980d6e3b53c65b9d42d1f011c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef85b287d0fc9611ac7ba4bade11d864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57045228fec057c04c8a9a3423ee9d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2014d34387ba31955241a88aa2c252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
8 . 对于实数
,用
表示不超过
的最大整数,例如
.已知
,则下列3个命题中真命题的个数为__________ .
(1)函数
是周期函数;
(2)函数
的图像关于直线
对称;
(3)方程
有2个实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d23555720f4938189847b3531bd7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2297ab933ad7b37e272c0ac367f150d.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec25b105130d71d3d529524671b6218.png)
(3)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f277209e43e8881f3b0ec4b1bc0df082.png)
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解题方法
9 . 已知
,且
,则点
在第__________ 象限.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca599151dae2ca77bd53af8b38b69684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9faccebbd12ce0332647b3ba6d2474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f42664269cd3e00de2e4dd8d02e886.png)
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解题方法
10 . 若
为锐角,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207b77aa3cf9351cf7ee25827f0688fd.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9da049c686ff81df5d6645ef51e993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207b77aa3cf9351cf7ee25827f0688fd.png)
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