解题方法
1 . 已知函数
.
(1)若
,写出不等式
的解集;
(2)从下列条件中只选出一个条件作答,使得函数
在
上有最小值,把选出的条件填在横线上,并写出
的单调区间及最小值;__________.(若选择的条件没有最小值,则本小题不得分)
①
;②
;③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
(3)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0377ee50123c2b689ae92f391ab5f387.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)从下列条件中只选出一个条件作答,使得函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69abe959988e4c8c0739f5857ccfb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
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2 . 某市有块三角形荒地,如图
所示,
(单位:米),现市政府要在荒地中开辟一块矩形绿地
,其中
点分别在线段
上,若要求绿地的面积不少于7500平方米,则
的长度(单位:米)范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab57c924a89e206d7831452f93795f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927456b0989846a2f1573844bbaa2105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e661d825b7a6061e4d26fe5c53df73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/18/cc6e2d1b-0b00-4db1-9fe6-bd8e42e70a75.png?resizew=127)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-10-17更新
|
241次组卷
|
2卷引用:北京市育才学校2023-2024学年高一上学期10月月考数学试题
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3 . (1)解关于x,y的方程组![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee94cad924f3bde7a583545b6ac84012.png)
(2)已知
和
是关于x,y的方程组
(k为参数)的两组不同实数解.
求证:①
,
;
②
;
③
(其中
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee94cad924f3bde7a583545b6ac84012.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3396ead2a01ebd1d6134732541008a7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a03b0e1c4de970668548ebb944fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494c830fbe4b161a0d1506c1aaf15cfb.png)
求证:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda10b954abfc6bcd2fa0fe54536bcfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa675d90df61bdb59aa45a3654c6a71.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d28790c9a69068d3ce4caafae10a967.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681683ea78209722151377053b34d082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2851fd014aec602364532b264691c271.png)
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4 . 证明:
(1)“
”是“
有两个不相等实数根”的充分不必要条件;
(2)设集合
,对集合A中的每一个
,不等式
均成立的一个必要不充分条件为
.
(1)“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6803e06223269e79138ac240d2d2f57f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c714411bfd70c6e1629da44953c590.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3a8ec8d0fc97bbbb2e81ed9e4600a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38052c45891d59e55514a7794c74d47b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ab6b598834b7cca86ed338dfbeea929.png)
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5 . 请同学们补全下面两个关于x的不等式的解答过程.
(1)
;
解:令
,
令
,计算
,
当
时,即
时,方程
不存在实根;
画
草图,
不等式的解集为______.
当
时,即______时,方程
的两根为______.
画
草图,
不等式的解集为______.
当
时,即______时,方程
的两根为______.
画
草图,
不等式的解集为______.
(2)
.
解:令
(*),
则方程(*)的三个根从小到大排列分别为
______;
______;
______.
把三个根分别标在x轴上,并完成表格,
请根据表格写出不等式
的解集.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458cbcd84273373e0a0bdab32ad42bad.png)
解:令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4317c59a6012372bc027d7badec24f.png)
令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06295591972865ce5a2fafb1427aa707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c70eef4e278303db019587ee2cc20f.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc39e3f9688bc77675ffdf0dd79da142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6232dc74b15e4acb0ac3482a1cbe6a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06295591972865ce5a2fafb1427aa707.png)
画
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925d9d720033e5e20561eb5f0722ecef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/b7500d30-d563-4620-8611-50152041ac5f.png?resizew=165)
不等式的解集为______.
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2b0eb6b8e515c616b5cdd4c37fefc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06295591972865ce5a2fafb1427aa707.png)
画
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925d9d720033e5e20561eb5f0722ecef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/f7cb6ca2-bf56-448e-896a-91b0659d6ed3.png?resizew=164)
不等式的解集为______.
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda1e6337ff7355c2fe9c19f9d619f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06295591972865ce5a2fafb1427aa707.png)
画
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925d9d720033e5e20561eb5f0722ecef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/3bdfb626-c867-473d-bcff-8423f5c61714.png?resizew=166)
不等式的解集为______.
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef1d654789c54f96acda1437cffb865.png)
解:令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8fa5322900d260782795939a4085c3.png)
则方程(*)的三个根从小到大排列分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e92f14fb20f920f88dcad2ccd1d53f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dad5a12f34bed0da0de93beae0eaa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7ad31dd3397f7d2830182a8d309289.png)
把三个根分别标在x轴上,并完成表格,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/6/9af896b0-08b8-4ac2-980e-9da2035e8cbd.png?resizew=271)
x的取值范围 | ||||
|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef1d654789c54f96acda1437cffb865.png)
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解题方法
6 . 已知________.
(1)解不等式
;
(2)若
的解集为R,求实数b的取值范围.
从下面条件①、条件②中任选一个,补充在上面的横线上作为已知,并作答.
①
的最小值是a;
②不等式
的解集是
.
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de9db115080b62ceb32d39f890b6d8f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c93a5df4808c014f0b4aeffefb3d05e.png)
从下面条件①、条件②中任选一个,补充在上面的横线上作为已知,并作答.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222d0ba81e913f1289c10e4783ce35db.png)
②不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce9a91332440ae5eb3495cbc4cbd64b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b05849c5aa6777c65d0035f08ad96e.png)
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7 . (1)不等式
的解集为______ ;
(2)
的值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3540d7cc7301c292e67aa24c57325cd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c987f63ed2a2b13fdb97af94808992.png)
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8 . 为宣传二十大,校宣传部计划设计一块面积为
的矩形海报.海报中间区域(图中空白处,记为矩形
)讲述党史故事.中间区域四周用宽为
的创意花纹进行装饰,设矩形海报与
平行的边长度为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/4a13c0a1-9642-4c41-84f4-71204ace3b96.png?resizew=169)
(1)若要求中间区域的一边
至少为
,且
比
至多长
,求
的取值范围;
(2)将中间区域的面积
表示为长度
的函数,在满足(1)的条件下,求
的最大值,并给出此时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a890a6467d817d6023af0b867486bc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da9429d1238ea3e979dd0de49dd2b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d0abc998ec2b780be50b061c3de05c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/4a13c0a1-9642-4c41-84f4-71204ace3b96.png?resizew=169)
(1)若要求中间区域的一边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3763241c95fae6af69a0f0485a1c6f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b66a88def6dd5747774ec95f3dd00f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)将中间区域的面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4acdc56ac9c45cba804fe2b8885580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5583e4c483558731bf8f2c6a6c3a3c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 . 若
,并且
,则
由小到大的顺序排列是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db099509012f0edaadf555324473fe85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bfa58b0f54825a3ba17ea96dd298459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0224cd2988d2cc1251543b2060190732.png)
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