名校
解题方法
1 . 命题
:“
,
”的否定形式为______ ;若
为真命题,则实数
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3052ca3322167f67e7293383bb4271ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 函数
的定义域是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0513aafc91ffd421ec137ecc82414d4b.png)
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3 . 在
中,写出不满足命题“若
,则
”的一组
、
的值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2a8bf5e05a07c93a7104839fc21849.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afde09d82ae96f00c135732baee64776.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b883d9703a1deaf8dbc18097c6b8bb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b4908b37cf23de34d38ae7a0bff278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2a8bf5e05a07c93a7104839fc21849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afde09d82ae96f00c135732baee64776.png)
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4 . 奇函数
在区间
上单调递增,且其图象经过点
,则不等式
的解集为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2372f424431ce7b547a66b7d61d75421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e88ebfb5c0d6cce558b515be06404d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1f94ec61d2c0ac73ab60713351fe01.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知函数
,其中
,
.
条件①:函数
图象相邻的两条对称轴之间的距离为
;
条件②:函数
图象关于点
对称;
条件③:函数
图象关于
对称.
从条件①、条件②、条件③这三个条件中选择两个作为已知条件,求:
(1)函数
的最小正周期;
(2)函数
在单调递增区间;
(3)函数
的图象可否由函数
的图象经过图象变换得到?如果可以,请设计一系列的图象变换过程,如果不可以,请说明理由.
注:如果选择不同条件组合分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a1b51fc74390c262bc0bcaeb20369c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d440669c516d6dff0fedaf3eed41aca8.png)
条件①:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
条件②:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b2b096238bd6eac8cd1ab2c4348fb9.png)
条件③:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8973254e0eeb29a0add0e4677ce5337b.png)
从条件①、条件②、条件③这三个条件中选择两个作为已知条件,求:
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
注:如果选择不同条件组合分别解答,按第一个解答计分.
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6 . 若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d394016b9fecac73f38cbc4ff18dee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdc546857baeab9b2fbad110ddd56bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38dd8aad9cfb5e1fe2a45d80923f1571.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知函数
,
,
.
(1)当
时,判断函数
的奇偶性并证明;
(2)当
且
时,利用函数单调性的定义证明函数
在
上单调递增;
(3)求证:当
且
时,方程
在
内有实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cc9b1b321520eae2bf944a9c85c9ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(3)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a871ef7bf13de3e15489d65b57a3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99caed81bfb141d6e7dac8f6fe9db069.png)
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8 . 当药品
注射到人体内,它在血液中的残余量会以每小时25%的速度减少.
(1)按照医嘱,护士给患者甲注射了
药品
两小时后,患者甲血液中药品
的残存量为
,求
的值;
(2)另一种药物
注射到人体内,它在血液中的残余量会以每小时10%的速度减少.如果同时给两位患者分别注射
药品
和
药品
,请你计算注射后几个小时两位患者体内两种药品的残余量恰好相等.(第(2)问计算结果保留2位小数)
参考值:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)按照医嘱,护士给患者甲注射了
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7428057b4757de6d1d510712f01465e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55354a714cdf174cf4ebd43a2f041bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)另一种药物
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2baea0d7b4cae52246ff279a41e460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618c8bb0c6e025b11eeb7da738183d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
参考值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49dc2827f437b3a1e7cbc25c680093c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51988fef1f0ae3f710f36865834790e5.png)
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9 . 把长为
的细铁丝截成两段,各自围成一个正方形,那么这两个正方形面积之和的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b1fe1b971b780e443a9b13621611c5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 下列函数中是奇函数且在上单调递增的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-03-31更新
|
411次组卷
|
2卷引用:北京市延庆区2023-2024学年高一上学期期末考试数学试卷