名校
解题方法
1 . 设矩形
的周长为
,其中
,如图所示,把它沿对角线
对折后,
交
于点
.设
,
.
![](https://img.xkw.com/dksih/QBM/2021/1/23/2642258797117440/2643643998265344/STEM/2043228943754950ad88f1d77487c8a6.png?resizew=199)
(1)将
表示成
的函数,并求定义域;
(2)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9199a3de404cb13ae7710f73db5c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2633a6f46b0847158eebb05c743561aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422714c2c8f13e3a0e9d30b1a0164b9.png)
![](https://img.xkw.com/dksih/QBM/2021/1/23/2642258797117440/2643643998265344/STEM/2043228943754950ad88f1d77487c8a6.png?resizew=199)
(1)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da7bcea5a45eeae211f5851f12a7517.png)
您最近一年使用:0次
2021-01-25更新
|
415次组卷
|
2卷引用:江苏省常州市教育学会2020-2021学年高一上学期期末数学试题
2 . “
”期间,某电商店铺
的活动为:全场商品每满
元返
元的优惠券,可叠加使用(比如,买
元的东西,可用两张优惠券,只需付
(元),其中
是不大于
的最大整数);另一电商店铺
的活动为:全场所有商品
折销售,如果单品件数超过
件,超出的每一件单品均享受
元/件的会员价,其中
为商品原价,
为超出的单品件数优惠店,
为常数,已知若购买某种商品
件,则第
件商品享受
折优惠.此外,在店铺优惠后,扣除店铺优惠后余下的金额,电商平台全场还提供每满
元减
元的优惠,可叠加使用(比如,店铺
原价
元的一单,最终价格是
(元)).
(1)小明打算在店铺
买一款
元的耳机和一款
元的音箱,是下两单(即耳机、音箱分两次购买)划算?还是下一单(即耳机、音箱一起购买)划算?
(2)小明打算趁“
”期间囤积某生活日用品至少
件,且预算不超过
元,该生活日用品两个店铺售价均为
元/件,小明打算全部在
店铺购买或者全部在
店铺购买,试分别计算在两家店铺购买多少件该生活日用品平均价格最低,最低平均价格分别是多少.(结果保留到小数点后两位)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d410e1a41e8b5eb3b250f52111bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b3779b4ea5477aebfe85113b0de1d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110e329d74716ab387dc602bb2b4f998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101d979a3432f77ae10fe6aae621bbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbddcdd55142662d6ff3a7d5a7ab3092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0b71b8d2c183154221f717ce09077b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0b71b8d2c183154221f717ce09077b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749082d415fedaedd79359ea0878ee14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba602bfa3a3ffb4fb43dc0f704a7f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b72ac611ae66b86761e080761d9aabc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf6be749959edcacf4c9d4a5ae8282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e777a20eaf4d7e451e2bb1c78ed196.png)
(1)小明打算在店铺
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f38eed00a39aae5a7232b72a4d3ed821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0ea43d65fc6a6bf339c60047941959.png)
(2)小明打算趁“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d410e1a41e8b5eb3b250f52111bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448aaa6640cb6ba29367c2204d8c9c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c7539ed297ea63b9ace6f5cc58ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
解题方法
3 . 2023年10月13日,中国花卉人的盛会—CFIC2023中花大会在无锡隆重开幕,“万物生花·惊艳绽放”,人在花中走,犹如画中游.某企业非常重视花卉苗木产业的培育和发展,决定对企业的某花卉进行一次评估,已知该花卉单棵售价为15元,年销售10万棵.
(1)据市场调查,若该花卉单棵售价每提高1元,销售量将相应减少5000棵,要使销售的总收入不低于原收入,问:该花卉单棵售价最多定为多少元?
(2)为了扩大该花卉的影响力,提高年利润,企业计划对该花卉进行种植技术革新和营销策略改革,预计在2024年投入
(
)万元作为技改费和宣传费用,单棵花卉的售价定为
元,预估单棵种植成本为
元,其销售量
的函数关系近似为
万棵,另每年需额外支出固定成本
万元,试问:该企业投入多少万元技改费和宣传费时,可获得最高利润,最高利润多少万元(利润=销售额-成本-技改费和宣传费).
(1)据市场调查,若该花卉单棵售价每提高1元,销售量将相应减少5000棵,要使销售的总收入不低于原收入,问:该花卉单棵售价最多定为多少元?
(2)为了扩大该花卉的影响力,提高年利润,企业计划对该花卉进行种植技术革新和营销策略改革,预计在2024年投入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0184fbac1a83242694b5357a1ed0a0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8bec66fde2dfe6efe4845a2dce176ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2607fee30515a61d1bd9aa73c9108828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e593828316139a54019e352dec883f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff1994863b2c3857e0c224d9456b901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66577f4cb97c0d2a213ab1a9a02d1324.png)
您最近一年使用:0次
解题方法
4 . 用清水漂洗衣服上残留的洗衣液,对用一定量的清水漂洗一次 的效果作如下假定:用1个单位量的水可洗掉衣服上残留洗衣液质量的一般,用水越多漂洗效果越好,但总还有洗衣液残留在衣服上.设用
单位量的清水漂洗一次 后,衣服上残留的洗衣液质量与本次漂洗前残留的洗衣液质量之比为函数
,其中
.
(1)试规定
的值,并解释其实际意义;
(2)根据假定写出函数
应该满足的条件和具有的性质,并写出满足假定的一个指数函数;
(3)设函数
.现有
(
)单位量的清水,可供漂洗一次,也可以把水平均分成2份后先后漂洗两次,试确定哪种方式漂洗效果更好?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72120311e5ee5b259439c87d5e9d599.png)
(1)试规定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
(2)根据假定写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f337750a735f32189b7e91fb83941e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55b6e9dc54f67d7f25e9aa6a65e14a5.png)
您最近一年使用:0次