解题方法
1 . 计算:
(1)
;
(2)求函数
的定义域.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdba66162f1db362d57038d6138fd1a4.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d52400df33b6bf2de776e679ab79fd.png)
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2 . (1)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f328740bf24bfa5307d5ba23cfaac1.png)
(2)已知
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f328740bf24bfa5307d5ba23cfaac1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d227c4e80e72eb343659193a06daff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e28564e8971ee3cd8deb50d1afab24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629abc79d5be8093ee40ef9f6eb19337.png)
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名校
3 . 按要求计算:
(1)分解因式:
;
(2)已知
,求
的值;
(3)
;
(4)已知
,求
的值.
(1)分解因式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfdb71089c581d4a65a944f18fcfc40.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ccf1328602bd22b09ca55faa023a3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac0218b480ef3eeec90ad04bdffb55f.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875e9e322ab55609bf86fbc632175bda.png)
(4)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80236b37de6f299b5ff05d1ff29850c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31f3398b18fc1b3285129af356f48e1.png)
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4 . 设
.当
时,
的值记为
;当
时,
的值记为
;…;当
时,
的值记为
.
(1)化简
,并计算
的值;
(2)若
,那么满足条件的正整数
共有多少个?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c50c7a6ce693e114b0ec7245ae32f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e583288ac625c357743cee940ba867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
(1)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe384602babc523297d4927d5503834.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc0d4d3d0d2e912d617830bc17bb1eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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21-22高一·湖南·课后作业
5 . 下表是中国近年来人口数据(不包括香港、澳门特别行政区和台湾省):
(1)在平面直角坐标系内标出这四个点,再把这些点连接成线;
(2)选择其中合适的两个点,建立一次函数模拟,用模拟函数预测2017年中国人口数;
(3)能否用“更好”的直线
来模拟这组数据的变化?也就是说,能否确定
,
的值,使式子
的值最小?(按如下步骤进行预测)
①化简S,使之成为字母
的二次三项式;
②当
取何值时(设为
),二次三项式S取最小值(设为
),这里
和
都应该是含字母
的式子,且
是字母
的二次三项式;
③求
的值
,使
取最小值;
④求出对应于上述
的
值;
⑤用一次函数
模拟数据的变化,用模拟函数预测2017年中国人口数.
(4)把所得到的两个预测数据和2017年中国实际人口数进行比较.
年份 | 2013 | 2014 | 2015 | 2016 |
人口数 | 13.61亿 | 13.68亿 | 13.75亿 | 13.83亿 |
(2)选择其中合适的两个点,建立一次函数模拟,用模拟函数预测2017年中国人口数;
(3)能否用“更好”的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e136e7637543c8ae92c8dcd55b31924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a6257593221fa41fec404fdaed0ac9.png)
①化简S,使之成为字母
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f562eb3c2a45d65cba066d712825a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f562eb3c2a45d65cba066d712825a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f562eb3c2a45d65cba066d712825a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
③求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f74901036e0163ee8f9e88e1d952aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f562eb3c2a45d65cba066d712825a5.png)
④求出对应于上述
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f74901036e0163ee8f9e88e1d952aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
⑤用一次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657439603ec9ae4dc349ceb40ccdd2f2.png)
(4)把所得到的两个预测数据和2017年中国实际人口数进行比较.
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21-22高一·湖南·课后作业
6 . 记
,
(
且
),写出
和
的具体表达式并化简.尝试说明这里的表达式和化简结果与对数的基本恒等式
和
的关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d76ee3b131ecd6aa1aacf7fb7b3eb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84518e68c9e73dee93a8a3cafce4d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df17d1b404651bf6dbc97b519d452e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3493c543f0eafc74f6a23e18869a6452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b84bc656ef4d2c8a195f5ca9a697728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/899f641f54f1563dd4b6d63c0b9a720c.png)
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21-22高一·湖南·课后作业
7 . 用计算器求值(结果精确到0.001):
(1)
;
(2)
;
(3)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d4b701e1ecf96f4af88b02f51bd48e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daee23d28b64f9cbf374be86f0eeeda9.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c14c41431abe9ae7ea91973b5392b8c.png)
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名校
8 . 如图,一质点在以O为圆心,2为半径的圆周上逆时针匀速运动,角速度为
,初始位置为
,
,x秒后转动到点
.设
.
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897254977765376/2901291588706304/STEM/dd9d2a5e-73df-4151-bc07-6c7ba9c932c2.png?resizew=176)
(1)求
的解析式,并化简为最简形式;
(2)如果曲线
与直线
的两个相邻交点间的距离为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a8e8037ab81db93b3f80e887ede647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e05d3ae5ff1fa8e8aa8451ef28651ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec550c01b4f075f22ab67f5e55ed5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7011feb19129e72f6fe8b56ec915d46.png)
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897254977765376/2901291588706304/STEM/dd9d2a5e-73df-4151-bc07-6c7ba9c932c2.png?resizew=176)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)如果曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f207bd173cac9d3fcabcae4687557a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4966e5af166b69a0a38a98abf555b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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2022-01-24更新
|
628次组卷
|
3卷引用:湖南省名校联考联合体2022-2023学年高一下学期入学考试数学试题