2022年人教A版数学必修五1.1.2《不等式与不等关系》导学案 .pdf

名师精编优秀教案高中数学必修 5 1.1.2 不等式与不等关系导学案姓名:班级:组别:组名:【学习目标】1感受在现实世界和日常生活中存在着大量的数量关系，了解不等式（组）的背景.2知道不等式的一些基本性质.3、二次函数、一元二次方程与一元二次不等式解集的关系.【重点难点】重点：1、不等式的基本性质.2、一元二次不等式的解法.难点：1、一元二次不等式的解法.2、理解二次函数、一元二次方程与一元二次不等式解集的关系.【知识链接】20XX年经济危机风暴继续在世界各国漫延，我国的房地产业受到很大的冲击，20XX年 8月深圳房价20570 元/2m，而到了10 月房价低于19680 元/2m，这三个月内平均降价的百分比是多少？你能列出不等式求解吗？【学习 过程】阅读课本第72 页至第 73 页的内容，去刻画客观事物的基本数量关系，尝试回答以下问题：知识点 1:不等关系与不等式基本性质问题 1完成课本第74 页练习 1、2，并举出几个现实生活中与不等式有关的例子.问题 2不等式的基本性质：性质 1：对称性abba?性质 2：传递性,ab bcac?性质 3：可加性abacbc?+性质 4：可乘性,0ab cacbc?性质 5：加法法则,ab cdacbd?+性质 6：乘法法则0,0abcdacbd?性质 7：乘方法则0(,2)nnababnN n?纬性质 8：开方法则0(,2)nnabab nN n?纬名师精编优秀教案练习：1、比较22xax-与2223aa-的大小(,)a xR?点拨：可用作差法比较大小，解题步骤：作差?分解因式或作差?确定符号?判断大小阅读课本第76 页至第 77 页的内 容，尝试回答以下问题：知识点 2:一元二次不等式的解法问题 1、从课本第77 页的图 3.2-2 可知，一元二次方程的根就是二次函数的零点.问题 2观察图3.2-2知：当x?，函数位于x轴上方，此时y 0，即25xx-0.当x?，函数位于y轴下方，此时y 0，即25xx-0.问题 3、从以上问题1、2 中可知观察函数图像可获得不等式解集问题 4、如何确定一元二次不等式20(0)axbxca+或20(0)axbxca+的解集.练习：解不等式28150 xx-+223xx-点拨：首先判断其所对应的一元二次方程判别式的符号，求根，然后根据不等号的方向及二次项函数的符号写出解集，这是解一元二次不等式的基本方法.知识点 3:一元二次不等式与二次函数及一元二次方程之间的联系.文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 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ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8名师精编优秀教案24bacD=-0D 0D=0D 的图像20(0)axbxca+=的根20(0)axbxca+的解集20(0)axbxca+解集知识点 4:一元二次不等式及可转化为一元二次不等式的指、对、分数不等式的解法例 1、求不等式24410 xx-+的解集问题 1、先求方程24410 xx-+=的根，再根据二次函数2441yxx=-+的图像写出解集问题 2、你能归纳求解一般一元二次不等式的过程吗？请试一试例 2、解不等式201xx-+问题 1、若0ab，则 只需a与b同号，即00abb?，则分式不等式201xx-+可转化为：问题 2、尝试写出本题的完整过程例 3、求解不等式2lg()lg(3)xxx+-文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 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ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8名师精编优秀教案点拨：利用对数函数单调性脱去对数符号时，必须使原不等式中的所有真数均大于零，而不仅仅是变形后的最简不等式中的真数大于零【基础达标】A1、解不等式22150 xx-221xx-222xx.C3、解不等式222306xxxx+-+C4定义在(1,1)上的奇函数()f x在定义域上式减函数，且2(1)(1)0fafa-+-，求a的取值范围.D5、若不等式20 xpxq+的解集为|12xx-的解集【小结】【当堂检测】若已知二次函数()yf x=的图像过原点，且有1(1)2f?，3(1)4f，求(2)f-的范围.【课后反思】本节课我最大的收获是我还存在的疑惑是我对导学案的建议是文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 ZJ8X5Y5M2P8文档编码:CZ4H6D8M5U1 HZ8M6G4Y2O7 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