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所在平台: Udemy |
课程主页: https://www.udemy.com/course/polynomials-coordinate-geometry-and-linear-equations/
课程评论：没有评论
**课程总结：多项式、坐标几何与线性方程** 本课程旨在帮助学习者构建对多项式、线性方程和坐标几何等核心数学概念的坚实理解。课程内容深入浅出，旨在提升学习者的理解、应用和分析能力，以应对从基本运算到高阶思维的各类问题。 **课程亮点：** * **多元化教学法：** 采用布鲁姆认知目标分类学的不同学习层次，确保学习者能够深入掌握知识。 * **丰富的实践练习：** 包含大量数学问题、案例研究以及断言与推理题，教授如何将理论知识应用于解决现实生活问题。 * **全面深入的内容：** * **多项式：** 涵盖变量、常数、系数、项、次数、零点与因式，零点与系数的关系，几何表示，运算，余数定理、因式定理、除法算法，HCF、LCM和多项式求平方根。 * **坐标几何：** 介绍笛卡尔坐标系，点斜式、直线方程，两线性方程的图解法，距离公式、分点公式（内分、外分）、中点公式、三等分点公式。深入探讨三角形的重心、内心、外心、垂心和旁心坐标，以及利用坐标计算三角形、四边形和多边形面积的公式，共线性条件，插值与外插法，图解法解应用题，欧拉线。 * **线性方程：** 讲解线性方程的类型，一元一次方程的解法，二元一次方程的解法，二元一次方程的图解表示。重点讲解二元一次方程组的可解性判断（包括不相容、相容和相依方程组），以及解方程组的各种方法，包括图解法。 * **实际应用导向：** 通过案例研究和断言与推理题，帮助学习者将所学知识融会贯通，应用于实际问题的解决。 本课程是erequisite，为进一步学习更复杂的数学主题打下坚实基础。
If you want to build a strong concept in very important topics like Polynomials, Linear equations, and Coordinate Geometry, this course will be helpful for you. I tried to implement different learning levels of Bloom's Taxonomy to improve your understanding, application, and analysis capability to solve basic to higher-order thinking problems. I solved enough mathematical problems, some case studies and assertion and reasoning-based questions to show you how to solve real-life problems by applying your learning and knowledge.The topics you will learn are:Variables, constants, coefficients, terms, degrees, zeroes and factors of polynomials.Relation of zeroes with numerical coefficients.Geometrical representation of polynomials.Mathematical operations on polynomials.Remainder theorem, factor theorem, division algorithm for polynomials.HCF, LCM and square root of polynomials.Cartesian coordinate geometry.Point slope formula, equations of straight lines.Solving two linear equations graphically.Distance formula, Internal section formula, external section formula, mid-point formula, point of trisection.Coordinate point of centroid, incentre, circumcenter, orthocenter and excentre of a triangle.Derive a formula to calculate the area of a triangle, quadrilateral and polygon from the coordinate points of three vertices.Condition of Collinearity.Interpolation and extrapolation method.Solving word problems graphically.Euler line.Types of linear equations.Methods of solving a single linear equation with one variable.Method of solving a single linear equation with two variables.Graphical representations of a single linear equation with two variables.Pair of linear equations with two variables and methods to find their solvability.Types of linear equations with two variables- inconsistent, consistent and dependent pair of linear equations.Methods of solving a pair of linear equations with two variables.Solving a pair of linear equations with two variables by graphical method.Case studies of the polynomial, coordinate geometry and linear equation chapters.Assertion and reasoning-based questions for polynomial, coordinate geometry and linear equation chapters.
