Polynomials, Coordinate Geometry And Linear Equations

What you'll learn
√ Variables, constants, coefficients, terms and degrees of polynomials.
√ Degrees, equations, factors, zeroes of polynomials.
√ Zeroes and the 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.
√ 2D coordinate geometry, Mirror image.
√ Slope, Intercept, Inclination and equations of straight lines.
√ Point Slope formula.
√ Solving two linear equations graphically.
√ Distance formula and application of distance formula.
√ Internal section formula, external section formula, mid-point formula, point of trisection.
√ Deriving formula to calculate centroid, incentre, circumcenter, orthocenter and excentre of a triangle.
√ Derive a formula to calculate the area of a triangle from coordinate points of three vertices.
√ Condition of Collinearity.
√ Calculation of the area of the quadrilateral polygon from coordinate points of vertices.
√ Area of a plane enclosed by straight lines.
√ Interpolation and extrapolation method.
√ Solving word problems graphically.
√ Euler line.
√ Types of linear equations.
√ Methods of solving linear equations with one variable.
√ Single linear equation with two variables, their solution and applications.
√ 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 pair 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.
Requirements
Some basic concepts of geometry and number system.
Description
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.
Overview
Section 1: Introduction
Lecture 1 Introduction
Lecture 2 What is Polynomials
Lecture 3 Global Positioning System and Coordinate Geometry
Lecture 4 Euler Line
Lecture 5 Types of Linear Equations
Section 2: Polynomials
Lecture 6 Variables, constants, coefficients, terms and degrees of polynomials.
Lecture 7 Degrees of polynomials, polynomial equations, factors and zeroes of polynomials.
Lecture 8 Relation of zeroes with numerical coefficients of polynomials.
Lecture 9 Geometrical representation of polynomials, part 1.
Lecture 10 Geometrical representation of polynomials, part 2 and mathematical problems.
Lecture 11 Mathematical operations on polynomials.
Lecture 12 Remainder Theorem, Factor Theorem, Division Algorithm for polynomials.
Lecture 13 HCF , LCM and square root of polynomials.
Lecture 14 Problems on polynomials Level 1 part 1.
Lecture 15 Problems on polynomials level 1 part 2.
Lecture 16 Problems on polynomials Leve 2 part 1.
Lecture 17 Problems on polynomials Level 2 part 2.
Lecture 18 Case study 1, polynomials.
Lecture 19 Case study 2, polynomials.
Lecture 20 Case Study 3, polynomials.
Lecture 21 Assertion and reasoning-based questions, polynomials.
Section 3: Coordinate Geometry
Lecture 22 2 Dimensional coordinate geometry, mirror image of a point with respect to axes.
Lecture 23 Slope, intercept, inclination and equations of straight lines.
Lecture 24 Problems using point slope formula, part 1
Lecture 25 Problem using point slope formula, part 2.
Lecture 26 Solving two linear equations graphically, part 1.
Lecture 27 Solving two linear equations graphically, part 2.
Lecture 28 Distance formula and mathematical problem.
Lecture 29 Application of distance formula.
Lecture 30 Internal section formula.
Lecture 31 External section formula, middle point formula, point of trisection.
Lecture 32 Mathematical problem on section formula.
Lecture 33 Centroid, incentre.
Lecture 34 Incircle, Circumcenter, Circumcircle
Lecture 35 Orthocenter.
Lecture 36 Excentre, part 1.
Lecture 37 Excentre, part 2.
Lecture 38 Mathematical problem on Centre of triangle.
Lecture 39 Area of triangle, problem on area of triangle.
Lecture 40 Condition of collinearity, area of quadrilateral and polygon.
Lecture 41 Area of a plane enclosed by straight lines, Interpolation, extrapolation method.
Lecture 42 Solving mathematical problem by interpolation and extrapolation method.
Lecture 43 Solving word problem graphically.
Lecture 44 Euler line.
Lecture 45 Mathematical Problem level 1 part 1.
Lecture 46 Mathematical problems Level 1 part 2
Lecture 47 Mathematical problem level 2 part 1.
Lecture 48 Mathematical problem level 2 part 2.
Lecture 49 Mathematical problem level 2 part 3.
Lecture 50 Case Study 1, Coordinate geometry.
Lecture 51 Case study 2, Coordinate geometry,
Lecture 52 Case study 3, Coordinate geometry.
Lecture 53 Assertion and reasoning -based questions, Coordinate geometry.
Section 4: Linear Equations.
Lecture 54 Types of linear equations.
Lecture 55 Methods of solving linear equations with one variable.
Lecture 56 Cross Multiplication method, word problem of linear equation with one variable.
Lecture 57 Single linear equation with two variables, solution and application.
Lecture 58 Graphical representation linear equation with two variables, pair of lines.
Lecture 59 Pair of linear equations with two variables, methods of finding solvability.
Lecture 60 Types of pair of linear equation with two variables, inconsistent pair of lines.
Lecture 61 Consistent pair of linear equations with two variables.
Lecture 62 Dependent pair of linear equations, finding types of linear equations.
Lecture 63 Methods of solving pair of linear equations with two variables.
Lecture 64 Solving pair of linear equations with two variables by graphical method.
Lecture 65 Mathematical problems level 1.
Lecture 66 Mathematical problems level 2.
Lecture 67 Case study 1, Linear equations.
Lecture 68 Case study 2, Linear equations.
Lecture 69 Case study 3, Linear equations.
Lecture 70 Assertion and reasoning-based questions, Linear equations.
Section 5: Tests
Current middle school/high school students. Anyone who wants to learn algebra.

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