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(Prove) Two distinct lines cannot have more than one point in common.ġ. Given two distinct points, there exists one and only one line through them. Showing the relationship between axiom and theorem, for example: (Axiom)ġ. Euclid's method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. History - Geometry in India and Euclid's geometry. The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations. UNIT 3: COORDINATE GEOMETRY COORDINATE GEOMETRY Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. Focus on linear equations of the type ax + by + c=0. Introduction to the equation in two variables. Recall of linear equations in one variable. Verification of identities:Īnd their use in factorization of polynomials. Recall of algebraic expressions and identities. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Statement and proof of the Factor Theorem. Motivate and State the Remainder Theorem with examples. Constant, linear, quadratic and cubic polynomials. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)ĭefinition of a polynomial in one variable, with examples and counter examples. Recall of laws of exponents with integral powers. Rationalization (with precise meaning) of real numbers of the type 1/(a+b√x) and 1/( √x + √y) (and their combinations) where x and y are natural number and a and b are integers.ĥ. Definition of nth root of a real number.Ĥ. every point on the number line represents a unique real number.ģ. Explaining that every real number is represented by a unique point on the number line and conversely, viz. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Examples of non-recurring/non-terminating decimals. Rational numbers as recurring/ terminating decimals. Review of representation of natural numbers, integers, and rational numbers on the number line. CBSE Class 9 Mathematics Syllabus 2023-24ġ.