Fundamentals of Mathematics

This topic covers concepts, such as Number System, Natural Numbers, Whole Numbers, Integers, Notation of Natural Numbers, Notation of Whole Numbers, Notation of Integers, Rational Numbers, Notation of Rational Numbers, Equivalent Rational Numbers, Co-prime Numbers, Subsets in Number System, Rational Numbers between Two Rational Numbers, Method of Means to Find Rational Numbers between Two Rational Numbers, Rational Numbers between Two Rational Numbers using Common Denominator, Infinite Rational Numbers between Two Rational Numbers & Number Line etc.

This topic covers concepts, such as Irrational Numbers, Need for Irrational Numbers, Transcendental Numbers, Real Numbers, Unique Representation of Real Numbers on Number Line, Representation of Irrational Numbers on Number Line, Representation of Square Root of Two on Number Line, Representation of Square Root of Three on Number Line & Square Root Spiral etc.

This topic covers concepts, such as Decimal Representation of Real Numbers, Representation of Rational Numbers as Terminating Decimal, Representation of Rational Numbers as Non-terminating Decimal, Decimal Representation of Irrational Numbers, Approximation of Sqrt(2), Irrational Numbers between Two Rational Numbers, Non-Terminating Decimals, Non Terminating Recurring Decimals, Non Terminating Non Recurring Decimals, Representing Real Numbers on the Number Line by Successive Magnification Method & Decimal Representation of Rational Numbers etc.

This topic covers concepts, such as Algebraic Operations on Real Numbers, Basic Properties of Algebraic Operations on Real Numbers, Sum of Rational and Irrational Numbers, Difference of Rational and Irrational Numbers, Multiplication of Rational and Irrational Numbers, Division of Rational and Irrational Numbers, Sum of Two Irrational Numbers, Difference of Two Irrational Numbers, Multiplication of Two Irrational Numbers, Division of Two Irrational Numbers & Rationalisation of Denominator etc.

This topic covers concepts, such as Surds, Radical Sign, Laws of Exponents for Real Numbers, Square Root of a Real Number, nth Root of a Real Number, Algebraic Identities Involving Square Roots, Algebraic Identities of Square Roots of Real Numbers, Quotient Property of Square Roots & Laws of Exponents for Real Numbers when Exponents Are Fractions etc.

This topic covers concepts, such as Linking Ratio with Fractions, Commensurable and Incommensurable Quantities, Case of Incommensurable Quantities, Duplicate Ratio, Compounded Ratio, Componendo and Dividendo Rule, Series of Equal Fractions, Cross Multiplication Method, Ratio of Greater and Lesser Inequality, Comparing Two Quantities by Division/by Taking the Ratio, Applications of Ratios in Real Life, Understanding Proportion as Equality of Ratios, Direct Proportion, Inverse Proportion, Continued Proportion & Comparison Between Algebraical and Geometrical Definitions of Propositions etc.

This topic covers concepts, such as Proportionality Constant, Joint Variation & Inverse Variation etc.

This topic covers concepts, such as Algebraic Solutions of Linear Inequalities in One Variable, Linear Inequalities, Quadratic Expressions Which are Always Positive/Negative, Solution of Simple Quadratic Inequalities, Solution of Rational Inequalities Involving Quadratic Expressions, Wavy Curve Method & Irrational Inequalities etc.

This topic covers concepts, such as Partial Fractions of f(x)/g(x) Where Both f(x) and g(x) are Polynomials, Partial Fractions of f(x)/g(x) When g(x) Contains Irreducible Factors, Partial Fractions of f(x)/g(x) When g(x) Contains Non–repeated Linear Factors & Partial Fractions of f(x)/g(x) When g(x) Contains Repeated and/or Non-repeated Linear Factors etc.

This topic covers concepts & such as Exponential Series etc.

This topic covers concepts & such as Logarithmic Series etc.