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Introduction to Functions
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Function: A Special Relation
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Terms Related to Functions
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Domain and Range of a Function
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Even Functions and Odd Functions
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Identity Function and Constant Function
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Understanding Polynomial Functions
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Quadratic Polynomial Function
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Problems Related to Quadratic Functions
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Rational Functions
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Understanding the Modulus Function
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Properties of Modulus Function
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Problems on the Modulus Function
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Understanding the Signum Function
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The Greatest Integer Function
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Problems on the Step Function
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Fractional Part Function
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e: A Special Number
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The Exponential Function
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The Logarithm Function
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Properties of Logarithms – 1
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Properties of Logarithms – 2
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Problems on the Domain and Range of Logarithms
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Graph of Logarithmic Functions
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Problems Related to Logarithmic Functions
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What Is an Angle?
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Introduction to Trigonometric Functions
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Definitions of Trigonometric Functions
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Observations on the Definition
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Domain, Range and Graph of the Sine Function
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Domain, Range and Graph of the Cosine Function
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Comparing Sine and Cosine Functions
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Domain, Range and Graph of the Cosecant and Secant Functions
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Domain, Range and Graph of the Tangent and Cotangent Functions
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Problems on Trigonometric Functions – 1
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Problems on Trigonometric Functions – 2
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Finding the Trigonometric Values of Some Specific Angles
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Problems on Finding the Values of Trigonometric Functions
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Introduction to One-to-One and Onto Functions
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Properties of One-to-One Functions
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Methods to Find One-to-One Functions
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Problems on One-to-One and Onto Functions
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Understanding Composition of Functions
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Properties of Composite Functions
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Defining the Inverse of a Function
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Properties of Inverse Functions
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Problems on Composite and Inverse Functions
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Introduction to Inverse Trigonometric Functions
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Sine and Cosine Inverse Functions
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Tangent and Cotangent Inverse Functions
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Cosecant and Secant Inverse Functions
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Problems on Inverse Trigonometric Functions
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Transformations of Graphs – 1
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Transformations of Graphs – 2
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Problems on Transformations of Graphs – 1
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Problems on Transformations of Graphs
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Periodic Functions
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Properties of Periodic Functions
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Functional Equations
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Solving Non-standard Functional Equations
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Finding the Number of Functions
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Problems on Finding the Number of Functions
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Practice Questions (Set 1)
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Practice Questions (Set 2)
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Practice Questions (Set 3)
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Practice Questions (Set 4)
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Introduction to Permutations and Combinations
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The Fundamental Principle of Counting
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Examples on the Fundamental Principle of Counting
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The Meaning of n!
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Number of Arrangements – Permutations
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Properties of nPr and Examples
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Number of Selections – Combinations
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Properties of nCr and Examples
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Examples of Permutations and Combinations
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Permutations of Alike Objects
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The Classical Problem of Seating Arrangements
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Game of Words: Lexicography and Dictionary
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Game of Digits and Divisibility Concept
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Permutations and Combinations of Playing Cards
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Circular Permutation
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Distribution of Identical Objects Into Groups – Part 1
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Distribution of Identical Objects Into Groups – Part 2
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Distribution of Distinct Objects Into Groups
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Practice Questions (Set 1)
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Practice Questions (Set 2)
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Practice Questions (Set 3)
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Practice Questions (Set 4)
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Introduction to Binomial Theorem
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Factorial and ⁿCᵣ
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Derivation of Binomial Expansion
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Problems on Binomial Expansion
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General Term and Middle Term
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Problems on the General Term
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Finding the Term From the End in a Binomial Expansion
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Problems on the Middle Term
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Problems on the Term Independent of ‘x’
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Numerically Greatest Term and Numerically Greatest Coefficient
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Problems on the Numerically Greatest Term
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Counting Rational and Irrational Terms
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Divisibility Problems – Type I
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Divisibility Problems – Type II
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Divisibility Problems – Type III
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Use of Differentiation in Binomial Theorem
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Binomial Expansion for Negative Index
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Problems on Binomial Expansion for Negative Index
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Practice Questions (Set 1)
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Practice Questions (Set 2)
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Practice Questions (Set 3)
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Practice Questions (Set 4)
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