23 Chapters

Mathematics Syllabus

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Basic Mathematics

Theory of Indices Linear Inequalities Properties of Modulus Function Properties of Logarithms Logarithmic Equations and Inequalities

Sets and Relations

Representation of Sets Types of Sets and Set Operations Cartesian Product of Sets Domain and Range of a Relation Types of Relations Equivalence Relations

Functions

Domain and Range of a Function Classification of Functions Even and Odd Functions Periodic Functions Composite Functions Inverse of a Function

Quadratic Equations

Solution of Quadratic Equations Relation Between Roots and Coefficients Nature of Roots Transformation of Equations Common Roots Maximum and Minimum Values of Quadratic Expressions Location of Roots

Sequence and Series

Arithmetic Progression (A.P.)Geometric Progression (G.P.)Harmonic Progression (H.P.)Arithmetic-Geometric Progression (A.G.P.)Relation Between A.M., G.M., and H.M.Sum of Special Series

Trigonometry

Trigonometric Ratios and Identities Trigonometric Functions of Compound Angles Multiple and Sub-multiple Angles Conditional Identities General Solution of Trigonometric Equations Properties of Triangles Heights and Distances

Inverse Trigonometric Functions

Principal Value Branches Domain and Range of Inverse Trigonometric Functions Properties of Inverse Trigonometric Functions Solving Inverse Trigonometric Equations

Straight Lines

Distance and Section Formulas Area of Triangle Slope of a Line Various Forms of Equations of a Line Angle Between Two Lines Distance of a Point from a Line Family of Lines Centroid, Incenter, Orthocenter, and Circumcenter

Circles

Standard and General Equation of a Circle Intercepts Made by a Circle Position of a Point with Respect to a Circle Equation of Tangent and Normal Length of Tangent and Chord of Contact Director Circle and Family of Circles Condition for Orthogonality

Conic Sections

Standard Equations of Parabola, Ellipse, and Hyperbola Foci, Directrices, and Eccentricity Parametric Equations Equation of Tangent and Normal Chord in terms of Midpoint Asymptotes of a Hyperbola Rectangular Hyperbola

Complex Numbers

Algebraic Operations on Complex Numbers Conjugate and Modulus Argand Plane and Polar Representation Euler's Form and De Moivre's Theorem Cube Roots and nth Roots of Unity Geometrical Applications of Complex Numbers

Permutations and Combinations

Fundamental Principle of Counting Factorial Notation Linear Permutations Circular Permutations Combinations and Selection Formation of Groups Derangement Principle

Binomial Theorem

Binomial Expansion for Positive Integral Index General Term and Middle Term Properties of Binomial Coefficients Greatest Term in Expansion Multinomial Theorem Binomial Theorem for any Index

Matrices and Determinants

Types of Matrices Algebraic Operations on Matrices Properties of Determinants Minors and Cofactors Adjoint and Inverse of a Matrix Solution of System of Linear Equations (Matrix Method and Cramer's Rule)

Limits, Continuity and Differentiability

Evaluation of Limits & L'Hopital's Rule Continuity at a Point and in an Interval Differentiability of a Function Relationship Between Continuity and Differentiability

Differentiation

Techniques of Differentiation Higher Order Derivatives Tangents, Normals and Rate Measure Monotonicity Maxima and Minima Mean Value Theorems

Indefinite Integration

Fundamental Integration Formulas Integration by Substitution Integration by Parts Integration using Partial Fractions Evaluation of Special Integral Forms

Definite Integration

Fundamental Theorem & Properties of Definite Integrals Newton-Leibniz & Reduction Formulas Definite Integral as a Limit of a Sum Area Bounded by Curves

Differential Equations

Order and Degree of a Differential Equation Formation of Differential Equations Variable Separable Method Homogeneous Differential Equations Linear Differential Equations Orthogonal Trajectories

Vector Algebra

Scalar and Vector Quantities Addition of Vectors Components of a Vector Scalar (Dot) Product Vector (Cross) Product Scalar Triple Product Vector Triple Product

Three Dimensional Geometry

Direction Cosines and Direction Ratios Equation of a Line in Space Angle Between Two Lines Shortest Distance Between Two Skew Lines Equation of a Plane Angle Between Two Planes Intersection of a Line and a Plane

Probability

Random Experiments and Sample Space Classical Definition of Probability Addition and Multiplication Theorems Conditional Probability Total Probability Theorem Bayes' Theorem Random Variables and Probability Distributions Binomial Distribution

Statistics

Measures of Central Tendency (Mean, Median, Mode)Measures of Dispersion Mean Deviation Variance and Standard Deviation