Types of sets, Union and intersection, Venn diagrams

Types of relations, Equivalence relation, Reflexive, Symmetric, and Transitive relations

Domain and range, Types of functions, Composition and inverse of functions

Algebra of complex numbers, Conjugate and modulus, Argand plane representation

Nature of roots, Sum and product of roots, Solving equations in complex numbers

Types of matrices, Addition and multiplication of matrices, Transpose and inverse of matrices

Properties of determinants, Cofactor and adjoint, Applications in solving linear equations (Cramer’s rule)

Basics of counting, Arrangements and selections

Factorial notation, Circular permutations, Restricted permutations

Selection of objects, Properties of combinations

Pascal’s Triangle, Binomial coefficients, General term, Expansion properties

Arithmetic Progression (AP), Geometric Progression (GP), Sum of n terms, Harmonic Progression (HP)

Distance formula, Section formula, Area of a triangle

Different forms of equations, Slope and intercepts, Angle between two lines

Equation of a circle, Tangent and normal, Chord properties

Standard equations of Parabola, Ellipse, Hyperbola, Foci, Directrix, Eccentricity

Definition, Relation between direction cosines

Equation of a line passing through a point, Angle between two lines

General form, Normal form, Distance from a point to a plane

Basic identities, Sin, Cos, Tan and their reciprocal relations

Applications of trigonometry in real-life problems

Principal values, Graphs, Properties of inverse functions

Basic logic, Contrapositive, Converse and Inverse

Measures of dispersion, Mean, Median, Mode, Variance, Standard deviation

Classical probability, Bayes’ theorem, Probability distributions

Definition, L’Hôpital’s Rule, Left-hand and Right-hand limits

Continuity of a function, Properties of continuous functions

Derivative as a rate of change, Differentiation rules, Mean value theorems

Basic integration formulas, Integration by substitution, Integration by parts

Properties, Fundamental Theorem of Calculus, Area under curves

Order and degree, Formation of equations, Solution of first-order differential equations

Definition and types, Addition and scalar multiplication of vectors

Dot product, Cross product, Applications in geometry

Proof by induction, Application in sequences and divisibility.

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