Unit-I: Sets and Functions | Sets | Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets, Subsets of a set of real numbers (intervals), Universal set, Venn diagrams, Union and Intersection of sets, Difference of sets, Complement, Properties of Complement. |
| Relations & Functions | Ordered pairs, Cartesian product of sets, Number of elements in Cartesian product, Cartesian product of reals, Definition of relation, pictorial diagrams, domain, co-domain, range, Function as a special type of relation, Real-valued functions and their types (constant, identity, polynomial, etc.), Sum, difference, product, and quotients of functions. |
Unit-I: Functions | Trigonometric Functions | Positive and negative angles, Measuring angles in radians/degrees, Conversion, Trigonometric functions via unit circle, Identity sin²x + cos²x = 1, Signs of trigonometric functions, Domain/range of trigonometric functions, Graphs, Expressing sin(x±y), cos(x±y), Deduction of trigonometric identities. |
Unit-II: Algebra | Complex Numbers & Quadratic Equations | Need for complex numbers (√−1), Solving quadratic equations, Algebraic properties of complex numbers, Argand plane. |
| Linear Inequalities | Linear inequalities, Algebraic solutions in one variable, Representation on the number line. |
| Permutations & Combinations | Fundamental principle of counting, Factorial n (n!), Permutations and combinations, Derivation of nPr and nCr, Simple applications. |
| Binomial Theorem | Historical perspective, Binomial theorem for positive integral indices, Pascal’s triangle, Simple applications. |
| Sequence and Series | Arithmetic Mean (A.M.), Geometric Progression (G.P.), General term, Sum of n terms of a G.P., Infinite G.P. and sum, Geometric mean (G.M.), Relationship between A.M. and G.M. |
Unit-III: Coordinate Geometry | Straight Lines | Review of 2D geometry, Slope of a line, Angle between two lines, Equations of a line (various forms), Distance of a point from a line. |
| Conic Sections | Circles, Ellipse, Parabola, Hyperbola, Standard equations and properties, Degenerated cases (point, line, pair of intersecting lines). |
| Introduction to 3D Geometry | Coordinate axes, Coordinate planes, Coordinates of a point, Distance between two points in three dimensions. |
Unit-IV: Calculus | Limits and Derivatives | Concept of Derivatives (rate of change), Limits (polynomials, rational, trigonometric, exponential, and logarithmic functions), Derivatives (sum, difference, product, quotient, and trigonometric functions). |
Unit-V: Statistics and Probability | Statistics | Measures of Dispersion: Range, Mean deviation, Variance, Standard deviation for ungrouped/grouped data. |
| Probability | Events, Occurrence of events, 'Not', 'And', 'Or' events, Exhaustive events, Mutually exclusive events, Set-theoretic probability, Probability of events ('not', 'and', 'or'). |
