Class XI: Mathematics Syllabus (Units 1–10)
Focus on algebra, geometry, and foundational calculus.
| Unit | Topic | Key Subtopics |
|---|---|---|
| 1 | Sets, Relations, and Functions | Sets (operations, types); relations (equivalence); functions (types, composition, inverse); binary operations. |
| 2 | Complex Numbers and Quadratic Equations | Complex numbers (Argand plane, modulus, argument, polar form); quadratic equations (roots, coefficients); algebra of complex numbers (conjugates, equations with real coefficients). |
| 3 | Matrices and Determinants | Matrices (types, operations, transpose, symmetric/skew-symmetric); determinants (properties, minors, cofactors); inverse (adjoint method); applications (system of equations). |
| 4 | Permutations and Combinations | Fundamental principle; permutations (repetitions, circular); combinations; binomial theorem (general term, middle term); properties of binomial coefficients. |
| 5 | Mathematical Induction | Principle of induction; applications to sums, inequalities. |
| 6 | Binomial Theorem and Its Simple Applications | Binomial expansion (positive/negative exponents); general/middle terms; approximations. |
| 7 | Sequences and Series | Sequences (arithmetic/geometric/harmonic); series (sum to n terms, infinite GP); AM-GM inequality. |
| 8 | Limits and Derivatives | Limits (algebraic/trigonometric, standard forms); continuity; derivatives (first principles, rules, chain rule); applications (tangents/normals, increasing/decreasing functions). |
| 9 | Coordinate Geometry | Straight lines (equations, distance, angle, concurrency); circles (equations, tangents); conic sections (parabola, ellipse, hyperbola—standard forms, foci, directrix, eccentricity, tangents). |
| 10 | Three Dimensional Geometry | Coordinates (direction cosines/ratios, lines, planes); distance between skew lines; shortest distance; angle between lines/planes; section formula; coplanarity. |
Class XII: Mathematics Syllabus (Units 11–16)
Emphasis on calculus applications, linear algebra, and probability.
| Unit | Topic | Key Subtopics |
|---|---|---|
| 11 | Relations and Functions | Relations (types); functions (one-one/onto, equivalence); inverse trigonometric functions (domain/range, principal values, properties). |
| 12 | Inverse Trigonometric Functions | Graphs; elementary properties; reduction formulae. |
| 13 | Continuity and Differentiability | Continuity/differentiability (polynomials/rational/trig/exponential/logarithmic); derivatives of implicit/composite functions; logarithmic differentiation; parametric forms; second-order derivatives; Rolle's/Lagrange's mean value theorems. |
| 14 | Applications of Derivatives | Rate of change; tangents/normals; increasing/decreasing/monotonicity; maxima/minima (first/second derivative tests); approximations; simple problems (errors, marginal cost). |
| 15 | Integrals | Indefinite integrals (basic forms, substitution, partial fractions, trig); definite integrals (properties, fundamental theorem); integration by parts; reduction formulae. |
| 16 | Applications of Integrals | Area under curves (bounded regions, between lines/parabolas); area between curves. |
| 17 | Differential Equations | Order/degree; general/particular solutions; formation; variable separable/homogeneous/linear first-order; applications (population growth, decay, mixtures). |
| 18 | Vector Algebra | Vectors (types, addition, scalar/vector products); projection; dot/cross products; scalar triple product; applications (geometry). |
| 19 | Three Dimensional Geometry | Direction cosines/ratios; lines/planes (equations, intersections, angles, coplanarity); shortest distance between skew lines. |
| 20 | Linear Programming | Objective function; feasible/non-feasible regions; graphical method; different objective types. |
| 21 | Probability | Random experiments; events (types, axioms); probability (conditional, multiplication/Bayes' theorem); independent events; random variables (Bernoulli, binomial distribution—mean/variance). |