Mathematics · Class 12

1. Relations & Functions

"Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions."

2. Inverse Trig Functions

"Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions."

3. Matrices

concept/notation/order/types · transpose · symmetric & skew-symmetric · addition · multiplication · scalar multiplication + simple properties · non-commutativity · non-zero matrices with zero product (order 2) · invertible matrices + uniqueness of inverse

4. Determinants

determinant up to 3×3 · minors · cofactors · area of triangle · adjoint · inverse · consistency/inconsistency · solving 2–3 variable systems (unique solution) by matrix inverse

5. Continuity & Differentiability

continuity · differentiability · chain rule · composite functions · derivatives of inverse trig · implicit functions · exponential/log · logarithmic differentiation · parametric forms · second-order derivatives

6. Applications of Derivatives

rate of change · increasing/decreasing · maxima and minima (first derivative test geometric, second derivative test as provable tool) · simple problems

7. Integrals

integration as inverse of differentiation · substitution · partial fractions · by parts · the ten listed special forms · Fundamental Theorem of Calculus (without proof) · basic properties of definite integrals and their evaluation

8. Applications of Integrals

area under simple curves — lines · circles/parabolas/ellipses (standard form only)

9. Differential Equations

definition · order and degree · general/particular solutions · separation of variables · homogeneous first-order first-degree · linear DE of dy/dx + py = q and dx/dy + px = q

10. Vector Algebra

vectors/scalars · magnitude/direction · direction cosines and ratios · types · position vector · negative · components · addition · scalar multiplication · position vector of a point dividing a segment in a given ratio (section formula) · scalar (dot) product · vector (cross) product — definition · geometrical interpretation · properties · application

11. Three-Dimensional Geometry

direction cosines/ratios of a line joining two points · Cartesian and vector equation of a line · skew lines · shortest distance between two lines · angle between two lines. Lines only — no planes.

12. Linear Programming

terminology · graphical method for two variables · feasible/infeasible regions (bounded/unbounded) · feasible/infeasible solutions · optimal feasible solutions (up to three non-trivial constraints)

13. Probability

conditional probability · multiplication theorem · independent events · total probability · Bayes' theorem. No random variable /distribution /mean /variance /binomial.