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Here is the CBSE Class 12 Maths Syllabus
CLASS XII
(Total Periods 240)
UNIT I: RELATIONS AND FUNCTIONS
- Relations and Functions (Periods 15)
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.
- Inverse Trigonometric Functions (Periods 15)
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.
UNIT II: ALGEBRA
- Matrices (Periods 25)
Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
- Determinants (Periods 25)
Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
UNIT III: CALCULUS
- Continuity and Differentiability (Periods 20)
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of exponential, logarithmic functions.
Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.
- Applications of Derivatives (Periods 10)
Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
- Integrals (Periods 20)
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts. Evaluation of simple integrals of the following types and problems based on them
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
- Applications of the Integrals (Periods 15)
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)
- Differential Equations (Periods 15)
Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type –
UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
- Vectors (Periods 15)
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar,
position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation,properties and application of scalar (dot) product of vectors, vector (cross) product of vectors
- Three-dimensional Geometry (Periods 15)
Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Angle between two lines,
Unit V: Linear Programming (Periods 20)
Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Unit VI: Probability (Periods 20)
Multiplications theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem. Random variable and its probability distribution, mean of random variable.
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