Mathematics Term II Syllabus for 2022 

Class 12 Maths Term II will consist of 1 paper. The  paper will be subjective in nature and consist of 40 marks.

Unit-III: Calculus

Integrals

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

Applications in finding the area under simple curves, especially lines, parabolas; area of circles /ellipses (in standard form only) (the region should be clearly identifiable).

Differential Equations

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential
equations of first order and first degree of the type:

dy+ py = q, where p and q are functions of x or constant.
dx

Unit-IV: Vectors and Three-Dimensional Geometry

Vectors

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

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Distance of a point from a plane.

Unit-VI: Probability

Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution.

CBSE Class 12 Mathematics: Important Topics

The important topics of class 12 maths are provided below:

Relations and Functions (20 Periods)

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one andonto functions, composite functions, inverse of a function. Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions, Elementary properties of inverse trigonometric functions

Matrices (25 Periods)

Concept, notation, order, equality, sorts of matrices, zero and unit matrix , transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non Commutativity of multiplication of matrices 

Determinants (25 Periods)

Determinant of a matrix (up to three x 3 matrices), minors, cofactors and applications of determinants find the world of a triangle. Adjoint and inverse of a square matrix.  solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Continuity and Differentiability (20 Period)

Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric Second order derivatives. 

Applications of Derivatives (10 Periods)

Applications of derivatives:  increasing/decreasing functions, tangents and normal, 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 topic also as real-life situations).

Integrals (20 Periods)

Integration as an inverse process of differentiation. Integration of a spread of functions by substitution, by partial fractions and by parts, Evaluation of straightforward integrals of the subsequent types and problems supported integral

Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.

Applications of the Integrals (10 Periods)

Applications find the world under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

Differential Equations (15 Periods)

Definition, order and degree, general and particular solutions of a equation . Solution of differential equations by method of separation of variables

Vectors (15 Periods)

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 some extent , negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of some extent dividing a line segment during a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors

Three-dimensional Geometry (15 Periods)

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane.  Distance of a point from a plane.

Linear Programming (20 Periods)

Introduction, related terminology like constraints, objective function, optimization, differing types of applied mathematics (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded), feasible and infeasible solutions, optimal feasible solutions (up to 3 non-trivial constraints).

Probability (30 Periods)

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, variate and its probability distribution.