# Class 12 Syllabus

## Course Structure

Maths Syllabus for Class 12 (2016-17)

Three Hours Max. Marks -100

 Unit Topic Marks I. Relations and Functions 10 II. Algebra 13 III. Calculus 44 IV. Vectors and 3D Geometry 17 V. Linear Programming 6 VI. Probability 10 Total 100

#### 1. Relations and Functions

• Types of relations: reflexive, symmetric, transitive and equivalence relations.
• One to one and onto functions, composite functions, inverse of a function.
• Binary operations.

#### 1. Matrices

• Concept, notation, order, equality, types of matrices, zero and identity 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 and existence of non-zero matrices whose product is the zero matrix.
• Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse.

#### 2. Determinants

• Determinant of a square matrix (up to 3 x 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 using inverse of a matrix.

#### 1. Continuity and Differentiability

• Continuity and differentiability, derivative of composite functions, chain rule, derivatives 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 forms. Second order derivatives.
• Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

#### 2. Applications of Derivatives

• Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals.
• Use of derivatives in approximation, maxima and minima.

#### 3. 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.
• Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).
• Basic properties of definite integrals and evaluation of definite integrals.

#### 4. Applications of the Integrals

Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses Area between any of the two above said curves (the region should be clearly identifiable).

#### 5. Differential Equations

• 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 solutions of homogeneous differential equations of first order and first degree.
• Solutions of linear differential equation of the type.

#### 1. 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, scalar triple product of vectors.

#### 2. 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.
• Angle between (i) two lines, (ii) two planes, (iii) a line and a plane, distance of a point from a plane.

#### Linear Programming

• Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming problems.
• Mathematical formulation of L.P. Problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

#### Probability

• Conditional probability, multiplication theorem on probability
• Independent events, total probability, Baye’s theorem, Random variable and its probability distribution, mean and variance of random variable.
• Repeated independent (Bernoulli) trials and Binomial distribution.