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# Mathematics Class 12th for CBSE

5,000

## Description

#### The entire syllabus has been divided into logical sections for better understanding of the students. All these sections will be covered sequentially as listed below.

 Chapter 1: Relations & Functions Relations Functions – Types of Function –  composite functions – Inverse of a function Chapter 2: Inverse Trigonometric Functions Introductions Inverse Trigonometric Functions Graphs of inverse trigonometric function Elementary properties of inverse trigonometric functions Chapter 3: Matrices Algebra of Matrices Existence of non-zero matrices whose product is the zero matrix Proof of the uniqueness of inverse , if exist Concept of Elementary row and column operations Chapter 4: Determinants Determinants Properties of Determinants Adjoint and Inverse of a Matrix Solution of Simultaneous Linear Equations Chapter 5: Continuity Continuity Differentiability Differentiation Higher Order Derivatives Mean Value Theorems Chapter 6: Applications of Derivatives Derivative as a Rate Measurer Differentials, Errors and Approximations Tangents and Normals Increasing and Decreasing Functions Maxima and Minima Chapter 7: Integrals Indefinite Integrals Definite Integrals Integration as limit as sum Chapter 8: Application of Integrals Area using vertical strips and horizontal strips Area between two curves Chapter 9: Differential Equations Degree of differential equations Formation of differential equations solution of differential equations Methods of solving first order first degree differential equation Variable separable differential equation Homogeneous differential equation Linear differential equation Applications of differential equations Chapter 10: Algebra of Vectors Algebra of Vectors Scalar Or Dot Product Vector or Cross Product Chapter 11: Three Dimensional Geometry Scalar Triple Product Direction Cosines and Direction Ratios Straight line in space The plane Chapter 12: Linear programming Solution of given LPP Mathematical formulation LPP & Unbounded Chapter 13: Probability Conditional theorem Multiplication theorem Total theorem of probability Bayes Theorem probability Mean and variance of a random variable Binomial Distribution

## Syllabus 2021-22

### The course will cover the full syllabus as under :

Unit-I: Relations and Functions

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.

1. Inverse Trigonometric Functions

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

Unit-II: Algebra

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. On[1]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).

1. Determinants

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors 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

1. Continuity and Differentiability

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 forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

1. 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 (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).

1. 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.

1. Applications of the Integrals

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

1. 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:

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

d????/d???? + px = q, where p and q are functions of y or constants.

Unit-IV: Vectors and Three-Dimensional Geometry

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.

1. 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.

Unit-V: Linear Programming

1. Linear Programming

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 (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI: Probability

1. Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Binomial probability distribution.

## Teacher Info

Ved Sir has 11 year of experience in teaching Mathematics. He has helped many students to get very impressive grades and to get selected into renowned institutes. Ved Sir has M.Sc. in Mathematics and B.Ed. Degrees. Some of his key achievements are –

• Teaching at Ables Education,Talwandi, Kota, Rajasthan.
• 100% results in Board exams for 11th and 12th grade students taught by him.
• Served as Vice Principal at KP School for 3 years.
• Has been examination head for many year and has very good understanding of CBSE exam pattern.