## Course Overview

### Class 12 Math Syllabus

#### 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
• Composition of function and invertible function

#### Inverse Trigonometric Functions

• Definition
• Range
• Domain
• Graphs of inverse trigonometric functions
• Properties of inverse trignometric functions

#### 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
• Noncommutativity 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

• 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

#### 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.

#### 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)
• Maximum and minimum value of function in closed interval

#### 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. • Geometric interpretation of indefinite integral
• Some properties of indefinite integrals
• Comparison between differentiation and integration

#### Applications of the Integrals

• Area under simple curves
• Concept of exponential and logarithmic functions.
• Area of a region bounded by curve and a line
• Area between two curves

#### Differential Equations

• Basic concepts
• Degree of a differential equation
• General and particular solutions of differential equation
• Formation of differential equation whose general solution is given
• Methods of solving first order, first degree differential equation
• Homogeneous differential equation
• Solutions of linear differential equation of the type: dy/dx + py = q, where p and q are functions of x or constants. dx/dy + px = q, where p and q are functions of y or constants.

#### Vectors

• Some basic concepts
• Types of vectors
• Multiplication of vector by a scalar: components of vector
• Vector joing two points
• Section formula
• Product of two vectors: scalar product and application
• Scalar triple product
• Cross product of two vectors

#### Three – dimensional Geometry

• Direction cosines and direction ratios of a line
• Equation of a line in space
• Angle between two lines
• Shortest distance between two lines
• Plane: equation of plane in normal form
• “Equation of a plane perpendicular to a given vector and passing through a given point”
• “Equation of plane passing through three non collinear points”
• “Intercept form of equation of line and a plane passing throug through the intersection of two given plane”
• Coplanarity of two lines
• Angle between two planes
• Distance of a point from a plane
• Angle between a line and a plane

#### Linear Programming

• Linear programming problem and its mathematical formulation
• Graphical method of solving linear programming problem
• Different types of linear programming problem

#### Probability

• Conditional 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

### Reference Books for Class 12 Math

• CBSE Chapter wise Solutions – Mathematics (Class 12) by Hemant Malhotra
• CBSE Examination Mathematics : 15 Sample Question Papers (Class 12) by Prem Kumar
• Mathematics (Class – XII) by NCERT
• Problems Plus In IIT Mathematics by A Das Gupta
• Senior Secondary School Math 12 by R. S. Aggarwal
• Solutions of Objective Mathematics: Solutions of Exercises and Chapter Tests by Dhanpat Rai

### NCERT Solutions for Class 12 Maths

Get 100 percent accurate NCERT Solutions for Class 12 Maths  explained by expert Science teachers. We provide step by step solutions for the questions given in Class 12 Maths textbook as per CBSE Board guidelines from the latest NCERT book for Class 12 Maths.

### CBSE Class 12 Maths,  Notes

Get Notes prepared by Ex-IITIan for CBSE Class 12 Maths

### Concept Maps and Important Questions Class 12 Maths

These concept maps and important questions will help you to revise the concepts quickly and get good marks. Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers of Class 12 Maths Chapter Relations & Functions are provided here for . I will help you online for any doubt / clarification.

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### CBSE Class 12 Maths R D Sharma and R S Agarwal Solution

Chapter wise solution of RD Sharma and R S Agarwal for Class 12 solved by Expert Mathematics Teachers (Ex- IITians) on https://www.IITianAcademy.com as per NCERT (CBSE) Book guidelines. All chapter wise RD Sharma Class 12 Maths Exercise Questions with Solutions to help you to revise the complete Syllabus make you ready for next Big thing – IIT JEE exam.

### Past Many Years Question Chemistry Class 12 Solutions

Past Many Years Question Papers Solutions for Class 12 Maths are provided here with simple step-by-step explanations. These solutions for are extremely popular among Class 12 students for Chemistry .  These Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Past Many Years Question Papers Book of Class 12 Maths Chapters are provided here for . I will help you online for any doubt / clarification.

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