# Class 12 Mathematics

The syllabus of Class 12 Mathematics is arranged in the form of courses that can be accessed by the members through this page.

## 1. Relations and Functions

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### Relations and Functions Class 12 Maths – (Part – 1)

Empty Relations, Universal Relations, Trivial Relations, Reflexive Relations, Symmetric Relations, Transitive Relations, Equivalence Relations, Equivalence Classes, and Questions based on the above topics from NCERT Textbook, Board’s Question Bank, RD Sharma, NCERT Exemplar etc.

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### Relations and Functions Class 12 Maths (Part – 2)

One to one andonto functions, composite functions, inverse of a function.

## 2. Inverse Trigonometric Functions

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### Inverse Trigonometric Functions Class 12 Maths

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

## 3. Matrices

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### Matrices Class 12 Maths

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 (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).

12 Months members only...

### Matrices Class 12 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

## 4. Determinants

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### Determinants Class 12 Maths

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.

12 months members only

### Determinants Class 12 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

## 5. Continuity and Differentiability

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### Continuity and Differentiability Class 12 Maths

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.

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### Continuity and Differentiability (Derivative Assignments) Class 12 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

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### Continuity and Differentiability (Differentiability Assignment – 3) Class 12 Assignments

This course is based on the Assignment - 3 Differentiability by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

## 6. Application of Derivatives

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### Applications of Derivatives Class 12 Maths

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).

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### Applications of Derivatives Class 12 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

## 7. Integrals

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### Integrals Class 12 Maths

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. \int{\frac{dx}{x^2 \pm a^2}}, \int{\frac{dx}{\sqrt{x^2 \pm a^2}}}, \int{\frac{dx}{\sqrt{a^2 - x^2}}}, \int{\frac{dx}{ax^2+bx+c}}, \int{\frac{dx}{\sqrt{ax^2+bx+c}}}, \int{\frac{px+q}{ax^2+bx+c}}dx, \int{\frac{px+q}{\sqrt{ax^2+bx+c}}}dx, \int{\sqrt{a^2 \pm x^2}}dx, \int{\sqrt{x^2-a^2}}dx, \int{\sqrt{ax^2+bx+c}}dx, \int{(px+q) \sqrt{ax^2+bx+c}}dx

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### Properties of Integrals Class 12 Maths

Properties of Definite Integrals : Derivations, Assignments, NCERT Exercise 7.11

## 8. Application of Integrals

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### Definite Integrals and its application

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).

## 9. Differential Equations

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### Differential Equations Class 12 Maths

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: \frac{dy}{dx}+ py = q, where p and q are functions of y or constants \frac{dx}{dy}+ px = q, where p and q are functions of y or constants

## 10. Vector Algebra

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### Vector Algebra Class 12 Maths

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.

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### Vector Algebra Class 12 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

## 11. Three Dimensional Geometry

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### Three Dimensional Geometry Class 12 Maths

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.

## 12. Linear Programming Problems

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### Linear Programming Problems Class 12 Maths

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).

## 13. Probability

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### Probability Class 12 Maths

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

## Deleted Part

### Deleted Syllabus Class 12 Maths

This course will have deleted syllabus of Class 12 Maths.