# Class 12 Maths

Ashish Kumar - Let's Learn provides an expanding number of detailed high-quality video lectures and study material for Full syllabus of Class 12 Maths. We aim to develop your ability to understand and analyse various types of mathematical problems through our expert created explanation from beginners to proficiency, questions starting from the basic concepts to the difficult and advanced level concepts, NCERT Solutions, R.D Sharma, R.S Aggarwal and Board’s Question Bank and Important Examples that you can access them directly to your desktop and mobile easily at any time and reach your educational goals by studying independently at your own pace. We also provide pdf notes and assignments for Class 12 Maths with detailed video lectures based on the assignments explained and prepared by expert teacher.

## Membership Details

This membership **includes**

- all 13 NCERT Chapters of Class 12 Mathematics in the form of 21 individual courses
- 3 months (90 Days) validity
- recorded videos of concepts, NCERT Exercise solutions, and NCERT Examples
- recorded videos of assignments based on RD Sharma, Boards questions bank, NCERT Exemplar problem etc.,
- PDFs of assignments
- Additional lectures based on Logarithms, Critical Points and Modulus as a separate 22
^{nd}Course

For complete details of membership content you can access the course description and course content index of all 22 membership courses on this page. As all chapters are different so does the content provided. Not all chapters have assignments, NCERT examples etc. A few topics of some chapters are not included in the membership. It is recommended to check the index and description of the courses before purchasing membership. This membership does not include doubts and live sessions.

Explanation Language: Hinglish (Hindi + English)

Membership: Class 12 Mathematics

Membership Mode: Online

Membership Topics: As per description

Membership Type: Self Learning

Assignment PDF: Yes

Assignment Video: Yes

Total Courses: 22

Validity: 3 Months (90 Days)

₹1,898

#### 10300+ minutes of videos

Membership will provide you 24×7 access to 10300+ minutes of class 12 maths videos

#### NCERT Exercises

Membership will provided you 24×7 access to the videos of NCERT Exercise solutions

#### Concepts explanations

Membership will provided you access to detailed explanation of concepts of Class 12 Maths

#### Assignments

Membership will provided you 24×7 access to the videos and PDFs of assignments from R.D. Sharma, NCERT Exemplar, Board's Questions bank etc.

## Ch01. Relations and Functions (Part – 1)

In this online course, you will learn Empty Relations, Universal Relations, Trivial Relations, Reflexive Relations, Symmetric Relations, Transitive Relations, Equivalence Relations, Equivalence Classes. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

## Ch01. Relations and Functions (Part – 2)

In this online course, you will learn One to one and onto functions, composite functions and inverse of a function. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

## Ch02. Inverse Trigonometric Functions

In this online course, you will learn definition, range, domain, principal value branch, graphs of inverse trigonometric functions and elementary properties of inverse trigonometric functions. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

## Ch03. Matrices Class 12 Maths

**THIS IS A COMBO OF TWO COURSES**

**COURSE – 1**

In this online course, you will learn 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. Concept of elementary row and column operations and Invertible matrices. This course also has solutions of NCERT Exercise questions.

Please note, this course comprises of live session recordings of Ashish Kumar (Agam Sir). Please ignore, if you have heard Agam Sir discussing about live session or doubts session in the course. Live sessions or doubts sessions are no longer offered.

**COURSE – 2**

This online course is an extended part of Ch03. Matrices Class 12 Maths. The course is based on the assignments by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course. Please note, the assignments do not have questions based on elementary operations.

## Ch04. Determinants Class 12 Maths

**THIS IS A COMBO OF TWO COURSES**

**COURSE – 1**

In this online course, you will learn 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, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.. This course also has solutions of NCERT Exercise questions.

Please note, this course comprises of live session recordings of Ashish Kumar (Agam Sir). Please ignore, if you have heard Agam Sir discussing about live session or doubts session in the course. Live sessions or doubts sessions are no longer offered.

**COURSE – 2**

This online course is an extended part of Ch04. Determinants Class 12 Maths. The course is based on the assignments by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course. Please note, the assignments do not have questions based on properties of determinants.

## Ch05. Continuity and Differentiability Class 12 Maths

The whole chapter Continuity and Differentiability is divided into three online courses. This online course is the part one. In this self study course, you will learn continuity, 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. This course also has NCERT Exercise solutions, some important NCERT Examples and assignment based on NCERT Exemplar, R.D. Sharma, board’s question bank etc. Please note, all three courses based on Continuity and Differentiability do not have Rolle’s Theorem, Mean Value Theorem, NCERT Exercise 5.8 and questions based on them in Miscellaneous exercise.

## Ch05. Continuity and Differentiability Assignment – 3

The whole chapter Continuity and Differentiability is divided into three online courses. This online course is the part 2. In this self study course, you will learn about differentiability. This course also has assignment that has questions from NCERT Exemplar, R.D. Sharma, board’s question bank etc. Please note, all three courses based on Continuity and Differentiability do not have Rolle’s Theorem, Mean Value Theorem, NCERT Exercise 5.8 and questions based on them in Miscellaneous exercise. The PDF of assignment can be downloaded within the course.

## Ch05. Continuity and Differentiability Assignments

The whole chapter Continuity and Differentiability is divided into three online courses. This online course is the part 3. The course is based on the assignments on Derivatives by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course. Please note, all three courses based on Continuity and Differentiability do not have Rolle’s Theorem, Mean Value Theorem, NCERT Exercise 5.8 and questions based on them in Miscellaneous exercise.

## Ch06. Applications of Derivatives

**THIS IS A COMBO OF TWO COURSES**

**COURSE – 1**

In this online course, you will learn 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). For further understanding of concepts and for examination preparation, this course has explanation of all NCERT Exercise questions and important NCERT Examples.

**COURSE – 2**

This online course is an extended part of Ch06. Applications of Derivatives. The course is based on the assignments by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course.

## Ch07. Integrals

In this online course, you will learn 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

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

For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that has questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

"Limit of Sum" and "Properties of Integrals" are not included in this course.

## Ch07. Properties of Integrals

This online course is an extended part of chapter 7 Integrals of Class 12 Maths. In this course, you will learn properties of definite Integrals and their derivations. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise 7.11, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

## Ch08. Limit of Sum & Application of Definite Integrals

In this online course, you will learn limit of sum, 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). For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

## Ch09. Differential Equations

In this online course, you will learn 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:

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

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

For further understanding of concepts and for examination preparation, this course has explanation of all NCERT Exercise questions. Also, there are self practice assignments that have questions from Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

## Ch10. Vector Algebra Class 12 Maths

**THIS IS A COMBO OF TWO COURSES**

**COURSE – 1**

In this online course, you will learn 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. This course also has solutions of NCERT Exercise and a few important examples. Please note, some of the part of this course comprises of live session recordings of Ashish Kumar (Agam Sir). Please ignore, if you have heard Agam Sir discussing about live session or doubts session in the course. Live sessions or doubts sessions are no longer offered.

**COURSE – 2**

This online course is an extended part of Ch10. Vector Algebra Class 12 Maths. The course is based on the assignments by Ashish Kumar (Agam Sir), which have questions from NCERT Exemplar, Board’s Question Bank, R. D. Sharma etc. The PDF of assignments can be downloaded within the course.

## Ch11. Three Dimensional Geometry Class 12 Maths

In this online course, you will learn 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. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course. Please note, this course comprises of live session recordings of Ashish Kumar (Agam Sir). Please ignore, if you have heard Agam Sir discussing about live session or doubts session in the course. Live sessions or doubts sessions are no longer offered.

## Ch12. Linear Programming Problems

In this online course, you will learn 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).

For further understanding of concepts and for examination preparation, this course has explanation of all NCERT Exercise questions (except Exercise 12.1). Also, there is practice assignment that has questions from Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignment can be downloaded within the course.

## Ch13. Probability

In this online course, you will learn conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable.

For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

## Other Important Topics for Maths and Physics

This online course contains supplementary / extra videos that will be required for better understanding of Maths and Physics but are not covered under the school syllabus.