New Notice regarding New Session 2024-25

                                                    

Information 

 

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**To:**

Topperwalagyan Users

**Subject:**

New Blog/Detailed Notes for Classes IX to XII in PCM Subjects

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Dear Students/Teachers,

In alignment with the standards outlined in the Quality Education Brochure for the upcoming academic session 2024-25, we are excited to introduce new courses meticulously crafted to foster deeper conceptual understanding. These materials have been developed under the guidance of Pawan Kumar (M.Phil. Candidate) and our esteemed team of subject matter experts (details kept confidential).

We've noticed recurring inquiries both at our offline centers and online platforms regarding the nature of our educational materials. Allow us to address some of these common queries:

1. **Quality of Study Materials:**

   Our study materials are meticulously designed to cover the theory and questions relevant to your academic level and syllabus, including those prescribed by your board or school. We also incorporate insights from renowned reference books for each respective class.

2. **Achieving High Marks:**

   Our approach to securing excellent marks in final exams revolves around comprehensive preparation. Upon completing the course content and associated practice sessions (DPP/DHPP), we delve into an intensive review of past examination papers spanning at least five years. This process is supervised by Mr. Pawan Kumar, alongside Dr. Shrivastavias and other distinguished educators and collaborators (details kept confidential).

Should you have any further inquiries or require additional assistance, please do not hesitate to reach out.

Warm regards,

Mr. Pawan Kumar  and Dr. Shrivastavias

Coordinator,

Topperwalagyan Science and Mathematics Department

			MR. Pawan kumar Head ,Science and Mathematics of Secondary school Education Department

 

 

                                                                                                                                                                                                                 

Class 12th Mathematics Syllabus

 Mathematics Syllabus For Class 12

 UNIT I. Relations and Functions 

1. Relations and Functions 15 Periods Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.

 2. Inverse Trigonometric Functions 15 Periods Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. 

UNIT II. Algebra 

1. Matrices 25 Periods Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of nonzero 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).

 2. Determinants 25 Periods Determinant of a square matrix (up to 3  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 (having unique solution) using inverse of a matrix. 

UNIT III. Calculus

 1. Continuity and Differentiability 20 Periods 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 10 Periods 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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Brief introduction to Chemistry For High school

 Introduction to Chemistry

Chemistry divided into three major group :

1. Physical chemistry

2. Organic chemistry

3. Inorganic chemistry

 

The mole, commonly abbreviated mol, is the SI base unit used to measure the amount of a substance. It is the number of representative particles, carbon atoms, in exactly 12 g of pure carbon-12. Through years of experimentation, it has been established that a mole of anything contains 6.022 136 7
1023 representative particles. A representative particle is any kind of particle such as atoms, molecules, formula units, electrons, or ions. The number 6.022 136 7
1023 is called Avogadro’s number in honor of the Italian physicist and lawyer Amedeo Avogadro who, in 1811, determined the volume of one mole of a gas. In this book, Avogadro’s number will be rounded to three significant figures—6.02
1023. If you write out Avogadro’s number, it looks like this. 602 000 000 000 000 000 000 000 Avogadro’s number is an enormous number, as it must be in order to count extremely small particles. As you can imagine, Avogadro’s number would not be convenient for measuring a quantity of marbles. Avogadro’s number of marbles would cover the surface of Earth to a depth of more than six kilometers! But you can see in Figure 11-2 that it is convenient to use the mole to measure substances. One-mole quantities of three substances are shown, each with a different representative particle. The representative particle in a mole of water is the water molecule, the representative particle in a mole of copper is the copper atom, and the representative particle in a mole of sodium chloride is the formula unit.

CO-PAWAN