I Amitesh Kumar from Patna, India have completed B.Tech from NIT Kurukshetra, Haryana(2015,8.8 CGPA). I have been teaching for about a decade to students of ICSE Board.

I  have represented NIT Kurukshetra at Govt. College of TechnologyJammu- Kashmir winning best project award and at MANTHAN, a program by CAG(Govt. of India) winning AIR 8th. I have also organized Interaction Program with Dr. A P J Abdul Kalam in guidance of Dean, NIT KURUKSHETRA , organized various workshops, won prizes at Cultural programs and also have solved questions of Physics present in various International Journals.

With a solid technical background in Conceptual Physics/Mathematics. I am into the process of learning and developing better teaching methodology  for better student development because I believe that a student can fail only when the teacher actually fails to evolve the student.

Degree: Bachelors of Technology - University: NIT Kurukshetra, Haryana

Degree:

Class 12 is a significant turning point in a student’s academic career because the Board test results determine their career path. Maths is a crucial subject and a substantial element of competitive Examinations, according to the ISC Class 12 Maths Syllabus, which includes several required courses that are an essential part of higher education.

• Learning Objectives:

  SECTION A:

  UNIT 1:Relations and Functions

  UNIT 2:Algebra

  UNIT 3:Calculus

  UNIT 4:Probability

   

  SECTION B:

  UNIT 5:Vectors

  UNIT 6:Three - Dimensional Geometry

  UNIT 7:Applications of Integrals

   

  SECTION C:

  UNIT 8:Application of Calculus

  UNIT 9:Linear Regression

  UNIT 10:Linear Programming

• Course Outline:

  SECTION A

  UNIT 1. Relations and Functions

  (i) Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, inverse of a function. Binary operations.

  (ii) Inverse trigonometric functions

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

  UNIT 2. Algebra Matrices and Determinants

  (i) 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. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order up to   3). 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).

  (ii) 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 3. Calculus

  (i) Continuity, Differentiability and Differentiation. 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.

  (ii) Applications of Derivatives

  Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normal , 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).

  
  (iii) 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.

  (iv) Differential Equations

  Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. 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. dx/dy + px = q, where p and q are functions of y or constants.

  UNIT 4. 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. Repeated independent (Bernoulli) trials and Binomial distribution. 

  SECTION B

  UNIT 5 . 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. 

  UNIT 6. 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 7 . Application of Integrals

  Application in finding the area bounded by simple curves and coordinate axes. Area enclosed between two curves. 

  SECTION C 

  UNITT 8 . Application of Calculus

  Application of Calculus in Commerce and Economics in the following:

  – Cost function, – Average cost, – Marginal cost and its interpretation – Demand function, – Revenue function,

  – Marginal revenue function and its interpretation, – Profit function and breakeven point. – Rough sketching of the following curves:

  AR, MR, R, C, AC, MC and their mathematical interpretation using the

  Concept of maxima & minima and increasing-decreasing functions. 

  UNIT 9 . Linear Regression

  – Lines of regression of x on y and y on x.

  – Scatter diagrams – The method of least squares. – Lines of best fit. – Regression coefficient of x on y and y on x. – Bxy x byx = r2, 0 ≤ bxy  ≤ byx ≤ 1 – Identification of regression equations – Angle between regression line and properties of regression lines. – Estimation of the value of one variable using the value of other variable from appropriate line of regression. 

  UNIT 10. 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 and unbounded), feasible and infeasible solutions, optimal feasible solutions

  (up to three non-trivial constraints). 

  
   

• Recomended Audience:

  The audience of this course is students of Grade-12 from ICSE Board. All the Chapters are well designed and its coverage as per latest curriculum released by the board. Still Student have complete flexibility to enhance or modify the course coverage during the course of learning process with Teacher. We are expecting that students of Grade-12 should drive their classes with Teacher as per chapters mentioned and also as per syllabus of their school and applicable School district or Board.

• Pre-Requisite Requirement:

  For attending this course, prior knowledge of Grade-11 Maths is required, this course assumes that students have prior experience with all the topics of Maths of Grade-4. This is not an introductory class for absolute beginners on Maths of Grade-11! Participants should already be familiar with the basic concepts which is taught in Grade-11.

• Course Level:
  Intermediate
• Language of Teaching:
  English, Hindi
• Class Schedule Availiability:
  Evening