ISC AND CBSE( CLASS 12 ):-
Features of this course:
1.Course Duration: 6 MONTHS(*After completing the syllabus you can join practice sessions and revision classes)
2.Every week one to one session for every student.
3.All class recording will be available so that you don’t have to miss any. Although it’s advised to attend Live lectures.
4.Assignments to help problem solving
(i) Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function.
(ii) Inverse Trigonometric Functions
Definition, domain, range, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
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 upto 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).
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.
(i) Differentiation, 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.
(ii) Applications of Derivatives
Applications of derivatives: increasing/decreasing functions, tangents and normals, 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).
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. 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.
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem.
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.
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.
Application in finding the area bounded b y simple curves and coordinate axes. Area enclosed between two curves.
Application of Calculus in Commerce and Economics.
– Lines of regression of x on y and y on x.
– Lines of best fit.
– Regression coefficient of x on y and y on x.
– Identification of regression equations
– Estimation of the value of one variable using the value of other variable from appropriate line of regression.
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
Relations and Functions
Article I. Relations and Functions
Article II. Inverse Trigonometric Functions
1. Continuity and Differentiability
2. Applications of Derivatives
4. Applications of the Integrals
5. Differential Equations
Vectors and Three-Dimensional Geometry
2. Three-dimensional Geometry
1) Linear programming
Article I. Multiplications theorem on probability
Section A: 65 Marks
Relations and Functions
Section B: 15 Marks
Application of Integral
Section C: 15 Marks
Application of Calculus
Relations and Functions
Vectors and Three – Dimensional Geometry
*PDF study materials will be provided for every chapter during the course.