Courses Grade 12

In this program student are going to learn about Relations and functions. Understanding difference between both of them,  Types of relations:

1) Reflexive

2) Symmetric

3) Transitive

4) Equivalence relations.

One to one and onto functions, composite functions, inverse of a function. Binary operations. These are some of the major points where we will focus on.

Every module is followed by various assignments and homework

In this program student will first recapitulate the concept of Trigonometry and various functions associated with it then they will move to this. They will learn various things like calculation of  range, domain, principal value branch. In depth  understanding of elementary properties of inverse trigonometric functions and various graphs associated with it is the main components of this program. The main focus here is that student should know all these concepts by the end of the program.

In this program student will learn about the concepts of Matrices. 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 commutatively 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. These are some of the major which student should know by the end of this program.

In this program students will learn about the  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. In depth analysis of  these topics is the key formulae for success in Matrices and Determinants.

In this program students will first recapitulate the concept of limits which they have learned in their previous grade then slowly they move to this topic which is the heart of calculus In this program student will learn 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. The main focus here to is make the student comfortable in calculus since it has a wide range of applications which will be used later on. All the topics are followed  with the help of various assignments and homework.

In this program student will first recapitulate the concept of Derivates then they will move on its application. In this program student will learn about basic application of derivatives and its uses.. Like 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), Word problems based on increasing/decresing functions and maxima minina. Once student is comfortable in these applications then they can move to advance level.

In this program student will learn about Integration and understand its inverse relationship with 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 . Basic propertiesof definite integrals and evaluation of definite integrals and indefinite integrals will be the main focus of this program.

In this program student will first recapsitute the concept of integrals its various types then further they will move on to its application. Applications of integrals includes finding the area under simple curves, which majorly includes clines, circles, parabolas. Once the student is comfortable in this part then they move to its further application which includes the calculation of area between any two of the above said curve. They will also learn double and triple integration which comes under area under the closed path with the help of various theorems and examples. All the above points are followed by various topics assignment and  proper homeworks.

In this program student will learn all about the differential equations its application and its uses. This include understanding of its definition, order and degree of differential equation, general and particular solutions of a differential equation in various forms  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 various type like

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.

 Main focus of this program is that by the end of the program  student should know how to form the equations and to solve it.

In this program student will learn about  majorly about vectors. Vectors and scalars, magnitude and direction of a vector.Representation of vector in various forms, 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. These are some of the main components where this program focus on.

In this program student will first recapitulate the basic concepts of geometry. They will learn about Geometry in three dimensions which include  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, section formulae. They will also strengthen the concept of three dimensional trigonometry. The main focus here is to by the end pof the program student should feel comfortable to analyze  a 3-D picture and perform related calculations based on that.

In this program student will first recapsitute the concept of probability which they learn in their previous grades. Once they feel comfortable they will learn  Conditional probability, multiplication theorem on probability. independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution. These are some of the points where student will focus on during th program. All the topics are followed by various assignments and homework.