Unit | Topic | Marks |
I. | Relations and Functions | 10 |
II. | Algebra | 13 |
III. | Calculus | 44 |
IV. | Vectors and 3-D Geometry | 17 |
V. | Linear Programming | 06 |
VI. | Probability | 10 |
Total | 100 |
Unit I: Relations and Functions
- Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.
- Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
Unit II: Algebra
- 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. Noncommutativity 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; (Here all matrices will have real entries).
- 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 III: Calculus
- Continuity and Differentiability
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.
- Applications of Derivatives
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).
- 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 propertiesof definite integrals and evaluation of definite integrals.
- Applications of the Integrals
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).
- 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 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 IV: Vectors and Three-Dimensional Geometry
- 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.
- 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 V: Linear Programming
- 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).
Unit VI: Probability
- Probability
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.
Total Course Fee (Annual) without Scholarship | 12000 INR | |
Scholarship Criteria | Scholarship Amount | Fee after Scholarship |
| 3000 INR | 9000 INR |
| 2000 INR | 10000 INR |
| 1500 INR | 10500 INR |
| 1000 INR | 11000 INR |
Other Charges excluding Tuition Fee
Charges for online test series per course 200 INR
Admission Fee | 100 INR Per Course |
AC Charges | 100 Rs Per Students/ Month (Course wise) |
Extra Charges of hard copy of Notes (1 Rs per Page) | |
Scholarships Available only on PCB and PCM Courses not on an independent Subject.
On the Basis of % in Class 10th
Following are the details of criteria and scholarship amount applicable.
Scholarship Criteria | Scholarship Amount (Per Course) |
| 3000 INR |
| 2000 INR |
| 1500 INR |
| 1000 INR |
The last date to get this scholarship scheme is 31st May 2020 for class 12th and 31 July 2020 for class 11th.
On the basis of Excellence Scholarship Scheme
Following are the details of criteria and scholarship amount applicable
Scholarship Criteria | Scholarship Amount (Per Course) |
| 3000 INR |
| 2000 INR |
| 1500 INR |
| 1000 INR |
The last date to get this scholarship scheme is 30th April 2020 for class 12th and 15 July 2020 for class 11th.
On the basis of performance in Educational, Sports, Cultural activities and social service award.
Following are the details of criteria and scholarship amount applicable
Scholarship Criteria | Scholarship Amount (Per Course) |
| 3000 INR |
| 2000 INR |
| 1500 INR |
| 1000 INR |
The last date to get this scholarship scheme is 30 june 2020
To a Only Girl Child
Scholarships for the single girl child do vent upon more on promising a bright and better future for the candidates and offering good roles to them in society.
This is a known situation that girl students are not getting the proper focus as that of the boys in various states of the country. It not only retards the country’s growth rather comes as a stagnant point in the smooth functioning of the educational bone of the nation.
So Academy of Excellence decided a Scholarship Scheme for Single Girl Child with an aim to compensate the cost of girl education for study in Academy of Excellence especially for such girls who happen to be the only girl child in their family.
Scholarship Scheme | Scholarship Amount (Per Course) |
Scholarship for a Single Girl Child of Parents | 3000 INR per Subject |
Student must have min 85% marks in 10th. (Annual income should be less than 2 lac)
The last date to get this scholarship scheme is 30 July 2020
To a Single Parent-Child
Raising a child on your own can be challenging, particularly since single-parent households tend to have significantly lower incomes. It can be a struggle to cover the cost of basic needs, much less save for a college education. Fortunately, we are providing scholarships to help children of single-parent.
Scholarship Scheme | Scholarship Amount (Per Course) |
Scholarship for a Single Parent-Child | 3000 INR per Subject |
Student must have min 85% marks in 10th. (Annual income should be less than 2 lac)
The last date to get this scholarship scheme is 30 July 2020
Chain Ram and Krishna Memorial Scholarship Scheme
This Scholarship is for those students which are good in study but financial condition of family is obstruction in their study.
Scholarship Criteria | Scholarship Amount in % (Per Course) |
| 50% of total Fee |
| 30% of Total Fee |
| 20% of Total Fee |
The last date to get this scholarship scheme is 30 june 2020
Eligibility Criteria
- Both male and female students can apply for this scholarship.
- Annual income of family should not be more than 1.2 lac from all resources.
- Candidates have to provide income Certificate.
- This Scholarship will be given only to selected students.
- Inspection team may visit your home or may inquire about you from all available resources.
- After collection of complete data, Academy of Excellence will send it to selection committee which is providing this scholarship.
- Final decision will be taken by Selection committee.
- Academy is not having any role in selection of students for scholarship.
Features of This Course
- Thoroughly revised Study Material as per the syllabus of CBSE and PSEB.
- Specially designed questions with mock tests.
- Doubt clearing sessions.
- Regular feedback and performance analysis sessions.
- Many shortcut tricks to solve question within seconds.
Faculty:
Master Champion of Mathematics with teaching experience of over 7 years with in St Joesph convent School and at Academy of Excellence, as a senior faculty, he intends to make a difference in the old traditional learning patterns by accentuating the need of new teaching standards and techniques. His experience, stature and the number of success stories are known to all and have attracted children from all across the Area to better their understanding and gain mastery of Mathematics. His favorite quote is from Albert Einstein “Logic will get you from A to B. Imagination will take you everywhere.”