AoE Mathematics 11th

Unit-I: Sets and Functions

1. Sets

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement Sets. Practical Problems based on sets.

2. Relations & Functions

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the sets of real (upto R x R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions: constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.

3. Trigonometric Functions

Positive and negative angles. Measuring angles in radians and in degrees and conversion of one into other. Definition of trigonometric functions with the help of unit circle. Truth of the sin²x+cos²x=1, for all x. Signs of trigonometric functions. Domain and range of trignometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application. Deducing identities like the following:

Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.

Unit-II: Algebra

1. Principle of Mathematical Induction

Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.

2. Complex Numbers and Quadratic Equations

Need for complex numbers, especially √1, to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system. Square root of a complex number.

3. Linear Inequalities

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical solution of system of linear inequalities in two variables. 

4. Permutations and Combinations

Fundamental principle of counting. Factorial n. (n!)Permutations and combinations, derivation of formulae and their connections, simple applications.

5. Binomial Theorem

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle term in binomial expansion, simple applications.

6. Sequence and Series

Sequence and Series. Arithmetic Progression (A.P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., Arithmetic and Geometric series infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formula for the following special sum:

Unit-III: Coordinate Geometry

1. Straight Lines

Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.

2. Conic Sections

Sections of a cone: circles, ellipse, parabola, hyperbola; a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

3. Introduction to Three–dimensional Geometry

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

Unit-IV: Calculus

1. Limits and Derivatives

Derivative introduced as rate of change both as that of distance function and geometrically.

Intutive idea of limit. Limits of polynomials and rational functions, trignometric, exponential and logarithmic functions. Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions. The derivative of polynomial and trignometric functions.

Unit-V: Mathematical Reasoning

1. Mathematical Reasoning

Mathematically acceptable statements. Connecting words/ phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words difference between contradiction, converse and contrapositive.

Unit-VI: Statistics and Probability

1. Statistics

Measures of dispersion; Range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

2. Probability

Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.

Other Charges excluding Tuition Fee

Charges for online test series per course 200 INR

On the Basis of % in Class 10th

Following are the details of criteria and scholarship amount applicable.

The last date to get this scholarship scheme is 31st May 2019 for class 12th and 31 July 2019 for class 11th.

On the basis of Excellence Scholarship Scheme

Following are the details of criteria and scholarship amount applicable

The last date to get this scholarship scheme is 30th April 2019 for class 12th and 15 July 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

The last date to get this scholarship scheme is 30 june 2019

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.

Student must have min 75% marks in 10th.
The last date to get this scholarship scheme is 30 July 2019

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. 

Student must have min 75% marks in 10th.
The last date to get this scholarship scheme is 30 July 2019

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.

The last date to get this scholarship scheme is 30 june 2019

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:

Nirmal Sharma

Master Champion of Mathematics with teaching experience of over 5 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.”