Courses Grade 11

In this program student will learn about, 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

In this program students will learn about 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 and greatest integer functions, with their graphs. Sum, difference, product and quotients of 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 trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application.

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.

In this Program students will learn about 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.

In this program student will learn in detail about how to solve 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.

In this program student will learn about fundamental principle of counting which is very important in context with Permutation and Combinations.  Student will strengthen the concept of Factorial n. (n!)Permutations and combinations, derivation of formulae and their connections, simple applications. The main focus here is to make student comfortable in arrangements and combinations.

In this program student are going to learn about Binomial Theorem, expansion of terms , its history, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, General and middle term in binomial expansion, simple applications. The main focus of this program is that by the end of this program student should know how to expand the large powers with the help of binomial theorem.

In this program student will learn about the Sequence and Series its type, formation and every thing about it.  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:

These are some of the main important points of this program.

In this program student will learn mainly about straight line and graphs which is one of the important topic in context with co-ordinate geometry. 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. These are the main points where we will focus in this program.

In this program student will learn about the  different 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. Problems solving and concept clearance based on these topics is the main focus of this program.

In this program student will learn about Coordinate geometry in three dimension. Relation between  axes and coordinate planes in three dimensions. lines, planes, equation of plane, intersection of planes, perpendicular planes, parallel planes , Coordinates of a point distance between two points, section formula, distance between a point and a plane, equations of a plane, orthogonal plane. These are some of the main topics where we will focus on. Every topic mentioned is followed by various assignments and homework's.

Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive idea of limit. Limits of polynomials and rational functions, trigonometric, 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 trigonometric functions.

In this program students will learn reasoning related to mathematics. The entire goal of this program is to make the student comfortable in 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. These are some of the important topics in mathematical reasoning where we will focus.

In this program student will learn about the various methods of data collection, mean, median, mode, range, deviation, Measures of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variance, calculate means and estimate means from frequency tables, construction of frequency polygons, concept of histograms, histogram formation, concept of quartile and interquartile, percentile. These are the important topics where we will focus on.

In this program student will first recapitulate the concept of probability what they have learned in their previous grade. They will strengthen their concepts of  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. The main focus here is to make the student perfect in Probability and theoretical distribution.