Maths (Class 11 / Grade 11)
The course deals with concepts of Mathematics of class XI. It develops the better understanding of basic concepts through animations and examples.User interactive simulation and quiz are added to each concept which provide learner with innovative and intresting practice environment.
Unit 1.1 Set Theory
This chapter includes basics of set theory, representation of sets, different types of sets, and operation performed on sets. Demorgan’s law and other identities.
Unit 1.2: Relations
This chapter includes Ordered pair, Cartesian product, domain, codomain,Range,and Relations.
Unit 1.3: Functions
This chapter includes representation of functions, function as a relation, domain, range and codomain of functions, and different types of functions.
Unit 2.1: Cartesian Coordinates of Point
This chapter includes Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus with examples, coordinates of in centre, ex centre, and centroid of a triangle.
Unit 2.2: Straight line
This chapter consists of concepts of straight line, slope of a line, parallel and perpendicular lines, angles between two lines, intercepts of a line on the coordinate axes, various forms of a line.
Unit 2.3: Circle
This chapter explains standard form of equation of a circle, general form of equation of a circle, various cases of a equation of a circle, and Diameter form of a circle.
Unit 2.4: Ellipse
This chapter explains ellipse as a section of a cone, standard equation of an ellipse, vertical ellipse equation, and different terms of ellipse, eccentricity theorem and simulation, And applications of elliptical concepts.
Unit 2.5: Parabola
This chapter explains parabola as a section of a cone, standard equation of parabola, terms of a parabola, different forms of parabola, eccentricity, and application of parabolic concepts.
Unit 2.6: Hyperbola
This chapter explains hyperbola as a section of a cone, standard equation of a hyperbola, terms of a hyperbola, conjugate hyperbola, eccentricity, and application of a hyperbolic concepts.
Unit 2.7:Three Dimensional Geometry
This chapter explains concept of three dimensional system, planes in three dimensional, point in a three dimensional system, octants, distance formula and section formula in three dimensional.
Unit 3.1: Measurements of Angles
This chapter explains angles, and different measuring systems as sexagesimal system, circular system, With arc radius relation, and some theorems of basic concepts.
Unit 3.2: Trigonometric Functions
This chapter gives the introduction to Trigonometric functions, signs of trigonometric functions, values of different trigonometric functions, and T-ratios of allied angles.
Unit 3.3: Graphs of Trigonometric Functions
Graph of basic Trigonometric functions as sin, cos, tan, cosec, sec and cot are shown with values
Unit 3.4: Trigonometric Ratios of Compound Angles
Cosine of difference and sum of two angles, sine of sum and difference of two angles,Tangent of sum and difference of two angles with examples.
Unit 3.5: Conditional Identities
This chapter explains Transformation formulae of products into sum, and sum into products.
Unit 3.6: Trigonometric Ratios of Multiple and Sub Multiple Angle
Trigonometric functions of multiple angles as 2A, and 3A. Trigonometric functions of submultiples angles as A/2, and values of trigonometric functions of 18 and 36. Conditional identities of Trigonometric functions.
Unit 3.7: Trigonometric Equations
Definition of Trigonometric functions and general solution of Trigonometric equations.
Unit 4.1: Limits
Introduction to limits , concept of limits,limit of a function at a point, left hand and right hand limits with examples, some standard results, Evaluation of Trigonometric limits.
Unit 4.2: Differentiation
This chapter deals with concept of differentiation, derivative at a point, derivative of function, physical significance and geometrical significance of derivative, various derivative formulae, derivative formulae for trigonometric functions, derivative of product of function, derivative of quotient of function.
Unit 5: Mathematical Reasoning
This unit explains mathematically acceptable statements .Connecting words/phrases and there use through variety of examples related to mathematics and real life. Validating the statements involving the connecting words , difference between contradiction, converse and contra positive. Truth tables,
Laws of algebra, and related examples .
Unit 6.1: Statistics
This chapter includes Meaning of measures of dispersion, Formula, Examples and merits demerits of Mean, mode and median for individual series and group data. Definition of standard deviation, Formula and example of standard deviation, shortcut method for standard deviation, coefficient of standard deviation, variance for individual series and frequency distribution. Relation between measures of dispersion.
Unit 6.2: Probability
This chapter includes random experiment, events, sample space, exhaustive events, mutually exclusive events, Probability of an event, Probability of ‘not’, ‘and’, & ‘or ’, events.
Unit 7.1: Principle of Mathematical Induction
This chapter explains principle of mathematical Induction, Relation of Dominos effect and Mathematical Induction, Processes of the proof by the induction, it’s simple applications.
Unit 7.2: Complex Numbers
This chapter includes, need for complex numbers, algebraic properties of complex numbers, polar representation of complex numbers, Equality of Complex Numbers, Modulus of Complex Numbers, Square roots of complex numbers.
Unit 7.3: Quadratic Equation
Introduction to Quadratic Equation, Roots of the equation, Methods of solving Quadratic equation, Nature of the roots, and solved Examples.
Unit 7.4: Linear Inequalities
This chapter explains meaning of linear inequalities, Algebraic solution of linear inequalities in one variable and their representation in on number line, Graphical solution of linear inequalities in two variables, Graphical solution of system of linear inequalities in two variables.
Unit 7.5: Permutations
This chapter includes fundamental principle of counting, Concept and examples related to Factorial (n!),Definition of permutation, animated practical problems involving permutations, circular permutation, Permutation with repetitions, Permutation of things not all different.
Unit 7.6: Combinations
This chapter includes difference between permutation and combination, definition of combination,Practical problems involving combinations, Division into groups, Combination when all things are not alike.
Unit 7.7: Binomial Theorem
This chapter explains Principle of Mathematical Induction, Pascal’s Triangle, Some observation of Pascal’s triangle, General Term, Middle terms, and particular terms with examples.
Unit 7.8: Arithmetic Progression
This chapter explains Concept of sequences, progression, and series. Definition of Arithmetic Progression, General term, sum of n terms of A.P. Some theorems and examples.
Unit 7.9: Geometric Progression
This chapter explains definition of Geometric Progression, General term, sum of n terms of G.P. Geometrical Mean and examples.
Unit 7.10: Special Sequences
This chapter includes Sequences of Natural numbers, sequences of squares of Natural numbers, sequences of cubes of natural numbers with examples.
Add to Cart