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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.

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.

In this session, you will learn logarithm and how to solve problem based on logarithm.

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.

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.

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.

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.

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

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

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:

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.

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.

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

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.

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

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.

Published 24-May-2017 Bilingual

- Sets and their representations
- Explain Empty set, Finite and Infinite sets, Equal sets, Subsets
- Subsets of a set of real numbers especially intervals (with notations)
- Discuss 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
**WHAT DO YOU STUDY IN RELATIONS AND FUNCTIONS?** - Ordered pairs 1
- Cartesian product of sets
- Number of elements in the Cartesian product of two finite sets
- Cartesian product of the sets of real (up to R × R)
- Definition of – Relation, Pictorial diagrams, Domain, Co-domain, 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, Greatest integer functions (with their graphs)
- Sum, difference, product and quotients of functions.
**WHAT DO YOU STUDY IN LOGORITHMS?** - Introduction of Logorithms
- Types of Logorithms
- Properties of LOGORITHMS
- Characteristics of Logorithms
- Explain Anti-Logorithms
**WHAT DO YOU STUDY IN TRIGONOMETRICS 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
- Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x
- General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.
**WHAT DO YOU STUDY IN MATHEMATICAL INDUCTION?** - Process of the proof by induction − 1
- 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
**WHAT DO YOU STUDY IN COMPLEX NUMBER?** - Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic 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
**WHAT DO YOU STUDY IN 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
**WHAT DO YOU STUDY IN PERMUTATION AND COMBINATION?** - Fundamental principle of counting
- Factorial n
- (n!) Permutations and combinations
- Derivation of formulae and their connections
- Simple applications.
**WHAT DO YOU STUDY IN BINOMIAL THEOREM?** - History of Binomial Theorem
- Statement and proof of the binomial theorem for positive integral indices
- Pascal's triangle
- General and middle term in binomial expansion
- Simple applications
**WHAT DO YOU STUDY IN SEQUENCES 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.
**WHAT DO YOU STUDY IN STRAIGHT LINES?** - 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.
- Equation of family of lines passing through the point of intersection of two lines
- Distance of a point from a line
**WHAT DO YOU STUDY IN 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, Hyperbola
- Standard equation of a circle
**WHAT DO YOU STUDY IN INTRODUCTION TO 3D GEOMETRY?** - Coordinate axes and coordinate planes in three dimensions.
- Coordinates of a point
- Distance between two points and section formula.
**WHAT DO YOU STUDY IN LIMITS AND DERIVATIVES?** - 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
**WHAT DO YOU STUDY IN STATISTICS?** - Measures of dispersion − 1. Range 2. Mean deviation 3. Variance 4.
- Standard deviation of ungrouped/grouped data
- Analysis of frequency distributions with equal means but different variances.
**WHAT DO YOU STUDY IN PROBABILITY?** - Random experiments − 1. Outcomes 2. Sample spaces (set representation)
- Events − 1. Occurrence of events, 'not', 'and' and 'or' events 2. Exhaustive events 3. Mutually exclusive events 4. Axiomatic (set theoretic) probability 5. Connections with the theories of earlier classes
- Probability of − 1. An event 2. probability of 'not', 'and' and 'or' events

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My highest qualification is MSc. in Mathematics from DU.

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