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Lecture 3: Statistics Part- 3

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Published    21-Apr-2017      Bilingual

MATHEMATICS COMPLETE COURSE OF CLASS 11TH CBSE

Study Khazana delivers CBSE Class 11th Mathematics, Sixty five video lectures by Gurpreet Singh on Mathematics Complete Course with complete solutions using sample paper based on NCERT Syllabus. This chapter covers the following topic to make students understand the topic and covers the whole chapter with all the question and answers.

WHAT DO YOU STUDY IN SETS?

• 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

HOW WE HELP THE STUDENTS???

These video lectures will make the subject easy for students. The free lecture is available as a demo. We provide mock exams after completion of the full course. These lectures are recording of the live session taken. it will include question and answers of the students undertaken during the class. CBSE Class 11th previous question papers and sample papers are also given to the students for practice. Video Lectures classes are taken by Study Khazana’s best faculties. Video lectures contain examples and formulas related to different topics. We have doubt sessions on YouTube related to students queries asked on WhatsApp. These classes are based on NCERT Syllabus. We offer pen drives and online-offline study mode to the students. We also have Android and IOS Study Khazana mobile app for helping students to study anywhere at any time.

Gurpreet Singh

 Phone: 09********90 Email: gse********@gmail.com Address: B-253A Street No -3 Majis Park Adarsh Nagar Delhi -110033 Institute: G.S Education

Teaching from last 19 years