S. No.
1
Chapter Name
Basics of Mathematics
2
3
Set Theory
4
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19
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59
Relation and function
LECTURE PLAN FOR JEE_MATHEMATICS (2022)
Topic Name
Wavy Curve Method & Inequalities.
Introduction, Sets, Representation of sets, Kinds of Sets, Analysis of two sets : Equal
sets, Equivalent sets, Subsets, Intervals as subset of R.
Power sets, Universe set, Venn diagram, Operation on sets : Union of sets, intersection
of sets, disjoint sets, difference two sets,
Complement of a set, Algebra on sets, Practical problems on union and intersection of
two sets
Introduction, Cartesian products of sets and Relations, function.
Methods to find out domain
Some basic functions and their graphs, Algebraic functions, Monomial function
polynomial function, constant function, Identity function
Methods of Finding Range-1
Rational function, Irrational functions. Modulus function and their properties
Signum function, Greatest integer and their properties.
Fractional part function and its properties.
Transcedental functions,-Trigonometric functions, Exponential function, logarithmic
function and their properties.
Logarithmic Function and related inequality.
Algebra of real function, replacement properties of function,
Transformations of Graphs
Angle, Important terms, system of measurement of angles, trigonometric function,
Values of trigonometric function for some specific angles
Trigonometric ratios of allied angles, Domain and ranges of trigonometric function,
Graph of trigonometric functions.
Transformation related to graph of Trigonometric Function
TRIGONOMETRY-I
Transformation formulae: trigonometric ratio of the sum and difference of two angles.
Transforming product into sum or difference, Transforming the sum or difference into
product.
Trigonometric ratio of multiple angles, sub-multiple angles.Conditional identities,
Tigonometric Series.
PRACTISE SESSION
Trigonometric equation: Types of trigonometric equation, Principal value, General
solution of basic trigonometric equation.
Trigonometric Ratios in submultiple angles in their domain, Analysis of the form y =
asinx + b cosx,
TRIGONOMETRY-II
Trigonomatric Equations, solution by reducing trigonometric equations to algebraic
one's, solution of the form
acos x + bsin x = c
Equation in which trigonometric function containing large exponent, Trigonometric
inequalities
HEIGHT & DISTANCES Height and Distance, PRACTISE SESSION
Statement of preposition, problem based on proving theorem or identities by the
Principle of mathematical principle of mathematical induction problem based on showing that a given expression
is divisible by an integer or by another expression, problem based on proving
induction
inequality by the principle of mathematical induction and target discussion
Introduction, Polynomial equation, Equation and identity, Quadratic equation:
Newton's Theorem nature of roots of quadratic equations ax2 + bx+ c= 0, Properties
related to nature of roots of quadratic equations.
Condition for common roots of quadratic equations, Quadratic expression y = ax2 + bx
+ c, sign of quadratic expression with graphical perspective
Quadratic Equations
Location of roots, Relation between roots of an equation, some useful results
Location of roots, Relation between roots of an equation, some useful results
Continued & Descartes rule of signs
Analysis of cubic equation,& Questions related to it.Transformation of equation &
Quadratic expression in two variables,
Introduction, square root of a negative number, definition of a complex number,
different particulars of a complex number,
different forms of a complex number, Algebra of complex number, Conjugate of a
complex number,Representation of conjugate of a complex number in Argand plane,
properties of conjugate, Modulus & Argument of a complex number, properties of
Complex number Part- I modulus, Properties of arguments,
properties of conjugate, Modulus & Argument of a complex number, properties of
modulus, Properties of arguments, continued
De moivre's theorem, Logarithm of a complex number, Square root of a complex
number, cube roots of unity,nth roots of unity, properties,
PRACTISE SESSION
Introduction, inequalities, some rules to solve inequalities, inequalities related to
modulus of a real numbers, Graphical solution of linear inequalities in two variables
Type-1: Problem based on solution of system of linear inequalities
Linear Inequalities
Type-2: Problem based on finding system of linear inequalities when their solution set
is given as a shaded region,
Introduction, Sequence, Series A.P, nth term of AP, properties of A.P. Sum of n term
of an AP
Arithmetic mean, Geometric progression, nth term, sum of n term of GP Geometric
mean,
AGP,Introduction to HP,
Sequence and Series
HM, Relation between AM, GM and HM, Sum of n terms of special series
Method of difference, Telescopic sums and products,
Exponential series, Logarithmatic series,
PRACTISE SESSION
limit, determinate and indeterminate form, justification for indeterminancy, evalution
of limit, Important properties of limits, working rule for evaluation of limits of 0/0
form
Evalution of ¥/¥, 0 × ¥ and ¥-¥ form, important results on limits, method for 1¥ form,
Limits and Derivatives
Derivatives, derivative of standard functions, Basic rules of differentation,
L’Hospital's rule,
PRACTISE SESSION
Measure of dispersion, Mean deviation for ungrouped and grouped data, mean
deviation about median, mean deviation about mean, Variance and standard deviation
Statistics
standard deviation of discrete frequency distribution, Analysis of frequency
distribution
Introduction, distance formula, section formula, area of triangle, definitions of
centroid, circumcentre and orthocentre of triangle,
slope of line, Angle between two lines, condition for two lines to be parallel and
perpendicular
Collinearly of three points, various forms of line: Horizontal and vertical line, point
slope form, Two point form, Slope intercept form, Intercept form
Normal form, Parametric form, reduction of General equation to standard form,
position of two points relative to a line
Position of a point which lies inside a triangle, Image of point w.r.t a line, foot of
perpendicular, perpendicular distance of a point from a line.
Straight Line
Analysis of two lines, family of lines, Equation of bisectors, analysis of three lines,
Transformation of axes
Holidays
No. of Lecture
1
Date of Lecture
20/08/2021
Date of Completion
28/05/2021
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01/11/2021
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25/08/2021
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08/10/2021
20/10/2021
21/10/2021
01/11/2021
09/11/2021
12/11/2021
26/11/2021
Date
Occasion
2021-07-21
Bakre-id
15/08/2021
Independence
Day
22/08/2021
Rakshabandhan
30/08/2021
Janmashtmi
02/10/2021
Gandhi Jayanti
15/10/2021
Dusshera
19/10/2021
Eid-e-Milad
04/11/2021
Diwali
05/11/2021
Diwali
10/11/2021
Chhat Pooja
19/11/2021
Guru Nanak
Jayanti
25/12/2021
Christmas Day
01/01/2022
New Year
26/01/2022
Republic Day
Straight Line
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108
Pair of straight line passing through origin, angle between lines represented by ax2 +
2hxy + by2 = 0, bisectors of angles between the lines represented by ax2 + 2hxy + by2
=0
General equation of second degree, Point of intersection, parallel lines and distance
between them, joint equation of pair of straight lines joining origin and points of
intersection of the curve and the line
Concept of Homogenisaiton
Definition of conic section, different form of a circle, general equation, centre, radius,
Diameter form parametric form, equation of circle passing through non-collinear
points,
equation of circle having tangent at (x1, y1), circle and a point, length of intercept on
coordinate axes
line and circle, condition for tangency to circle, Equation of tangent to a circle, length
CIRCLE
of tangent from an external point,
director circle equation of normal chord with a given mid-point
Equation of chord of contact, equation of pair of tangents, pole, polar, length of
intercept on a line
Family of circles, analysis of two circles, radical axis, coaxial system
Locus Problems, PRACTISE SESSION
Standard equation of parabola, parametric equation, position of a point,
Properties of Focal Chord, line as tangent, condition for tangency
Equation of tangent in different form, point of intersection of tangents
Normal, co-normal points, properties of co-normal points, important points related to
parabola, Equation of chord having mid-point (x1, y1) equation of pair of tangents,
pole and polar
PRACTISE SESSION
Standard equation of ellipse, auxilliary circle, position of a point,
line and ellipse, equation of tangent, director circle
Conic Section
Normal, equation of chord having mid-point (x1, y1),
pair of tangents, conjugate diameters chord of contact
PRACTISE SESSION
Standard equation of hyperbola, auxilliary circle, Line and hyperbola equation of
tangent,
Equation of normal, director circle, chord with a given midpoint conjugate diameters
Asymptotes, Rectangular hyperbola, Parametric form, Tangent, Normal.
Asymptotes, Rectangular hyperbola, Parametric form, Tangent, Normal continued
PRACTISE SESSION
Geometry of complex numbers, section formulae, condition, for quadrilateral
Complex number Part- II Rotation of complex number
Straight line in Argand plane, circle,
Introduction: Notation of factorial and definition of C(n, r) and P(n, r) Pascal triangle,
Binomial theorem for a positive integer index, Some special forms of binomial
theorem, problem based on direct expansion,
General term in the expansion of (a + x)n, middle term in the expansion of (a + x)n
Greatest binomial coefficient, numerically greatest term in the binomial expansion,
Binomial theorem
properties of Binomial coefficients, use of differentiation and integration, Binobinomial series.
Multinomial expansion, binomial theorem for any index.
Uses of Binomial Theorem(Finding remainder, Last digits, Finding Integral Part…)
Fundamental principle of counting, multiplication principle, addition rule, factorial
notation, Permutation of things all distinct.
Permutation of things not all distinct, Different types of problem based on Permutation,
circular permutation,
Rank of a word, Combinations, Difference between a permutation, Combination of
Permutation and
different type of objects
Combination
Special use of nCr, Divisors, sum of the numbers formed by n digits.
Division into groups, Equal division of objects, Arrangement into groups.
Number of integral solution of an equation, application of multinomial expansion.
Exponent of a prime number in a factorial, Derangement.
Basic definition, Random experiment, Types of events exhaustive events, Mutually
exclusive events
Probability
Axiomatic approach of probability addition rule of probability, Miscellaneous problem
based on P & C
Introduciton to 3-D
Introduction to 3-D geometry, octant, distance formula, section formula
Geometry
Introduction, mathematical statement, New statement from old, negation of statement,
Mathematical Reasoning compound statement,Special words/phrases AND or ‘OR’ implication, contra positive
and converse
Properties of triangle, sine rule and cosine rule and Basic questions.
Napier's analogy, projection formulae, Area of triangle in different form.,Half angle
TRIGONOMETRY-III formula and question Related to them.
Different Centre Related to Triangle:Circum centre, incentre, Ortho centre, Centroid.
Escribed circle, Regular polygon, Assignment discussion of properties of triangle.
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01/02/2022