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Challenger > Mathematics

Systematic order of all the topics and their subtopics we provide in Mathematics of Challenger (class 12th) with a description in detail.

DIFFERENTIAL CALCULUS RELATION

INTRODUCTION TO RELATIONS
TYPES OF RELATIONS
CLASSIFICATION OF RELATIONS

FUNCTION

REAL VALUED FUNCTIONS OF A REAL VARIABLE
DOMAIN AND RANGE OF FUNCTIONS
INTO, ONTO AND ONE – TO – ONE FUNCTIONS
SUM, DIFFERENCE, PRODUCT AND QUOTIENT OF TWO FUNCTIONS
COMPOSITE FUNCTIONS
ABSOLUTE VALUE, POLYNOMIAL, RATIONAL, TRIGONOMETRIC, EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
EVEN AND ODD FUNCTION
GRAPH OF SIMPLE FUNCTIONS


INVERSE TRIGONOMETRY FUNCTION

DOMAIN, RANGE AND GRAPHS OF INVERSE TRIGONOMETRY FUNCTION
PROPERTIES OF INVERSE TRIGONOMETRIC FUNCTIONS
SIMPLIFICATION AND TRANSFORMATION OF INVERSE FUNCTION BY ELEMENTARY SUBSTITUTION AND THEIR GRAPHS
EQUATIONS INVOLVING INVERSE TRIGONOMETRIC FUNCTIONS
SIMULTANEOUS IN-EQUATIONS INVOLVING ITF
SUMMATION OF SERIES USING ITF


LIMIT, CONTINUITY AND DIFFERENTIABILITY

CONCEPT OF LIMIT
EXISTENCE OF LIMIT
0/0 FORM – FACTORISATION
0/0 FORM – RATIONALIZATION
0/0 FORM – STANDARDIZATION
INFINITY BY INFINITY FORM
(ZERO INTO INFINITY) AND (INFINITY INTO INFINITY) FORM
LIMIT OF TRIGONOMETRIC FUNCTIONS – PART 1
LIMIT OF TRIGONOMETRIC FUNCTIONS – PART 2
LIMIT USING SERIES EXPANSION
LIMIT OF EXPONENTIAL FUNCTIONS
LIMIT OF LOGARITHMIC FUNCTIONS
ONE TO THE POWER INFINITY FORM
BUILT-IN LIMIT
APPLICATION OF LIMIT IN GEOMETRY
LIMIT OF COMPOSITE FUNCTIONS
L’HOSPITAL RULE
(ZERO TO THE POWER ZERO) AND (INFINITY TO THE POWER INFINITY) FORM
SANDWICH THEOREM
CONCEPT OF CONTINUITY
FORMULATIVE DEFINITION
REASON AND TYPES OF DISCONTINUITIES
CONTINUITY IN AN INTERVAL
CONTINUITY OF FUNCTION DEFINED BY FUNCTIONAL RULE
CONTINUITY OF COMPOSITE FUNCTIONS
INTERMEDIATE VALUE THEOREM (IMVT)
IMPORTANT POINTS ABOUT CONTINUITY
CONTINUITY OVER COUNTABLE SET
CONCEPT OF DERIVATIVE
EXISTENCE OF DERIVATIVE
DERIVABILITY AND CONTINUITY
ALGEBRA OF DIFFERENTIABILITY
IMPORTANT CONCEPTS
DETERMINATION OF FUNCTION SATISFYING THE FUNCTIONAL RULE


DIFFERENTIATION

DERIVATIVE OF A FUNCTION
DERIVATIVE OF THE SUM, DIFFERENCE, PRODUCT AND QUOTIENT OF TWO FUNCTIONS
CHAIN RULE
DERIVATIVES OF POLYNOMIAL, RATIONAL, TRIGONOMETRIC, EXPONENTIAL AND LOGARITHMIC FUNCTIONS
DERIVATIVES OF IMPLICIT FUNCTIONS
DERIVATIVES UP TO ORDER TWO
GEOMETRICAL INTERPRETATION OF THE DERIVATIVE

 

APPLICATION OF DERIVATIVE

TANGENTS AND NORMALS
INCREASING AND DECREASING FUNCTIONS
MAXIMUM AND MINIMUM VALUES OF A FUNCTION
ROLLE’S THEOREM AND LAGRANGE’S MEAN VALUE THEOREM

 

INTEGRAL CALCULUS INDEFINITE INTEGRATION

INTEGRATION AS THE INVERSE PROCESS OF DIFFERENTIATION
INDEFINITE INTEGRALS OF STANDARD FUNCTIONS
INTEGRATION BY PARTS
INTEGRATION BY THE METHODS OF SUBSTITUTION PARTIAL FRACTIONS

 

DEFINITE INTEGRATION

DEFINITE INTEGRALS AND THEIR PROPERTIES
FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS
INTEGRATION BY PARTS
INTEGRATION BY THE METHODS OF SUBSTITUTION PARTIAL FRACTIONS

 

AREA

 

INTRODUCTION TO AREA UNDER CURVE
AREA BETWEEN TWO CURVES
SOME STANDARD AREAS
AREA WHERE THE CURVE SKETCHING IS SIGNIFICANT
AREAS DEALING WITH INEQUALITIES
AREA BY SHIFTING OF ORIGIN
AREA FOR CURVES REPRESENTED PARAMETRICALLY
AREA ENCLOSED BY INVERSE FUNCTION
DETERMINATION OF UNKNOWN PARAMETERS
CONCEPT OF VARIABLE AREA
DIFFERENTIAL EQUATION

 

FORMATION OF ORDINARY DIFFERENTIAL EQUATIONS
SOLUTION OF HOMOGENEOUS DIFFERENTIAL EQUATIONS
SEPARATION OF VARIABLES METHOD, LINEAR FIRST ORDER DIFFERENTIAL EQUATIONS
GEOMETRIC APPLICATIONS OF DIFFERENTIAL EQUATION
ORTHOGONAL CURVE
SOLUTION OF INTEGRAL EQUATIONS
ANALYTICAL GEOMETRY 3D

 

DIRECTION COSINES
DIRECTION RATIOS
EQUATION OF A STRAIGHT LINE IN SPACE
EQUATION OF A PLANE
DISTANCE OF A POINT FROM A PLANE
VECTOR

ADDITION OF VECTORS
SCALAR MULTIPLICATION
DOT AND CROSS PRODUCTS
SCALAR TRIPLE PRODUCTS AND THEIR GEOMETRICAL INTERPRETATIONS

 

MATRICES MATRIX

MATRICES AS A RECTANGULAR ARRAY OF REAL NUMBERS
EQUALITY OF MATRICES
ADDITION, MULTIPLICATION BY A SCALAR AND PRODUCT OF MATRICES
TRANSPOSE OF A MATRIX
DETERMINANT OF A SQUARE MATRIX OF ORDER UP TO THREE
INVERSE OF A SQUARE MATRIX OF ORDER UP TO THREE
PROPERTIES OF THESE MATRIX OPERATIONS, DIAGONAL, SYMMETRIC AND SKEW-SYMMETRIC MATRICES AND THEIR PROPERTIES
SOLUTIONS OF SIMULTANEOUS LINEAR EQUATIONS IN TWO OR THREE VARIABLES

 

STATISTICS PROBABILITY

ADDITION AND MULTIPLICATION RULES OF PROBABILITY
CONDITIONAL PROBABILITY
BAYES THEOREM
INDEPENDENCE OF EVENTS
COMPUTATION OF PROBABILITY OF EVENTS USING PERMUTATIONS AND COMBINATIONS
PROBABILITY USING BINOMIAL DISTRIBUTION
GEOMETRIC PROBABILITY

 

STATISTICS

MEASURE OF CENTRAL TENDENCY – ARITHMETIC MEAN
PROPERTIES OF ARITHMETIC MEAN
MEASURE OF CENTRAL TENDENCY – WEIGHTED MEAN AND COMBINED MEAN
HARMONIC MEAN AND GEOMETRIC MEAN
MEASURE OF CENTRAL TENDENCY – MEDIAN
MEASURE OF CENTRAL TENDENCY – MODE
MEASURES OF DISPERSION – RANGE AND MEAN DEVIATION
MEASURES OF DISPERSION – VARIANCE AND STANDARD DEVIATION
PROPERTIES OF VARIANCE

 

MATHEMATICAL REASONING

LOGICAL OPERATOR: AND AND OR
LOGICAL OPERATOR: CONDITIONAL AND BI-CONDITIONAL
ALGEBRA OF STATEMENTS