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MHT - CET Mathematics

Mathematics is the branch of science, which deals with numbers, involves calculations and mainly focuses on the study of quantity, shapes, measurements etc.In more simple words, math is the science, deals with structures, numbers, geometry etc.

Sets

  * Introduction
  * Types of Sets(empty set,finite set,infinte set,equal set)
  * Subsets of a set of real numbers especially intervals (with notations)
  * Power set
  * Universal set
  * Introduction to Venn diagrams
  * Union and Intersection of sets
  * Difference of sets
  * Complement of a set(introduction,properties of complement set)
  * Proofs using properties of set
  * Proofs where properties of set cant be applied using element

Mock MCQ Videos

Relations

  * Introduction
  * Cartesian product of sets
  * Equality of two ordered pairs
  * Number of elements in the cartesian product of two finite sets
  * Cartesian product of the sets of real (up to R × R)
  * Relation Definition
  * Finding Relation-(set builder form given,arrow depiction given)
  * Types of relations
  * Number of relations
  * Empty and Universal Relation
  * Types of relations − Reflexive , Symmetric , transitive and equivalence relation,One to one and onto functions,composite functions,inverse of a function,Binary operations
  * To prove relation reflexive,trasitive,symmetric and equivalent
  * Finding number of relations

Mock MCQ Videos

Functions

  * Defintion and its types(Odd and Even functions , Inverse Functions and Periodic functions)
  * Finding value at certain points
  * 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
  * Different functions and their graphs
  * Finding domain and range(by drawing graphs and by general methods)
  * "Real valued functions, domain and range of these functions"
  * −(Constant,Identity,Polynomial,Rational,Modulus,Signum,Exponential,Logarithmic,Greatest integer functions (with their graphs))
  * Piece-wise defined and special functions
  * Algebra of real functions(Sum, difference, product and quotients of functions)
  * Definition
  * To prove one - one and onto (injective , surjective , bijective)
  * Composite functions,composite functions and one - one onto
  * finding inverse
  * inverse function - Proof questions
  * Binary operation - defintion
  * whether binary commutative/associative or not
  * binary operation - identity element
  * binary operation - inverse

Mock MCQ Videos

Angle and its Measurement

  * Positive and negative angles
  * Measuring angles in radians and in degrees and conversion of one into other
  * Arc length

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Trigonometry - I

  * Introduction
  * Finding value of trignometric functions (given other functions,given angle)
  * Signs of trigonometric functions
  * Domain and range of trigonometric functions and their graphs
  * Fundamental Identities and Periodicity of trigonometric functions
  * Polar Co-ordinates

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Trigonometry - II

  * Introduction
  * Truth of the sin2x + cos2x = 1, for all x
  * (x+y) formula (Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application) 2x,3x formula (Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x)
  * Factorization formulae,Trigonometric functions of angles of a triangle.
  * General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.

Mock MCQ Videos

Trignometric Functions

  * Trignometric Functions and their solution
  * Polar Co-ordinates,relation between systems
  * Solving a triangle
  * Sine and Cosine formula
  * Projection rule
  * Applications of sine rule,cosine rule and the projection rule
  * Some more formulae, Principle Solution and its algorithm
  * Examples based on Solutions of Trigonometric Equation
  * Examples based on Solutions of Trigonometric Equations
  * Question type-By Factorisation and by introducing auxiliary argument
  * Question type-By converting product to sum form and sum to product form
  * Question type- By changing the variable and by introducing a new variable
  * Question type- Using boundedness of function and by solving equations of the form f(x)= vf(x)

Mock MCQ Videos

Principle of Mathematical Induction

  * Introduction to Mathematical Induction
  * Equal addition,equal upon addition,equal multiplication,divisible
  * 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

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Complex Numbers and Quadratic Equations

  * Need for complex numbers, especially √1, to be motivated by inability to
  * solve some of the quadratic equations
  * Classification and geometrical representation of complex numbers, integral power of 'i'
  * Algebra(addition, multiplication,subtraction,division)
  * Conjugate and modulus of Complex Numbers
  * Argument of Complex numbers
  * Representation of Complex Numbers
  * Properties of modulus, conjugate and argument
  * Argand plane and polar representation of complex numbers
  * Concept of rotation
  * Demoivre's Theorem
  * Cube roots of unity
  * Geometry of Complex Numbers
  * Geometry of Complex Numbers
  * Logarithm of Complex Quantity
  * Solution of quadratic equations in the complex number system
  * Square root of a complex number
  * triangle inequality, cube roots of unity, geometric interpretations
  * Convert to a+ib form
  * identities(square,cube of two complex numbers)
  * Quadratic equations with real coefficients
  * relations between roots and coefficients
  * formation of quadratic equations with given roots
  * symmetric functions of roots

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Permutations and Combinations

  * Fundamental principle of counting
  * Factorial n
  * Definition and its formula
  * Derivation of formulae and their connections(for repeating and non-repeating)
  * Theorem Related To Application of Permutation And Combination
  * Formation of Groups
  * Permutation of Alike Objects
  * Circular Permutation
  * Total Number of Combination Or Selection
  * Problems Based On Number Theory
  * Summation of Numbers(2 Different Ways)
  * Distribution of Alike Objects
  * Derangements And Some Important Results About Points

Mock MCQ Videos

Binomial Theorem and distribution

  * History
  * Explanation of Binomial Theorem-number evaluation
  * Statement and proof of the binomial theorem for positive integral indices
  * Numerically Greatest Term
  * Binomial Coefficients and Properties
  * Pascal's triangle
  * Coefficient
  * General and middle term in binomial expansion
  * Miscellanous - Multinomial
  * Binomial theorem for a positive integral index, properties of binomial coefficients
  * Binomial distribution
  * Mean and variance of binomial distribution

Mock MCQ Videos

Sequence and Series

  * Introduction
  * Finding sequences
  * AP formula based
  * Statement of AP,calculation based and proofs
  * Inserting AP between two numbers
  * Arithmetic mean
  * Finding sequences
  * GP formula based
  * Statement of GP,calculation based and proofs
  * Inserting GP between two numbers
  * Geometric mean
  * General term of a G.P
  * Sum of n terms of a G.P.
  * Arithmetic and Geometric series infinite G.P. and its sum
  * Relation between A.M. and G.M.
  * AP and GP mix questions
  * Finding sum from series
  * infinite geometric series, sums of squares and cubes of the first n natural numbers
  * Finding sum from nth number
  * Harmonic Progression - definition,general terms,harmonic mean

Mock MCQ Videos

Straight Lines

  * Introduction to Basic Concepts of Co-ordinate Geometry and Straight Lines
  * Brief recall of two dimensional geometries from earlier classes
  * Shifting of origin
  * Slope definition-(Finding slope,perpendicularity)
  * Angle between two Straight Lines
  * Collinearity of three points by slope,point slope form
  * Parallel to axis
  * Point-slope form
  * Slope-intercept form
  * Two-point form
  * Intercept form
  * Normal form
  *   * General equation of a line
  * Position of point w.r.to line and Concurrency
  * Bisectors of Angles between two Lines
  * Homogenisation
  * Distance of a point from a line
  * Equation of family of lines passing through the point of intersection of two lines
  * Pair of straight lines
  * Distance between two parallel lines
  * Distance of a point from a line along a line
  * Problems Based On area of triangle formed
  * Problem based on three lines concurrent
  * Images given and find slope

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Circles

  * Standard form of equation of a circle
  * general form of the equation of a circle
  * Its radius and centre
  * equation of a circle
  * when the endpoints of a diameter are given
  * points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle
  * equation of the tangent.

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Conic Sections

  * Circles,Ellipse,Parabola,Hyperbola − a point, a straight line and a pair of
  * intersecting lines as a degenerated case of a conic section.
  * Introduction to Conic Sections
  * Introduction to Parabola
  * Forms of Parabola
  * Checkpoint (Introduction to Parabola)
  * Points and Lines w.r.t. Parabola
  * Tangents and Normals
  * Checkpoint (Tangent and Normals)
  * Chord, Diameter & Important Results
  * Check Point (Chord and Imp. Results)
  * Sub-tangent, Sub-normal and Properties of Parabola
  * Miscellaneous topics
  * Parabola basic questions
  * Parabola arch and mirror problem
  * Parabola - Triangle in Parabola Problem
  * Beam Problem in Parabola
  * Introduction to Ellipse
  * Important Concepts Related to Ellipse
  * Tangents to Ellipse
  *  of Tangents and Normals
  *  Polar, Diameter and Eq wrt to Lines
  * Path Traced
  * Definition of Hyperbola
  * Equation of Tangents-Hyperbola
  * Equation of Normals and properties of Hyperbola

Mock MCQ Videos

Introduction to Three–dimensional Geometry

  * Coordinate axes and coordinate planes in three dimensions
  * Coordinates of a point
  * Defintion and formula
  * Distance between two points - Definition
  * Distance between two points - Collinear
  * Distance between two points - Set of points
  * Section - Definition,collinear
  * Plane dividing line segment,centroid,median
  * Direction Cosines, Direction Ratios, Angle between two lines
  * Different forms of equations of planes
  * Family of planes, angle between two planes
  * Symmetric and unsymmetric form

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Limits

  * Introduction
  * Derivative introduced as rate of change both as that of distance function and geometrically
  * Limits - Definition
  * Limits - 0/0 form,x^n formula,of trignometric functions,limts exist
  * Limits of Polynomials and rational functions,Trigonometric, exponential and logarithmic functions
  * Limit and continuity of a function
  * limit and continuity of the sum,difference,product and quotient of two functions

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Mathematical Reasoning (mathematical logic)

  * Mathematically acceptable statements
  * Statement and Conjunction
  * Disjunction, Negation and Quantifiers
  * Implication, Contrapositive and Converse
  * Tautology, Fallacy and Algebra of Statements
  * Connecting words/ phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or",
  * "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics
  * Validating the statements involving the connecting words difference between contradiction, converse and contrapositive
  * Proving not true/false
  * Proving true - if and only if
  * Proving True - By contrapositive
  * Proving True - By Contradiction
  * Necessary and sufficient condition
  * Application of logic to switching circuits
  * Switching table

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Measures of dispersion

  * Introduction to Statistics and Measures of Central Values
  * Calculation of Median
  * Mode
  * Range and Mean Deviation
  * Variance, Standard Deviation and Coefficient of Variation

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Probability - 1

  * Introduction
  * Outcomes
  * Sample spaces (set representation)
  * Occurrence of events, 'not', 'and' and 'or' events,independent events
  * Exhaustive events,Mutually exclusive events
  * Axiomatic (set theoretic) probability,Connections with the theories of earlier classes
  * An event ,probability of 'not', 'and' and 'or' events
  * Conditional Probability
  * Total Probability Theorem
  * Baye's Theorem
  * Binomial Trails & Distribution
  * calculation of probability by basic formula
  * calculation of probability by using formula sets
  * calculation of probability by using permutation
  * calculation of probability by using combinations

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Inverse Trigonometric Functions

  * Definition, range, domain, principal value branch
  * Graphs of inverse trigonometric functions
  * Elementary properties of inverse trigonometric functions
  * Simplification & Transformation of Inverse Functions
  * Equations Involving IT
  * Simultaneous Equations & In-equations Involving IT
  * Summation of Series
  * Changing of trignometric variables and then applying formula

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Matrices

  * Definition,formation
  * notation,order of matrices
  * Types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices
  * Operation on matrices: Addition and multiplication and multiplication with a scalar
  * Simple properties of addition, multiplication and scalar multiplication
  * Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2)
  * Transpose of matrices
  * Concept of elementary row and column operations
  * Inverse of matrix using elementary transformation
  * Minors and cofactors,Adjoint of a matrix
  * Rank of a matrix
  * System of equations(Cramer's rule)
  * solutions of simultaneous linear equations in two or three variables
  * Matrix method and Augmented matrix
  * Method of inversion
  * Method of reduction
  * Test of consistency
  * Statement question - Addition and Subtraction of matrices
  * Statement question -multiplication of matrices
  * finding unknown element and matrices
  * proof using property of transpose
  * proof using mathematical induction

Mock MCQ Videos

Determinants

  * Introduction
  * Determinant of a square matrix (up to 2 × 2 matrices)
  * Determinant of a square matrix (up to 3 × 3 matrices)
  * Ad joint and inverse of a square matrix
  * minors, co-factors
  * properties of determinants
  * Finding the area of a triangle
  * Equation of line using determinant
  * Consistency, inconsistency and number of solutions of system of linear equations by examples
  * solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix

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Continuity

  * Continuity of function
  * Reasons and Types of Discontinuity
  * Theorems of Continuity
  * Checking continuity at a given point
  * Checking continuity at a any point
  * checking continuity using LHL and RHL
  * Algebra of continous functions
  * continuity of composite function

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Differentiation - 1

  * Introduction
  * 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
  * The derivative of trigonometric functions
  * checking if function is differentiable
  * derivative of composite functions
  * derivative of functions by chain rule
  * derivatives of inverse trigonometric functions, derivative of implicit functions
  * Derivatives of logarithmic and exponential functions
  * Derivative in parametric form
  * "Relationship between Continuity and Differentiability."
  * Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions

Mock MCQ Videos


Applications of Derivatives

  * Monotonicity
  * Maxima and Minima
  * Tangent and Normal
  * rate of change
  * Finding second order derivative - normal form
  * Finding second order derivative - implicit form
  * Rolle's Theorems (without proof) and their geometric interpretation
  * Lagrange's Mean Value Theorems (without proof) and their geometric interpretation
  * To show increasing/decreasing in whole domain
local maxima/minima
  * Absolute minima/maxima
  * To show increasing/decreasing in intervals
  * Find intervals of increasing/decreasing
  * Finding slope of tangent/normal
  * Finding point when tangent is parallel/perpendicular
  * Finding equation of tangent/normal when point and curve is given
  * Finding equation of tangent/normal when slope and curve is given
  * Finding apporximate value of numbers
  * Finding apporximate value of function
  * Finding approximate value - statement questions
  * Finding minimum and maximum values from graph
  * Minima/maxima - Number questions
  * Minima/maxima - geometry questions
  * Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)

Mock MCQ Videos

Integrals - Indefinite integration

  * Integration as the inverse process of differentiation
  * indefinite integrals of standard functions
  * definite integrals and their properties
  * By using formula ( Indirect, Derived)
  * By using trignometric formulae
  * Integration by substitution(algebric,exponential,log function,trignometric identities)
  * Integration using trigo identities(sine and cos formula,a-b formula,2x formula,3x formula,CD and CD inv formulae,Inv trigo formula)
  * Integration by parts(exponential function)
  * Integration by partial function
  * Integration by Specific Formula
  * application of definite integrals to the determination of areas involving simple curves

Mock MCQ Videos

Integrals - Definite Integration

  * Introduction
  * Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof)
  * Basic properties of definite integrals and evaluation of definite integrals
  * Definite Integrals - By formulae
  * Definite Integrals - By Partial Fraction
  * Definite Integrals - By e Fraction
  * Definite Integrals - By substitution
  * Definite Integrals - By propeties

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Applications of the Integrals

  * Introduction to integrals
  * Area under curve
  * Area bounded by curve and horizontal or vertical line
  * Area between curve and line
  * Area between curve and curve
  * Some Standard Areas Numericals
  * Curve Tracing
  * Variable Area, Greatest & Least value, Average Value of a Function

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Differential Equations

  * Definition, order, degree and formation of differential equations
  * general and particular solutions of a differential equation
  * Formation of differential equation whose general solution is given
  * Solution of differential equations and variable separable form
  * Reducible to variable separable type
  * Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree
  * Homogeneous and reducible to homogeneous differential equations
  * Linear differential equations(dy/dx + py = q, where p and q are functions of x or constants,dx/dy + px = q, where p and q are functions of y or constants)
  * Solving differential equation when equation is given or statement is given
  * Solving Linerar differential equation when equation is given or statement is given

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Vectors

  * Meaning & types of vectors - Vectors and scalars, magnitude and direction of a vector
  * "Vectors and its Types (Zero Vector,Unit Vector Position Vector,Co-initial Vector,Like and UnlikeVectors,Co-planar Vector,Collinear Vector,Equal Vector,Displacement Vector,Negative of a Vector)"
  * Triangle and Parallelogram Laws of Vector Addition
  * Direction cosines and direction ratios of a vector
  * Section Formula
  * Orthogonal system of unit vectors, scalar product and properties
  * Vector product of two vectors & related properties
  * Scalar Triple Product & Properties
  * Vector triple product and reciprocal system of vectors
  * Linear Combination of vectors
  * Applications of Vectors in Geometry
  * Collinearity of two products and 3 points or 3 position vectors

Mock MCQ Videos

Three - dimensional Geometry(line and plane)

  * Direction cosines and direction ratios of a line joining two points
Cartesian equation and vector equation of a line, coplanar and skew lines
  * Equation of line - given point and vector
  * Equation of line - given two points
  * Two lines
  * Two planes
  * A line and a plane
  * shortest distance between two lines- two parallel lines, two skew lines
  * Distance of a point from a plane
  * Equation of Plane - in normal form
  * Equation of Plane - perpendicular to vector and passing through point
  * Equation of Plane - pasing through 3 non collinear point
  * Equation of Plane - intercept form
  * Equation of Plane - passing through intersection of planes
  * Coplanarity of two lines
  * Angle between two planes
  * Distance of point from plane
  * Angle between line and plane
  * Equation of line under planes condition
  * Point with lines and planes

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Linear Programming

  * Introduction and Mathematical Description of LP
  * Mathematical Formulation of Optimal Product Line, Diet and Transportation Problems
  * Constraints
  * Objective function
  * Optimization
  * Different types of linear programming (L.P.) Problems
  * Mathematical formulation of L.P. Problems
  * Graphical method of solution for problems in two variables
  * Feasible and infeasible regions (bounded and unbounded)
  * Feasible and infeasible solutions
  * Optimal feasible solutions (up to three non-trivial constraints)
  * Corner Point Method
  * Iso- Profit/ Iso-Cost Method
  * Different Types of LPP
  * Linear equation given - bounded
  * Linear equation given - not feasible
  * Linear equation given - unbounded
  * Diet problems
  * Manufacturing problems
  * Transport problems

Mock MCQ Videos

Probability - 2(Probability distribution)

  * Introduction to Probability
  * Different methods to find probability
  * Conditional probability
  * Multiplication theorem on probability
  * Independent events, total probability
  * Baye's theorem
  * Definition
  * Probability distribution
  * Probability mass function
  * cumulative distribution function
  * Probability distribution function
  * Mean or Expectation of random variable
  * Variance and Standerd deviation of random variable
  * Bernoulli trials
  * PYQ for JEE Mains

Mock MCQ Videos

Pair of straight lines

  * Introduction
  * Combined equation of a pair lines
  * Homogeneous equation of degree two
  * angle between lines
  * general second degree equation in x and y

Mock MCQ Videos

Differentiation - 2

  * Introduction
  * Derivative of composite functions
  * Derivative of inverse functions
  * Derivative of implicit functions
  * Higher order derivatives
  * Geometrical meaning of derivative
  * Logarithmic differentiation
  * Derivatives of Parametric functions

Mock MCQ Videos

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