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Maharasthra Board 11 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
  * Proofs using properties of set
  * Proofs where properties of set cant be applied using element

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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

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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)

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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.

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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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Linear inequalities

  * Introduction to Linear inequalities
  * System of Inequalities
  * Rational Inequalities
  * Modulus Inequalities
  * Logarithm Inequalities
  * Logarithm Inequalities Complexities
  * Trignometric inequalities
  * Application of System of Inequalities
  * Application of Rational Inequalities
  * Modulus Inequalities Complexities
  * 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
  * Solving one side
  * Solving both side
  * Solving on number line (one graph)
  * Solving on number line (two graph)
  * Solving inequality-statement questions

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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

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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
  * Mean and variance of binomial distribution

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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

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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

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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

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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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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

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