Mathematics

Below is the detailed Mathematics curriculum for the academic year 2022-23 as per the latest CBSE notification given. Mathematics is one of the most difficult and scoring subjects in 11th standard. So candidates should prepare for it properly to get good scores.

Unit-I: Sets and Functions

• Sets
• • Sets and their representations
  • Empty sets
  • Finite and Infinite sets
  • Equal sets
  • Subsets
  • Subsets of a set of real numbers especially intervals (with notations) 
  • Universal set
  • Venn diagrams
  • Union and Intersection of sets
  • Difference of sets
  • Complement a set
  • Properties of Complement
• Relations & Functions
  • Ordered pairs
  • Cartesian product of sets
  • Number of elements in the Cartesian product of two finite sets
  • Cartesian product of the set of reals with itself (up to R x R x R)
  • Definition of relation, pictorial diagrams, domain, co-domain, and range of a relation
  • Function as a special type of relation
  • 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 and greatest integer functions, with their graphs
  • Sum, difference, product and quotients of functions
• Trigonometric Functions
  • Positive and negative angles
  • Measuring angles in radians and in degrees and conversion from one measure to another
  • Definition of trigonometric functions with the help of unit circle
  • Truth of the identity 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 applications

Unit-II: Algebra

• Complex Numbers and Quadratic Equations 
  • The need for complex numbers, especially√−1, is motivated by the inability to solve some of the quadratic equations
  • Algebraic properties of complex numbers
  • Argand plane
• Linear Inequalities
  • Linear inequalities
  • Algebraic solutions of linear inequalities in one variable and their representation on the number line
• Permutations and Combinations 
  • A fundamental principle of counting
  • Factorial n. (n!) 
  • Permutations and combinations, derivation of formulae for nPr and nCr and their connections, simple applications
• Binomial Theorem 
  • Historical perspective, statement and proof of the binomial theorem for positive integral indices
  • Pascal’s triangle, simple applications
• Sequence and Series 
  • Sequence and Series
  • Arithmetic Mean (A.M.) 
  • Geometric Progression (G.P.) is, the general term of a G.P., the sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), the relation between A.M. and G.M

Unit-III: Coordinate Geometry

• Straight Lines
  • Brief recall of two-dimensional geometry from earlier classes
  • The slope of a line and the 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
  • Distance of a point from a line

• 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 and hyperbola
  • Standard equation of a circle
• Introduction to Three-dimensional Geometry
  • Coordinate axes and coordinate planes in three dimensions
  • Coordinates a point
  • Distance between two points

Unit-IV: Calculus

• Limits and Derivatives 
  • A derivative is introduced as a rate of change both as that of distance function and geometrically
  • The intuitive idea of limit
  • Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions
  • Definition of derivative relates it to the scope of a tangent of the curve, a derivative of the sum, difference, product, and quotient of functions
  • Derivatives of polynomial and trigonometric functions

Unit-V: Statistics and Probability

• Statistics 
  • Measures of Dispersion
    • Range, Mean deviation, variance and standard deviation of ungrouped/grouped data
• Probability 
  • Events
  • Occurrence of events, ‘not’, ‘and’ and ‘or’ events
  • Exhaustive events
  • Mutually exclusive events
  • Axiomatic (set theoretic) probability
  • Connections with other theories of earlier classes
  • Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events