# Mathematics

Want to know the latest CBSE Class 11 2022 Exam subject-wise syllabus? Here is the complete syllabus for 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