NCERT Solutions for Class 12 Maths PDF - All Chapters - Free PDF Download

Unit I: Sets and functions

Sets 

• ·Sets and their representations.
• Empty set.Finite and Infinite sets
• Equal sets.Subsets.Subsets of a set  of  real  numbers  especially  intervals  (with  notations).
• Power  set.  Universal  set.
• Venn diagrams.
• Union and Intersection of sets.Difference of sets
• Complement of 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 (upto R × R × 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 and cosy and their simple applications.

Unit-II: Algebra

Principle of Mathematical Induction

• Process of proof by induction.
• 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.

Complex Numbers and Quadratic Equations

• Need for complex numbers, especially √−1, motivated by the inability to solve some quadratic equations.
• Algebraic properties of complex numbers.
• Argand plane and polar representation of complex numbers.
• Statement of Fundamental Theorem of Algebra.
• Solution of quadratic equations (with real coefficients) in the complex number system.
• Square root of a complex number.

Linear Inequalities

• Linear inequalities.
• Algebraic solutions of linear inequalities in one variable and their representation on the number line.
• Graphical solution of linear inequalities in two variables.
• Graphical method of finding a solution of a system of linear inequalities in two variables.

Permutations and Combinations

• Fundamental principle of counting.
• Factorial n (n!).
• Permutations and combinations.
• Derivation of formulae for nPr and nCr and their connections.
• Simple applications.

Binomial Theorem

• History, statement and proof of the binomial theorem for positive integral indices.
• Pascal's triangle.
• General and middle terms in binomial expansion.
• Simple applications.

Sequence and Series

• Sequence and Series.
• Arithmetic Progression (A.P.).
• Arithmetic Mean (A.M.).
• Geometric Progression (G.P.).
• General term of a G.P.
• Sum of n terms of a G.P.
• Infinite G.P. and its sum.
• Geometric Mean (G.M.).
• Relation between A.M. and G.M.

Unit-III: Coordinate Geometry

Straight Lines

• Brief recall of two-dimensional geometry from earlier classes.
• Shifting of origin.
• Slope of a line and 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 and normal form.
• General equation of a line.
• Equation of family of lines passing through the point of intersection of two lines.
• Distance of a point from a line.

Conic Sections

• Sections of a cone: circles, ellipse, parabola, hyperboloids, a point, a straight line and a pair of intersecting lines as degenerated cases 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 of a point.
• Distance between two points and section formula.

Unit-IV: Calculus

Limits and Derivatives

• Derivative introduced as rate of change both as that of distance function and geometrically.
• Intuitive idea of limit.
• Limits of polynomials and rational functions, trigonometric, exponential and logarithmic functions.
• Definition of derivative and its relation to slope of tangent to a curve.
• Derivative of sum, difference, product and quotient of functions.
• Derivatives of polynomial and trigonometric functions.

Unit-V: Mathematical Reasoning

Mathematical Reasoning

• Mathematically acceptable statements.
• Connecting words/phrases – understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists".
• Use through a variety of examples related to real life and Mathematics.
• Validating statements involving connecting words.
• Difference among contradiction, converse and contrapositive.

Unit-VI: Statistics and Probability

Statistics

• Measures of Dispersion: Range, Mean Deviation, Variance and Standard Deviation of ungrouped/grouped data.
• Analysis of frequency distributions with equal means but different variances.

Probability

• Random experiments, outcomes and sample spaces (set representation).
• Events and occurrence of events.
• 'Not', 'And' and 'Or' events.
• Exhaustive events and mutually exclusive events.
• Axiomatic (set theoretic) probability.
• Connections with probability theories of earlier classes.
• Probability of an event.
• Probability of 'Not', 'And' and 'Or' events.