Class 11 Maths Syllabus : Details, Important, Preparation, Exam

1. Sets 

Sets and their representations, Empty sets, Finite and Infinite sets, Equal sets, Subsets, and Subsets of a set of real numbers especially intervals (with notations). Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement.

2. Relations & Functions

Ordered pairs. Cartesian product of sets. Several 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.

3. Trigonometric Functions

Positive and negative angles. Measuring angles in radians and degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. The 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 sex, siny, cost & cosy and their simple applications.

1. Complex Numbers and Quadratic Equations 

Need for complex numbers, especially √−1, to be motivated by the inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane

2. Linear Inequalities

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.

3. Permutations and Combinations

The fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of Formulae for nPr and nCr and their connections, simple applications.

4. Binomial Theorem

Historical perspective, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, simple applications.

5. Sequence and Series

Sequence and Series. Arithmetic Mean (A.M.) Geometric Progression (G.P.), 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.

1. 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 the axis, point-slope form, slope-intercept form, two-point form, intercept form, and Distance of a point from a line.

2. Conic Sections

Sections of a cone: circles, ellipses, parabolas, hyperbolas, a point, straight lines 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.

3. Introduction to Three-dimensional Geometry

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points.

1. Limits and Derivatives 

Derivative introduced as 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. The definition of derivative relates to the slope of the tangent of the curve, a derivative of the sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

1. Statistics 

Measures of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/grouped data.

2. 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.