Class 11 Mathematics Syllabus West Bengal Board 2025 PDF

Marks: 40

CONTACT HOURS: 100 Hours

UNIT-I: SETS AND FUNCTIONS

1) Sets CONTACT HOURS- 15 and MARKS- 4

Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets, Subsets of the 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 sets.

2) Relations and Functions CONTACT HOURS- 15 and MARKS- 4

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 × 𝑅 × 𝑅). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. 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. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, exponential, logarithmic, signum and greatest integer functions with their graphs. sum, difference, product and quotients of functions.

3) Trigonometric Functions CONTACT HOURS- 15 and MARKS- 7

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 sinଶ 𝑥 + cosଶ 𝑥 = 1, for all 𝑥. Signs of trigonometric functions, domain, range and sketch their graphs. Expressing sin(𝑥 ± 𝑦) and cos(𝑥 ± 𝑦) in terms of sin 𝑥 , cos 𝑥, sin 𝑦 and cos 𝑦.

Deducing identities like the following:

Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solutions of trigonometric equations of the type sin 𝜃 = sin 𝛼 , cos 𝜃 = cos 𝛼 and tan 𝜃 = tan 𝛼.

UNIT-II: ALGEBRA

1) Complex Numbers and Quadratic Equations CONTACT HOURS- 13 and MARKS- 6

Need for complex numbers, especially √−1, to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane, polar representation of complex numbers, modulus, argument. solution of quadratic equation in complex number system.

2) Linear inequalities CONTACT HOURS- 5 and MARKS- 4

Linear inequalities. Algebraic solutions of linear inequalities in one variable and modulus function and their representation on the number line. Graphical solution of linear inequalities in two.

3) Permutations and Combinations CONTACT HOURS- 12 and MARKS- 5

Fundamental principle of counting. Factorial 𝑛 (𝑛!). Permutations and combinations, derivation of formulae for npr and ncr and their connections, simple applications

UNIT-III: CALCULUS

1) Limits and Derivatives CONTACT HOURS- 25 and MARKS- 10

Intuitive idea of limit. Limits of polynomials and rational functions, trigonometric, exponential and logarithmic functions. Derivative introduced as rate of change both as that of distance function and geometrically. Definition of derivative, relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

Marks: 40

CONTACT HOURS: 80 Hours

UNIT-I: ALGEBRA

1) Principle of Mathematical Induction CONTACT HOURS- 7 and MARKS- 3

Process of the proof by induction motivating the application of method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications

2) Binomial theorem CONTACT HOURS- 13 and MARKS- 6

History, Statement and proof of the binomial theorem for positive integral indices. Pascal’s Triangle, General and middle term in Binomial expansion, Simple applications.

3) Trigonometric Functions CONTACT HOURS- 15 and MARKS- 6

Sequence and series. Arithmetic Progression (A.P.), Arithmetic Mean (A.M.), Geometric Progression (G.P.), Geometric Mean (G.M,) relation between A.M. & G.M., Arithmetic-Geometric Progression Series (AGP series), infinite G.P. and its sum, sum to n terms of the special series

UNIT-II: COORDINATE GEOMETRY (2D)

1) Straight lines CONTACT HOURS- 10 and MARKS- 5

Brief recall of two dimensional geometry from earlier classes. 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, distance of a point from a line.

2) Conic sections CONTACT HOURS- 20 and MARKS- 10

Sections of a Cone: circle, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of conic section; Standard equation of circle, general equation of circle, Standard equations and simple properties of Parabola, Ellipse and Hyperbola.

UNIT-III: STATISTICS AND PROBABILITY

1) Statistics  CONTACT HOURS- 5 and MARKS- 3

Measures of dispersion: Range, mean deviation, variance and standard deviation of ungrouped/ grouped data.

2) Probability CONTACT HOURS- 10 and MARKS- 7

Random experiments, outcomes, Sample spaces (set representation), 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.

[ Note:20 Hours reserved for Remedial classes, Tutorials and Home Assignments.]

Course: Project for Class XI

Full Marks: 20

Projects should be conducted regularly throughout the year. A project notebook is to be prepared by each and every student where all the below mentioned activities should be recorded. There should be a project assessment once a year (once in Class XI and once in Class XII) where the student will be asked to do one of the activities and write it in his/her script provided for the purpose. The student should carry his/her project notebook during the assessment. A viva should also be conducted during the assessment to test the knowledge of the student regarding the project activity.

List of Projects for Class XI