CBSE Class 11 Mathematics

Unit-I: Sets and Functions (23 Marks)

• 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). 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 (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. Deducing identities like the following: tan(x ± y) = (tan x ± tan y) / (1 ∓ tan x tan y), cot(x ± y) = (cot x cot y ∓ 1) / (cot y ± cot x), sin α ± sin β = 2 sin ½(α ± β) cos ½(α ∓ β), cos α + cos β = 2 cos ½(α + β) cos ½(α - β), cos α - cos β = -2 sin ½(α + β) sin ½(α - β). Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x.

Note for Students: This unit establishes the foundational language of mathematics through set theory and functions, while building a robust understanding of trigonometric identities required for calculus.

Unit-II: Algebra (25 Marks)

• Complex Numbers and Quadratic Equations: 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.
• Linear Inequalities: Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.
• Permutations and Combinations: Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of Formulae for ⁿPᵣ, 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.), 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.

Note for Students: This unit focuses on algebraic structures and counting techniques, providing essential tools for solving higher-order equations and understanding mathematical patterns.

Unit-III: Coordinate Geometry (12 Marks)

• Straight Lines: 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.
• 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 of a point. Distance between two points.

Note for Students: Coordinate geometry bridges algebra and geometry, teaching students how to visualize equations and analyze the properties of various geometric shapes in both 2D and 3D planes.

Unit-IV: Calculus (08 Marks)

• 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 relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions of polynomial and trigonometric functions.

Note for Students: This introductory calculus unit focuses on the concept of limits and the definition of derivatives, serving as a critical gateway to advanced mathematical analysis.

Unit-V: Statistics and Probability (12 Marks)

• 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.

Note for Students: This unit provides practical tools for data interpretation and quantifying uncertainty, which are vital for research, economics, and scientific experimentation.