11.I.1.1 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.
11.I.2 Relations and Functions
11.I.2.1 Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the reals with itself (up to R X R X R).
11.I.2.2 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 function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions.
11.I.3.1 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 and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: tan (x ± y) = (tan x ± tan y)/(1 ± tan x x tan y), cot(x ± y)= (cot x cot y ± 1)/(cot y ± cot x), sin x + sin y = 2sin (x + y)/2 x cos (x - y)/2, cos x + cos y = 2 cos (x + y)/2 cos (x - y)/2, sin x - sin y = 2cos (x + y)/2 sin (x - y)/2, cos x - cos y = -2sin (x + y)/2 sin (x - y)/2.
11.I.3.2 Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. General solution of trigonometric equations of the type sin θ = sin α, cos θ = cos α and tan θ = tan α. Proofs and simple applications of sine and cosine formulae.
11.II.1 Principle of Mathematical Induction
11.II.1.1 Processes of the 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.
11.II.2 Complex Numbers and Quadratic Equations
11.II.2.1 Need for complex numbers, especially √-1 , to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system.
11.II.3.1 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. Solution of system of linear inequalities in two variables – graphically.
11.II.6.1 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., geometric mean (G.M.), relation between A.M. and G.M. Sum to n terms of the special series: ∑n, ∑n² and ∑n³.
11.III.1.1 Brief recall of 2D from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form. General equation of a line. Distance of a point from a line.
11.III.2.1 Sections of a cone: Circles, ellipse, parabola, hyperbola, a point, a straight line and 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.
11.III.3 Introduction to Three-dimensional Geometry
11.III.3.1 Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.
11.IV. Limits and Derivatives
11.IV.1 Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. lim as x → 0 (loge(1 + x))/x, lim as x → 0 (e to the x power - 1)/x. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.
11.V.1 Mathematically acceptable statements. Connecting words/phrases – consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words – difference between contradiction, converse and contrapositive.
11.VI.2.1 Random experiments: Outcomes, sample spaces (set representation). Events: Occurrence of events, 'not', 'and' & 'or' events, exhaustive events, mutually exclusive events. Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of 'not', 'and' & 'or' events.