Unit 1: Sets & Functions | Sets | - Sets and their representationsEmpty 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 set Difference of sets Complement of a set Properties of Complement sets |
Relations & Functions | - Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto 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. 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. Pictorial representation of a function, domain, co-domain and range of a function.Sum, difference, product and quotients of functions.
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Trigonometric Functions | - Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Signs of trigonometric functions and sketches of their graphs. Expressing sin (x+ y) and cos (x + y) in terms of sin x, sin y, cos x and cos y.Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2 x + cos2 x = 1, for all x.
- Deducing the identities like the following:
 - Proofs and simple applications of sine and cosine formulae. Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type sinθ = sin α, cosθ = cosα and tanθ = tan α.
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Unit 2: Algebra | Principle of mathematical induction | - The principle of mathematical induction and simple applications.Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers.
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Complex numbers & quadratic equations | - Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Need for complex numbers, especially √−1, to be motivated by inability to solve every quadratic equation. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system, Square-root of a Complex number.
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Linear inequalities | - Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables - graphically. Linear inequalities, Algebraic solutions of linear inequalities in one variable and their representation on the number line.
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Permutations & combinations | - Fundamental principle of counting. Factorial n. Permutations and combinations derivation of formulae and their connections, simple applications
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Binomial theorem | - History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications
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Sequence & 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. Arithmetic and geometric series, infinite G.P. and its sum, geometric mean (G.M.). Relation between A.M. and G.M. Sum to n terms of the special series : ∑n, ∑n2, and ∑n3
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Unit 3: Coordinate Geometry | Straight lines | - 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. Brief recall of 2-D from earlier classes, shifting of origin. 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.
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Conic sections | - Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle. 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.
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Introduction to three-dimensional geometry | - Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula
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Unit 4: Calculus | Limits & derivatives | - Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit.Derivatives of polynomial and trigonometric functions
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Unit 5: Mathematical Reasoning | Mathematical Reasoning | - 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.
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Unit 6: Statistics & Probability | Statistics | - Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances
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Probability | - Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’, & ‘or’ events. Random experiments: outcomes, sample spaces (set representation). Events: Occurrence of events, ‘not’, ‘and’ & ‘or’ events, exhaustive events, mutually exclusive events.
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