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Skills available for India class XI maths curriculum

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National Council of Education Research and Training Syllabus: CISCE Class XI National Council of Education Research and Training Syllabus: CISCE Class XI
National Council of Education Research and Training Syllabus: Class XI National Council of Education Research and Training Syllabus: Class XI

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11.I Sets and Functions

11.I.1 Sets
- 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 Trigonometric 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.V Mathematical Reasoning

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 Statistics and Probability

11.VI.1 Statistics
- 11.VI.1.1 Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.
  - Mean absolute deviation (XI-FF.4)
  - Variance and standard deviation (XI-FF.5)
11.VI.2 Probability
- 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.

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11.I Sets and Functions

11.I.1 Sets

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.3 Trigonometric Functions

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 Algebra

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.3 Linear Inequalities

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.4 Permutations and Combinations

11.II.4.1 Fundamental principle of counting. Factorial n. Permutations and combinations, derivation of formulae and their connections, simple applications.

11.II.5 Binomial Theorem

11.II.5.1 History, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, general and middle term in binomial expansion, simple applications.

11.II.6 Sequence and Series

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 Coordinate Geometry

11.III.1 Straight Lines

11.III.2 Conic Sections

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 Calculus

11.IV. Limits and Derivatives

11.V Mathematical Reasoning

11.VI Statistics and Probability

11.VI.1 Statistics

11.VI.1.1 Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

11.VI.2 Probability