NCERT Class 11 Maths Syllabus
Unit 1. Sets and Functions
Unit 2. Algebra
Unit 3. Coordinate Geometry
Unit 4. Calculus
Unit 5. Mathematical Reasoning
Unit 6. Statistics and Probability
TERM I (2021 -2022)
Unit-I: Sets and Functions 1. 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). Power set. Universal set. Venn diagrams. Union and Intersection of sets. 2. 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 ( R x R only).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. Unit-II: Algebra 1. Complex Numbers and Quadratic Equations Need for complex numbers, especially√−1, to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers. Argand plane. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system. 2. Sequence and 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., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Unit-III: Coordinate Geometry 1. 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 and normal form. General equation of a line. Distance of a point from a line. Unit-IV: Calculus 1. Limits Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions Unit-V: Statistics and Probability 1. Statistics Measures of Dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped data.
TERM II ( 2021 - 2022)
Unit-I: Sets and Functions 1. 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 sinα ± sinβ = 2sin 1 2 (α ± β)cos 1 2 (α ∓ β) cosα + cosβ = 2cos 1 2 (α + β)cos 1 2 (α − β) 𝑐𝑜𝑠𝛼 − 𝑐𝑜𝑠𝛽 = −2𝑠𝑖𝑛 1 2 (𝛼 + 𝛽)𝑠𝑖𝑛 1 2 (𝛼 − 𝛽) Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x. Unit-II: Algebra 1. Linear Inequalities 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. Graphical method of finding a solution of system of linear inequalities in two variables. 2. Permutations and Combinations Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, formula for nPr and nCr, simple applications. Unit-III: Coordinate Geometry 1. Conic Sections Sections of a cone: circles, ellipse, parabola, hyperbola. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle. 2. Introduction to Three-dimensional Geometry Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula. Unit-IV: Calculus 1. Derivatives 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. Unit-V: Statistics and Probability 1. Probability Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.
The syllabus provides an overview of the Maths topics. Maths is a subject that requires daily practice. So knowing the syllabus will help students in creating a daily study plan. Students can easily keep a record of topics that they have completed. Students will feel confident during the exam as the question paper will be designed from the syllabus.
Mathematics, study material, class 11
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