Class XI
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The Updated Syllabus Taken From CBSE Website
Unit One: Sets and Functions
Unit Two: Algebra
Unit Three: Co-ordiante Geometry
Unit Four: Calculus
Unit Five: Statistics and probability
- 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 (upto 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 sin^2 x + cos^2 x = 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:- Compound angle formula
- Double angle formula
- Transformtion formula
- Complex Numbers
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 and 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.
- 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.
- 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. Derivatives of polynomial and trigonometric functions.
- 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.
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Chapters
1. Sets and Properties
Unit 1
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on writing of set, finite and infinite sets, etc. | |
Concept Exploration Exercise (CEE)-02 | Based on concepts of subsets, number of subsets, power set. | |
Concept Exploration Exercise (CEE)-03 | Based on various operations on sets. | |
Concept Exploration Exercise (CEE)-04 | Based on union-intersection formula, Venn-diagram, etc. | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
2. Relations and Functions
Unit 1
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Ordered pairs, and Cartesian product of two sets. | |
Concept Exploration Exercise (CEE)-02 | Based on Relation on sets, domain and range. | |
Concept Exploration Exercise (CEE)-03 | Based on Functions, domain, and range. | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
3. Trigonometric Functions
Unit 1
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on conversion of units and relation between arc, radius and angle | |
Concept Exploration Exercise (CEE)-02 | Based on sign of T-functions in different quadrants | |
Concept Exploration Exercise (CEE)-03 | Based on reference angle and co-relation identities | |
Concept Exploration Exercise (CEE)-04 | Based on Compound Angle Identities | |
Concept Exploration Exercise (CEE)-05 | Based on Transformation Identities | |
Concept Exploration Exercise (CEE)-06 | Based on Multiple Angle Identities | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
4. Complex Numbers
Unit 2
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on power of iota, basic operations on complex numbers, Conjugate, Modulus | |
Concept Exploration Exercise (CEE)-02 | Based on argument of complex number, properties of argument, polar form | |
Concept Exploration Exercise (CEE)-03 | Based on Square root of complex number, cube roots of unity, complex roots equation | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
6. Permutation And Combination
Unit 2
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Fundamental Counting | |
Concept Exploration Exercise (CEE)-02 | Based on Factorial Calculation | |
Concept Exploration Exercise (CEE)-03 | Based on Permutation | |
Concept Exploration Exercise (CEE)-04 | Based on Combination | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
7. Binomial Theorem
Unit 2
8. Sequence and Series
Unit 2
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Definition of sequence | |
Concept Exploration Exercise (CEE)-02 | Based on Arithmetic Progression | |
Concept Exploration Exercise (CEE)-03 | Based on Geometric Progression | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
9. Straight Lines
Unit 3
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Distance Formula, Area, etc. | |
Concept Exploration Exercise (CEE)-02 | Based on Slope of Line | |
Concept Exploration Exercise (CEE)-03 | Based on Equation of Lines | |
Concept Exploration Exercise (CEE)-04 | Length of perp. Image, Foot of Perp. | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
10. Conic Sections
Unit 3
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Circles | |
Concept Exploration Exercise (CEE)-02 | Based on Parabola | |
Concept Exploration Exercise (CEE)-03 | Based on Ellipse | |
Concept Exploration Exercise (CEE)-04 | Based on Hyperbola |
12. Limits & Derivatives
Unit 4
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Evaluating the Limits | |
Concept Exploration Exercise (CEE)-02 | Based on Derivatives | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
13. Statistics
Unit 5
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Mean Deviation | |
Concept Exploration Exercise (CEE)-02 | Variance and Standard Deviation | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 20 plus questions with answers | Download |
14. Probability
Unit 5
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Describing the Events | |
Concept Exploration Exercise (CEE)-02 | Finding Out the Probabilities | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 20 plus questions with answers | Download |
Start practicing the language of numbers and patterns, for in the disciplined pursuit of mathematics lies the power to unravel complexities and forge a path to intellectual excellence.