Math Olympiad For Class 11 | Olympiad Preparation Online | IMO | Math Olympiad Books
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NCERT Solutions for Class 11 Maths
Read Notes and Videos,Practice,Mock Tests for Class 11 Maths
Practice questions and NCERT Solutions for Class 11
Maths is one of the vital subject and it is also of very much importance while preparing for various competitive exams and hence it is essential to prepare it from the very beginning. Understanding the concepts and applying them in the provided situation can improvise your analytical as well as logical thinking.
Maths is a very important resource for students of CBSE Class 11. Maths is an interesting subject for the enhancement of analytical and problem solving skills.
Unfortunately, many students find it difficult because of no interest or lack of better knowledge to comprehend. Maths is really a difficult subject but very interesting when comprehended well and practice with easy to hard problems and students find it difficult because most of them do not have their basics clear for the subject. Lack of sufficient practice tool is a major reason why solving Mathematical problems seems a tough nut to crack.
School Connect Online students are not only solving and understanding questions from Maths from NCERT or Syllabus but also they are solving questions to practice Maths Olympiad this helps students to become expert
To help you with this, we have learning notes and videos, Practice questions for NCERT,JEE Main and Advance,IIT JEE Main and Advance, with Solutions for Class 11 Maths.
Practice Solutions for Class 11 Maths
NCERT solutions of Class 11 Maths includes solutions of all questions and more to help and support practice with more relevant and important questions. These solutions have been provided and prepared by the most experienced teachers and important resources. A very simple approach has been followed while solving the questions and designing the NCERT Solutions for Class 11 Maths. Students will find it extremely easy to understand the problems and how to go about solving them.
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Unlike other subjects, rote learning cannot help you to excel in Maths as it requires more analytical approach and critical ability to think and solve. Even for other subjects, rote learning is not recommended as it won’t be of much use after a point of time. Maths, from the very beginning, needs one to think logically to enhance analytical ability. But just because the subject needs logical thinking and analytical skills does not mean it is tough. Maths needs practice and with practice, anything can be perfected, even the way you think and analyze.
So, it is of utmost importance to take Maths seriously right from your early school life. Getting your basics clear at this point will make it easier for you to handle difficult concepts as you grow older.
Maths of Class 11 standard plays a vital role in strengthening the fundamentals of the subject with comprehensive analysis. It is at this point, Maths goes beyond simple addition, subtraction, multiplication, and division and move onto more complex concepts to practice and understand . So, one must prepare for this subject in a serious manner and get all their doubts clear,with maximum practice more and more to master the problem solving skill. Otherwise, they won’t be able to cope with the subject later, especially if they are planning to take up Science in their Higher Secondary level.Subject like Maths and Maths in higher classes has Maths base to solve and analyse.
IIT JEE Main And Advance Paper Analysis for Maths
Maths
Maths was the easiest paper amongst the three. Most questions were calculative. There were 10 questions asked from the 11th standard syllabus and 20 questions from the 11th standard syllabus. This section had 3 difficult questions, 14 moderate questions and 13 easy questions.
This is a breakup of chapters which had the toughest and easiest questions:
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Tough Questions
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Easy questions (11th Standard)
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Easy questions (11th Standard)
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Hyperbola
Parabola
Sets
Relations and Functions
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Mathematical Induction and Reasoning
Parabola
Permutations and Combinations
Quadratic Equations
Sequences and Series
Statistics
Trigonometry
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3D Geometry
Determinants
Differential Equations
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This is the breakup of marks between different topics of the Maths section:
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Topic
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Marks Allotted
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Algebra
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56
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Calculus
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28
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Trigonometry
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8
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Conics
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16
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Vector Algebra
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11
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Maths Syllabus for Class 11
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Unit
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Topic
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Marks
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I.
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Sets and Functions
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29
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II.
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Algebra
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37
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III.
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Co-ordinate Geometry
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13
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IV.
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Calculus
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6
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V.
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Mathematical Reasoning
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3
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VI.
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Statistics and Probability
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12
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Total
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100
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Unit-I: Sets and Functions
1. Sets
- Sets and their representations.
- Finite and Infinite sets.
- Empty set. Power set. Equal sets. Subsets.
- Properties of Complement Sets.
- Venn diagrams. Difference of sets.
- Complement of a set.
- Universal set. Subsets of a set of real numbers especially intervals (with notations).
- Union and Intersection of sets.
- Practical Problems based on sets.
2. Relations & Functions
- Ordered pairs, Cartesian product of sets.
- Cartesian product of the sets of real (up to R x R).
- Pictorial representation of a function, domain, co-domain, and range of a function. Function as a special kind of relation from one set to another.
- Definition of relation, pictorial diagrams, domain, co-domain, and range of a relation. Number of elements in the cartesian product of two finite sets.
- Sum, difference, product and quotients of functions.
- Real-valued functions, domain and range of these functions: modulus, exponential, constant, polynomial, identity, rational, Signum, logarithmic and greatest integer functions, with their graphs.
3. Trigonometric Functions
- Positive and negative Angles.
- Definition of trigonometric functions with the help of the unit circle.
- Truth of the sin2x+cos2x=1, for all x.
- Signs of trigonometric functions
- Domain and range of trigonometric functions and their graphs.
- Measuring angles in radians and in degrees and conversion of one into other. Expressing sin (x±y) and cos (x±y) in terms of sin x, sin y, cos x & cos y and their simple application.
- Deducing identities like the following: Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x.
- General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.
Unit-II: Algebra
1. Principle of Mathematical Induction
- 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.
- The principle of mathematical induction and simple applications.
2. Complex Numbers and Quadratic Equations
- 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 and polar representation of complex numbers.
- Statement of Fundamental Theorem of Algebra, solution of Quadratic equations in the complex number system. Square root of a complex number.
3. 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 solution of system of linear inequalities in two variables.
4. Permutations and Combinations
- Fundamental principle of counting.
- Factorial n. (n!)Permutations and combinations,
- Derivation of formulae and their connections, simple applications.
5. 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.
6. 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., Arithmetic and Geometric series infinite G.P. and its sum, geometric mean (G.M.),
- Relation between A.M. and G.M.
- Formula for the following special sum
Unit-III: Coordinate Geometry
1. Straight Lines
- Brief recall of two dimensional geometry from earlier classes. Shifting of origin.
- 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. Equation of family of lines passing through the point of intersection of two lines.
- Distance of a point from a line.
2. 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.
3. 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. 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 slope of tangent of a curve, derivative of sum, difference, product and quotient of functions.
- The derivative of polynomial and trigonometric functions.
Unit-V: Mathematical Reasoning
1. 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 Maths.
- Validating the statements involving the connecting words difference between contradiction, converse and contrapositive.
Unit-VI: Statistics and Probability
1. Statistics
- Measures of dispersion; Range, mean deviation, variance and standard deviation of ungrouped/grouped data.
- Analysis of frequency distributions with equal means but different variances.
2. Probability
- Random experiments; outcomes, sample spaces (set representation).
- Events; occurrence of events, ‘not’, ‘and’ 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’ and ‘or’ events.
IIT JEE Syllabus for Maths
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Algebra
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Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.
Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
Logarithms and their properties.
Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.
Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.
Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.
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Trigonometry
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Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.
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Analytical Geometry
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Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).
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Two dimensions
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Cartesian coordinates, distance between two points, section formulae, shift of origin
Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle. Equation of a circle in various forms, equations of tangent, normal and chord.
Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal. Locus Problems.
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Three dimensions
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Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.
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Differential calculus
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Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions.
Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.
Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, Rolle’s Theorem and Lagrange’s Mean Value Theorem.
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Integral calculus
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Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, Fundamental Theorem of Integral Calculus. Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves. Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.
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Vectors
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Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.
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Tips and Tricks to prepare for Maths
Attempt as many conceptual questions on those derivations as you can. This will give you a better understanding of the subject.
- Look for new questions on similar context from previous year’s question papers, sample papers and other model test papers.
- Always time yourself while solving sample papers as it will help you better manage time during the exam.
- Revision of notes and memorizing the formulas and the definition of difficult terms helps a lot while last minute preparation. Keep a few lists of topics separately for quick revision and it must contain the important formulae, derivations and important definitions.
- Solve as many Class 11 sample papers you can.Practice past year question papers & model test papers.
- Time management is a must; take out time for re-creation as well along side preparation.
- Try and finish all the topics and questions in the NCERT books.CBSE board questions are majorly based on the question in this book only.
Reference Links –
Other National and International Level Olympiads
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AI Olympiad
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International Artificial Intelligence Olympiad
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Coding Olympiad
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International Coding Olympiad
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IMO
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International Maths Olympiad
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ISO
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International Science Olympiad
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KVPY
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Kishore Vaigyanik Protsahan Yojana
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