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Triangles Class 10 Maths

Definitions, examples, counter examples of similar triangles. 1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. 2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. 4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. 5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar. 6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other. 7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. 8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. 9. (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right angle.

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Area related to Circles Class 10 Maths

Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

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Derivatives Class 11 Maths

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.

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Quadratic Equations Class 10 Maths

Standard form of a quadratic equation ax²+bx+c=0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.

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Polynomials Class 10 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 10 Mathematics.

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Polynomials Class 10 Maths

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

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Pair of Linear Equations in Two Variables Class 10 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 10 Mathematics.

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Determinants Class 12 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

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Determinants Class 12 Maths

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

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Continuity and Differentiability (Differentiability Assignment – 3) Class 12 Assignments

This course is based on the Assignment - 3 Differentiability by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

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Limits Class 11 Maths

Intuitive idea of limit.Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions.

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Matrices Class 12 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

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Applications of Derivatives Class 12 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

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Continuity and Differentiability (Derivative Assignments) Class 12 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 12 Mathematics.

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Real Numbers Class 10 Maths

Euclid’s division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality, Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

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Binomial Theorem Class 11 Assignments

This course is based on the Assignments by Ashish Kumar (Agam Sir). The assignments have questions from NCERT Exemplar, Board's Question Bank, R. D. Sharma etc., under the syllabus of Class 11 Mathematics.

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Arithmetic Progression Class 10 Maths

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

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Integrals Class 12 Maths

Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.

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Pair of Linear Equations in Two Variables Class 10 Maths

Pair of linear equations in two variables and graphical method of their solution, consistency / inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations.

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Applications of Derivatives Class 12 Maths

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

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Applications of Trigonometry Class 10 Maths

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, 60°.

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Matrices Class 12 Maths

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on Matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

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Trigonometric Functions Class 11 Maths

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.

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Continuity and Differentiability Class 12 Maths

Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions.Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

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Probability Class 12 Maths

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable.

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Other Important Topics for Maths and Physics

This course contains supplementary / extra videos that will be required for better understanding of Maths and Physics but are not covered under the school syllabus.

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Practice & Exam Preparation Tips

This is 12 Months Members Only Course consisting of Agam Sir tips and wisdom for practice and exam preparations.

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Agam Wisdom

Motivational Videos by Agam Sir will be posted in this course from time to time. This course is available for all members.

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(Domain – Range) Relations and Functions Class 11 Maths

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.

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Linear Inequalities Class 11 Maths

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.

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Relations and Functions Class 11 Maths

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. Sum, difference, product and quotients of functions.

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Sets Class 11 Maths

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. Difference of sets. Complement of a set. Properties of Complement.

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Complex Numbers Class 11 Maths

Need for complex numbers, especially $$\sqrt{-1}$$, to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers.Argand plane and polar representation of complex numbers.Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system.Square root of a complex number.

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Principle of Mathematical Induction Class 11 Maths

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.

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Binomial Theorem Class 11 Maths

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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Permutations and Combinations Class 11 Maths

Fundamental theorem of counting, factorial, permutations and combinations. All the NCERT solutions from the Exercise 7.1, 7.2, 7.3, 7.4 and the miscellaneous exercise.

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Inverse Trigonometric Functions Class 12 Maths

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions Elementary properties of inverse trigonometric functions.

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Relations and Functions Class 12 Maths (Part – 2)

One to one andonto functions, composite functions, inverse of a function.

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Relations and Functions Class 12 Maths – (Part – 1)

Empty Relations, Universal Relations, Trivial Relations, Reflexive Relations, Symmetric Relations, Transitive Relations, Equivalence Relations, Equivalence Classes, and Questions based on the above topics from NCERT Textbook, Board’s Question Bank, RD Sharma, NCERT Exemplar etc.

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