## Class 10 Maths

### 1. Real Numbers

12 Months Members Only ### 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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### 3. Pair of Linear Equations in Two Variables

Members Only ### 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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Members Only ### 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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Members Only ### 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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### 6. Triangles

Members Only ### 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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### 8. Introduction to Trigonometry

12 Months Members Only ### Introduction to Trigonometry Class 10 Maths

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0°, 90°. Values of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios. Proof and applications of the identity sin²A + cos²A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

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### 12. Area Related to Circles

Members Only ### 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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## Class 11 Maths

### 1. Sets

Student ### 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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### 2. Relations and Functions

Members Only ### 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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Members only ### (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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### 3. Trigonometric Functions

Members Only ### 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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### 5. Complex Numbers and Quadratic Equations

Members Only ### 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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Members Only ### Complex Numbers and Quadratic Equations 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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### 6. Linear Inequalities

Members Only ### 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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12 Months Members Only ### Linear Inequalities Assignments Class 11 Maths

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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### 9. Sequences and Series

Members Only ### Sequences and Series Class 11 Maths

Syllabus: 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.

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### 10. Straight Lines

Members Only ### Straight Lines Class 11 Maths

Syllabus: 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.

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### 16. Probability

Members Only ### Probability Class 11 Maths

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.

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## Class 12 Maths

### 1. Relations and Functions

Members Only ### 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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### 3. Matrices

Members Only ### 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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### 4. Determinants

Members only ### 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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### 5. Continuity and Differentiability

Members Only ### 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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Members Only ### 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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Members Only ### 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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### 6. Application of Derivatives

Members Only ### 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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### 7. Integrals

Members Only ### 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. $$\int{\frac{dx}{x^2 \pm a^2}}$$, $$\int{\frac{dx}{\sqrt{x^2 \pm a^2}}}$$, $$\int{\frac{dx}{\sqrt{a^2 - x^2}}}$$, $$\int{\frac{dx}{ax^2+bx+c}}$$, $$\int{\frac{dx}{\sqrt{ax^2+bx+c}}}$$, $$\int{\frac{px+q}{ax^2+bx+c}}dx$$, $$\int{\frac{px+q}{\sqrt{ax^2+bx+c}}}dx$$, $$\int{\sqrt{a^2 \pm x^2}}dx$$, $$\int{\sqrt{x^2-a^2}}dx$$, $$\int{\sqrt{ax^2+bx+c}}dx$$, $$\int{(px+q) \sqrt{ax^2+bx+c}}dx$$

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### 9. Differential Equations

Members only ### Differential Equations Class 12 Maths

Definition, order and degree, general and particular solutions of a differential equation. formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: $$\frac{dy}{dx}+ py = q$$, where p and q are functions of y or constants $$\frac{dx}{dy}+ px = q$$, where p and q are functions of y or constants

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### 10. Vector Algebra

Members Only ### Vector Algebra Class 12 Maths

Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

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### 11. Three Dimensional Geometry

Members Only ### Three Dimensional Geometry Class 12 Maths

Direction cosines and direction ratios of a line joining two points.Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines.Cartesian and vector equation of a plane.Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.Distance of a point from a plane.

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### 12. Linear Programming Problems

Members Only ### Linear Programming Problems Class 12 Maths

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

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## Deleted Syllabus

Deleted syllabus will be provided after October 2020 to those members who need them. For more details check FAQ.