###### Give Responsive Preparation to Dream IIT with Syllabus for IIT JEE

May 20, 2022###### Syllabus for IIT JEE Mains- First and Major Concern for the Strategic Learning.

May 20, 2022The syllabus for IIT JEE Math gets rid of what to study and what not to? Aspirants require concentration as well as pure dedication to crack the exam. Numerous amount of students appears every year in JEE exam. However, very few get a chance to sit in the prestigious IITs. So, knowing the syllabus is very important for exam preparation.

## Syllabus for JEE Mains

**Syllabus** **for IIT JEE** **Math** – **JEE Mains**

The syllabus for IIT JEE Math filters the topic for you to prepare as well as practice for them. Also, it will help you formulate a proper strategy for studying in an organized manner. For mathematics, the most important thing that students need to have is rigorous practice. Additionally, the more problems students practice, the better they will be at solving questions with accuracy and speed.

So, let us have a look over the syllabus for IIT JEE Math:

**Sets, Relations, and Functions**

Sets and their representation. Union, intersection, and complement of sets and their algebraic properties. Powerset. Relation, Types of relations, equivalence relations. Functions; one-one, into and onto functions, and also the composition of functions.

**Complex Numbers and Quadratic Equations**

Complex numbers as ordered pairs of reals. Representation of complex numbers in the form (a+ib) and their representation in a plane, Argand diagram. Algebra of complex numbers, modulus and argument of a complex number, square root of a complex number. Triangle inequality. Quadratic equations in real and complex number system and their solutions. The relation between roots and coefficients, the nature of roots, and also the formation of quadratic equations with given roots.

**Matrices**

Algebra of matrices, types of matrices, and matrices of order two and also of three.

**Determinants**

Properties of determinants, evaluation of determinants, the area of triangles using determinants. Ad-joint and evaluation of inverse of a square matrix using determinants and elementary transformations. Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and also matrices.

**Permutations and Combinations**

The fundamental principle of counting. Permutation as an arrangement and also combination as a selection. The meaning of P (n,r) and C (n,r). Simple applications.

**Mathematical Induction**

The Principle of Mathematical Induction as well as its simple applications.

**Binomial Theorem**

Binomial theorem for a positive integral index. General term and middle term. Properties of Binomial coefficients and simple applications.

**Sequence and Series**

Arithmetic and Geometric progressions, insertion of arithmetic. Geometric means between two given numbers. The relation between A.M. as well as G.M. Sum up to n terms of special series: Sn, Sn2, Sn3. Arithmetic Geometric progression.

**Limit, Continuity, and Differentiability**

Real-valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity, and also differentiability. Differentiation of the sum, difference, product, and also the quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite, and implicit functions; derivatives of order up to two. Rolle’s as well as Lagrange’s Mean Value Theorems. Also applications of derivatives: Rate of change of quantities, monotonic increasing and decreasing functions, Maxima. As well as minima of functions of one variable, tangents, and normal.

**Integral Calculus**

Integral as an antiderivative. Fundamental integrals involve algebraic, trigonometric, exponential, and logarithmic functions. Integration by substitution, by parts, and by partial fractions. Integration using trigonometric identities. Also Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals, evaluation of definite integrals, and also determining areas of the regions bounded by simple curves in standard form.

**Differential Equations**

Ordinary differential equations, their order, and degree. Formation of differential equations. The solution of differential equations by the method of separation of variables. The solution of homogeneous as well as linear differential equations of the type.

**Coordinate Geometry**

Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus, and its equation, translation of axes, the slope of a line, parallel and also perpendicular lines, intercepts of a line on the coordinate axes. Various forms of equations of a line, intersection of lines, angles between two lines, and conditions for concurrence of three lines. Distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of the centroid, ortho-center, and then circumcenter of a triangle, equation of the family of lines passing through the point of intersection of two lines.

Circles, conic sections: Standard form of the equation of a circle, the general form of the equation of a circle, its radius and center, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the center at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, also condition for y = mx + c to be a tangent and point of tangency.

**3D Geometry**

Coordinates a point in space, the distance between two points. Section formula, direction ratios, and direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them, as well as its equation. Equations of a line and a plane in different forms, the intersection of a line as well as a plane, coplanar lines.

**Vector Algebra**

Scalars and Vectors. Addition, subtraction, multiplication, and division of vectors. Vector’s Components in 2D and 3D space. Scalar products and vector products as well as triple product.

**Statistics & Probability**

Measures of Dispersion: Calculation of mean, mode, median, variance, standard deviation, and mean deviation of ungrouped as well as grouped data.

**Probability**

Probability of events, multiplication theorems, addition theorems, Baye’s theorem, Bernoulli trials, Binomial distribution, and also probability distribution.

**Trigonometry**

Identities of Trigonometry and Trigonometric equations. Functions of Trigonometry. Properties of Inverse trigonometric functions. Problems on Heights and also Distances.

Mathematical Reasoning: Statements and logical operations: or, and, implied by, implies, only if and if. Understanding of contradiction, tautology, contrapositive, and also converse.

## Syllabus for JEE Advanced

**Syllabus for IIT JEE Math – JEE Advanced**

**Complex Numbers**

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**

Quadratic equations with real coefficients. Relations between roots and coefficients. Formation of quadratic equations with given roots. As well as Symmetric functions of roots.

**Sequences and Series**

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**

Logarithms and their Properties.

**Permutations and Combinations**

Problems on Permutations and Combinations

**Binomial Theorem**

Binomial theorem for a positive integral index. Properties of binomial coefficients.

**Matrices and Determinants**

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, the inverse of a square matrix of order up to three. Properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties. Additionally, solutions of simultaneous linear equations in two or three variables.

**Probability**

Addition and multiplication rules of probability, conditional probability. Bayes Theorem, independence of events. Computation of probability of events using permutations as well as combinations.

**Trigonometric Functions**

Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae. Formulae involving multiple and submultiple angles. Also, the general solution of trigonometric equations.

**Inverse Trigonometric Functions**

Relations between sides and angles of a triangle, sine rule, cosine rule. Half-angle formula and the area of a triangle. Inverse trigonometric functions (thus principal value only).

**Properties of Vectors**

The addition of vectors, scalar multiplication. Dot as well as cross products. Scalar triple products and also their geometrical interpretations.

**Functions**

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 also logarithmic functions. Even as well as odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

**Limits and Continuity**

Limit and continuity of a function. Limit and continuity of the sum, difference, product and also quotient of two functions. Also, L’s Hospital rule of evaluation of limits of functions.

**Derivatives**

The derivative of a function, the derivative of the sum, difference, product and quotient of two functions. Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and also logarithmic functions. Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative. Tangents as well as normals, increasing and decreasing functions, maximum and minimum values of a function. Rolle’s Theorem and Lagrange’s Mean Value Theorem.

**Integration**

Integration as the inverse process of differentiation. Indefinite integrals of standard functions, definite integrals, as well as their properties. Fundamental Theorem of Integral Calculus. Integration by parts, integration by the methods of substitution and also partial fractions.

**Application of Integration**

Application of definite integrals to the determination of areas involving simple curves.

**Differential Equations**

Formation of ordinary differential equations. The solution of homogeneous differential equations, separation of variables method. Also, Linear first-order differential equations.

**Wrapping Up**

For understanding such a complicated and huge amount of syllabus, one needs proper guidance. If you are looking for an IIT JEE Coaching institute Kautilya IIT Academy is a perfect place for it. With top IIT graduates as teachers, you will get a lot of academic as well as career guidance. Also, the institute provides integrated schooling with Navjeevan CBSE Academy and Navjeevan Science School which are co-units of the institute. The institute has the highest selection ratio from its origin. Well-furnished infrastructure, top faculties, integrated schooling, as well as a healthy learning environment make the institute a perfect place for JEE preparation.