# JEE Mathematics Syllabus

Mathematics is one of the three subjects involved in the National level examination i.e. JEE. In order to prepare well for JEE Mathematics, candidates need to be well aware with the JEE Main Mathematics Syllabus. Being well aware with the syllabus will definitely help students to know about the important topics included in the JEE Main Mathematics syllabus. Usually, students are afraid of Mathematics, so in order to overcome their fear, JEE aspirants are advised to start preparing this subject pretty well in advance. Also, candidates are advised to practice a large number of IIT JEE previous years question papers. By regularly solving previous years papers, candidates will be able to know the type of questions that might be available in the question paper and will also be able to check their preparation level. Keep reading the further details to get detailed IIT JEE Mathematics Syllabus for JEE Main & JEE Advanced.

- 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, composition of functions

- 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 (or amplitude) 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, nature of roots, the formation of quadratic equations with given roots.

- Matrices: Algebra of matrices, types of matrices, and matrices of order two and three.
- Determinants: Properties of determinants, evaluation of determinants, the area of triangles using determinants.
- Adjoint 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 matrices.

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

- The principle of Mathematical Induction and its simple applications.

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

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

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

- Integral as an antiderivative.
- Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions.
- Integration by substitution, by parts, and by partial fractions.
- Integration using trigonometric identities.
- Integral as limit of a sum.
- Evaluation of simple integrals:

- Fundamental Theorem of Calculus.
- Properties of definite integrals, evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

- 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 and linear differential equations of the type:

- 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 perpendicular lines, intercepts of a line on the coordinate axes.
- Straight lines: Various forms of equations of a line, intersection of lines, angles between two lines, 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 centroid, orthocentre, and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.
- Circles, conic sections: Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre 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, condition for y = mx + c to be a tangent and point (s) of tangency.

- Coordinates of 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 and its equation.
- Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

- Vectors and scalars, the addition of vectors.
- Components of a vector in two dimensions and three-dimensional space.
- Scalar and vector products, scalar and vector triple product.

- Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
- Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

- Trigonometric identities and equations.
- Trigonometric functions.
- Inverse trigonometric functions and their properties.
- Heights and Distances.

- Statements, logical operations and, or, implies, implied by, if and only if.
- Understanding of tautology, contradiction, converse, and contrapositive.

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