JEE Main Maths Syllabus
1. 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, the composition of functions. 2. 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 (or amplitude) of a complex number, square root of a complex number. Triangle inequality; Quadratic equations in real and complex number systems and their solutions; The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots. 3. Matrices and Determinants 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. 4. Permutations and Combinations The fundamental principle of counting; Permutation as an arrangement and combination as selection; The meaning of P (n,r) and C (n,r). Simple applications. 5. Mathematical Induction The principle of Mathematical Induction and its simple applications. 6. Binomial Theorem Binomial theorem for a positive integral index; General term and middle term; Properties of Binomial coefficients and simple applications. 7. Sequence and Series 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; Arithmetic Geometric progression. 8. 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 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. 9. Integral Calculus 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. 10. 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 and linear differential equations. 11. 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 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 the centroid, orthocentre, and circumcentre of a triangle, equation of the 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. 12. 3D Geometry 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. 13. 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, triple products. 14. Statistics and Probability Measures of Dispersion: Calculation of mean, mode, median, variance, standard deviation, and mean deviation of ungrouped and grouped data; Probability: Probability of events, multiplication theorems, addition theorems, Bayes theorem, Bernoulli trials, Binomial distribution and probability distribution. 15. Trigonometry Identities of Trigonometry and Trigonometric equations; Functions of Trigonometry; Properties of Inverse trigonometric functions. Problems on Heights and Distances. 16. Mathematical Reasoning Statements and logical operations: or, and, implied by, implies, only if and if; Understanding of contradiction, tautology, contrapositive and converse.
Important Topics Expected weightage Coordinate Geometry 12% Integral and Differential Calculus 30% Trigonometry 7% Sequence and Series 7% Matrices and Determinants 7% Differential Equations 7% Topic Number of questions Sets, Relations and Functions 1 Complex Numbers and Quadratic Equations 3 Matrices and Determinants 2 Permutations and Combinations 1 Mathematical Induction 1 Binomial Theorem and its simple applications 1 Sequences and Series 2 Limit, Continuity and Differentiability 4 Integral Calculus 3 Differential Equations 1 Coordinate Geometry 5 Three-Dimensional Geometry 3 Vector Algebra 1 Statistics and Probability 2 Trigonometry 2 Mathematical Reasoning 1
IIT JEE Advanced Math Syllabus
Algebra 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, Sum 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 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, 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.
Probability Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.
Trigonometry Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, and general solution of trigonometric equations. Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric
Analytical Geometry Two dimensions Cartesian coordinates, the distance between two points, section formulae, the shift of origin. Equation of a straight line in various forms, angle between two lines, a 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, and, 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, and equations of tangent and normal.
Locus problems Three dimensions: Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.
Differential Calculus 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 normal, increasing and decreasing functions, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem.
Integral Calculus 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.
Vectors Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.
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