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JEE Main Mathematics Syllabus 2026
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Units
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Topics
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SETS, RELATIONS AND FUNCTIONS
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Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relations, type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions.
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COMPLEX NUMBERS AND QUADRATIC EQUATIONS
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Complex numbers as ordered pairs of reals, Representation of complex numbers in the forma +iband their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, Quadratic equations in real and complex number systems and their solutions; Relations between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.
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MATRICES AND DETERMINANTS
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Matrices, algebra of matrices, type of matrices, determinants and matrices of order two and three, evaluation of determinants, area of triangles using determinants; Adjoint and inverse of a square matrix; Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
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PERMUTATIONS AND COMBINATIONS
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The fundamental principle of counting, permutations and combinations; Meaning of P(n, r) and C(n, r). Simple applications.
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BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS
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Binomial theorem for a positive integral index, general term and middle term and simple applications.
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SEQUENCE AND SERIES
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Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M
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LIMIT, CONTINUITY AND DIFFERENTIABILITY
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Real–valued functions, algebra of functions; polynomial, rational, trigonometric, logarithmic and exponential functions; inverse functions. Graphs of simple functions. Limits, continuityanddifferentiability. 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 upto two, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable.
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INTEGRAL CALCULAS
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Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the type
∫ dx / (x² + a²),
∫ dx / (x² ± a²),
∫ dx / (a² − x²),
∫ dx / √(a² − x²),
∫ dx / (ax² + bx + c),
∫ dx / √(ax² + bx + c),
∫ (px + q) dx / (ax² + bx + c),
∫ (px + q) dx / √(ax² + bx + c),
∫ √(a² ± x²) dx,
∫ √(x² − a²) dx
The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard forms.
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DIFFRENTIAL EQUATIONS
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Ordinary differential equations, their order and degree, the solution of differential equation by the method of separation of variables, solution of a homogeneous and linear differential equation of the type
dy/dx + p(x)·y = q(x)
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CO-ORDINATE GEOMETRY
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Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and situation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis. Straight line: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, the distance of a point form a line, co-ordinate of the centroid, orthocentre and circumcentre of a triangle. Circle, conic sections: A standard form of equations of a circle, the 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 sections of conics, equations of conic sections(parabola, ellipse and hyperbola) in standard forms.
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THREE DIMENSIONAL GEOMETRY
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Coordinates of a point in space, the distance between two points, section formula, direction ratios and direction cosines and the angle between two intersecting lines. Equation of a line; Skewlines, the shortest distance between them and its equation.
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VECTOR ALGEBRA
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Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional spaces, scalar and vector products.
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STATISTICS AND PROBABILITY
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Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data, calculationofstandard 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 variable.
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TRIGONOMETRY
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Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions and their properties.
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