JEE Main Mathematics
Algebra, Calculus, Coordinate Geometry, Vectors & 3D, Trigonometry, Statistics and Probability — chapter-wise notes for JEE Main.
Sets, Relations and Functions
Set operations, types of relations, equivalence relations, domain and range, one-one and onto functions, composition and inverse.
Complex Numbers
Algebra of complex numbers, modulus and argument, Argand plane, polar and Euler form, cube roots of unity, locus problems.
Quadratic Equations
Nature of roots, relation between roots and coefficients, symmetric expressions, location of roots and common roots.
Matrices and Determinants
Types of matrices, transpose, adjoint and inverse, properties of determinants, system of linear equations.
Permutations and Combinations
Counting principles, arrangements with and without repetition, selections, circular permutations and distributions.
Binomial Theorem
General term, middle term, term independent of x, greatest coefficient and properties of binomial coefficients.
Sequences and Series
AP, GP, AM–GM inequality, sums of special series and the method of differences.
Limits, Continuity and Differentiability
Standard limits, L’Hospital’s rule, continuity, differentiability and methods of differentiation.
Applications of Derivatives
Rate of change, tangents and normals, increasing and decreasing functions, maxima and minima.
Integral Calculus
Standard integrals, substitution, integration by parts, partial fractions, definite integrals and area under curves.
Differential Equations
Order and degree, variable separable, homogeneous and linear differential equations.
Straight Lines
Slope, forms of a line, distance of a point from a line, angle between lines, family of lines.
Circles
Equations of a circle, tangents and normals, chord of contact, position of a point and of two circles.
Conic Sections
Parabola, ellipse and hyperbola — standard forms, focus, directrix, eccentricity, latus rectum and tangents.
Three Dimensional Geometry
Direction cosines, equations of lines and planes, angles, shortest distance and image of a point.
Vector Algebra
Vector operations, dot and cross products, projections, scalar triple product and coplanarity.
Statistics
Mean, median, mode, variance and standard deviation of grouped and ungrouped data, and the effect of changing data.
Probability
Classical probability, addition and multiplication theorems, conditional probability, Bayes’ theorem and binomial distribution.
Trigonometry
Identities, trigonometric equations, inverse trigonometric functions and properties of triangles.