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JEE Main Mathematics Syllabus: Units, Sub-Topics & Key Concepts
This comprehensive guide covers all essential units and sub-topics included in the Class 11 and 12 Mathematics syllabus. From foundational topics like Sets, Relations and Functions, to advanced chapters such as Differential Calculus, Vector Algebra, and Three-Dimensional Geometry, each unit is well-structured with concept-based sub-topics. Students will also explore core areas like Complex Numbers, Quadratic Equations, Matrices and Determinants, Permutations and Combinations, Binomial Theorem, Probability, Coordinate Geometry, and Trigonometry. Topic-wise links from Aakash are provided for deeper conceptual clarity and revision support. This structured breakdown helps students strengthen fundamentals and prepare effectively for competitive exams such as JEE and NEET.
| Units | Unit Name | Sub Topics |
|
Unit 1
|
Sets, Relations and Functions
|
Sets and their representation |
| Union, intersection, and complement of sets | ||
| Algebraic properties of sets | ||
| Power set | ||
| Relations and types of relations | ||
| Equivalence relations | ||
| Functions: one-one, onto, into | ||
| Composition of functions | ||
|
Unit 2
|
Complex Numbers and Quadratic Equations
|
Complex numbers as ordered pairs of reals |
| Form a + ib and representation in the plane | ||
| Argand diagram | ||
| Algebra of complex numbers | ||
| Modulus and argument (amplitude) | ||
| Quadratic equations in real and complex number systems | ||
| Relations between roots and coefficients | ||
| Nature of roots | ||
| Formation of quadratic equations with given roots | ||
|
Unit 3
|
Matrices and Determinants
|
Types and algebra of matrices |
| Determinants of order 2 and 3 | ||
| Evaluation of determinants | ||
| Area of triangle using determinants | ||
| Adjoint and inverse of square matrix | ||
| Test of consistency | ||
| Solving simultaneous linear equations in 2 or 3 variables | ||
|
Unit 4
|
Permutations and Combinations
|
Fundamental principle of counting |
| Permutations: P(n, r) | ||
| Combinations: C(n, r) | ||
| Simple applications | ||
|
Unit 5
|
Binomial Theorem
|
Binomial theorem for positive integral index |
| General term | ||
| Middle term | ||
| Simple applications | ||
|
Unit 6
|
Sequences and Series
|
Arithmetic progression (A.P.) |
| Geometric progression (G.P.) | ||
| Insertion of A.M. and G.M. between two numbers | ||
| Relation between A.M. and G.M. | ||
|
Unit 7
|
Differential Calculus
|
Real-valued functions: polynomial, rational, trigonometric, logarithmic, exponential |
| Inverse functions and their graphs | ||
| Limits, continuity, and differentiability | ||
| Derivatives of sum, difference, product, quotient of functions | ||
| Derivatives of trigonometric, inverse trigonometric, exponential, logarithmic, composite, and implicit functions | ||
| Higher-order derivatives (up to second order) | ||
| Applications: rate of change, monotonicity, maxima and minima | ||
|
Unit 8
|
Integral Calculus
|
Integral as anti-derivative |
| Fundamental integrals (algebraic, trigonometric, exponential, logarithmic) | ||
| Integration by substitution, parts, and partial fractions | ||
| Integration using trigonometric identities | ||
| Properties and evaluation of definite integrals | ||
| Area under curves (bounded regions) | ||
|
Unit 9
|
Differential Equations
|
Order and degree of ODEs |
| Solution by separation of variables | ||
| Homogeneous and linear differential equations | ||
| Standard form: dy/dx + P(y) = Q(x) | ||
|
Unit 10
|
Co-ordinate Geometry (2D)
|
Cartesian coordinate system |
| Distance formula, section formula | ||
| Locus and its equation | ||
| Slope of line, parallel & perpendicular lines | ||
| Line equations (various forms) | ||
| Intersection of lines and angle between them | ||
| Concurrence of lines | ||
| Distance of a point from a line | ||
| Centroid, orthocentre, circumcentre of triangle | ||
| Circle: standard and general forms, center & radius, diameter endpoints, line-circle intersections | ||
| Conic sections: parabola, ellipse, hyperbola (standard equations) | ||
|
Unit 11
|
Three Dimensional Geometry
|
Coordinates in space |
| Distance between two points | ||
| Section formula | ||
| Direction ratios and direction cosines | ||
| Angle between intersecting lines | ||
| Equation of a line in 3D | ||
| Skew lines and shortest distance | ||
|
Unit 12
|
Vector Algebra
|
Scalars and vectors |
| Addition of vectors | ||
| Components of vectors in 2D and 3D | ||
| Scalar (dot) product | ||
| Vector (cross) product | ||
|
Unit 13
|
Statistics and Probability
|
Measures of dispersion: mean, median, mode (grouped and ungrouped) |
| Standard deviation, variance, mean deviation | ||
| Probability of an event | ||
| Addition and multiplication theorems | ||
| Bayes’ theorem | ||
| Probability distribution of random variable | ||
|
Unit 14
|
Mathematical Reasoning and Trigonometry
|
Trigonometric identities and functions |
| Inverse trigonometric functions | ||
| Properties of inverse trig functions | ||
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