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JEE Mathematics — Topic Guide
Full JEE Math Syllabus
JEE Mathematics — Complete Topic List
All important topics & subtopics arranged for JEE Main & Advanced preparation. Use this as your study map — practice, revise, and test.
CORE
Estimated hours: 200+
Difficulty: Medium–High
Tip: Start with Algebra & Coordinate Geometry — they yield higher marks for lower time. Use timed mock tests weekly.
Syllabus Overview
Algebra
Polynomials, complex numbers, theory of equations, inequalities, sequences & series
Explore →Detailed Topics (click to expand)
Algebra — Key subtopics
- Polynomials: zeroes, factor theorem, division algorithm, symmetric functions
- Complex Numbers: a + ib form, modulus, argument, De Moivre’s theorem
- Theory of Equations: roots, relation between roots & coefficients, multiple roots
- Inequalities: AM-GM, Cauchy-Schwarz, rearrangement, Jensen (basic)
- Sequences & Series: arithmetic, geometric, harmonic, binomial expansions, tests for convergence
- Matrices & Determinants: inverse, rank, solution of linear equations, properties
- Permutations & Combinations (basic combinatorics)
Calculus — Key subtopics
- Limits & Continuity
- Differentiation: rules, chain rule, implicit differentiation, higher order derivatives
- Applications of Derivative: maxima/minima, tangents & normals, curve sketching, rate problems
- Integration: definite & indefinite integrals, substitution, parts, partial fractions
- Applications of Integration: area, volume, length of curves
- Differential Equations: first order (linear), separable, second order (basic)
- Sequences & Series (power series, Taylor & Maclaurin basics)
Coordinate Geometry — Key subtopics
- Straight Lines: slope, intercept form, angle between two lines, distance from point to line
- Circles: equation, chord, tangent, radical axis
- Conic Sections: parabola, ellipse, hyperbola — standard forms & properties
- Locus problems & basic transformations (translation & rotation)
Vectors & 3D Geometry — Key subtopics
- Vector operations: addition, scalar multiplication, dot & cross product
- Projection, components
- 3D geometry: equations of line & plane, angle between & distance formulae
Other Important Topics
- Probability & Statistics: conditional probability, Bayes theorem, mean, variance
- Complex Numbers (advanced problems for JEE Advanced)
- Linear Algebra: vector spaces, linear transformations (basics)
- Mathematical Reasoning: statements, logical operations, proofs
- Trigonometry: identities, equations, inverse trigonometric functions
- Misc: Inequalities, functional equations (selective)
Quick 30-Day Revision Plan
- Days 1–6: Algebra fundamentals + problems
- Days 7–12: Coordinate Geometry + practice tests
- Days 13–18: Differential Calculus + application
- Days 19–24: Integral Calculus + problems
- Days 25–28: Vectors, 3D & Probability
- Days 29–30: Full-length mock tests + revision