GATE Mathematics Syllabus

GATE Mathematics: topic-wise syllabus

1. 1

   Algebra

   ~1 marks

   Sets, Relations, Functions, Equations, Per GATE Official Notification

   • Sets, Relations, Functions, Venn Diagrams, Inverse, Composition
   • Complex Numbers, Quadratic Equations, Polynomials, Roots, Modulus-Argument Form
   • Sequences and Series — AP, GP, HP, Sum, Mean, Variance, Infinite Series, Binomial
   • Permutation-Combination, Probability, Conditional, Bayes Theorem, Random Variables
   • Matrices and Determinants, System of Equations, Linear Programming, Eigenvalues
   • Logarithms, Partial Fractions, Mathematical Induction, Mathematical Reasoning
   • Boolean Algebra, Logic, Number Theory, Recursion, Mathematical Olympiad
2. 2

   Calculus & Geometry

   ~1 marks

   Differentiation, Integration, Trigonometry, Per GATE Official Notification

   • Limits, Continuity, Differentiability, Derivatives, Methods
   • Applications of Derivatives — Maxima, Minima, Rate of Change, Tangent, Normal
   • Integration — Definite, Indefinite, Methods, Reduction Formulas, Areas, Volumes
   • Differential Equations — First Order, First Degree, Applications, Higher Order
   • Trigonometric Ratios, Identities, Equations, Inverse Trig, Heights & Distances, Properties
   • Coordinate Geometry — Straight Lines, Circles, Conics, 3D, Vectors
   • Mathematical Reasoning, Statistics, Probability, Linear Algebra, Modern Math
3. 3

   Arithmetic (MBA Quant)

   ~3 marks

   Number System, Percentages, Profit-Loss, SI-CI

   • Number System, HCF-LCM, Indices, Surds, Simplification, Approximation
   • Percentages, Profit-Loss, Discount, SI-CI, Growth Rate, Population Growth
   • Ratio, Proportion, Mixture-Alligation, Partnership, Ages
   • Time-Work, Work-Wages, Pipes & Cisterns, Efficiency
   • Time-Speed-Distance, Trains, Boats, Races, Clocks, Calendar
   • Averages, Mixture Problems, Alligation, Allegation Method
   • Mensuration, Geometry, Coordinate Geometry, Trigonometry
   • Data Interpretation — Tables, Bar, Pie, Line, Caselet, Data Sufficiency
   • Modern Math — Permutation, Combination, Probability, Sets, Functions
   • Commercial Math — Stocks, Shares, Dividends, Brokerage, GST, True Discount
4. 4

   Algebra (MBA Quant)

   ~3 marks

   Equations, Functions, P&C, Probability

   • Linear Equations, Quadratic Equations, Polynomials, Identities
   • Functions, Graphs, Inequalities, Logarithms, Modulus, Domain, Range
   • Sequences and Series, AP, GP, HP, Sum of n terms, Special Series
   • Permutation, Combination, Binomial Theorem, Probability
   • Matrices, Determinants, Linear Programming, System of Equations
   • Set Theory, Relations, Functions, Venn Diagrams, Cardinality
   • Trigonometry — Ratios, Identities, Heights and Distances, Equations
   • Coordinate Geometry — Lines, Circles, Conics, Distance, Slope
   • Calculus — Limits, Derivatives, Integrals, Maxima, Minima, Applications
   • Statistics — Mean, Median, Mode, Variance, Skewness, Correlation, Regression
5. 5

   Data Interpretation

   ~3 marks

   Charts, Tables, Caselets, Data Sufficiency

   • Table DI — Direct, Calculation-Based, Multi-Step
   • Bar Graph DI — Single, Double, Stacked, Comparison
   • Pie Chart DI — Sector Angle, Percentage, Comparison, Multiple Pie
   • Line Graph DI — Trend, Multiple Lines, Comparison, Growth Rate
   • Caselet DI — Story-Based, Multi-Step, Verbal Reasoning with Data
   • Data Sufficiency — Two-Statement, Three-Statement, Multi-Condition
   • Comparison DI — Ratio, Percentage, Difference, Growth Rate
   • Missing Data DI — Find the Missing Value, Estimate, Calculate
   • Quant-Based DI — Averages, Ratios in Data, Business Scenarios, HR Data
   • Radar, Web, Mixed Chart DI, Business Scenarios — Revenue, Cost, Profit, Market Share
6. 6

   English

   ~3 marks

   Verbal Ability, Grammar, Vocabulary, RC

   • Reading Comprehension — Factual, Inferential, Critical, Editorial, Business
   • Cloze Test, Fill in the Blanks, Sentence Completion
   • Spotting Errors, Sentence Correction, Sentence Improvement
   • Para Jumbles, Sentence Rearrangement, Paragraph Completion
   • Vocabulary — Synonyms, Antonyms, One-Word Substitutes, Idioms, Phrasal Verbs
   • Grammar — Tenses, Voice, Narration, Prepositions, Articles, Modals
   • Word Usage, Foreign Words, Root Words, Etymology, Confusables
   • Essay Writing, Letter Writing, Email Writing, Report, Précis
   • Business Reading — Business News, Annual Reports, Strategies, Case Studies
   • Critical Reading — Argument Analysis, Flaw Identification, Strengthen/Weaken
7. 7

   Logical Reasoning

   ~3 marks

   Puzzles, Arrangements, Logic, Decisions

   • Seating Arrangement — Linear, Circular, Square, Rectangular, Hexagonal
   • Floor/Ladder Puzzles, Box Puzzles, Scheduling (Day/Month/Year)
   • Venn Diagrams, Sets, Family Tree, Blood Relations, Direction
   • Number Series, Letter Series, Coding-Decoding, Pattern Recognition
   • Syllogisms, Statement-Conclusion, Assumption, Inference, Course of Action
   • Critical Reasoning, Paradox, Brainteasers, Logic Games
   • Decision Making, Selection, Prioritization, Optimization, Negotiation
   • Data Sufficiency, Input-Output, Scheduling, Ranking
   • Verbal Reasoning — Analogies, Classification, Odd-Man-Out, Series
   • Visual Reasoning, Pattern Completion, Embedded Figures, Mirror, Water
8. 8

   Mechanics (Physics)

   ~4 marks

   Kinematics, Dynamics, Rotational Motion, Gravitation

   • Kinematics — Motion in 1D/2D/3D, Projectile, Circular, Relative Motion
   • Newton's Laws of Motion, Friction, Pseudo Forces, Constraint Motion
   • Work, Energy, Power, Kinetic and Potential Energy, Conservation
   • Circular Motion, Banking of Roads, Conical Pendulum, Vertical Circle
   • Rotational Mechanics — Torque, Angular Momentum, Moment of Inertia, Rolling
   • Gravitation — Kepler's Laws, Universal Law, Gravitational Field, Satellite
   • Elasticity — Stress, Strain, Hooke's Law, Young's Modulus, Bulk Modulus, Shear Modulus
   • Fluid Mechanics — Pressure, Buoyancy, Bernoulli's Theorem, Viscosity, Surface Tension
   • Mechanical Waves — SHM, Oscillations, Spring, Pendulum, Wave Motion, Sound
   • Properties of Matter, Units, Dimensions, Error Analysis, Significant Figures
9. 9

   Heat & Thermodynamics (Physics)

   ~4 marks

   Heat Transfer, Laws, Kinetic Theory

   • Heat and Temperature — Scales, Thermometry, Thermal Expansion
   • Calorimetry — Specific Heat, Latent Heat, Heat Capacity
   • Heat Transfer — Conduction, Convection, Radiation, Thermal Conductivity
   • Thermodynamics — Zeroth, First, Second, Third Law, PV Diagram, Work, Heat
   • Kinetic Theory of Gases — Pressure, RMS Speed, Mean Free Path, Degrees of Freedom
   • Gas Laws — Boyle's, Charles', Gay-Lussac's, Ideal Gas Equation, Real Gases
   • Thermodynamic Processes — Isothermal, Adiabatic, Isobaric, Isochoric, Cyclic
   • Heat Engines, Refrigerators, Carnot Cycle, Entropy
   • Calorimetry, Phase Changes, Latent Heat, Triple Point, Critical Point
   • Thermal Radiation, Black Body, Stefan-Boltzmann Law, Wien's Displacement Law
10. 10

    Optics & Modern Physics

    ~4 marks

    Light, EM Waves, Relativity, Quantum, Nuclear

    • Ray Optics — Reflection, Refraction, Total Internal Reflection, Prism
    • Lenses and Mirrors — Image Formation, Formulae, Power, Combination
    • Optical Instruments — Microscope, Telescope, Magnifying Glass, Camera
    • Wave Optics — Interference, Diffraction, Polarization, Young's Double Slit
    • Electromagnetic Waves — EM Spectrum, Properties, Maxwell's Equations
    • Photoelectric Effect — Einstein's Equation, Work Function, Threshold Frequency
    • Bohr's Atomic Model, Hydrogen Spectrum, Atomic Structure
    • Nuclear Physics — Atomic Structure, Radioactivity, Half-Life, Decay
    • Modern Physics — Photoelectric Effect, X-rays, Lasers, Optical Fibers
    • Semiconductor Physics — Diode, Transistor, Logic Gates, Communication
11. 11

    Atomic Structure & Chemical Bonding

    ~4 marks

    Quantum, Periodic Table, Bonds

    • Atomic Structure — Bohr's Model, Quantum Numbers, Electronic Configuration, Shapes
    • Atomic Models — Thomson, Rutherford, Bohr, Schrodinger (Qualitative), Heisenberg
    • Photoelectric Effect, Wave-Particle Duality, de Broglie Wavelength, Heisenberg
    • Periodic Table — Periodicity, Atomic Radius, Ionization Energy, Electronegativity
    • Chemical Bonding — Ionic, Covalent, Coordinate, Hydrogen Bonding, Metallic
    • Hybridization — sp, sp2, sp3, sp3d, sp3d2 with Examples (CH4, NH3, H2O)
    • VSEPR Theory, VBT (Valence Bond Theory), MOT (Molecular Orbital Theory)
    • Bond Parameters — Bond Length, Angle, Energy, Polarity, Dipole Moment
    • Resonance, Hyperconjugation, Inductive Effect, Mesomeric Effect, Electromeric
    • Lattice Energy, Born-Haber Cycle, Fajan's Rules, Polarizing Power
12. 12

    States of Matter & Solutions

    ~4 marks

    Gas, Liquid, Solid, Solutions, Colloids

    • Gas Laws — Boyle's Law, Charles' Law, Gay-Lussac's Law, Avogadro's Law, Ideal Gas
    • Kinetic Molecular Theory — Postulates, Derivation of Gas Laws, RMS Speed
    • Real Gases — van der Waals Equation, Critical Constants, Liquefaction
    • Liquid State — Properties, Vapor Pressure, Surface Tension, Viscosity
    • Solid State — Crystalline, Amorphous, Crystal Systems, Bravais Lattices
    • Unit Cell, Coordination Number, Packing Efficiency, Density Calculations
    • Imperfections in Solids — Point Defects, Schottky, Frenkel, F-Centers
    • Solutions — Types, Concentration (Molarity, Molality, Normality, Formality)
    • Colligative Properties — Lowering of VP, Elevation of BP, Depression of FP, Osmotic
    • Colloids — Types, Preparation, Properties, Emulsions, Gels, Tyndall Effect
13. 13

    Algebra (Advanced)

    ~4 marks

    Sets, Relations, Functions, Complex Numbers, P&C

    • Sets, Relations, Functions, Venn Diagrams, Equivalence Relations
    • Complex Numbers — Algebra, Argand Plane, Modulus-Argument, De Moivre's
    • Quadratic Equations, Polynomials, Identities, Factorization, Remainder Theorem
    • Sequences and Series — AP, GP, HP, Sum, Special Series, Method of Differences
    • Permutations and Combinations, Binomial Theorem, Multinomial Theorem
    • Probability — Conditional, Bayes, Independent Events, Random Variables
    • Matrices and Determinants — Types, Operations, Inverse, Cramer's Rule
    • Linear Algebra — Vector Spaces, Eigenvalues, Linear Programming, Graph Theory
    • Logarithms, Antilogarithms, Partial Fractions, Induction, Mathematical Reasoning
    • Number Theory — Divisibility, Modular Arithmetic, Fermat's, Wilson's Theorem
14. 14

    Trigonometry (Advanced)

    ~4 marks

    Ratios, Identities, Equations, Inverse, Heights

    • Trigonometric Ratios (sin, cos, tan, cot, sec, cosec) — Sign Conventions
    • Trigonometric Identities — Pythagorean, Sum-Difference, Product-to-Sum
    • Trigonometric Equations — General Solutions, Specific Solutions
    • Inverse Trigonometric Functions — sin^-1, cos^-1, tan^-1, Properties
    • Heights and Distances — Angle of Elevation, Depression, Problems
    • Properties of Triangles — Sine Rule, Cosine Rule, Half-Angle, Napier Analogy
    • Trigonometric Series — Taylor Series, Maclaurin Series for sin, cos
    • Multiple and Sub-multiple Angles — sin 2θ, cos 2θ, sin 3θ, cos 3θ
    • Conditional Trigonometric Identities, Maxima and Minima
    • Heights and Distances — Bearing, Compass, Survey Problems, Real-World Applications
15. 15

    Coordinate Geometry (Advanced)

    ~4 marks

    2D/3D, Conics, Vectors, Transformations

    • Straight Lines — Slope, Equation, Distance, Angle Between Lines, Family of Lines
    • Circles — Standard Form, General Form, Tangent, Normal, Chord of Contact, Pole-Polar
    • Conic Sections — Parabola, Ellipse, Hyperbola (Standard Forms, Focus, Directrix, Eccentricity)
    • 3D Coordinate Geometry — Distance, Section Formula, Direction Cosines, Ratios
    • Plane and Line in 3D — Equation, Angle, Distance, Symmetric Form
    • Sphere, Cone, Cylinder — Equations, Tangent Plane, Generator, Curved Surface
    • Vectors — Types, Addition, Subtraction, Dot, Cross, Triple Product
    • Vector Algebra — Position Vector, Section Formula, Projection, Resolution
    • Coordinate Transformations — Translation, Rotation, Reflection, Scaling
    • Locus, Curve Tracing, Parametric Equations, Applications to Motion