U.P. EDUCATION SERVICE SELECTION COMMISSION, PRAYAGRAJ

TGT MATHEMATICS SYLLABUS 2026

Subject Code - 03 (English Medium)

Sets, Relations and Functions, Types of Relations, Equivalence Relations, Composition of Functions, Inverse Functions. Theory of Equations: Quadratic equations and expressions, Roots and coefficients, Symmetric functions of roots, Transformation of equations. Progressions: Arithmetic, Geometric and Harmonic Progressions (AP, GP, HP), Sum of n terms, Means. Permutations and Combinations: Fundamental principles of counting, Formulas for nPr and nCr, Applications. Binomial Theorem: Positive, negative, and fractional indices, General and middle terms, Exponential and Logarithmic Series.

Matrices: Types of matrices, Addition, Subtraction, and Multiplication of matrices, Transpose of a matrix, Symmetric and Skew-symmetric matrices, Adjoint and Inverse of a matrix. Determinants: Properties of determinants, Expansion, Minors and Cofactors, System of linear equations and solution using Cramer's Rule and Matrix Inversion Method, Rank of a Matrix.

Trigonometric ratios and identities, Compound angles, Multiple and Sub-multiple angles, Transformation formulas. Trigonometric Equations and General Solutions. Properties of Triangles: Sine rule, Cosine rule, Projection formulas, In-radius, Ex-radii, Circum-radius, and Solution of Triangles. Inverse Trigonometric Functions: Properties and solutions. Heights and Distances. Complex Numbers: De Moivre's Theorem and its simple applications, Hyperbolic Functions.

2D Geometry: Cartesian coordinates, Distance formula, Section formula, Area of a triangle. Straight Lines: Angle between two lines, Pair of straight lines, Distance of a point from a line. Circles: Standard and general equation, Tangent and Normal, Condition of tangency, Family of circles. Conic Sections: Standard equations, properties, tangents and normals of Parabola, Ellipse, and Hyperbola. 3D Geometry: Direction Cosines and Direction Ratios, Planes and Straight Lines in 3D, Shortest distance between two skew lines, Sphere.

Differential Calculus: Limits, Continuity, and Differentiability. Derivatives of standard functions, Chain rule, Implicit and Parametric differentiation. Tangents and Normals, Monotonicity, Rolle's Theorem and Lagrange's Mean Value Theorem, Maxima and Minima of functions of one variable, Successive differentiation, Expansion of functions. Integral Calculus: Indefinite and Definite integrals, Integration by substitution, parts, and partial fractions. Properties of definite integrals, Area bounded by plane curves. Differential Equations: Order and degree, First order and first degree differential equations (Variable separable, Homogeneous, Linear differential equations).

Vector Algebra: Vectors and Scalars, Addition of vectors, Position vector, Scalar and Vector products of two and three vectors (Dot, Cross, Scalar Triple Product, Vector Triple Product) and their geometric applications. Statics: Coplanar forces, Equilibrium conditions, Moments, Couples, Resultant of concurrent and parallel forces, Center of Gravity. Dynamics: Motion in a straight line, Rectilinear motion with uniform acceleration, Projectiles, Motion under gravity, Work, Power, and Energy, Laws of Motion.

Statistics: Measures of Central Tendency (Mean, Median, Mode), Measures of Dispersion (Range, Mean Deviation, Variance, Standard Deviation), Frequency distribution. Correlation and Regression coefficients, Lines of regression. Probability: Random experiments, Sample space, Events, Axiomatic definition of probability, Addition and Multiplication theorems, Conditional probability, Bayes' Theorem, Binomial and Poisson distributions.

UP TGT SCIENCE SYLLABUS 2026

Subject Code - 05

1. General Physics (Mechanics)

Units and Dimensions, Vector and Scalar quantities, Product (Scalar and Vector products), Gradient, Divergence and Curl, Gauss, Stokes Theorem and applications. Motion, Force and Acceleration, Equations of Motion, Kinetic and Potential Energy, Linear and Angular momentum. Conservation of Energy and Momentum, Conservative and Non-conservative forces, Rotational motion, Centrifugal and Centripetal force, Gravitational force, Central force, Kepler's laws of planetary motion, Geostationary satellites, Gravitational acceleration, Escape velocity, Simple and Compound pendulum, Moment of Inertia, Parallel and Perpendicular axes theorem, Moment of Inertia of sphere, ring, disc and cylinder, Angular momentum and torque. Streamlined and turbulent flow, Critical velocity, Stokes and Poiseuille's formulas, Bernoulli's theorem and applications. Surface tension, Excess pressure inside curved surfaces of liquids, Surface energy, Flow of liquid in a capillary. Elasticity: Elastic constants, mutual relations between them, Bending moment, Cantilever. Theory of Relativity, change in length, time and mass, Mass-Energy equivalence.

2. Heat

Concept of heat and temperature, Various temperature measuring scales, Absolute temperature, Thermal expansion of solids, gases and liquids, Conductors and Insulators, Radiation of heat, Black body radiation, Rayleigh-Jeans and Wien's laws, Planck's radiation formula, Newton's law of cooling, Stefan's law, Internal energy, Isothermal and Adiabatic changes, First and Second laws of thermodynamics, Carnot engine, Entropy, Maxwell's thermodynamic relations, Joule-Thomson effect, Clausius-Clapeyron equation.

3. Waves and Oscillations

Simple harmonic motion, Progressive and Stationary waves, Phase and Group velocity, Damped harmonic motion, Forced oscillations and resonance, Resonance sharpness. Superposition of waves, Beats and Lissajous figures, Doppler effect.

4. Optics

Spherical mirrors and lenses, Refractive index, Formulas for focal lengths, Coaxial system, Combination of thin lenses, Eyepieces, Ramsden and Huygens eyepieces, Chromatic aberration of lenses, Human eye, Long-sightedness, Short-sightedness. Basic concepts of Interference, Diffraction and Polarization, Biprism, Newton's rings, Fresnel-Fraunhofer diffraction, Rayleigh criterion, Resolving power, Zone plate and working principles of gratings. Double refraction, Plane, circular and elliptical polarization, Quarter and Half-wave plates, General concept of Laser, Ruby and Helium-Neon lasers.

5. Electricity and Magnetism

Primary and Secondary cells, Internal resistance, Electromotive force, Laws of combination of resistances and capacitors, Current, Drift velocity and Conductivity, Galvanometer, Ammeter and Voltmeter, Wheatstone bridge and its applications, Electric Field, Electric Potential, Gauss Law, Biot-Savart law, Ampere's circuital law, Electromagnetic induction, Faraday's and Lenz's laws. Self-induction and Mutual induction, Alternating current, Series and Parallel (LCR) circuits, Introductory knowledge of dia-, para- and ferro-magnetism, Electromagnetic Maxwell's equations, Displacement current, Electromagnetic waves.

6. Modern Physics

Structure of atom, Vector and Bohr's model of atom, Pauli's Exclusion Principle, Optical and X-ray Spectra, Photoelectric effect, Compton effect, Zeeman, Paschen-Back and Raman effect, de Broglie Waves, Uncertainty principle, Schrödinger equation, Radioactivity, Metals, Semiconductors and Insulators, P-N Junction, Zener Diode, Transistor and their uses. Logic gates, Truth tables, Boolean algebra.

1. Matter & Laws of Chemical Combinations

Matter: Nature and behaviour, types of matter, elements and their classification (metals and non-metals), compounds and their mixtures. Laws of Chemical Combinations: Laws of constant proportions, multiple proportions and reciprocal proportions, Gay-Lussac's law of gaseous volumes, Mitscherlich's law of isomorphism.

2. Structure of Matter & Atomic Structure

Structure of Matter: Dalton's atomic theory, atoms, molecules and their characteristics. Atomic structure: Discovery of the electron, proton, and neutron. Rutherford's alpha-ray scattering experiment and discovery of the nucleus. Atomic models of Rutherford, Bohr and Sommerfeld. Quantum numbers, modern atomic theory. de Broglie equation, Heisenberg Uncertainty principle, shape of s, p and d orbitals, Electronic configuration based on Aufbau principle, Hund's rule and Pauli's exclusion principle.

3. Radioactivity

Discovery of radioactivity, radioactive rays and their characteristics, half life and average life, laws of radioactive decay, nuclear fission and fusion, artificial radioactivity. Isotopes, Isobars and Isoelectronics.

4. Chemical Bonding

Fundamental concepts of valency, electronic theory, octet rule, exceptions to octet rule, electrovalent, covalent and coordinate bonds. Characteristics of ionic, covalent and coordinate compounds. Polarization and Fajans' rule. Inert pair effect, valence bond theory of covalency (for hydrogen molecule), hybridization and shapes of sp, sp², sp³ hybrid orbitals.

5. Chemical Reactions & Types

Symbols, ions, and formulas, presentation of chemical reactions by chemical equations. Physical and chemical changes and their differences. Types of chemical reactions: Displacement, addition, dissociation, decomposition, double decomposition, slow, fast, exothermic, endothermic and catalysed reactions.

6. Electrochemical Cells

Voltaic cell and its mechanism of working, Dry cell, lead storage battery, reversible cell, electrode potential, Nernst equation and its applications.

7. Periodic Classification of Elements

Mendeleeff's periodic classification and its basis, Merits and demerits of the Mendleeff's periodic table, modified form of the periodic table and its important features, periodic properties of elements (atomic and ionic radii, ionization potential, electron affinity and electronegativity), variation of periodic properties in groups and periods. General properties of s and p block elements. Discussion of the properties of first row transition elements (3d block elements) with reference to their electronic configuration, oxidation state, colour, magnetic properties and complex compounds formation.

8. General Organic Chemistry

Inductive, electromeric and mesomeric effects, Hyperconjugation, resonance and their applications, electrophilic and nucleophilic reagents, free radicals, carbocations and carbanions. Hydrogen bonding and its effects. Classification and nomenclature of organic compounds.

9. Isomerism & Organic Compounds

Isomerism: Structural and stereoisomerism, concept of mechanism of organic reactions, mechanism of simple substitution, addition and neutralization reactions. Methods of preparation of the following Organic compounds and their properties: alkanes, alkenes, alkynes, alkyl halides, ketones, acids and their derivatives. Benzene, its preparation, properties and structure.

ADHYAYANAM

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UP TGT SCIENCE

(Subject Code — 05)

Complete Syllabus  •  Structured Study Modules  •  Previous-Year Question-Paper Pattern Analysis

2026 BATCH  |  RECORDED VIDEO LECTURES + LIVE STREAM CLASSES

EXAMINATION SCHEME

The table below summarises the current UP TGT written-examination pattern that this course is mapped against. Candidates preparing for the Science paper should treat the Concerned Subject section as the highest-priority area of study.

This document compiles the official UP TGT Science syllabus (Subject Code 05) into a structured, teachable module — organised exactly the way the Adhyayanam faculty team delivers it through recorded video lectures and live stream classes. Each topic has been broken down into manageable units, mapped to an estimated question-paper weightage derived from an analysis of previous years' papers, and paired with a video-lecture count so that students can plan their preparation timeline with precision.

The syllabus is divided into two sections as prescribed: Section A – Physics and Section B – Chemistry. Detailed module-wise breakdowns for both sections follow on the next pages.

Six modules covering complete Physics as per the prescribed UP TGT Science syllabus.

Section A Total: 6 Modules  |  100 Recorded Video Lectures

Nine modules covering complete Chemistry as per the prescribed UP TGT Science syllabus.

Section B Total: 9 Modules  |  100 Recorded Video Lectures

Based on Adhyayanam faculty's analysis of previous years' UP TGT Science papers, the relative emphasis given to each topic within Physics and Chemistry is summarised below. These figures are indicative planning estimates — used internally to sequence the video curriculum and mock-test difficulty — and should be read alongside the official syllabus, not as a substitute for it.

Section A — Physics

Section B — Chemistry

High-priority zones (highest bars above) receive proportionally more recorded lectures, extra practice sheets and dedicated live doubt-clearing sessions in the Adhyayanam study plan.

The complete UP TGT Science course is delivered as a blend of self-paced recorded lectures and scheduled live classes, so that working candidates and full-time aspirants can both follow the same structured timeline.

What the Course Includes

•  Topic-wise recorded video lectures (watch anytime, unlimited replays for course validity)

•  Live interactive stream classes with faculty, held on a weekly timetable

•  Printable / downloadable module notes for every topic listed in this syllabus

•  Section-wise and full-length mock tests modelled on the previous-year paper pattern

•  Weekly live doubt-clearing sessions

•  Performance tracking dashboard and topic-wise scorecards

•  Dedicated WhatsApp / Telegram support group for announcements and quick queries

Choose the plan that fits your preparation style. EMI options are available on all plans; scholarship discounts apply for early enrolment.

* Fees are indicative and subject to change. Please confirm current fees, active offers and EMI terms directly with the Adhyayanam admissions team before enrolling.

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