UP TGT Maths Syllabus 2026: Subject-wise Topics, Exam Pattern & PDF

UP TGT Maths Syllabus 2026 Highlights

Particulars

Details

Exam Name

UP TGT Recruitment Exam 2026

Conducting Body

Uttar Pradesh Education Service Selection Commission (UPESSC), Prayagraj

Subject

Mathematics

Post

Trained Graduate Teacher (TGT)

Exam Mode

Offline (OMR-Based)

Question Type

Multiple Choice Questions (MCQs)

Official Syllabus

Released by UPESSC

Selection Process

Written Examination

Official Website

upessc.up.gov.in

UP TGT Maths Syllabus 2026 Subject-wise Topics

Topic

Important Topics Covered

Commercial Mathematics

Work and Time, Speed and Time, Simple Interest, Compound Interest, Banking, Taxation

Statistics

Frequency Distribution, Pictorial Representation of Data, Measures of Central Tendency, Measures of Dispersion, Birth and Death Statistics, Index Numbers

Algebra

Surds, Polynomials, Factorization, HCF of Polynomials, Linear Equations, Simultaneous Equations, Quadratic Equations, Logarithms, Ratio and Proportion, Number System, Determinants (up to 3×3), Cramer's Rule, Matrices, Transpose, Symmetric & Skew-Symmetric Matrices, Inverse Matrix Method, Theory of Equations, Symmetric Functions of Roots, AP, GP, HP, Sum of Squares & Cubes, Permutations & Combinations, Binomial Theorem, Exponential & Logarithmic Series

Probability

Addition Theorem, Multiplication Theorem

Set Theory

Set Algebra, Equivalence Relation, Mapping, Composition of Mapping, Inverse Mapping, Peano's Postulates, Mathematical Induction, Group, Group Homomorphism, Cyclic Groups, Subgroups, Cosets, Lagrange's Theorem

Real Analysis

Axioms of Real Numbers, Countable Sets, Metric Spaces, Open & Closed Sets, Dense & Perfect Sets, Bolzano-Weierstrass Theorem, Sequences, Limits, Convergence, Divergence, Monotonic & Bounded Sequences, Cauchy Sequences, Continuity, Types of Discontinuity, Rolle's Theorem

Trigonometry

Circular Measure, Trigonometric Ratios, Compound Angles, Multiple & Submultiple Angles, Trigonometric Identities, Trigonometric Equations, Solution of Triangles, Properties of Circumcircle, Incircle, Excircle, Inverse Trigonometric Functions

Complex Numbers

Operations on Complex Numbers, De Moivre's Theorem, Height & Distance, Exponential, Circular & Hyperbolic Functions, Separation into Real & Imaginary Parts

Geometry

Baudhayana-Pythagoras Theorem, Circle, Sector, Arc, Chord, Tangent, Alternate Segment Theorem, Congruence of Linear & Plane Figures

Coordinate Geometry

Cartesian Plane, Pair of Straight Lines, Angle Bisectors, Circle, Parabola, Ellipse, Hyperbola, Transformation of Axes, Tangent & Normal, Parametric Equations, Polar Equations, Three-Dimensional Geometry (Sphere, Cone, Cylinder)

Calculus

Differentiation of Algebraic, Trigonometric, Exponential & Logarithmic Functions, Tangents & Normals, Maxima & Minima, Curve Tracing, Integration by Parts, Substitution, Partial Fractions, Definite Integrals, Area Between Curves, Volume & Surface Area, Differential Equations (First Order & First Degree)

Vector Analysis

Position Vectors, Displacement Vector, Unit Vector, Direction Cosines, Vector Addition & Subtraction, Relative Velocity, Scalar Product, Vector Product, Triple Product, Applications in Work & Moment of Force

Statics

Equilibrium of Bodies, Lami's Theorem, Triangle Law of Forces, Resolution of Forces, Conditions of Equilibrium, Centre of Gravity, Common Catenary

Dynamics

Projectile Motion, Motion in a Plane, Radial & Transverse Velocity, Tangential & Normal Velocity, Acceleration