UP PGT Mathematics Syllabus 2026
Complete Mathematics Syllabus • Subject Code 08 • General Knowledge • Exam Pattern • Algebra • Calculus • Geometry • Abstract Algebra • Linear Algebra • Vector Calculus • Mechanics • Trigonometry • Official PDF
📘 UP PGT Mathematics Syllabus 2026 – Complete Guide
UP PGT Mathematics Syllabus 2026 की तैयारी करने वाले अभ्यर्थियों के लिए यह page उपलब्ध syllabus PDF को आसान, व्यवस्थित और reader-friendly format में प्रस्तुत करता है।
Official syllabus document में Mathematics–PGT (Secondary Education), Subject Code–08 दिया गया है। Mathematics syllabus में Algebra, Calculus, Ordinary Differential Equations, Co-ordinate Geometry, Vectors and Three Dimensional Geometry, Abstract Algebra, Linear Algebra, Vector Calculus, Mechanics और Trigonometry जैसे प्रमुख areas शामिल हैं।
इसी document के pages 5–6 में TGT एवं PGT के लिए common General Knowledge syllabus दिया गया है, जिसमें 30 Questions निर्धारित हैं।
📄 UP PGT Mathematics & General Knowledge Official Syllabus PDF
UP PGT Mathematics तथा TGT/PGT common General Knowledge syllabus के उपलब्ध PDF को नीचे दिए गए button से सीधे open/download करें।
Document: PGT Mathematics and GK Syllabus
Subject: Mathematics–PGT (Secondary Education)
Subject Code: 08
📥 VIEW / DOWNLOAD OFFICIAL MATHEMATICS SYLLABUS PDF📊 UP PGT Mathematics 2026 – Quick Overview
| Particular | Details |
|---|---|
| Examination | UP PGT / Lecturer |
| Subject | Mathematics |
| Subject Code | 08 |
| Concerned Subject | 90 Questions – 270 Marks |
| General Knowledge | 30 Questions – 90 Marks |
| Written Examination | 120 Questions – 360 Marks |
| Interview | 40 Marks |
| Total Selection Framework | 400 Marks |
📝 UP PGT Mathematics Exam Pattern 2026
| Section | Questions | Marks |
|---|---|---|
| General Knowledge / General Studies | 30 | 90 |
| Concerned Subject – Mathematics | 90 | 270 |
| Written Examination | 120 | 360 |
| Interview | — | 40 |
| Total Selection Framework | — | 400 |
∑ UP PGT Mathematics Syllabus 2026 – Main Sections
🔵 Algebra & Probability
Relations and Functions, Matrices, Determinants, equations, Arithmetic/Geometric/Harmonic Progressions, Permutations and Combinations, Binomial Theorem, Exponential and Logarithmic Series and Probability.
🟢 Calculus & Differential Equations
Functions of one variable, limits, continuity, differentiation, mean value theorems, integration, definite integrals, areas, Riemann integration and ordinary differential equations.
🟠 Geometry, Algebra & Mechanics
Co-ordinate Geometry, Vectors, Three Dimensional Geometry, Abstract Algebra, Linear Algebra, Vector Calculus, Mechanics and Trigonometry.
1️⃣ Algebra
Relations and Functions
- Types of relations – reflexive, symmetric and transitive relations
- Equivalence relations
- Equivalence class
- One-one and onto functions
- Composite of functions
- Inverse of functions
- Binary operations
Matrices
- Types of matrices
- Transpose of a matrix
- Symmetric and skew-symmetric matrices
- Addition and multiplication of matrices
- Singular and non-singular matrices
- Invertible matrices
Determinants
- Properties of determinants
- Adjoint and inverse of a square matrix
- Consistency and number of solutions of system of linear equations
- Solving systems of linear equations in two or three variables
Equations, Progressions and Series
- Theory of equations of degree greater than or equal to two
- Arithmetic Progression
- Geometric Progression
- Harmonic Progression
- Permutations and Combinations
- Binomial Theorem
- Exponential Series
- Logarithmic Series
Probability
- Multiplication theorem of probability
- Conditional probability
- Independent events
- Total probability
2️⃣ Calculus
Function of One Variable
- Limit of a function
- Continuity
- Differentiability of a function
- Derivative of composite function
- Rolle’s theorem
- Lagrange’s mean value theorem
- Cauchy’s mean value theorem
- Maclaurin’s and Taylor’s series
- L. Hospital’s rule
- Successive differentiations
- Leibnitz theorem
- Equation of tangent and normal to a given curve
- Maxima and minima
- Increasing and decreasing functions
Integration
- Methods of integration
- Definite integration as a limit of sum
- Basic properties of definite integrals
- Evaluation of definite integrals
- Applications in finding the area under simple curves
- Riemann integration
3️⃣ Ordinary Differential Equations
- Order and degree of differential equations
- Formation of differential equations
- Solution of differential equations of first order and first degree
- Singular solutions
- Linear differential equations with constant coefficients
- Homogeneous differential equations
4️⃣ Co-ordinate Geometry of Two Dimensions
- General equation of second degree in two variables (x, y)
- Classification to pair of straight lines
- Circle
- Parabola
- Ellipse
- Hyperbola
- Equation of tangents and normals
- Common tangents to conics
- Pair of tangents
- Chord of contact
5️⃣ Vectors and Three Dimensional Geometry
Vector
- Vectors and scalars
- Unit vectors
- Direction cosines and ratios of a vector
- Multiplication of a vector by scalar
- Dot product
- Cross product of vectors
- Applications of vector products
Three Dimensional Geometry
- Direction cosines and ratios of a line joining two points
- Cartesian and vector equation of a straight line
- Coplanar and skew lines
- Shortest distance between two lines
- Cartesian and vector equation of a plane
- Angle between two lines
- Angle between two planes
- Angle between a line and a plane
- Distance of a point from a plane
- Intersection of two lines
- Intersection of a line and plane
- Intersection of two planes
- Equations of sphere, cone and cylinder
6️⃣ Abstract Algebra
- Group and its examples
- Subgroups
- Homomorphism and isomorphism
- Properties of homomorphism
- Order of an element in a group
- Cyclic group
- Symmetric group
- Sn
- Lagrange’s theorem and its applications
- Normal subgroups
- Fundamental theorem of homomorphism
- Ring and Field with examples
7️⃣ Linear Algebra
- Vector space with examples
- Subspace
- Linear dependence and independence
- Basis and dimension of a vector space
- Quotient space
- Linear sum and direct sum of subspaces
- Linear transformation
- Kernel and image
- Rank and nullity of a linear transformation
- Rank-nullity theorem
- Composite of linear transformations
- Singular and non-singular linear transformations
- Transpose of a linear transformation
- Matrix of a linear transformation
8️⃣ Vector Calculus
Vector Differentiation
- Scalar and vector fields
- Gradient
- Divergence
- Curl
- Vector identities
- Directional derivatives
Vector Integration
- Line integral
- Surface integral
- Volume integral
- Green’s theorem
- Gauss-divergence theorem
- Stokes’ theorem
- Simple applications of these theorems
9️⃣ Mechanics
Statics
- Equilibrium of a body under the action of three forces
- Coplanar forces
- Equilibrium under a system of coplanar forces
- Centre of gravity
- Moment of inertia
- Moment and properties
Dynamics
- Motion of a projectile in vertical plane under gravity
- Work
- Power and energy
- Radial and transverse velocity and acceleration
- Tangential and normal velocity and acceleration
- Central orbits
🔟 Trigonometry
- Trigonometric equations
- Properties of triangles
- Inverse circular functions
- Height and distance
- Complex numbers
- De Moivre’s theorem
- Applications of De Moivre’s theorem
🧠 General Knowledge Syllabus – 30 Questions
उपलब्ध Mathematics PDF के pages 5–6 में Trained Graduate Teacher (TGT) and Post Graduate Teacher (PGT) के लिए General Knowledge का common syllabus दिया गया है। Number of Questions: 30.
Unit 1 – Current Affairs
- Current Events of State, National and International Importance
- Personalities in News
- Sports
Unit 2 – Indian History, Indian Polity, Indian Economy and Indian Geography
- Indian History and Indian National Movement
- Indian Constitution and Polity
- Legal and Constitutional Development related with Educational System
- Indian Economy
- Basic Indian Geography
- Population
Unit 3 – General Science, Information and Communication Technology
- General Science, Technology and Environment in contemporary context
- Human Health and Hygiene
- Vitamins
- Minerals
- Diseases and Deficiency Diseases
- Hormones and Enzymes
- Computer and Internet Terminology
- ICT uses
- Development in Educational Technology
🇮🇳 UP PGT गणित सिलेबस 2026 – हिन्दी में
विषय कोड–08
1. बीज गणित
संबंध एवं फलन, आव्यूह, सारणिक, समीकरणों की संगति एवं हलों की संख्या, दो तथा तीन चरों के समीकरण, अंकगणितीय/गुणोत्तर/हारात्मक श्रेणियाँ, क्रमचय एवं संचय, द्विपद प्रमेय, घातीय एवं लघुगणकीय श्रेणियाँ तथा प्रायिकता।
2. कलन
एक चर के फलन, सीमा, सततता, अवकलनीयता, अवकलज, माध्य मान प्रमेय, मैक्लॉरिन एवं टेलर श्रेणियाँ, लघुगणितीय अवकलन, स्पर्शी एवं अभिलम्ब, उच्चिष्ठ एवं निम्निष्ठ तथा समाकलन।
3. साधारण अवकल समीकरण
अवकल समीकरण की कोटि एवं घाति, अवकल समीकरण की व्युत्पत्ति, प्रथम कोटि एवं प्रथम घाति के अवकल समीकरण, विशेष हल तथा स्थिर गुणांकों वाले रैखिक अवकल समीकरण।
4. द्विविमीय निर्देशांक ज्यामिति
दो चर वाले द्विघात समीकरण, सरल रेखा युग्म, वृत्त, परवलय, दीर्घवृत्त, अतिपरवलय, स्पर्शी एवं अभिलम्ब तथा शंकुओं से संबंधित स्पर्शी topics।
5. सदिश एवं त्रिविमीय ज्यामिति
सदिश एवं अदिश, इकाई सदिश, दिशा कोज्या, सदिश गुणन, डॉट एवं क्रॉस गुणन, रेखा एवं समतल के समीकरण, skew lines, shortest distance तथा गोला, शंकु और बेलन के समीकरण।
6. अमूर्त बीजगणित
समूह, उपसमूह, समाकारिता एवं तुल्याकारिता, cyclic group, symmetric group, Lagrange theorem, normal subgroups, homomorphism तथा Ring और Field।
7. रेखीय बीजगणित
Vector space, subspace, linear dependence/independence, basis, dimension, quotient space, linear transformation, kernel, image, rank, nullity तथा linear transformations के matrix।
8. सदिश कलन
Scalar और vector fields, gradient, divergence, curl, directional derivatives, line/surface/volume integrals तथा Green’s, Gauss-divergence और Stokes’ theorem।
9. यान्त्रिकी
Statics में equilibrium, coplanar forces, centre of gravity और moment of inertia; Dynamics में projectile motion, work, power, energy, velocity, acceleration और central orbits।
10. त्रिकोणमिति
त्रिकोणमितीय समीकरण, त्रिभुजों के गुण, inverse circular functions, height and distance, complex numbers तथा De Moivre’s theorem।
🎯 UP PGT Mathematics Preparation Strategy 2026
1. पहले पूरे syllabus को 10 blocks में divide करें
Algebra, Calculus, Ordinary Differential Equations, Co-ordinate Geometry, Vectors & 3D, Abstract Algebra, Linear Algebra, Vector Calculus, Mechanics और Trigonometry को अलग-अलग preparation blocks में रखें।
2. Algebra को मजबूत आधार बनाएं
Relations and Functions, Matrices, Determinants, equations, progressions, series, permutations, combinations, binomial theorem और probability को व्यवस्थित रूप से तैयार करें।
3. Calculus के concepts को practice के साथ पढ़ें
Limits, continuity, differentiation, mean value theorems, Taylor/Maclaurin series, integration, definite integrals और Riemann integration की नियमित practice करें।
4. Abstract और Linear Algebra को अलग revision blocks दें
Groups, subgroups, homomorphism, isomorphism, vector spaces, basis, dimension, linear transformation, rank और nullity को concept-wise revise करें।
5. Geometry और Vector Calculus पर नियमित practice करें
Two-dimensional geometry, 3D geometry, vector products, gradient, divergence, curl और integral theorems को questions के साथ अभ्यास करें।
6. Mechanics और Trigonometry को नजरअंदाज न करें
Statics, dynamics, projectile motion, work, power, energy, central orbits, trigonometric equations, complex numbers और De Moivre’s theorem को syllabus के अनुसार तैयार करें।
7. GK के 30 Questions के लिए अलग समय रखें
Current Affairs, Indian History, Indian National Movement, Constitution, Polity, Economy, Geography, General Science, Technology, Environment, Human Health, Computer/Internet terminology, ICT और Educational Technology को नियमित रूप से revise करें।
8. Previous Papers और Mock Tests का अभ्यास करें
Mathematics syllabus पूरा करने के बाद topic-wise questions, previous papers और mock tests के माध्यम से accuracy तथा time management पर काम करें।
📚 UP PGT New Syllabus 2026 – Other Subject Posts
Mathematics के साथ Objective English पर उपलब्ध अन्य PGT syllabus resources भी देखें।
📚 UP TGT New Syllabus 2026 – Related Subject Resources
PGT Mathematics preparation के साथ UP TGT New Syllabus series के उपलब्ध subject-wise resources भी देखें।
🧭 UP TGT & PGT New Syllabus 2026 – Master Guide
TGT और PGT के revised syllabus, examination framework, General Knowledge, subject questions, negative marking और selection-related information को एक जगह समझने के लिए हमारा Master Guide देखें।
📚 UP TGT PGT NEW SYLLABUS 2026 – MASTER GUIDE New Exam Pattern • 90 Subject + 30 General Studies Questions • Negative Marking • Selection Process📑 UP PGT Recruitment & Previous Solved Papers
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Students को अलग-अलग careers को समझने, eligibility, qualifications, subjects, entrance examinations और career roadmap जैसी जानकारी व्यवस्थित रूप से समझाने के लिए हमारा career guidance platform।
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Visit 10th Class Website →🔗 Important Official & Study Resources
❓ UP PGT Mathematics Syllabus 2026 – FAQs
उपलब्ध official syllabus PDF में Mathematics–PGT (Secondary Education) का Subject Code–08 दिया गया है।
उपलब्ध syllabus में 10 मुख्य sections हैं: Algebra, Calculus, Ordinary Differential Equations, Co-ordinate Geometry, Vectors and Three Dimensional Geometry, Abstract Algebra, Linear Algebra, Vector Calculus, Mechanics और Trigonometry।
Relations and Functions, Matrices, Determinants, equations, progressions, permutations and combinations, Binomial Theorem, exponential/logarithmic series और Probability शामिल हैं।
हाँ। Calculus section में differentiation के साथ methods of integration, definite integration, area under simple curves और Riemann integration शामिल हैं।
हाँ। Group, Subgroups, Homomorphism, Isomorphism, Cyclic Group, Symmetric Group, Lagrange’s Theorem, Normal Subgroups तथा Ring and Field syllabus में दिए गए हैं।
हाँ। Vector Space, Subspace, Linear Dependence/Independence, Basis, Dimension, Linear Transformation, Kernel, Image, Rank, Nullity तथा संबंधित topics शामिल हैं।
उपलब्ध PDF में TGT एवं PGT के common General Knowledge section के लिए Number of Questions – 30 दिया गया है।
Current Affairs, Indian History and National Movement, Constitution and Polity, Indian Economy, Geography and Population, General Science, Technology, Environment, Human Health, Computer/Internet Terminology, ICT तथा Educational Technology शामिल हैं।
इस page पर दिए गए Official Mathematics & GK PDF button से उपलब्ध syllabus document को directly open/download किया जा सकता है।
Recruitment, examination, application, marking और selection से संबंधित अंतिम तथा नवीनतम information के लिए UPESSC की official website और latest official notification को प्राथमिक source मानें।
✅ UP PGT Mathematics Syllabus 2026 – Final Checklist
🏆 UP PGT Mathematics Preparation Formula
📌 Official Source Note
इस article में Mathematics subject syllabus तथा common General Knowledge syllabus को उपलब्ध PGT Mathematics and GK Syllabus PDF के आधार पर व्यवस्थित किया गया है।
उपलब्ध document में Mathematics–PGT (Secondary Education), Subject Code–08 तथा Mathematics के 10 major sections दिए गए हैं।
PDF के pages 5–6 में TGT एवं PGT के लिए common General Knowledge syllabus और 30 questions का उल्लेख है।
Examination pattern, marking, recruitment, application और selection से संबंधित अंतिम/नवीनतम बदलाव के लिए UPESSC द्वारा जारी latest official notification/instructions को प्राथमिक source माना जाना चाहिए।
Official Commission: Uttar Pradesh Education Service Selection Commission (UPESSC)
📢 UP PGT Mathematics 2026 Preparation
Mathematics के पूरे syllabus को section-wise समझें, Algebra और Calculus जैसे core areas को मजबूत करें, Geometry, Abstract Algebra, Linear Algebra, Vector Calculus, Mechanics और Trigonometry की नियमित practice करें तथा common GK के 30 questions के लिए भी अलग preparation रखें।