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UP GIC Lecturer Maths Syllabus 2025, Download PDF, Exam Pattern

authorImageNazish Fatima16 Sept, 2025
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UP GIC Lecturer Maths Syllabus 2025

UP GIC Lecturer Maths Syllabus 2025 will cover Relations and Functions, Algebra, Calculus, Coordinate Geometry, Vectors, and 3D Geometry. It includes advanced chapters such as Groups, Linear Programming, Differential Equations, Probability, and Matrices. 

Candidates should have a good understanding of the basic and advanced topics of Maths. The goal is to provide the aspiring candidates with the knowledge so they will be effective in teaching and be successful when taking the competitive exam for UP GIC Lecturer Recruitment 2025.

UP GIC Lecturer Maths Syllabus 2025 Overview

The UPPSC GIC Lecturer Notification 2025 covers the syllabus for the Maths exam. It is designed to test a candidate’s deep understanding of mathematical topics. It covers a wide range of topics, including advanced chapters such as Groups, Linear Programming, Differential Equations, Probability, and Matrices—preparing candidates for teaching roles in senior secondary government schools.

UP GIC Lecturer Maths Syllabus 2025 Overview
Recruitment Body Uttar Pradesh Public Service Commission (UPPSC)
Post Name Lecturer (Male/Female) Government Inter College, Special GIC, and Lecturer in UP Jail Training School
Total Vacancies 1518 (Male GIC: 777, Female GIC: 694, Special GIC: 45, Jail Training School: 2)
Pay Scale Level-8 ₹47,600 – ₹1,51,100 (Most posts)Level-7 ₹44,900 – ₹1,42,400 (Jail Training School)
Application Mode Online (OTR-based)
Application Dates Start: 12 August 2025Last Date (Fee & Submit): 12 September 2025Correction Window: 19 September 2025
Exam Pattern – Prelims 120 Questions (80 Subject + 40 General Studies)
Exam Pattern – Mains Paper 1: General Hindi & Essay – 100 Marks (2 hrs)Paper 2: Subject paper – 300 Marks (3 hrs)
Difficulty Level Post-Graduate/PG Level
 Syllabus Scope Relations and Functions, Algebra, Calculus, Coordinate Geometry, Groups, Linear Programming, Differential Equations, Probability, and Matrices 
Official Website uppsc.up.nic.in

UP GIC Lecturer Maths Syllabus 2025

Candidates can easily download the complete UP GIC Lecturer Maths Syllabus PDF from the official UPPSC portal and leading education websites. The PDF includes unit-wise topics, listing all subunits and core concepts that may be asked in the main examinations. The detailed Maths syllabus for the UP GIC Lecturer Exam is tabulated below:

UP GIC Lecturer Maths Syllabus 2025
Topic Category Topics Covered
Relations and Functions
  • Reflexive, Symmetric, Transitive, Equivalence Relations
  • Equivalence Class
  • One-one and Onto Functions
  • Composite & Inverse of Functions
  • Binary Operations
Matrices
  • Types of Matrices
  • Zero Matrix
  • Transpose
  • Symmetric & Skew-symmetric Matrices
  • Addition, Scalar & Matrix Multiplication
  • Singular & Non-singular
  • Invertible Matrices
Determinants
  • Determinant of Square Matrix (up to 3x3)
  • Properties- Adjoint and Inverse
  • System of Linear Equations (Consistency, Solutions, Examples)
Algebra
  • Equations of Degree ≥ 2
  • Arithmetic, Geometric, Harmonic Progressions
  • Permutations & Combinations
  • Binomial Theorem
  • Exponential & Logarithmic Series
Probability
  • Multiplication Theorem
  • Conditional Probability
  • Independent Events
  • Total Probability
  • Bayes’ Theorem
Calculus - Differentiation
  • Continuity & Differentiability
  • Chain Rule, Rolle's & Lagrange Theorems
  • Maclaurin’s & Taylor’s Series
  • L’Hospital’s Rule
  • Partial & Successive Differentiation
  • Leibnitz Theorem
  • Tangent & Normal Equations
  • Maxima/Minima
  • Increasing/Decreasing Functions
Calculus - Integration
  • Methods of Integration
  • Definite Integrals as Limit of Sum
  • Properties & Evaluation of Definite Integrals
  • Area under Curves, Spheres, Cones, Cylinders
Differential Equations
  • Order & Degree
  • Formation of Equations
  • First Order & First Degree Solutions
  • Linear Equations with Constant Coefficients
  • Homogeneous Differential Equations
Coordinate Geometry
  • Pair of Straight Lines
  • Classification of Second Degree Equations
  • Tangents & Normals to Conics
  • Common Tangents, Chord of Contact, Polar Lines
Vectors & 3D Geometry
  • Scalars & Vectors
  • Unit Vectors, Direction Cosines/Ratios
  • Scalar Multiplication
  • Dot & Cross Product
  • Vector & Cartesian Line Equations
  • Coplanar/Skew Lines, Shortest Distance
  • Equation of Plane- Angles Between Lines/Planes
  • Distance of Point to Plane
  • Intersection of Lines/Planes
  • Plane from Two Plane Intersection
Group Theory
  • Groups: nth Roots of Unity, Modulo nnn & ppp
  • Subgroups, Homomorphisms, Isomorphisms
  • Order, Cyclic & Symmetric Groups
  • Lagrange, Fermat’s Theorems
  • Normal Subgroups, Fundamental Theorem
  • Endomorphism, Automorphism, Isomorphism Theorems
Rings and Fields
  • Definitions & Examples: (Zn,+,⋅), (Zn​,+,⋅), (Zp,+,⋅), (Zp​,+,⋅)
Vector Spaces
  • Definitions & Examples
  • Subspace, Linear Dependence/Independence
  • Basis & Dimension
  • Quotient, Sum & Direct Sum
  • Linear Transformations
  • Kernel, Image
  • Rank, Nullity, Rank
  • Nullity Theorem
  • Matrix Representation
  • Singular/Non-singular Transformations
Vector Calculus
  • Gradient, Divergence, Curl
  • Directional Derivatives
  • Line, Surface & Volume Integrals
  • Green’s, Gauss, Stokes’s Theorems
Integration of Special Functions
  • Discontinuous Function Integration
  • Lower & Upper Integrals
  • Step & Signum Function Integration
Statics & Dynamics
  • Equilibrium under 3 Forces
  • Coplanar Forces, Systems
  • Centre of Gravity, Catenary, Friction
  • Projectile Motion, Work, Power, Energy
  • Direct Impact of Smooth Bodies
  • Radial, Transverse, Tangential & Normal Acceleration
Trigonometry & Miscellaneous
  • Trigonometric Equations
  • Triangle Properties
  • Inverse Circular Functions
  • Heights & Distances- Complex Numbers- De Moivre’s Theorem- nthn^{th}nth Roots of Unity- Linear Programming- Logarithmic Differentiation- Implicit Differentiation- Applications of Derivatives- Straight Line Equations (Various Forms)

UP GIC Lecturer Maths Syllabus PDF

Candidates are advised to download the UP GIC Lecturer Notification released by the exam conducting authority. The detailed notifications PDF covers the Maths syllabus and its exam pattern. Visit the official website and download the notification, and find the Maths section under it. A direct link to download the UP GIC Lecturer Maths Syllabus PDF is available here. Click the button below to download.

UP GIC Lecturer Maths Exam Pattern

The UP GIC Lecturer Maths Exam Pattern comprises descriptive written papers in the mains, featuring questions from all topic areas of the syllabus. The duration of the exam is three hours and carries 300 marks. Here is the structured exam pattern for the UP GIC Lecturer Maths recruitment 2025:

UP GIC Lecturer Maths Exam Pattern
Exam Stage Number of Questions/Pattern Marks Time Negative Marking
Mains Paper 2 Maths (Descriptive, 20 Questions) 300 3 hours None
 

 

UP GIC Lecturer Maths Syllabus 2025 FAQs

What topics are covered in UP GIC Lecturer Maths Syllabus 2025?

Relations and Functions, Algebra, Calculus, Coordinate Geometry, Groups, Linear Programming, Differential Equations, Probability, and Matrices

Is the UP GIC Lecturer Maths syllabus based on NCERT or PG level?

It combines NCERT Class XI-XII and postgraduate level topics, reflecting the requirements for teaching at inter colleges

Is there negative marking in the UP GIC Lecturer maths exam? .

A3: Yes, there is a negative marking of 1/3rd mark for each wrong answer in the Preliminary exam

What are the exam modes?

Both Prelims and Mains are offline (OMR / descriptive).
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