UP PGT Maths Syllabus PDF: Detailed Unit-Wise Syllabus

Candidates preparing for the UP PGT Maths exam should understand the complete syllabus before starting their preparation. The UP PGT Maths syllabus is divided into ten units covering different areas of Mathematics. Knowing the syllabus helps candidates focus on the right topics and prepare in a planned manner.

The syllabus includes important topics such as Algebra, Calculus, Geometry, Mechanics, Trigonometry, and other key areas prescribed for the examination. Going through each unit carefully can help candidates build a strong preparation strategy and avoid missing any important topics.

UP PGT Maths Syllabus Overview

The UP PGT Maths syllabus is prescribed by UPESSC for the Mathematics (PGT) post in Secondary Education. It is divided into ten units covering different areas of Mathematics. Candidates should understand all the units before starting their preparation. The table below provides a quick overview of the UP PGT Maths syllabus and its basic details.

UP PGT Maths Syllabus PDF

Candidates can download the official UP PGT Maths Syllabus PDF released by UPESSC to check the complete unit-wise Mathematics syllabus. Referring to the official PDF helps ensure that your preparation is based on the latest syllabus and prescribed topics.

UP PGT Maths Unit-wise Syllabus in Detail

The UP PGT Maths syllabus is divided into ten units covering different areas of Mathematics. Below is the detailed unit-wise syllabus with the important topics included in each unit.

1. Algebra

This unit covers:

• Relation and Function: Types of relations (reflexive, symmetric, transitive, and equivalence relations), equivalence class, one-one and onto functions, composite of function, inverse of function, and 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, and invertible matrices.

• Determinants: Properties of determinants, adjoint and inverse of a square matrix, consistency and number of solutions of a system of linear equations, and solving a system of linear equations in two or three variables.

• Theory of equations of degree greater than or equal to two, arithmetic, geometric, and harmonic progressions, permutations and combinations, binomial theorem, and exponential and logarithmic series.

• Probability: Multiplication theorem of probability, conditional probability, independent events, and total probability.

2. Calculus

This unit includes:

• Function of one variable: Limit of a function, continuity and differentiability of a function, derivative of a composite function, Rolle's theorem, Lagrange and Cauchy mean value theorems, Maclaurin's and Taylor's series, L'Hospital's rule, successive differentiation, Leibnitz theorem, equation of tangent and normal to a given curve, increasing and decreasing functions, and maxima and minima.

• Integration: Methods of integration, definite integration as a limit of sum, basic properties of definite integrals and their evaluation, applications in finding the area under simple curves, and Riemann integration.

3. Ordinary Differential Equations

Topics include 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, and homogeneous differential equations.

4. Co-ordinate Geometry of Two Dimensions

This unit covers the general equation of second degree in two variables (x, y) and its classification into pairs of straight lines, circle, parabola, ellipse, and hyperbola. It also includes the equation of tangents and normals, common tangents to two conics, pair of tangents, and chord of contact.

5. Vectors and Three Dimensional Geometry

• Vector: Vectors and scalars, unit vectors, direction cosines and ratios of a vector, multiplication of a vector by a scalar, dot product, cross product of vectors, and their simple applications.

• 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 (a) two lines, (b) two planes, and (c) a line and a plane. Also included are the distance of a point from a plane, intersection of two lines, intersection of a line and a plane, intersection of two planes, and equations of sphere, cone, and cylinder.

6. Abstract Algebra

This unit includes group and its examples, subgroups, homomorphism and isomorphism, properties of homomorphism, order of an element in a group, cyclic group, symmetric group (Sn), Lagrange theorem, Fermat's theorem and its application, normal subgroups, the fundamental theorem of homomorphism, and ring and field with examples.

7. Linear Algebra

Topics covered are 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 of a linear transformation, rank and nullity of a linear transformation, the rank-nullity theorem, composite of linear transformations, singular and non-singular linear transformations, transpose of a linear transformation, and matrix of a linear transformation.

8. Vector Calculus

• Vector differentiation: Scalar and vector fields, gradient, divergence and curl, vector identities, and directional derivatives.

• Vector integration: Line integral, surface integral, volume integral, Green's theorem, Gauss-divergence theorem, Stokes' theorem, and their simple applications.

9. Mechanics

• Statics: Equilibrium of a body under the action of three forces, coplanar forces, equilibrium of a body under the action of a system of coplanar forces, centre of gravity, common catenary and its properties, and moment of inertia.

• Dynamics: Motion of a projectile in a vertical plane under gravity, work, power and energy, radial and transverse velocity and acceleration, tangential and normal velocity and acceleration, and central orbits.

10. Trigonometry

This unit covers trigonometric equations, properties of triangles, inverse circular functions, height and distance, complex numbers, De Moivre's theorem, and its application.