RPSC 1st Grade Math Syllabus 2026

Prepare with confidence for the Rajasthan Public Service Commission (RPSC) examinations using the comprehensive RPSC 1st Grade Math Syllabus 2026. Carefully organized into single points for clear understanding. Mastering the complete RPSC 1st Grade Math Syllabus 2026 is your guaranteed path to an exceptional score.[cite: 1]

Part-I: Senior Secondary Level (भाग-I: उच्च माध्यमिक स्तर) - RPSC 1st Grade Math Syllabus 2026

1. Sets, Relations and Functions (समुच्चय, संबंध और फलन) - RPSC 1st Grade Math Syllabus 2026

• Sets and their representations [cite: 1]
• Different kinds of sets [cite: 1]
• Sub set [cite: 1]
• Universal set [cite: 1]
• Venn diagrams [cite: 1]
• Operation on Sets [cite: 1]
• De-Morgan's laws and practical problems based on them [cite: 1]
• Ordered pair [cite: 1]
• Cartesian product of sets [cite: 1]
• Relation [cite: 1]
• Domain, co-domain and range of relation [cite: 1]
• Equivalence relation [cite: 1]
• Function as a special case of relation [cite: 1]
• Domain, co-domain, range of functions [cite: 1]
• Invertible functions [cite: 1]
• Even and odd functions [cite: 1]
• Into, onto and one-to-one functions [cite: 1]
• Special functions (polynomial, trigonometric, exponential, logarithmic, absolute value, greatest integer etc.) [cite: 1]
• Sum, difference, product and composition of functions [cite: 1]

2. Trigonometry (त्रिकोणमिति) - RPSC 1st Grade Math Syllabus 2026

• Measuring angles in radians and in degrees [cite: 1]
• Trigonometric functions and their graphs [cite: 1]
• Trigonometric identities [cite: 1]
• General solution of trigonometric equations [cite: 1]
• Inverse trigonometric functions (principal value only) [cite: 1]
• Elementary properties of inverse trigonometric functions [cite: 1]

3. Algebra (बीजगणित) - RPSC 1st Grade Math Syllabus 2026

• Quadratic equation with real coefficients [cite: 1]
• Formation of quadratic equation with given roots [cite: 1]
• Relation between roots and coefficients [cite: 1]
• Symmetric functions of roots [cite: 1]
• Linear and quadratic inequations [cite: 1]
• Algebra of complex numbers [cite: 1]
• Addition, multiplication, conjugation of complex numbers [cite: 1]
• Polar representation of complex numbers [cite: 1]
• Properties of modulus and principal argument [cite: 1]
• Triangle inequalities [cite: 1]
• Cube roots of unity [cite: 1]
• Geometric interpretations of complex number [cite: 1]
• Arithmetic and geometric progressions [cite: 1]
• n^th term and sum of n terms [cite: 1]
• Arithmetic and geometric means [cite: 1]
• Infinite geometric series [cite: 1]
• Arithmetico-Geometric Progression [cite: 1]
• Sum of the first 'n' natural numbers [cite: 1]
• Sums of squares and cubes of the first 'n' natural numbers [cite: 1]
• Fundamental principle of counting [cite: 1]
• Factorial n (n!) [cite: 1]
• Permutations and Combinations and simple applications [cite: 1]
• Exponential and logarithmic series [cite: 1]
• Binomial theorem and simple applications [cite: 1]
• General term and middle term [cite: 1]
• Properties of binomial coefficients [cite: 1]

4. Matrices and Determinants (आव्यूह और सारणिक)

• Matrices and algebra of matrices [cite: 1]
• Type of matrices [cite: 1]
• Transpose of a matrix [cite: 1]
• Symmetric and skew symmetric matrices [cite: 1]
• Operations on matrices: Addition, multiplication and multiplication with a scalar [cite: 1]
• Determinants of order two and three [cite: 1]
• Properties of determinants [cite: 1]
• Minors and co-factors [cite: 1]
• Applications of determinants in finding the area of a triangle [cite: 1]
• Adjoint and inverse of a square matrix [cite: 1]
• Inverse of matrix using elementary transformations [cite: 1]
• Test of consistency [cite: 1]
• Solution of simultaneous linear equations in two and three variables using determinants and matrices [cite: 1]

5. Two-Dimensional Geometry (द्विमीय ज्यामिति)

• Cartesian coordinates [cite: 1]
• Distance between two points [cite: 1]
• Section formulae [cite: 1]
• Shift of origin [cite: 1]
• Equation of a straight line in various forms [cite: 1]
• Slop of line and angle between two lines [cite: 1]
• Distance of a point from a line [cite: 1]
• Lines through the point of intersection of two given lines [cite: 1]
• Equation of the bisector of the angle between two lines [cite: 1]
• Concurrency of lines [cite: 1]
• Centroid, orthocenter, incentre and circumcenter of a triangle [cite: 1]
• Equation of a circle in various forms [cite: 1]
• Equation of tangent, normal and chord of a circle [cite: 1]
• Parametric equations of a circle [cite: 1]
• Intersection of a circle with a straight line/ circle [cite: 1]
• Equation of a circle through the points of intersection of two circles [cite: 1]
• Equation of a circle through points of a circle and a straight line [cite: 1]
• Equation of a parabola, ellipse, hyperbola and their foci [cite: 1]
• Directrices and eccentricity [cite: 1]
• Parametric equations, equations of tangent and normal [cite: 1]
• Problems based on locus [cite: 1]
• General equation of second degree [cite: 1]
• Nature of conic [cite: 1]
• Polar equation of a conic [cite: 1]
• Polar equation of tangent and normal [cite: 1]
• Asymptotes and chord of contact [cite: 1]
• Auxiliary circle and director circle of a conic and related problems [cite: 1]

6. Calculus (कलन) - RPSC 1st Grade Math Syllabus 2026

• Limits, continuity and differentiability [cite: 1]
• Differentiation of the sum, difference, product and quotient of two functions [cite: 1]
• Chain rule [cite: 1]
• Derivative of composite functions [cite: 1]
• Derivatives of trigonometrical and inverse trigonometric functions [cite: 1]
• Derivative of implicit functions [cite: 1]
• Derivatives of logarithmic and exponential functions [cite: 1]
• Logarithmic differentiation [cite: 1]
• Derivative of functions expressed in parametric forms [cite: 1]
• Second and third order derivatives [cite: 1]
• Rolle's and Lagrange's Mean value Theorems [cite: 1]
• Rate of change of quantities [cite: 1]
• Monotonic increasing and decreasing functions [cite: 1]
• Maxima and minima of functions of one variable [cite: 1]
• Tangent and normal [cite: 1]
• Integral as an anti-derivative [cite: 1]
• Integration of a variety of functions by substitution [cite: 1]
• Integration by partial fractions and by parts [cite: 1]
• Integration of rational and irrational functions [cite: 1]
• Definite integral and their properties [cite: 1]
• Application of definite integrals in finding the area under simple curves [cite: 1]
• Area of lines, arcs of circles/parabolas/ellipses/hyperbola [cite: 1]
• Area between the said curves (the region should be clearly identifiable) [cite: 1]

7. Vector Algebra (सदिश बीजगणित)

• Vectors and scalars [cite: 1]
• Magnitude and direction of a vector [cite: 1]
• Direction cosines/ratios of vectors [cite: 1]
• Types of vectors (equal, unit, zero, parallel and collinear vectors etc.) [cite: 1]
• Position vector of a point [cite: 1]
• Negative of a vector [cite: 1]
• Components of a vector [cite: 1]
• Addition of vectors [cite: 1]
• Multiplication of a vector by a scalar [cite: 1]
• Position vector of a point dividing a line segment in a given ratio [cite: 1]
• Scalar (dot) product of vectors [cite: 1]
• Projection of a vector on a line [cite: 1]
• Vector (cross) product of vectors [cite: 1]
• Scalar and Vector triple product and problems related to them [cite: 1]

8. Statistics and Probability (सांख्यिकी और प्रायिकता)

• Measures of dispersion: Standard deviation, variance and mean deviation for grouped and ungrouped data [cite: 1]
• Probability of an event [cite: 1]
• Addition and multiplication theorems of probability [cite: 1]
• Conditional probability [cite: 1]
• Bayes' theorem and total probability [cite: 1]
• Probability distribution of a random variate [cite: 1]
• Bernoulli trials and binomial distribution [cite: 1]

Part-II: Graduation Level (भाग-II: स्नातक स्तर) - RPSC 1st Grade Math Syllabus 2026

1. Abstract Algebra (अमूर्त बीजगणित)

• Definition and example of groups [cite: 1]
• General properties of groups [cite: 1]
• Order of an element of a group [cite: 1]
• Cyclic group [cite: 1]
• Permutations: Even and Odd permutations [cite: 1]
• Groups of permutations [cite: 1]
• Cyclic permutation and Alternating group [cite: 1]
• Subgroups and Cosets [cite: 1]
• Lagrange's theorem [cite: 1]
• Normal subgroup [cite: 1]
• Conjugate elements and conjugate complexes [cite: 1]
• Centre of a group and Simple group [cite: 1]
• Normaliser of an element and of a complex [cite: 1]
• Quotient Groups [cite: 1]
• Group homomorphism and isomorphism with elementary basic properties [cite: 1]
• Fundamental theorem of homomorphism in groups [cite: 1]
• Isomorphism theorems of groups [cite: 1]
• Cayley's theorem [cite: 1]
• Ring Theory: Introduction to Rings [cite: 1]
• Zero divisors [cite: 1]
• Division ring, Integral Domain and Fields, their examples and properties [cite: 1]
• Ideals of a ring [cite: 1]
• Quotient rings [cite: 1]

2. Complex Analysis (सम्मिश्र विश्लेषण) - RPSC 1st Grade Math Syllabus 2026

• Functions, Limits, Continuity and Differentiability of complex functions [cite: 1]
• The extended plane and its spherical representation [cite: 1]
• Concept of an analytic function [cite: 1]
• Cartesian and Polar form of Cauchy-Riemann equations [cite: 1]
• Harmonic functions [cite: 1]
• Construction of an analytic function [cite: 1]
• Conformal mapping [cite: 1]
• Bilinear transformation and its properties [cite: 1]
• Fixed points [cite: 1]
• Cross ratio [cite: 1]
• Inverse point [cite: 1]

3. Advance Calculus (उन्नत कलन)

• Polar Co-ordinates [cite: 1]
• Angle between radius vector and the tangent [cite: 1]
• Angle between two curves in polar form [cite: 1]
• Length of polar tangent, sub-tangent, normal and subnormal [cite: 1]
• Pedal equation of a curve [cite: 1]
• Derivatives of an arc [cite: 1]
• Curvature and various formulae [cite: 1]
• Centre of curvature and chord of curvature and related problems [cite: 1]
• Partial differentiation [cite: 1]
• Euler's theorem on homogeneous functions [cite: 1]
• Chain rule of partial differentiation [cite: 1]
• Total differentiation [cite: 1]
• Maxima and Minima of functions of two independent variables [cite: 1]
• Maxima and Minima of three variables connected by a relation [cite: 1]
• Lagrange's Method of undetermined multipliers [cite: 1]
• Asymptotes and double points [cite: 1]
• Curve tracing [cite: 1]
• Envelopes and evolutes [cite: 1]
• Theory of Beta and Gamma functions [cite: 1]
• Differentiation and integration under the sign of integration [cite: 1]
• Double integral [cite: 1]
• Change of order of integration and changing into polar co-ordinates [cite: 1]
• Applications in finding areas [cite: 1]
• Triple integral and application to find volume [cite: 1]
• Dirichlet's integral [cite: 1]
• Quadrature and Rectification [cite: 1]
• Volume and Surface area of solids of revolution [cite: 1]

4. Ordinary and Partial Differential Equations (साधारण और आंशिक अवकल समीकरण)

• Order and degree of differential equation [cite: 1]
• Ordinary differential equations of first order and first degree [cite: 1]
• Differential equations of first order but not of first degree [cite: 1]
• Clairaut's equations [cite: 1]
• General and singular solutions [cite: 1]
• Linear differential equations with constant coefficients [cite: 1]
• Homogeneous differential equation [cite: 1]
• Second order linear differential equations [cite: 1]
• Simultaneous linear differential equations of first order [cite: 1]
• Partial differential equations of the first order [cite: 1]
• Linear partial differential equation with constant coefficient [cite: 1]

5. Vector Calculus (सदिश कलन) - RPSC 1st Grade Math Syllabus 2026

• Vector differentiation: Curl, Gradient and Divergence [cite: 1]
• Identities involving these operators and related problems [cite: 1]
• Vector integration: line and surface integral [cite: 1]
• Problems based on Stoke, Green and Gauss theorems [cite: 1]

6. Three-Dimensional Geometry (त्रिविमीय ज्यामिति)

• Distance between two points [cite: 1]
• Direction cosines and direction ratios [cite: 1]
• Equation of a straight line in space in various form [cite: 1]
• Skew lines [cite: 1]
• Shortest distance between two lines [cite: 1]
• Equation of a plane in various form [cite: 1]
• Distance of a point from a plane and a line [cite: 1]
• Cartesian and vector equation of a plane and a line [cite: 1]
• Angle between two lines [cite: 1]
• Angle between two planes [cite: 1]
• Angle between a line and a plane [cite: 1]
• Coplanar lines [cite: 1]
• Sphere: Equation of a sphere in various forms [cite: 1]
• Tangent plane, Pole and Polar [cite: 1]
• Intersection of two spheres and Orthogonal spheres [cite: 1]
• Cone, Enveloping cone and Tangent plane [cite: 1]
• Reciprocal cone and three mutually Perpendicular generators [cite: 1]
• Right circular cone [cite: 1]
• Cylinder, right circular cylinder and Enveloping cylinder [cite: 1]

7. Statics and Dynamics (स्थैतिकी और गतिकी)

• Composition and resolution of co-planer forces [cite: 1]
• Component of a force in two given directions [cite: 1]
• Equilibrium of concurrent forces, parallel forces and moment [cite: 1]
• Equilibrium of a body under several coplaner forces [cite: 1]
• Friction [cite: 1]
• Virtual work and common catenary [cite: 1]
• Velocity and acceleration [cite: 1]
• Velocities and accelerations along radial and transverse directions [cite: 1]
• Velocities and accelerations along tangential and normal directions [cite: 1]
• Simple linear motion under constant acceleration [cite: 1]
• Laws of motion [cite: 1]
• Projectile [cite: 1]
• Simple Harmonic Motion [cite: 1]
• Rectilinear motion under variable laws [cite: 1]
• Hook's law [cite: 1]
• Linear motion in resisting medium [cite: 1]
• Constrained motion on smooth plane curves (circular and cycloidal motion) [cite: 1]

Part-III: Post Graduation Level (भाग-III: स्नातकोत्तर स्तर) - RPSC 1st Grade Math Syllabus 2026

1. Real Analysis (वास्तविक विश्लेषण) - RPSC 1st Grade Math Syllabus 2026

• Real numbers as a complete ordered field [cite: 1]
• Linear sets [cite: 1]
• Lower and upper bounds [cite: 1]
• Limit points [cite: 1]
• Closed and open sets [cite: 1]
• Real sequence [cite: 1]
• Limit and convergence of a sequence [cite: 1]
• Convergence of series [cite: 1]
• Tests for convergence of a series [cite: 1]
• Absolute convergence [cite: 1]
• Uniform convergence of sequence and series of functions [cite: 1]

2. Linear Algebra and Metric Spaces (रैखिक बीजगणित और मीट्रिक रिक्त स्थान)

• Definition and examples of a vector space [cite: 1]
• Subspace of a vector space [cite: 1]
• Linear combination [cite: 1]
• Linear dependence and independence of vectors [cite: 1]
• Direct product of vector spaces and internal direct sums of subspaces [cite: 1]
• Bases and dimension of a finitely generated spaces [cite: 1]
• Quotient space [cite: 1]
• Isomorphism [cite: 1]
• Linear transformation (Homomorphism) [cite: 1]
• Rank and nullity of linear transformation [cite: 1]
• The characteristic equation of a matrix [cite: 1]
• Eigen values and Eigen vectors [cite: 1]
• Cayley-Hamilton theorem [cite: 1]
• Definition and example of a metric space [cite: 1]
• Diameter of a set [cite: 1]
• Bounded set [cite: 1]
• Open sphere [cite: 1]
• Interior point and Interior of a set [cite: 1]
• Derived and Closure of set [cite: 1]
• Closed set and Closed Sphere [cite: 1]
• Properties of Open and Closed sets [cite: 1]
• Boundary point of set [cite: 1]
• Convergent and Cauchy sequences [cite: 1]
• Complete metric space [cite: 1]
• Cantor's Intersection theorem [cite: 1]
• Bolzano-Weierstrass theorem [cite: 1]
• Heine-Borel theorem [cite: 1]
• Compactness and connectedness [cite: 1]
• Cantor's ternary set [cite: 1]

3. Integral Transforms and Special Function (समाकलन रूपांतरण और विशेष फलन)

• Laplace transform: Definition and its properties [cite: 1]
• Rules of manipulations [cite: 1]
• Laplace theorems of derivatives and integrals [cite: 1]
• Properties of Inverse Laplace transforms [cite: 1]
• Convolution theorem [cite: 1]
• Complex inversion formulas [cite: 1]
• Applications to the solutions of ordinary differential equations with constant and variable coefficients [cite: 1]
• Fourier Transform: Definition and properties of Fourier sine, cosine and complex transforms [cite: 1]
• Convolution theorem [cite: 1]
• Legendre's polynomial/ Functions: Legendre's differential equation and associated Legendre's differential equations [cite: 1]
• Simple properties of Legendre's functions of first and second kind [cite: 1]
• Bessel functions and Generating function [cite: 1]
• Integral formulae [cite: 1]
• Recurrence relations [cite: 1]
• Addition formula and other properties of Bessel functions [cite: 1]

4. Differential Geometry and Tensors (अवकल ज्यामिति और टेन्सर)

• Differential Geometry: Curves in Space- Space curves [cite: 1]
• Contact of a curve and a surface [cite: 1]
• Definition of unit tangent vector and tangent line [cite: 1]
• Principal Normal, Binormal and Normal plane [cite: 1]
• Tensors: Transformation of coordinates [cite: 1]
• Contravariant, covariant and mixed tensors [cite: 1]
• Second order tensors and Higher order tensors [cite: 1]
• Addition, subtraction and multiplication of tensors [cite: 1]
• Contraction and Quotient Law [cite: 1]
• Symmetric and skew symmetric tensors [cite: 1]
• Conjugate symmetric tensors of the second order [cite: 1]
• Fundamental tensor and Associated tensors [cite: 1]
• Christoffel symbols and Transformation law of Christoffel symbols [cite: 1]
• Covariant differentiation of vectors and tensors [cite: 1]

5. Numerical Analysis (संख्यात्मक विश्लेषण)

• Difference operators and factorial notation [cite: 1]
• Differences of polynomial [cite: 1]
• Newton's formulae for forward and backward interpolations [cite: 1]
• Divided differences [cite: 1]
• Relation between divided differences and Simple difference [cite: 1]
• Newton's general interpolation formulae [cite: 1]
• Lagrange interpolation formula [cite: 1]
• Central differences [cite: 1]
• Gauss, Stirling and Bessel interpolation formulae [cite: 1]
• Numerical Differentiation [cite: 1]
• Numerical integration [cite: 1]
• Newton-Cotes quadrature formula [cite: 1]
• Gauss's quadrature formulae [cite: 1]
• Trapezoidal, Simpson's and Weddle's rules [cite: 1]
• Estimation of errors [cite: 1]
• Transcendental and polynomial equations [cite: 1]
• Bisection method [cite: 1]
• Iteration method [cite: 1]
• Regula Falsi method [cite: 1]
• Newton Raphson method [cite: 1]

6. Optimization Technique (अनुकूलन तकनीक) - RPSC 1st Grade Math Syllabus 2026

• Convex sets and their properties [cite: 1]
• Simplex Method [cite: 1]
• Concepts of duality in linear programming [cite: 1]
• Framing of dual programming [cite: 1]
• Assignment problems [cite: 1]
• Transportation problems [cite: 1]
• Theory of Games: Competitive strategies [cite: 1]
• Minimax and maximin criteria [cite: 1]
• Two-person zero-sum games with and without saddle point [cite: 1]

Part-IV: Pedagogy, TLM & ICT (भाग-IV: शिक्षाशास्त्र और आईसीटी) - RPSC 1st Grade Math Syllabus 2026

• Pedagogy and Teaching Learning Material (Instructional Strategies for Adolescent Learner) [cite: 1]
• Communication skills [cite: 1]
• Use of various verbal and non verbal classroom communication strategies [cite: 1]
• Teaching models- advance organizer and inquiry training (information processing) [cite: 1]
• Group Investigation (Social Interaction) [cite: 1]
• Non-Directive model (Personal development) [cite: 1]
• Preparation and use of teaching-learning material during teaching [cite: 1]
• Cooperative learning [cite: 1]
• Use of Computers and Information Technology in Teaching Learning [cite: 1]
• Concept of ICT and Digital learning [cite: 1]
• E-learning and Virtual Classroom [cite: 1]
• Technology integration in teaching-learning and assessment [cite: 1]

Most Asked Questions: RPSC 1st Grade Math Syllabus 2026

Welcome to the most comprehensive and highly requested FAQ section dedicated entirely to the RPSC 1st Grade Math Syllabus 2026. As thousands of candidates prepare for the upcoming examination, having absolute clarity on every single point of the RPSC 1st Grade Math Syllabus 2026 is mandatory for securing top ranks. Review these expertly crafted answers to accelerate your preparation journey.