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UPSC Mains Optional

Mathematics Optional test series with All-India Ranking

UPSC-style normalization across all 48 optionals

26 tests (12 sectional + 14 full-length), each evaluated by experts within 2 hours, with model answers written around your own style. Every test gets your All-India rank and your Mathematics rank.

₹9,999for all 26 tests

26tests
2 hoursevaluation
1500+question bank
330+target score

Choose your plan

Everything is delivered and submitted on WhatsApp. Evaluated reports and analytics appear on your dashboard.

Test series

Mathematics test series

12 sectional + 14 full-length tests

₹9,999

  • Expert evaluation within 2 hours
  • Model answers built on your writing style
  • Your score vs UPSC weightage graphs
  • 12 years of topic and subtopic analytics
  • Personalise your test dates after joining

Daily practice

One test a day (3 questions), on the days you choose

₹6,000 6 months

  • Plan your topic priority and test dates
  • Same-day evaluation and feedback
  • Model solutions for every test
  • Delivered and submitted on WhatsApp

Topic-wise PYQs

Last 10 years, organised by topic

₹250

  • Average yearly weightage per topic
  • UPSC focus areas highlighted
  • Quick reference for revision

PYQ solutions

2014-2024 model solutions, topic-wise

₹1,250

  • Detailed, easy-to-follow solutions
  • Learn how strong answers are structured
  • Built to lift your score toward 330+

Test schedule

12 sectional tests followed by 14 full-length mocks.

TestTypeTopicDate
1 Sectional – Paper I Linear Algebra 24-Oct
2 Sectional – Paper I Calculus 25-Oct
3 Sectional – Paper I Analytic Geometry 31-Oct
4 Sectional – Paper I Ordinary Differential Equations 01-Nov
5 Sectional – Paper I Dynamics and Statics 07-Nov
6 Sectional – Paper I Vector Analysis 08-Nov
7 Sectional – Paper II Modern Algebra 14-Nov
8 Sectional – Paper II Real Analysis 15-Nov
9 Sectional – Paper II Complex Analysis & Linear Programming 21-Nov
10 Sectional – Paper II Partial Differential Equations 22-Nov
11 Sectional – Paper II Numerical Analysis and Computer Programming 28-Nov
12 Sectional – Paper II Mechanics and Fluid Dynamics 29-Nov
13 Full-Length Test Paper I – Full Syllabus 05-Dec
14 Full-Length Test Paper II – Full Syllabus 06-Dec
15 Full-Length Test Paper I – Full Syllabus 12-Dec
16 Full-Length Test Paper II – Full Syllabus 13-Dec
17 Full-Length Test Paper I – Full Syllabus 19-Dec
18 Full-Length Test Paper II – Full Syllabus 20-Dec
19 Full-Length Test Paper I – Full Syllabus 26-Dec
20 Full-Length Test Paper II – Full Syllabus 27-Dec
21 Full-Length Test Paper I – Full Syllabus 02-Jan
22 Full-Length Test Paper II – Full Syllabus 03-Jan
23 Full-Length Test Paper I – Full Syllabus 09-Jan
24 Full-Length Test Paper II – Full Syllabus 10-Jan
25 Full-Length Test Paper I – Full Syllabus 16-Jan
26 Full-Length Test Paper II – Full Syllabus 17-Jan

Dates don't suit you? You can personalise your test schedule after joining.

Mathematics Optional syllabus

The UPSC syllabus this test series covers, topic by topic.

Paper-I

Linear Algebra
Vector spaces over R and C linear dependence and independence subspaces bases dimension Linear transformations rank and nullity Algebra of matrices including row or column reduction echelon form congruences similarity Rank and inverse of a matrix Solving linear systems Eigenvalues and eigenvectors characteristic polynomial Cayley–Hamilton theorem Properties of symmetric skew symmetric Hermitian skew Hermitian orthogonal and unitary matrices and their eigenvalues
Calculus
Real functions limits continuity differentiability Mean value theorem Taylor theorem with remainder Indeterminate forms Maxima and minima Asymptotes Curve tracing Multivariable functions limits continuity partial derivatives maxima and minima including Lagrange multipliers Jacobian Integration Riemann definite integrals indefinite integrals Improper integrals Double and triple integrals evaluation techniques only Area surface and volume calculations
Analytic Geometry
Cartesian and polar coordinates in three dimensions Quadratic surfaces in three variables reduction to canonical forms Straight lines Shortest distance between two skew lines Planes spheres cones cylinders paraboloids ellipsoids hyperboloids one or two sheets and their properties
Ordinary Differential Equations
Formulation of differential equations First order equations integrating factors orthogonal trajectories Clairaut equation singular solutions Second and higher order linear ODEs with constant coefficients complementary function particular integrals Variable coefficient cases Euler–Cauchy Variation of parameters Laplace and inverse Laplace transforms and applications to initial value problems for second order linear equations with constant coefficients
Dynamics and Statics
Rectilinear motion simple harmonic motion motion in a plane projectiles constrained motion Work and energy conservation laws Kepler laws central force orbits Equilibrium of particle systems work potential energy friction common catenary virtual work principle stability of equilibrium three dimensional force equilibrium
Vector Analysis
Scalar and vector fields differentiation of vector fields with respect to a scalar variable Gradient divergence curl in Cartesian and cylindrical coordinates Higher order derivatives Vector identities and equations Geometry applications curves in space curvature and torsion Serret–Frenet formulae Integral theorems Gauss theorem Stokes theorem Green identities

Paper-II

Modern Algebra
Groups subgroups normal subgroups homomorphisms quotient groups First Second Third isomorphism theorems Sylow theorems and applications Rings ideals integral domains fields Ring homomorphisms Field extensions Finite fields
Real Analysis
The real number system as a complete ordered field Sequences limits Cauchy sequences completeness Series convergence tests absolute or conditional convergence Continuity and uniform continuity Properties of continuous functions on compact sets Riemann integration improper integrals Fundamental theorems of calculus Uniform convergence of sequences and series of functions continuity differentiability integrability Multivariable partial derivatives maxima and minima
Complex Analysis
Analytic functions and the Cauchy–Riemann equations Cauchy integral theorem and formula Taylor and Laurent series Residue theorem and applications
Linear Programming
Linear programming problems basic concepts Graphical method Simplex method Duality and its interpretation
Partial Differential Equations
Geometry of curves and surfaces in three dimensions Formulation of PDEs First order PDEs Second order linear PDEs with constant coefficients Standard PDEs vibrating string heat equation Laplace equation
Numerical Analysis and Computer Programming
Numerical methods root finding bisection regula falsi Newton Raphson Linear systems by Gaussian elimination or Gauss Jordan methods Numerical interpolation Newton forward and backward Lagrange Numerical integration trapezoidal Simpson rules Numerical ODE solution Euler Runge Kutta Programming in C data types operators input output control structures functions
Mechanics and Fluid Dynamics
Generalized coordinates and Lagrange equations with simple applications Central force motion Rigid body motion in two dimensions Mechanics of particle systems equations of motion for mass moments Fluid mechanics continuity equation Euler equation for perfect fluids streamlines particle paths potential flow two dimensional and axisymmetric flows sources sinks vortex motion flow past a circular cylinder method of images

Free 2014 PYQ solutions

Expert-solved previous year questions. Read them free to see our answer quality.

Linear AlgebraRead free Real AnalysisRead free

Want every year? Get topic-wise solutions for 2014-2024.

UPSC weightage analytics

Where UPSC has awarded marks, topic by topic. Focus on what scores, and compare your test results once you join.

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