UPSC National Defence Academy

Mathematics syllabus (8 sections)

1. 1
   Algebra — sets, De Morgan laws, Cartesian product/relations, complex numbers, binary numbers, AP/GP/HP, quadratic equations, linear inequations, permutations & combinations, binomial theorem, logarithms
2. 2
   Matrices and Determinants — types and operations on matrices, determinants, adjoint and inverse of a square matrix, Cramer's rule, applications of the matrix method
3. 3
   Trigonometry — trigonometric ratios and identities, sum/difference formulae, multiple and sub-multiple angles, inverse trigonometric functions, applications to heights and distances, properties of triangles
4. 4
   Analytical Geometry of Two and Three Dimensions — Cartesian coordinate systems, straight lines, circles, conic sections (parabola, ellipse, hyperbola), points/planes/spheres in three dimensions
5. 5
   Differential Calculus — functions, limits, continuity, derivatives, applications to maxima and minima
6. 6
   Integral Calculus and Differential Equations — techniques of integration, definite integrals and areas, ordinary differential equations
7. 7
   Vector Algebra — vectors in two and three dimensions, dot and cross products, applications of vectors
8. 8
   Statistics and Probability — classification and graphical representation of data, measures of central tendency and variance, correlation and regression, probability theory, Bayes' theorem, binomial distribution