UPSC Combined Defence Services

Elementary Mathematics syllabus (six areas, objective, IMA/INA/AFA only)

1. 1
   Arithmetic — Number System (natural/integer/rational/real numbers, fundamental operations, square roots, decimal fractions, unitary method, time/distance/work, percentages, simple/compound interest, profit/loss, ratio/proportion, variation); Elementary Number Theory (division algorithm, prime/composite numbers, tests of divisibility, HCF/LCM, Euclidean algorithm, logarithms)
2. 2
   Algebra — basic operations, simple factors, Remainder Theorem, HCF and LCM, theory of polynomials, solutions of quadratic equations, relation between roots and coefficients, simultaneous linear equations and inequations in two variables/graphs, set language and set notation, rational expressions and conditional identities, laws of indices
3. 3
   Trigonometry — sine, cosine, tangent of an angle 0-90°, values at 0/30/45/60/90°, simple trigonometric identities, use of trigonometric tables, simple cases of heights and distances
4. 4
   Geometry — lines and angles, plane figures, theorems on angles at a point/parallel lines/sides and angles of a triangle/congruency of triangles/similar triangles/medians and altitudes/parallelograms-rectangles-squares properties/circles and tangents, loci
5. 5
   Mensuration — areas of squares, rectangles, parallelograms, triangles and circles; surface area and volume of cuboids, cones, cylinders and spheres
6. 6
   Statistics — classification and tabulation of statistical data, graphical representation (histogram, pie chart, frequency polygon), measures of central tendency