UPSC CDS Syllabus I) Objective Test : A) English Syllabus This section contains questions on : • Synonyms, • Antonyms, • Reading Comprehension, • Para Jumbles, • Error Spotting, • Jumbled Sentences, • Sentence Correction and • Fill in the Blanks. B) General Knowledge Syllabus This section contains questions on : • History • Political Science • Economics • Geography • Environmental Science • Science & Technology • Current Affairs C) Elementary Mathematics Syllabus This section contains questions on : Arithmetic • Number System - Natural numbers, Integers, Rational and Real numbers. Fundamental operations addition, subtraction, multiplication, division, Square roots, Decimal fractions. • Unitary method - time and distance, time and work, percentages, applications to simple and compound interest, profit and loss, ratio and proportion, variation. • Elementary Number Theory - Division algorithm. Prime and composite numbers. Tests of divisibility by 2, 3, 4, 5, 9 and 11. Multiples and factors. Factorisation Theorem. H.C.F. and L.C.M. Euclidean algorithm, Logarithms to base 10, laws of logarithms, use of logarithmic tables. Algebra Basic Operations, simple factors, Remainder Theorem, H.C.F., L.C.M. Theory of polynomials, solutions of quadratic equations, relation between its roots and coefficients (Only real roots to be considered). Simultaneous linear equations in two unknowns-analytical and graphical solutions. Simultaneous linear equations in two variables and their solutions. Practical problems leading to two simultaneous linear equations or inequations in two variables or quadratic equations in one variable & their solutions. Set language and set notation, Rational expressions and conditional identities, Laws of indices. Trigonometry Sine x, cosine x, Tangent x when 0 < x < 90 degrees, Values of sin x, cos x and tan x, for x = 0, 30, 45, 60 and 90 degrees, Simple trigonometric identities, Use of trigonometric tables, simple cases of heights and distances. Geometry Lines and angles, Plane and plane figures, Theorems on (i) Properties of angles at a point (ii) Parallel lines, (iii) Sides and angles of a triangle, (iv) Congruency of triangles, (v) Similar triangles, (vi) Concurrence of medians and altitudes, (vii) Properties of angles, sides and diagonals of a parallelogram, rectangle and square (viii) Circles and its properties including tangents and normals, (ix) Loci. Mensuration Areas of squares, rectangles, parallelograms, triangle and circle. Areas of figures which can be split up into these figures (Field Book), Surface area and volume of cuboids, lateral surface and volume of right circular cones and cylinders, surface area and volume of spheres. Statistics Collection and tabulation of statistical data, Graphical representation frequency polygons, histograms, bar charts, pie charts, etc. Measures of central tendency.