Union Public Service Commission (UPSC) organizes Combined Defence Service Examination. Through CDS Exam, candidates get admission to the courses at Indian Military Academy, Indian Naval Academy, Air Force Academy and Officers Training Academy.
Exam date – 14 Feb 2016
Syllabus of CDS Exam – Here we will provide you the detailed syllabus of Elementary Mathematics for the CDS exam.
Paper-3.Elementary Mathematics - It consists of various topics like Arithmetic’s, Geometry, Mensuration etc. Here we will provide the detailed syllabus of Elementary Mathematics---
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 in equations in two variables or quadratic equations in one variable & their solutions. Set language and set notation, rational expressions and conditional identities, Laws of indices.
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, Factorizations Theorem. H.C.F. and L.C.M. Euclidean algorithm, Logarithms to base 10, laws of logarithms, use of logarithmic tables.
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 normal (ix) Loci.
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.
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, Measures of central tendency.