Elementary Mathematics CDS Syllabus
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Arithmetic
Number SystemNatural numbers, Integers, Rational and Real numbers. Fundamental operations addition, subtraction, multiplication, division, Square roots, Decimal fractions.
Unitary methodtime and distance, time and work, percentages, applications to simple and compound interest, profit and loss, ratio and proportion, variation.
Elementary Number TheoryDivision algorithm. Prime and composite numbers. Tests of divisibility by 2, 3, 4, 5, 9 and 11. Multiples and factors. Factorisation Theorem. HCF and LCM Euclidean algorithm, Logarithms to base 10, laws of logarithms, use of logarithmic tables.
Algebra
Basic Operations, simple factors, Remainder Theorem, HCF, LCM, Theory of polynomials, solutions of quadratic equations, relation between its roots and coefficients (Only real roots to be considered). Simultaneous linear equations in two unknownsanalytical 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 deg < x < 90 deg
Values of sin x, cos x and tan x, for x = 0 deg, 30 deg, 45 deg, 60 deg and 90 deg
Simple trigonometric identities.
Use of trigonometric tables.
simple cases of heights and distances.
Geometry
 Lines and angles, Plane and plane figures
 Theorems on

 Properties of angles at a point
 Parallel lines
 Sides and angles of a triangle
 Congruency of triangles
 Similar triangles
 Concurrence of medians and altitudes
 Properties of angles, sides and diagonals of a parallelogram, rectangle and square
 Circles and its properties including tangents and normals
 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.