UPSC CDS Syllabus and Exam Pattern 2021

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 the coefficients (Only real roots are to be considered)
• Simultaneous linear equations in two unknown variable— the analytical and graphical solutions
• Simultaneous linear inequations in the two variables and their respective solutions
• The practical problems which are leading to two simultaneous linear equations or inequations in the two variables or quadratic equations in the one variable with their solutions
• Set language and set notation
• Rational expressions and conditional identities
• Laws of indices

Arithmetic

• Number System: Natural, Rational & Real numbers and Integers
• Fundamental operations such as addition, subtraction, multiplication, division, Square roots, Decimal fractions, etc.
• 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.
• Factorization Theorem
• H.C.F. and L.C.M.
• Euclidean algorithm
• Logarithms to base 10
• laws of logarithms
• use of logarithmic tables

Trigonometry

• The values of Sine ×, cosine ×, Tangent × when 0° < × < 90°
• The values of sine ×, cosine ×, and tangent ×, for ×= 0°, 30°, 45°, 60°, and 90°
• Simple trigonometric identities
• Use of trigonometric tables
• Simple cases of heights and distances

Geometry

• Lines and angles
• Plane and plane figures
• Theorems on the 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 their properties including the 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
• The lateral surface area and volume of the right circular cones and cylinders
• The 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