• Number System
• Natural numbers
• Integers
• Rational and Real numbers.
• Fundamental operations
• addition
• subtraction
• multiplication
• division
• Square roots
• Decimal fractions
• Unitary method
• time and work
• time and distance
• percentages
• Applications of profit and loss
• simple and compound interest
• ratio and proportion
• variation

• 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
• use of logarithmic tables
• laws of logarithms

• Basic operations and Simple factors
• Remainder Theorem
• H.C.F. and L.C.M
• Theory of polynomials
• relation between its roots and coefficients (Only real roots to be considered), solutions of quadratic equations
• Simultaneous linear equations in two unknowns — analytical & graphical solutions
• Simultaneous linear inequalities in two variables & their solutions
• Practical issues with solutions that result in two simultaneous linear equations, inequalities in two variables or quadratic equations in one variable
• Set notation and set language
• Rational expressions and conditional identities
• Laws of indices

• Sine x, cosine x, Tan x when 0° < x < 90° , Values of sin x, cos x & tan x, for x = 0°, 30°, 45°, 60° & 90°.
• Simple trigonometric identities.
• Use of trigonometric tables.
• Simple cases of heights and distances.

• Plane and plane figures
• Lines and angles
• Theorems on:
• Properties of angles at a point
• Parallel lines
• Sides and angles of a triangle
• Congruence of triangles
• Similar triangles
• Concurrence of medians and altitudes
• Properties of sides, angles and diagonals of a rectangle, parallelogram and square
• Circles and their properties including tangents and normals
• Loci

• Areas of parallelograms
• squares, rectangles
• triangles and circles
• Areas of figures can be split up into these figures (Field Book)
• lateral surface and volume of right circular cones and cylinders
• Surface area and volume of cuboids
• surface area and volume of spheres

• Collection and tabulation of statistical data
• Graphical representation of frequency polygons
• bar charts
• histograms
• pie charts etc
• Measures of central tendency

Best UPSC CDS Books for Elementary Mathematics
For the Elementary Mathematics section, candidates should focus on building a strong foundation. Here are the recommended books:

Mathematics for CDS by R.S. Aggarwal: Tailored for CDS aspirants, this book covers topics frequently asked in the examination with detailed explanations and practice sets.
Quantitative Aptitude for Competitive Examinations by R.S. Aggarwal: Ideal for clearing various math topics from basics, this book provides a variety of solved examples and practice sets.
Pathfinder for CDS by Arihant Publications: Widely followed by aspirants, this book covers the entire syllabus of mathematics and other crucial subjects for CDS. Economic Times): Regular reading of newspapers is essential to stay updated on relevant topics for the exam.

Here's a breakdown on how to tackle Quantitative Aptitude for the CDS exam:

Build a Strong Foundation:

• The CDS quant section primarily focuses on Arithmetic, Algebra, Geometry, Trigonometry, and Mensuration. Make sure you have a clear grasp of the basic concepts and formulas in these areas. Textbooks like R. S. Aggarwal's Quantitative Aptitude for Competitive Examinations can be helpful resources [Reference Book].
• Conceptual Clarity:

Don't just memorize formulas - understand why they work

•  This will help you apply them to different problems and avoid getting stuck on rote learning.

Practice Regularly:

• Once you're comfortable with the basics, dive into practice problems. Solve questions from previous years' CDS exams to get a feel for the question format and difficulty level [Previous Years' Papers].
• Regularly practicing mock tests and sectional tests will help you identify your weak areas and improve your time management skills, which are crucial in the actual exam.

Pro Tips:

• Focus on Shortcuts and Techniques: Mastering time-saving tricks and shortcuts can give you an edge, especially when dealing with lengthy calculations. But remember, these should come after a strong foundation in concepts.
• Develop your Approach: While there might be multiple ways to solve a problem, experiment and find an approach that works best for you. This will boost your confidence and speed.

Revision is Key: Regularly revise formulas and concepts to keep them fresh in your mind.