CDS

CDS Mathematics Important Formulas: Chapter-Wise Formula Sheet

CDS Mathematics Important Formulas, chapter wise,

CDS Maths Formulas for all 8 chapters of the Elementary Mathematics paper, organized as a quick-revision, chapter-wise formula sheet.

CDS Maths Formulas for the Elementary Mathematics paper fall into 8 chapters: Number System, Algebra, Arithmetic (Percentage, Profit & Loss, Simple and Compound Interest), Ratio, Average and Time & Work, Speed Time & Distance, Geometry and Mensuration, Trigonometry, and Statistics. This sheet lists the core formula for each, so revision doesn't mean flipping through an entire textbook the night before your exam.

The Elementary Mathematics paper carries 100 marks and applies to IMA, INA, and AFA candidates. OTA candidates don't attempt this paper at all.

Most aspirants don't lose marks in CDS Maths because a concept was too hard. They lose marks because a formula didn't come to mind fast enough under time pressure.

This guide puts all the CDS Maths Formulas you actually need in one chapter-wise sheet, so revision stays fast and nothing important gets missed.

CDS Mathematics Exam Pattern: A Quick Recap

Before the CDS Maths Formulas below, here's the structure they apply to.

Detail

Value

Total marks

100

Duration

2 hours

Applicable to

IMA, INA, AFA candidates

Not applicable to

OTA candidates

Question type

Objective, multiple-choice, OMR-based

Negative marking

One-third mark deducted per wrong answer

Since every question is objective, recalling the right CDS Maths Formulas quickly matters more than showing full working, which is exactly what this sheet is built for.

Chapter 1: Number System

Number System questions test divisibility, factors, and basic number properties, usually solved faster with a rule than with long division.

Concept

Formula / Rule

Divisibility by 2

Last digit is 0, 2, 4, 6, or 8

Divisibility by 3

Sum of digits divisible by 3

Divisibility by 9

Sum of digits divisible by 9

Divisibility by 11

Difference of (sum of digits at odd places) and (sum at even places) is 0 or divisible by 11

HCF (Highest Common Factor) × LCM (Lowest Common Multiple)

HCF × LCM = Product of the two numbers

Chapter 2: Algebra

Algebra formulas in CDS Maths are almost entirely built around a handful of standard identities.

Identity

Formula

Difference of squares

(a + b)(a − b) = a² − b²

Square of a sum

(a + b)² = a² + b² + 2ab

Square of a difference

(a − b)² = a² + b² − 2ab

Square of a trinomial

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Sum of cubes

a³ + b³ = (a + b)(a² − ab + b²)

Difference of cubes

a³ − b³ = (a − b)(a² + ab + b²)

Three-term cube identity

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

Chapter 3: Percentage, Profit & Loss, and Interest

These three topics show up constantly in CDS Maths, and they share the same underlying percentage logic.

Concept

Formula

Percentage

(Value / Total) × 100

Profit percentage

(Profit / Cost Price) × 100

Loss percentage

(Loss / Cost Price) × 100

Simple Interest (SI)

SI = (Principal × Rate × Time) / 100

Compound Interest (CI)

CI = Principal × (1 + Rate/100)ⁿ − Principal

Chapter 4: Ratio, Average, and Time & Work

These three topics are grouped together because CDS Maths questions frequently combine them in the same problem.

Concept

Formula

Ratio and proportion

If a : b = c : d, then a × d = b × c

Average

Sum of all observations ÷ Number of observations

Time and work

Work done = Time × Rate of work (efficiency is inversely proportional to time taken)

Chapter 5: Speed, Time & Distance

Speed, Time and Distance questions extend into boats, streams, and trains, but every variation still starts from the same base formula.

Concept

Formula

Base formula

Distance = Speed × Time

Unit conversion

x km/hr = x × (5/18) m/sec

Average speed (two equal distances)

2xy / (x + y) km/hr, where x and y are the two speeds

Boats and streams (downstream)

Speed downstream = Boat speed + Stream speed

Boats and streams (upstream)

Speed upstream = Boat speed − Stream speed

Chapter 6: Geometry and Mensuration

Geometry in CDS Maths focuses on circles, triangles, and quadrilaterals, while Mensuration covers area, volume, and surface area.

Concept

Formula

Right triangle (Pythagoras)

a² + b² = c², where c is the hypotenuse

Area of a triangle

½ × base × height

Area of a rectangle

length × breadth

Area of a circle

π × r²

Volume of a cylinder

π × r² × h

Volume of a cone

(1/3) × π × r² × h

Volume of a sphere

(4/3) × π × r³

Chapter 7: Trigonometry

Trigonometry questions in CDS Maths lean on standard angle values and one core identity.

Concept

Formula

Core identity

sin²θ + cos²θ = 1

Tangent

tanθ = sinθ / cosθ

sin 30°, 45°, 60°, 90°

½, 1/√2, √3/2, 1

cos 30°, 45°, 60°, 90°

√3/2, 1/√2, ½, 0

Heights and distances

Uses tanθ = Opposite side / Adjacent side to find unknown heights

Chapter 8: Statistics

Statistics questions in CDS Maths are usually the most straightforward, testing basic central tendency measures.

Concept

Formula

Mean

Sum of all observations ÷ Number of observations

Median

Middle value when data is arranged in order

Mode

The value that occurs most frequently in the data

How to Use This CDS Maths Formula Sheet Effectively

Having all these CDS Maths Formulas in one place only helps if they're used the right way during preparation.

  1. Build the concept first, memorize second. A formula recalled without understanding where it comes from breaks down the moment a question is phrased differently than expected.

  2. Solve at least 5 previous CDS papers using this sheet as a quick-reference, not a crutch. Repetition under exam-like conditions is what actually locks a formula into memory.

  3. Take full-length, timed mock tests and review every mistake against this sheet afterward, so gaps show up before the actual exam does.

  4. Use elimination on tough MCQs instead of solving from scratch every time. Ruling out two clearly wrong options before applying a formula saves valuable time.

  5. Practice quick calculation techniques, like two-digit multiplication shortcuts, so applying a formula doesn't become the slow part of your answer.

Common Mistakes Aspirants Make With CDS Maths Formulas

  1. Memorizing formulas in isolation, without practicing where each one actually applies in a mixed question.

  2. Skipping the "why" behind an identity, which makes it harder to adapt the formula when a question twists the standard format.

  3. Ignoring speed-solving techniques, so even correct formula knowledge doesn't translate into a completed paper on time.

  4. Not revising Geometry and Mensuration formulas regularly, since these have the most individual formulas to keep straight compared to other chapters.

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Bringing It Together

CDS Maths Formulas aren't difficult individually. The challenge is having all of them ready to recall instantly across 8 different chapters, under a strict two-hour, negative-marking exam.

This chapter-wise sheet is built for exactly that: a fast, structured reference to revise against, not a replacement for understanding each concept properly the first time.

Frequently Asked Questions

How many chapters do CDS Maths Formulas cover? CDS Mathematics formulas span 8 chapters: Number System, Algebra, Percentage/Profit & Loss/Interest, Ratio/Average/Time & Work, Speed Time & Distance, Geometry and Mensuration, Trigonometry, and Statistics.

Is the CDS Maths paper compulsory for every candidate? No. The Elementary Mathematics paper applies only to IMA, INA, and AFA candidates. OTA candidates do not attempt this paper.

Which CDS Maths chapter has the most formulas to remember? Geometry and Mensuration typically has the most individual formulas, covering area, volume, and surface area across multiple shapes, along with core geometry theorems.

Is Vedic Mathematics useful for solving CDS Maths faster? Yes, provided the underlying concept is already clear. Techniques like two-digit multiplication shortcuts help speed up calculation once a formula is chosen correctly, but they shouldn't replace understanding the formula itself.

How should I revise CDS Maths Formulas in the final days before the exam? Use a chapter-wise sheet like this one purely for quick recall, alongside timed mock tests and error review, rather than trying to relearn full concepts at the last minute.

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