50+ Important Formulas for CAT 2025 Preparation: Topic-Wise Formulas

50+ formulas for CAT 2025 preparation cover topics like profit and loss, algebra, number system, permutation & combination, percentages, etc. It is essential that every candidate be aware of several key CAT formulas aside from these topics for CAT 2025 exam preparation. CAT formulas are mostly relevant to the Quantitative Aptitude section, which includes Maths topics. Strategies mentioned in the CAT 2025 preparation tips in addition to these important formulas can help you perform better in the exam. There are many formula-based questions in CAT 2025 where all you need to do is use a formula to reach the answer. You must learn all the formulas mentioned here to the best of your abilities to ensure a stellar performance in CAT 2025!

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Important Formulas in CAT 2025 Preparation

There are a number of important formulas in CAT preparation 2025 that you must become fluent in. All of the formulas used in CAT are from up to the Class 12th level. You must already be familiar with these formulas from their school days. However, since there is at least a 3 to 4-year gap between Class 12th and CAT preparation, it becomes easy to forget these formulas. Hence, it makes sense to regularly revise and practice using formulas when solving CAT questions. Before moving on further, here is a quick glance at the revised exam pattern of CAT 2025.

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The QA section of CAT 2025 includes many topics such as Percentages, Ratio & Proportion, Profit & Loss, HCF & LCM, Mensuration, Geometry, etc. Here are some important formulas to remember for each topic.

Important CAT 2025 Formulas for Algebra

Square of a + b

• (a + b)(a – b) = (a ² – b ² )

• (a + b) ² = (a ² + b ² + 2ab)

• (a – b) ² = (a² + b² – 2ab)

Square of a + b + c

• (a + b + c) ² = a ² + b ² + c ² + 2(ab + bc + ca)

Cube of a + b

• (a + b) ³ = a ³ + 3a ² b + 3ab ² + b ³

• (a – b) ³ = a ³ – 3a ² b + 3ab ² – b ³

• (a ³ + b ³ ) = (a + b)(a ² - ab + b ² )

• (a ³ – b ³ ) = (a – b)(a ² + ab + b ² )

• (a ³ + b ³ + c ³ – 3abc) = (a + b + c)(a ² + b ² + c ² – ab – bc – ac)

• When a + b + c = 0, then a ³ + b ³ + c ³ = 3abc

Root Formula

Important CAT 2025 Formulas for Number System

• (1 ² + 2 ² + 3 ² + ….. + n ² ) = n ( n + 1 ) (2n + 1) / 6

• 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2

• (1 ³ + 2 ³ + 3 ³ + ….. + n ³ ) = (n(n + 1)/ 2) ²

• Sum of first n odd numbers = n ²

• Sum of first n even numbers = n (n + 1)

Important CAT 2025 Formulas for Permutation and Combination

• Combination: ⁿ C _r = n! / (n-r)!r! = ⁿ P _r / r!

• Permutation: ⁿ P _r = n! / (n-r)!

Important CAT 2025 Formulas for Percentages

• Percentage Change = {(Final Value – Initital Value) / Initial Value} x 100

• Total Percentage Change for two successive changes of a% and b% = (a + b + ab/100)%
  eg. for two successive changes of 10% and 20%, the total percentage change will be = (10 + 20 + 10*20/100)% = 32%

Important Fractions and Their Percentage Values

Also Read : 15+ CAT 2025 Percentage Questions

Important CAT 2025 Formulas for Averages

• Average = Total Sum / Total Number

• Weighted Average = (w ₁ x ₁ + w ₂ x ₂ + w ₃ x ₃ .... + w _n x _n ) / (w ₁ + w ₂ + ..... + w _n)

Important CAT 2025 Formulas for Simple Interest and Compound Interest

• Amount = Principle + Interest

• Simple Interest = P x r x n

• Compound Interest = P(1 + r) ⁿ – P

Important CAT 2025 Formulas for Profit, Loss and Discount

• Profit = SP – CP

• Profit Percentage = (SP – CP)/CP x 100

• Loss = CP – SP

• Loss Percentage = (CP – SP)/CP x 100

• Discount = MP – SP

• Discount Percentage = (MP – SP)/MP x 100

• Total Discount on successive discounts of a% followed by b% = (a + b – ab/100)%

• If articles worth Rs. b are free along with articles worth Rs. a, Discount = y/(x+y) x 100

Important CAT 2025 Formulas for HCF and LCM

• HFC of Fractions = (HCF of numerators) / (LCM of denominators)

• LCM of Fractions = (LCM of numerators) / (HCF of denominators)

• LCM x HCF = Product of Numbers

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Important CAT 2025 Formulas for Set Theory & Function

Demorgan’s Law is the basic and most important formula for sets, which is defined as

• (A ∩ B) ‘ = A’ U B’ and (A U B)’ = A’ ∩ B’

The relation R⊂A×AR⊂A×A is said to be called:

• Reflexive Relation: If a R a ∀∀ a ∈∈ A.

• Symmetric Relation: If aRb, then bRa ∀∀ a, b ∈∈ A.

• Transitive Relation: If aRb, bRc, then aRc ∀∀ a, b, c ∈∈ A.

If any relation R is reflexive, symmetric, and transitive in a given set A, then that relation is known as an equivalence relation.

Important CAT 2025 Formulas for Logarithms

• log _x 1 = 0

• log _x x = 1

• log _x (mn) = log _x m + log _x n

• log _x (m/n) = log _x m – log _x n

• log _x a ^b = b log _x a

• log _x a ^x = a

• log _x m = (log _y n) x (log _a n)

Important CAT 2025 Formulas for Surds and Indices

Important CAT 2025 Formulas for Time, Speed, and Distance

• Speed = Distance / Time

• 1 km/h = 5/18 m/s

• 1 m/s = 18/5 km/h

Important CAT 2025 Formulas for Boats and Streams

• S _downstream = S _boat + S _stream

• S _upstream = S _boat - S _stream

Important CAT 2025 Formulas for Mixtures and Alligations

Alligation: It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of the desired price.

Mean Price: The cost of a unit quantity of the mixture is called the mean price.

Rule of Alligation:

If two ingredients are mixed, then

• (Quantity of cheaper / Quantity of dearer) = (C.P. of dearer – Mean Price / Mean price – C.P. of cheaper)

Important CAT 2025 Formulas for Trigonometry

• sin A = Perpendicular / Hypoteneuse = a / c

• cos A = Base / Hypoteneuse = b / c

• tan A = Perpendicular / Base = a / b

• cot A  = 1 / tan A

• sec A = 1 / cos A

• cosec A = 1 / sin A

Trigonometric Identities:

• Sine=Opposite/Hypotenuse

• Cosine=Adjacent/Hypotenuse

• Tangent=Opposite/Adjacent

• Secant=Hypotenuse/Adjacent

• Co−Secant=Hypotenuse/Opposite

• Co−Tangent=Adjacent/Opposite

The reciprocal identities:

• sinΘ=1/CosecΘ

• cosΘ=1/secΘ

• tanΘ=1/cotΘ

• CosecΘ=1/sinΘ

• secΘ=1/cosΘ

• cotΘ=1/tanΘ

Important CAT 2025 Formulas for Mensuration

Plane Figures

Solids

NOTE: (3.14) is an approximation of pi.

Important CAT 2025 Formulas for Probability

Important CAT 2025 Formulas for Coordinate Geometry

There are various methods, mnemonics, and learning tricks you can use to remember the important formulas. If your basic mathematical concepts are clear, you may even be able to figure out some of the formulas used in CAT 2025 without the need to learn them.

• As an example , if we imagine a Cylinder as infinite disks stacked on top of each other, the Curved Surface Area of a Cylinder becomes equal to the Perimeter of the Base Circle times Height. Hence, 2 (3.14) r multiplied by h.

However, the best way to remember important formulas for CAT is to use them in solving questions. Practicing will help you become familiar with important formulas. It will also train you to use these formulas with more speed and accuracy.

Why are CAT Formulas Important?

While studying for the CAT 2025 exam, efficiency in preparation is necessary. In order to solve difficult questions quickly, one requires the suitable formulas by their side. The CAT formulas are important because:

• Quick Revision: Instead of going through various books, the formulas can be referred to in one place for fast revision
• Better Time Management: When you are aware of the formulas, you can solve the problems faster, which is crucial in a time-limited exam such as CAT.
• Enhanced Retention: Repeatedly practicing with the formulas helps improve long-term memory.
• Increased Accuracy: Knowing the basics of formulas helps you to make fewer mistakes during the exam, especially while dealing with CAT quant formulas.

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