**Important Formulas for CAT Preparation -** Proceeding further towards CAT important formulas, let's get familiar with the “Importance of CAT Formulas”. When it comes to CAT 2021 preparation basically for the Quantitative Aptitude section, the most important aspect is remembering the formulas and theorems and by knowing such key formulas one will get to know when and how to apply them. Thus, it becomes more important than a candidate will have to be well versed with the basic formulas as it is required to solve the questions with good speed and accuracy rate.The questions in the QA section are from various topics such as Profit, Loss and Discount, Number System, Time and Work, LCM and HCF, Logarithm, Averages, Set theory & Function, Probability, Permutation & Combination, Trigonometry, Mensuration, Coordinate Geometry, etc. Formulae are the basic and indispensable part of ace the quantitative section in the CAT Exam. They may be proved to be an elixir to the section if one does their preparation in an appropriate manner. So as one starts their CAT preparation 2021, here is the list of important formulae that one needs to master to crack the Common Admission Test successfully.

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(a + b)² = (a² + b² + 2ab)

(a – b)² = (a² + b² – 2ab)

(a + b)(a – b) = (a² – b²)

(a + b)² = (a² + b² + 2ab)

(a³ – b³) = (a – b)(a² + ab + b²)

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

(a³ + b³) = (a + b)(a² – ab + b²)

When a + b + c = 0, then a³ + b³ + c³ = 3abc

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

(a + b)n = an + (nC1)an-1b + (nC2)an-2b² + … + (nCn-1)abn-1 + bn

**CAT Important Formulas for Number System**

(1² + 2² + 3² + ….. + n²) = n ( n + 1 ) (2n + 1) / 6

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

(1³ + 2³ + 3³ + ….. + n³) = (n(n + 1)/ 2)²

Sum of first n odd numbers = n²

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

**Formulas for LCM and HCF**

LCM × HCF = Product of the Numbers

LCM of Co-prime Numbers = Product Of The Numbers

**Mathematical Formulas for Profit, Loss and Discount**

Profit % = Profit/(C P)×100

Profit/Gain = (S.P.) – (C.P.)

C P = 100/(100+gain %)×S P

S P = (100+gain % )/100 ×C P

Loss % = Loss/(C.P.)×100

Loss = (C.P.) – (S.P.)

C P = 100/(100-loss %)×S P

S P = (100-loss %)/100×C P

**Formulae for Percentages**

Find what percentage of X is Y: Y/X x 100

Increase N by S% = N(1+S/100)

Decrease N by S% = N(1 - S/100)

**Important Formulas for Speed, Time and Distance**

Speed= Distance/ Time

Distance= Speed x Time

Time= Distance/ Time

**Time and Work Formulas (Basic Formulas)**

If X can do a piece of work in ‘n’ days, then X’s 1 day’s work= 1/n

If X’s 1 day’s work= 1/n, then X can finish the work in n days.

**Averages Formula**

Average= Sum of observations/ Number of observations

**Simple and Compound Interest Formula**

Simple Interest: P x i x n (P= Principle, i= interest rate and n= term of the loan)

Compound Interest:

Compound Interest = [P(1+i)n] - P

Compound Interest = P[(1+i)n-1]

**Mathematical Logarithm Formulas**

If n and a are positive real numbers, and a is not equal to 1, then If ax = n, then log a n = x

log of 1 to any base is 0 (log b 1 = 0)

log of any number to base as itself is 1, log a a = 1

Logarithm of a Product (log a pq = log a p + loga q)

Logarithm of a Fraction (log a (p/q) = log a p – log a q)

log a pn = n log a p

a(log a p) = p

Base Change Rule of Logarithms: (log a n = log b n × log a b)

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Trigonometric Identities

Sine=Opposite/Hypotenuse

Secant=Hypotenuse/Adjacent

Cosine=Adjacent/Hypotenuse

Tangent=Opposite/Adjacent

Co−Secant=Hypotenuse/Opposite

Co−Tangent=Adjacent/Opposite

The reciprocal identities are given as

CosecΘ=1/sinΘ

secΘ=1/cosΘ

cotΘ=1/tanΘ

sinΘ=1/CosecΘ

cosΘ=1/secΘ

tanΘ=1/cotΘ

**Mathematical Mensuration Formulas**

Rectangle

Area = lb

Perimeter = 2(l+b)

Square

Perimeter = 4a

Area = a×a

Triangle

Area =b×h/2 or √s(s-a)(s-b)(s-c)______where s=a+b+c/2

Cube

Volume: V = l3

Surface Area: S = 6s2

Diagonal (d) = √3l

Lateral surface area = 4a2

Circle

Circumference = 2πr or πd

Area = πr² or πd²/4

Area of sector of a circle = (θπr² )/360

Cuboid

Total surface area = 2 (lb + bh + hl) or 6l2

Volume of cuboid: lbh

Length of diagonal =√(l²+b²+h²)

**Formulas for Coordinate Geometry**

AB² = (Bx – Ax)² + (By – Ay)²

The midpoint of the line joining the points (x1, y1) and (x2, y2) is:

[½(x1 + x2), ½(y1 + y2)]

**Read more;**CAT Question Papers 2021 with Solutions PDFCAT Quantitative Aptitude Syllabus 2021

**Mixtures and Allegation Formula**

If 2 ingredients are mixed, then

(Quantity of cheaper/ Quantity of dearer) = (C.P of dearer - Mean price/ Mean price - C.P of cheaper)

**Also Check;**CAT 2021 Preparation StrategyCAT 2021 Preparation Tips for Beginners

**Permutation and Combination Formula for CAT 2021**

Permutation Formula

Combination Formula

**Formulas for Set Theory and Function**

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

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