Mathematics Formula Sheet

Essential formulas for quantitative aptitude competitive exams

Category: MATH

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MATH PHYSICS CHEMISTRY RSCIT REASONING COMPUTER SCIENCE BIOLOGY ENGLISH

Formula Collection

Arithmetic

Percentage

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x% of y = (x/100) × y = y% of x

Profit/Loss

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Profit % = [(SP - CP)/CP] × 100, Loss % = [(CP - SP)/CP] × 100

Simple Interest

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SI = (P × R × T)/100, Amount = P + SI

Compound Interest

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CI = P[(1 + R/100)ⁿ - 1], Amount = P(1 + R/100)ⁿ

Ratio & Proportion

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a:b = c:d ⇒ a/b = c/d, Product of means = Product of extremes

Average

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Average = Sum of observations / Number of observations

Time & Work

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Work = Rate × Time, Combined work rate = Sum of individual rates

Time, Speed & Distance

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Speed = Distance/Time, Average speed = Total distance/Total time

Algebra

Quadratic Equation

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ax² + bx + c = 0, Roots = [-b ± √(b² - 4ac)]/2a

Arithmetic Progression

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nth term = a + (n-1)d, Sum = n/2[2a + (n-1)d]

Geometric Progression

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nth term = arⁿ⁻¹, Sum = a(rⁿ - 1)/(r - 1) for r≠1

Special Products

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(a+b)² = a² + 2ab + b², (a-b)² = a² - 2ab + b², (a+b)(a-b) = a² - b²

Binomial Theorem

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(a+b)ⁿ = Σ [nCr × aⁿ⁻ʳ × bʳ] where r=0 to n

Logarithms

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logₐ(mn) = logₐm + logₐn, logₐ(m/n) = logₐm - logₐn, logₐmⁿ = n logₐm

Geometry

Pythagoras Theorem

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In right triangle: a² + b² = c²

Area of Triangle

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½ × base × height, √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2

Area of Circle

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πr², Circumference = 2πr

Area of Rectangle

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length × breadth, Perimeter = 2(l+b)

Area of Square

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side², Perimeter = 4 × side

Volume of Cube

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side³, Surface area = 6 × side²

Volume of Cylinder

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πr²h, Curved surface area = 2πrh

Volume of Sphere

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(4/3)πr³, Surface area = 4πr²

Trigonometry

Basic Identities

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sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ

Sum & Difference

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sin(A±B) = sinA cosB ± cosA sinB, cos(A±B) = cosA cosB ∓ sinA sinB

Double Angle

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sin2θ = 2 sinθ cosθ, cos2θ = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ

Product to Sum

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2 sinA cosB = sin(A+B) + sin(A-B), 2 cosA cosB = cos(A+B) + cos(A-B)

Quick Shortcuts & Tips

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Percentage: To find x% of y, you can find y% of x (often easier)

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Square of numbers ending with 5: (a5)² = a×(a+1) followed by 25

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Multiplication by 11: abc × 11 = a (a+b) (b+c) c

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Division by 5: Multiply by 2 and divide by 10

How to Use This Formula Sheet

Learn, Don't Memorize

Understand the derivation and application of each formula. Knowing why a formula works is more important than memorizing it.

Practice Application

Immediately after learning a formula, solve 5-10 problems using it. This reinforces learning and builds problem-solving skills.

Create Your Own Sheet

Copy formulas you frequently forget onto a physical sheet. The act of writing helps memory retention.

Regular Revision

Review formulas weekly. Use spaced repetition: next day, after 3 days, after 1 week, then monthly.

Common Formula Mistakes to Avoid

Unit Confusion

Always check units before applying formulas. Convert all measurements to consistent units (all in meters or all in centimeters).

Formula Misapplication

Ensure you're using the right formula for the given problem type. Don't force a formula that doesn't fit the situation.

Sign Errors

Pay attention to positive/negative signs, especially in physics and coordinate geometry formulas.

Approximation Errors

When using π = 22/7 or √2 = 1.414, be consistent. Don't mix exact and approximate values in the same calculation.

Practice with Formulas

Apply Formulas

Practice questions where you can use these formulas

Quick Revision

Review key concepts along with formulas

Study Guide

Detailed explanations of formulas and concepts

Previous Year Questions

Practice with past exam questions using these formulas