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PRERNA FOR IAS
MATH FORMULA
(CSAT)
1. Percentage
Percentage represents a part of a whole expressed out of 100. It is calculated as:
Percentage = (Value ÷ Total Value) × 100
Percentages are widely used in examinations, business, statistics, finance, and everyday calculations. They help compare quantities easily and measure increases, decreases, profits, losses, and overall performance.
2. Average
Average, also called the arithmetic mean, represents the central value of a set of observations. It is calculated by dividing the total sum by the number of observations.
Average = Sum of Observations ÷ Number of Observations
Average helps summarize data and is widely used in statistics, economics, and education.
3. Ratio
A ratio compares two quantities of the same kind. It is expressed as a:b or a/b. Ratios help show relationships between quantities and are commonly used in mathematics, business, maps, and daily life. Simplifying ratios makes comparisons easier and more meaningful for analysis.
4. Proportion
A proportion is an equality between two ratios, written as a:b = c:d. It shows that two ratios represent the same relationship. Proportions are useful in scaling, maps, recipes, and solving mathematical problems involving direct and indirect comparisons between quantities.
5. Simple Interest
Simple Interest is the interest calculated only on the principal amount.
SI = (P × R × T) ÷ 100
where P is principal, R is rate of interest, and T is time. It is commonly used in banking, loans, and financial calculations involving fixed interest rates.
6. Speed
Speed measures how fast an object moves.
Speed = Distance ÷ Time
It is usually measured in kilometers per hour (km/h) or meters per second (m/s). Speed is an important concept in transportation, physics, and daily life, helping determine travel time and movement efficiency.
7. Profit and Loss
Profit occurs when the selling price exceeds the cost price, while loss occurs when the cost price is higher than the selling price.
Profit = SP – CP
Loss = CP – SP
These concepts are important in business, trade, commerce, and financial decision-making.
8. Fraction
A fraction represents a part of a whole and is written as a/b, where b ≠ 0. The top number is called the numerator, and the bottom number is the denominator. Fractions are used in measurements, calculations, percentages, and many real-life mathematical applications.
9. Quadratic Formula
The quadratic formula helps find the roots of a quadratic equation:
x = (-b ± √(b² – 4ac)) ÷ 2a
It is used when solving equations of the form ax² + bx + c = 0. The formula provides exact solutions and is fundamental in algebra.
10. Heron’s Formula
Heron’s Formula calculates the area of a triangle when all three sides are known.
Area = √[s(s-a)(s-b)(s-c)]
where s = (a+b+c)/2 is the semi-perimeter. It eliminates the need to know the triangle’s height and is widely used in geometry and surveying.
11. Pythagoras Theorem
The Pythagoras Theorem applies to right-angled triangles and states:
c² = a² + b²
where c is the hypotenuse and a, b are the other sides. It is one of the most important theorems in geometry and is used in construction, engineering, and navigation.
12. Volume of Cylinder
The volume of a cylinder measures the space it occupies.
V = πr²h
where r is the radius and h is the height. This formula is commonly used in engineering, architecture, manufacturing, and practical calculations involving tanks, pipes, and containers.
13. Laws of Indices
Laws of indices simplify calculations involving powers and exponents. Important rules include:
aᵐ × aⁿ = aᵐ⁺ⁿ
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
These rules make multiplication, division, and simplification of exponential expressions easier and are fundamental in algebra and higher mathematics.
14. Logarithms
A logarithm is the inverse operation of exponentiation.
logₐ b = c means aᶜ = b
Logarithms simplify complex calculations involving large numbers and exponents. They are widely used in mathematics, science, engineering, statistics, and computer science for solving exponential equations.
15. Trigonometric Ratios
Trigonometric ratios relate the sides of a right-angled triangle to its angles.
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
These ratios are essential in geometry, navigation, astronomy, surveying, engineering, and many real-world applications involving angles and distances.
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Master essential math formulas for CSAT: percentage, average, ratio, simple interest, quadratic equations, geometry, and logarithms with clear explanations.
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