Table of Contents
Preparing for the Exceptional Performance in the Civil Services Preliminary Examination (EXCPT) requires a solid understanding of essential math formulas. These formulas form the backbone of quantitative reasoning and problem-solving, helping candidates to solve questions efficiently and accurately. This article provides a comprehensive overview of the key formulas that every EXCPT candidate should master.
Algebra Formulas
- Quadratic Equation: ax2 + bx + c = 0
- Sum of roots: α + β = -b/a
- Product of roots: αβ = c/a
- Factorization: a(x – r)(x – s)
Arithmetic Progression (AP)
- n-th term: an = a + (n – 1)d
- Sum of n terms: Sn = n/2 [2a + (n – 1)d]
Geometric Progression (GP)
- n-th term: an = arn – 1
- Sum of n terms: Sn = a( rn – 1 ) / ( r – 1 )
Percentage and Ratio
- Percentage: (Part / Whole) × 100
- Ratio: Part : Part or Part / Part
- Percentage Increase/Decrease: [(New Value – Original Value) / Original Value] × 100
Profit and Loss
- Profit: Selling Price (SP) – Cost Price (CP)
- Loss: Cost Price (CP) – Selling Price (SP)
- Profit Percentage: (Profit / Cost Price) × 100
- Loss Percentage: (Loss / Cost Price) × 100
Simple and Compound Interest
- Simple Interest (SI): (P × R × T) / 100
- Compound Interest (CI): P(1 + R/100)T – P
- Amount with CI: P(1 + R/100)T
Basic Geometry Formulas
- Area of Triangle: ½ × base × height
- Area of Rectangle: length × breadth
- Area of Circle: πr2
- Circumference of Circle: 2πr
- Perimeter of Square: 4 × side
Coordinate Geometry
- Distance between two points: √[(x2 – x1)2 + (y2 – y1)2]
- Midpoint: ((x1 + x2)/2, (y1 + y2)/2)
Probability
- Probability of an event: Number of favorable outcomes / Total outcomes
- Complement: 1 – P(event)
Mastery of these formulas will significantly enhance your problem-solving speed and accuracy in the EXCPT exam. Regular practice and application of these formulas in various contexts will prepare you to tackle questions confidently and effectively.