Quantitative Aptitude Quick Revision
Essential formulas, shortcuts, and concepts for mathematics
Select Revision Category
Topic-wise Revision Points
Arithmetic
- Percentage shortcuts: x% of y = y% of x
- Profit/Loss: SP = CP × (100 ± P%)/100
- Simple Interest: SI = P×R×T/100
- Compound Interest: CI = P[(1 + R/100)ⁿ - 1]
Algebra
- Quadratic equation: ax² + bx + c = 0, roots = [-b ± √(b² - 4ac)]/2a
- Arithmetic progression: nth term = a + (n-1)d, sum = n/2[2a + (n-1)d]
- Geometric progression: nth term = arⁿ⁻¹, sum = a(rⁿ - 1)/(r - 1) for r≠1
- Special products: (a+b)², (a-b)², (a+b)(a-b), (a+b)³
Geometry
- Pythagoras theorem: a² + b² = c²
- Area formulas: Triangle = ½×b×h, Circle = πr², Rectangle = l×b
- Volume formulas: Cube = a³, Cylinder = πr²h, Sphere = 4/3πr³
- Important triangles: 3-4-5, 5-12-13, 7-24-25, 8-15-17
Trigonometry
- sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ
- sin(A+B) = sinA cosB + cosA sinB
- cos(A+B) = cosA cosB - sinA sinB
- tan(A+B) = (tanA + tanB)/(1 - tanA tanB)
Memory Aids & Mnemonics
Trigonometry ratios: Some People Have Curly Black Hair Through Proper Brushing (Sin=Perp/Hyp, Cos=Base/Hyp, Tan=Perp/Base)
BODMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction
Quadratic formula: Minus B plus or minus square root of B squared minus 4AC over 2A
Important Formulas & Rules
Speed = Distance/Time
Work = Rate × Time
Mixture: Quantity of cheaper/Quantity of dearer = (Price of dearer - Mean price)/(Mean price - Price of cheaper)
Partnership: Profit share ratio = Investment × Time period ratio
Revision Strategy
First Pass (30 minutes)
Quickly scan all topics. Identify areas where you feel less confident. Mark them for focused revision.
Deep Revision (60 minutes)
Study marked topics thoroughly. Write down key points. Create your own mnemonics for difficult concepts.
Practice (45 minutes)
Solve 10-15 questions from this category. Apply the formulas and techniques you just revised.
Final Review (15 minutes)
Go through mnemonics and formulas one more time. Note down any remaining doubts for later clarification.