मात्रात्मक — Number System, Algebra र Statistics
यस नोटमा संख्या पद्धति, बीजगणितीय shortcut र basic statistics को अभ्यास गरिन्छ।
Number System
Divisibility Rules
| Divisor | Rule |
|---|---|
| 2 | अन्तिम digit 0,2,4,6,8 |
| 3 | Digits को sum 3 ले भाग लाग्छ |
| 4 | अन्तिम 2 digits 4 ले भाग |
| 6 | 2 र 3 दुवैले भाग लाग्छ |
| 8 | अन्तिम 3 digits 8 ले भाग |
| 9 | Digits को sum 9 ले भाग |
| 11 | (Odd digits sum) − (Even digits sum) = 0 or 11 |
LCM र HCF
| Concept | Detail |
|---|---|
| HCF (GCD) | Maximum common factor — भाग विधि वा Prime factor |
| LCM | Minimum common multiple — Prime factor method |
| LCM × HCF | = Product of two numbers (two numbers only) |
Algebraic Identities
| Identity | Formula |
|---|---|
| (a+b)² | a² + 2ab + b² |
| (a−b)² | a² − 2ab + b² |
| a²−b² | (a+b)(a−b) |
| (a+b)³ | a³ + 3a²b + 3ab² + b³ |
| a³+b³ | (a+b)(a²−ab+b²) |
| a³−b³ | (a−b)(a²+ab+b²) |
Statistics (तथ्यांकशास्त्र)
Central Tendency
| Measure | Formula | Use |
|---|---|---|
| Mean (औसत) | ΣX/n | Normal distribution |
| Median (मध्यिका) | Middle value (sorted) | Skewed data |
| Mode (बहुलक) | Most frequent | Categorical data |
| Range | Max − Min | Spread measure |
Surds र Indices
| Rule | Formula |
|---|---|
| Multiplication | aᵐ × aⁿ = aᵐ⁺ⁿ |
| Division | aᵐ ÷ aⁿ = aᵐ⁻ⁿ |
| Power of power | (aᵐ)ⁿ = aᵐⁿ |
| Negative index | a⁻ⁿ = 1/aⁿ |
| Zero index | a⁰ = 1 |
| Fractional index | a^(1/n) = ⁿ√a |
Quick Recall:
• Div by 11: (Odd pos sum) − (Even pos sum) = 0 or ±11
• LCM × HCF = Product of 2 numbers
• Mean = ΣX/n | Median = middle | Mode = most frequent
• (a+b)² = a²+2ab+b² | a²−b²=(a+b)(a−b)
• Div by 11: (Odd pos sum) − (Even pos sum) = 0 or ±11
• LCM × HCF = Product of 2 numbers
• Mean = ΣX/n | Median = middle | Mode = most frequent
• (a+b)² = a²+2ab+b² | a²−b²=(a+b)(a−b)