Error Analysis

---
name: error-analysis
description: Specific calculation errors that cost marks in Math and Physics. Not conceptual mistakes but mechanical errors — sign errors, unit mismatches, decimal slips. The 2-3 marks that separate 495 from 498.
---

# Error Analysis — Mechanical Mistakes That Cost 2-5 Marks Per Paper

## The 495+ Gap
```
Student knows all concepts: ~490 marks
Student who ALSO avoids mechanical errors: ~498 marks

The difference between 490 and 498 is NOT knowledge — it's CAREFULNESS.
These 8 marks come from fixing these specific error types:
```

## Error Type 1: Sign Errors (most common — costs 1-2M per paper)
```
WHERE: Quadratic formula, coordinate geometry, mirror/lens formula

COMMON MISTAKES:
  ❌ (-b)² = -b² instead of b²
  ❌ Forgetting negative in distance formula: (x₂-x₁) when x₁ > x₂
  ❌ Mirror formula: u is always negative but students write +
  ❌ Lens formula: 1/v - 1/u (not 1/v + 1/u like mirror)

FIX: After solving, substitute answer back into original equation
  → If it doesn't satisfy → sign error somewhere
```

## Error Type 2: Unit Conversion (costs 0.5-1M per paper)
```
COMMON MISTAKES:
  ❌ Power of lens: f=20cm → P=1/20=0.05D (WRONG: need m → P=1/0.2=5D)
  ❌ Resistivity: area in mm² not converted to m²
  ❌ Mensuration: mixing cm and m in same problem
  ❌ Speed: km/hr not converted to m/s when needed (× 5/18)

FIX: Write units at EVERY step, not just the final answer
  → If units don't match → conversion error somewhere
```

## Error Type 3: Decimal/Fraction Errors (costs 1M per paper)
```
COMMON MISTAKES:
  ❌ 22/7 × 49 = 22 × 7 = 154 (CORRECT) but student writes 144
  ❌ √3 ≈ 1.73, √2 ≈ 1.41 (students mix these up)
  ❌ Moving decimal: 0.002 × 1000 = 2 (not 0.2 or 20)
  ❌ Fraction addition: 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 (not 2/9)

FIX: Do arithmetic on the SIDE of your answer sheet as rough work
  → Circle the final calculated value before writing in answer
```

## Error Type 4: Formula Misapplication (costs 1-2M per paper)
```
COMMON MISTAKES:
  ❌ Using mode formula when question asks for median
  ❌ Using CSA when question asks for TSA
  ❌ Series resistance formula used for parallel circuit
  ❌ Applying BPT ratio incorrectly (which sides correspond)

FIX: Before calculating, write the formula name:
  "Using median formula: Median = l + [(n/2-cf)/f] × h"
  → This forces you to THINK about which formula is correct
```

## Error Type 5: Misreading the Question (costs 2-3M per paper)
```
COMMON MISTAKES:
  ❌ "Find the RATIO" but student finds the actual values
  ❌ "In terms of π" but student calculates decimal value
  ❌ "Use π = 22/7" but student uses 3.14
  ❌ "How MANY terms" but student finds the sum
  ❌ "2 resistors" but student reads as 3

FIX: Underline key instruction words during reading time
  → Ratio? Terms? Values? Use 22/7? Draw diagram?
```

## Error Type 6: Copying Errors (costs 0.5M per paper)
```
COMMON MISTAKES:
  ❌ Copying 37 from question but writing 73 in solution
  ❌ Carrying forward wrong intermediate value
  ❌ Writing correct working but wrong final answer line

FIX: After completing each question, re-read your Given values
  → Do they match the question paper? If not → copying error
```

## Pre-Submission Checklist (Last 15 Minutes)
```
□ All MCQs have an option marked (no blanks)
□ All numericals have units
□ All diagrams are labeled
□ All chemical equations are balanced with state symbols
□ Question numbers match (didn't write Q15's answer under Q16)
□ Supplementary sheets are numbered and attached
```