Quick Revision Notes

---
target: 495+/500
author: Senior Sibling
name: quick-revision-notes
description: >-
  Ultra-condensed 1-page summaries for Grade 12 (PCMB/PCMC). 
  The "Night-Before-Exam" recall file for high-stakes units.
---

# Quick Revision Notes — Grade 12 Topper Scan

## 📐 Mathematics (35M Calculus Focus)
```latex
• Continuity: LHL = RHL = f(a)
• Chain Rule: d/dx[f(g(x))] = f'(g(x))g'(x)
• Integration by Parts: ∫ uv dx = u∫v dx - ∫[u'∫v dx] dx (ILATE rule)
• King Property: ∫_0^a f(x) dx = ∫_0^a f(a-x) dx
• Diff Eq: I.F. = e^{∫P dx} for dy/dx + Py = Q
• Vectors: Shortest Distance d = |(b1xb2).(a2-a1)| / |b1xb2|
• Matrices: A^{-1} = 1/|A| * adj(A)
• LPP: Corner point method for objective function Z = ax + by
```

## 🔭 Physics (18M Optics & 16M Electro Focus)
```latex
• Gauss Law: Φ = q/ε₀ (Infinite wire: E = λ/2πε₀r)
• Capacitance: C = ε₀A/d (With dielectric: C' = K * C)
• Drift Velocity: I = neAv_d
• KVL/KCL: ΣV = 0 (Loop), ΣI = 0 (Junction)
• Biot-Savart: dB = (μ₀/4π) * Idl sinθ / r²
• Resonance (AC): ω = 1/√(LC)
• Lens Maker: 1/f = (n-1)(1/R1 - 1/R2)
• YDSE: Fringe width β = λD/d
• Photoelectric: K_max = hν - Φ₀
```

## 🧪 Chemistry (33M Organic Focus)
```markdown
PHYSICAL:
• Nernst: E_cell = E⁰_cell - (0.0591/n) log Q
• Kinetics: k = (2.303/t) log([R]₀/[R]) (First Order)
• Solutions: ΔT_f = i * K_f * m

INORGANIC:
• VBT: Inner (d²sp³) vs Outer (sp³d²) complexes.
• CFT: Strong field (pairing) vs Weak field (no pairing).

ORGANIC (Named Reactions):
• Aldol: Dilute NaOH, α-hydrogen mandatory.
• Cannizzaro: Conc. NaOH, NO α-hydrogen.
• Reimer-Tiemann: Phenol + CHCl₃ + NaOH → Salicylaldehyde.
• Lucas Test: 3° (fast), 2° (5 min), 1° (heat needed).
```

## 🧬 Biology (20M Genetics Focus)
```markdown
• DNA Replication: S-phase, semiconservative, DNA Polymerase (5'→3').
• Transcription: Promoter → Structural Gene → Terminator (TATA box).
• Lac Operon: Inducer (Lactose) binds to repressor, allowing transcription.
• Biotech: PCR steps (Denaturation 94°C, Annealing 54°C, Extension 72°C).
• Ecology: 10% law, Population growth (Logistic: dN/dt = rN[(K-N)/K]).
```

## 💻 Computer Science (40M Python Focus)
```python
• File Modes: 'r', 'w', 'a' (Text); 'rb', 'wb', 'ab' (Binary).
• Pickle: dump(data, f) for write, load(f) for read.
• SQL: SELECT * FROM Table GROUP BY Column HAVING Condition.
• Stack: LIFO, Push (append), Pop (pop). Check for Underflow.
```

## 📖 English Core
```markdown
• Flamingo: The Last Lesson (M. Hamel), Deep Water (Douglas), Indigo (Gandhi).
• Vistas: The Third Level (Charlie), The Enemy (Dr. Sadao).
• Formats: Notice (Box!), Letter (Bio-data for Job App), Report (Byline).
```