Concept Graph

---
target: 495+/500
author: Senior Sibling
name: concept-graph
description: >-
  NCERT chapter dependency graph for 12th Grade Math, Physics, and Biology. 
  Shows prerequisite chains (e.g., Integration needs Differentiation) to fix root causes of weakness.
---

# Concept Graph Navigator — 12th Grade Edition

## The "Prerequisite" Trap in 12th Grade
12th Grade subjects are highly **Linear**. You cannot understand Chapter 7 if Chapter 1 is weak. Most students struggle with "Calculus" because their "Trigonometry" or "Limits" from 11th grade (and basic Algebra) are shaky.

---

## 📐 Mathematics Dependency Graph

```mermaid
graph TD
    REL["Relations & Functions"] --> ITF["Inverse Trig Functions"]
    ITF --> DIFF["Differentiation (Calculus)"]
    DIFF --> AOD["Apps of Derivatives"]
    DIFF --> INT["Integrals"]
    INT --> AOI["Apps of Integrals"]
    INT --> DE["Differential Equations"]
    
    MAT["Matrices"] --> DET["Determinants"]
    DET --> VEC["Vectors"]
    VEC --> 3D["3D Geometry"]
    
    LP["Linear Programming"]
    PROB["Probability (Bayes' Theorem)"]
```

**Critical Chain:** Differentiation $\to$ Integration $\to$ Differential Equations. If you break this chain, you lose 35 marks instantly.

---

## 🔭 Physics Dependency Graph

```mermaid
graph TD
    EC["Electrostatics"] --> CAP["Capacitors"]
    EC --> CE["Current Electricity"]
    CE --> MAG["Magnetism (Biot-Savart)"]
    MAG --> EMI["Electromagnetic Induction"]
    EMI --> AC["Alternating Current"]
    
    RAY["Ray Optics"] --> WAVE["Wave Optics"]
    WAVE --> MODERN["Modern Physics (Dual Nature)"]
    MODERN --> ATOMS["Atoms & Nuclei"]
    ATOMS --> SEMI["Semiconductors"]
```

**Critical Chain:** Electrostatics is the "Grammar" of Physics. If you don't understand *Electric Field*, you will struggle with *Magnetic Force* and *AC Circuits*.

---

## 🧪 Chemistry Dependency Graph

```mermaid
graph TD
    SOL["Solutions (Colligative Props)"] --> EL["Electrochemistry"]
    EL --> KIN["Chemical Kinetics"]
    
    HAL["Haloalkanes & Haloarenes"] --> ALC["Alcohols & Phenols"]
    ALC --> ALD["Aldehydes & Ketones"]
    ALD --> AMINES["Amines"]
    AMINES --> BIO["Biomolecules"]
```

**Critical Chain:** Organic Chemistry is a single unit. Haloalkanes is the foundation. If you miss the "Nucleophilic Substitution" logic in Ch 1, you will fail the rest of Organic.

---

## 🧬 Biology Dependency Graph

```mermaid
graph TD
    REP["Reproduction (Plant/Human)"] --> GEN["Genetics (Principles)"]
    GEN --> MOL["Molecular Basis"]
    MOL --> BT["Biotechnology"]
    BT --> HEAL["Human Health & Disease"]
    HEAL --> ECO["Ecology"]
```

**Critical Chain:** Genetics $\to$ Molecular Basis $\to$ Biotechnology. This block is 30% of your paper.

---

## /graph-path Command Logic

Whenever the student says "I'm struggling with [Topic]", the AI should run the `/graph-path` analysis:

**EXAMPLE:**
> Student: "I can't solve Differential Equations."
> AI Analysis: 
> 1. Target: Differential Equations
> 2. Root 1: Basic Integration (Ch 7)
> 3. Root 2: Basic Differentiation (Ch 5)
> 4. Fix: Revise the 'Integrating Factor' logic and basic derivative formulas first.

---

## 💡 The Senior Sibling Advice
Don't jump to the hardest chapter first. Look at this graph. Fix the **Root Node** (the chapter at the top of the chain) first, and the rest of the tree will fall into place.