🤖 ALL-CHAPTERS AI STUDY HANDBOOK
Class 9–12 & JEE All-Chapters AI Notes.
Complete AI-generated chapter notes, formula cheatsheets, calculus integration rules, matrix determinants, conic sections, and solved theorems curated by Ajay Yadav.
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All-Chapters AI Mathematics Master Handbook
Curated by: Ajay Yadav (Math King of Katargam | 15+ Yrs Experience | 2nd Rank TAT High School Exam)
📘 PART 1: CLASS 12 & JEE ADVANCED
1. Integrals & Calculus
King's Property: ∫ₐᵇ f(x) dx = ∫ₐᵇ f(a+b-x) dx
Integration by Parts: ∫ u·v dx = u∫v dx - ∫(u'∫v dx) dx
Integration by Parts: ∫ u·v dx = u∫v dx - ∫(u'∫v dx) dx
2. Differential Equations
Linear DE: dy/dx + P(x)y = Q(x) ⇒ IF = e^(∫P dx) ⇒ y·IF = ∫(Q·IF) dx + C
3. Matrices & Determinants
Inverse Matrix: A⁻¹ = (1 / |A|) · adj(A)
Determinant Property: |adj(A)| = |A|ⁿ⁻¹, |kA| = kⁿ|A|
Determinant Property: |adj(A)| = |A|ⁿ⁻¹, |kA| = kⁿ|A|
4. Vectors & 3D Geometry
Dot Product Angle: cosθ = (a · b) / (|a||b|)
Shortest Distance: d = |(a₂ - a₁) · (b₁ × b₂)| / |b₁ × b₂|
Shortest Distance: d = |(a₂ - a₁) · (b₁ × b₂)| / |b₁ × b₂|
📗 PART 2: CLASS 11 & JEE MAIN
5. Trigonometric Functions
sin(A ± B) = sin A cos B ± cos A sin B
cos(A ± B) = cos A cos B ∓ sin A sin B
tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)
cos(A ± B) = cos A cos B ∓ sin A sin B
tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)
6. Conic Sections (Coordinate Geometry)
- Parabola: y² = 4ax (Focus: (a,0), Directrix: x = -a)
- Ellipse: x²/a² + y²/b² = 1 (Eccentricity e = √(1 - b²/a²))
- Hyperbola: x²/a² - y²/b² = 1 (Eccentricity e = √(1 + b²/a²))
🏆 PART 3: CLASS 10 BOARD EXAM
7. Quadratic Equations & Arithmetic Progressions
Quadratic Roots: x = (-b ± √(b² - 4ac)) / 2a
AP nth Term: aₙ = a + (n-1)d
AP Sum: Sₙ = (n/2)[2a + (n-1)d]
AP nth Term: aₙ = a + (n-1)d
AP Sum: Sₙ = (n/2)[2a + (n-1)d]
📙 PART 4: CLASS 9 FOUNDATIONAL
8. Heron's Formula & Geometry
Semi-perimeter: s = (a + b + c) / 2
Triangle Area = √[s(s-a)(s-b)(s-c)]
Triangle Area = √[s(s-a)(s-b)(s-c)]