CBSE Class 11-12 Advanced Formulas — Math, Physics & Chemistry
CBSE Class 11 and 12 are the most academically demanding years. These classes introduce advanced concepts in calculus, thermodynamics, organic chemistry, electromagnetic induction, and more — all critical for board exams and competitive exams like JEE Main, JEE Advanced, and NEET. This comprehensive formula sheet covers the most important Class 11 and Class 12 formulas across Mathematics, Physics, and Chemistry.
Whether you are preparing for CBSE board exams or aiming for JEE/NEET, use this resource for quick revision, formula recall practice, and exam-day reference. All formulas are aligned with the current NCERT syllabus for Class 11 and 12.
Mathematics Formulas — Class 11 & 12
Trigonometry (Class 11)
- sin(A+B) = sinA cosB + cosA sinB
- cos(A+B) = cosA cosB − sinA sinB
- sin 2A = 2 sinA cosA; cos 2A = cos²A − sin²A
- tan 2A = 2tanA / (1 − tan²A)
Calculus — Differentiation (Class 12)
- d/dx(xⁿ) = nxⁿ⁻¹
- d/dx(sin x) = cos x; d/dx(cos x) = −sin x
- d/dx(eˣ) = eˣ; d/dx(ln x) = 1/x
- Product rule: d/dx(uv) = u'v + uv'
- Chain rule: d/dx[f(g(x))] = f'(g(x)) · g'(x)
Integration (Class 12)
- ∫xⁿ dx = xⁿ⁺¹/(n+1) + C
- ∫eˣ dx = eˣ + C; ∫(1/x) dx = ln|x| + C
- ∫sin x dx = −cos x + C; ∫cos x dx = sin x + C
Physics Formulas — Class 11 & 12
Thermodynamics (Class 11)
- First Law: ΔU = Q − W
- Ideal Gas Law: PV = nRT
- Efficiency of Carnot engine: η = 1 − T₂/T₁
Electromagnetic Induction (Class 12)
- Faraday's Law: ε = −dΦ/dt
- Induced EMF: ε = Bvl (for straight conductor)
- Self-inductance: ε = −L(dI/dt)
Modern Physics (Class 12)
- Photoelectric effect: KEₘₘₙ = hf − φ
- de Broglie wavelength: λ = h/mv
- Energy of photon: E = hf = hc/λ
Chemistry Formulas — Class 11 & 12
Electrochemistry (Class 12)
- Nernst equation: E = E° − (RT/nF) ln Q
- Faraday's law of electrolysis: m = (M × I × t) / (n × F)
- ΔG° = −nFE°ₜₗₗ
Chemical Kinetics (Class 12)
- Rate law: Rate = k[A]ⁿ[B]ᵐ
- Integrated rate law (1st order): ln[A]ₜ − ln[A]ₜ₀ = −kt
- Half-life (1st order): t½ = 0.693/k
Frequently Asked Questions
- What are the most important calculus formulas for Class 12 CBSE?
- Key calculus formulas: d/dx(xⁿ) = nxⁿ⁻¹, chain rule, product rule, ∫xⁿ dx = xⁿ⁺¹/(n+1)+C, and definite integral using fundamental theorem. Integration by parts: ∫u dv = uv − ∫v du.
- Which Class 12 Physics chapters are most important for JEE?
- For JEE, the most important Class 12 Physics chapters are Electrostatics, Current Electricity, Electromagnetic Induction & AC, Optics (wave optics and ray optics), and Modern Physics. Together these carry 55-60% of Physics in JEE Main.
- What organic chemistry reactions are important for Class 12 CBSE and NEET?
- Important Class 12 organic reactions: Aldol condensation, Cannizzaro reaction, Sandmeyer reaction, Kolbe reaction, Williamson synthesis, Hoffmann degradation, and reactions of alcohols, aldehydes, ketones, and carboxylic acids with named reagents.
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