Mathematical Tools for Physics Class 11 & 12: Complete JEE Formula Sheet with Free PDF Download
Mathematical Tools for Physics Formula Sheet — Competishun
Mathematical Tools for Physics Class 11 & 12: Complete JEE Formula Sheet with Free PDF Download
Physics is not just about physics, it is built on maths. Before you can solve a single question in kinematics, electrostatics or modern physics, you need a solid grip on a set of maths concepts called the mathematical tools. That is exactly why Mathematical Tools is one of the very first chapters in Class 11 physics, and why it stays useful right through Class 12 and all of JEE.
This page gives you a complete Mathematical Tools for Physics formula sheet, covering trigonometry, logarithms, differentiation, integration, vectors and approximations, everything you need for JEE physics in one place. Grab the free PDF below and keep it handy for quick revision.
Download the Mathematical Tools Formula Sheet PDF
Get the complete Class 11 & 12 Mathematical Tools for Physics formula sheet in one clean PDF, free. Perfect for last-minute JEE physics revision.
Download Free PDFWhat Are Mathematical Tools in Physics?
Mathematical tools are the maths concepts you use as tools to solve physics. They are not physics themselves, they are the language physics is written in. Master them once, and every physics chapter becomes easier.
Here is what the Mathematical Tools chapter covers, and what this formula sheet includes:
1. Trigonometry Formulas
Trigonometry appears in vectors, waves, oscillations and projectile motion. These are the essentials.
| Concept | Formula |
|---|---|
| Pythagorean identities | sin²θ + cos²θ = 1 | 1 + tan²θ = sec²θ | 1 + cot²θ = cosec²θ |
| Sum of angles | sin(A ± B) = sinA cosB ± cosA sinB |
| Sum of angles | cos(A ± B) = cosA cosB ∓ sinA sinB |
| Double angle | sin2θ = 2 sinθ cosθ | cos2θ = 2cos²θ − 1 |
| Standard values | sin0=0, sin30=½, sin45=1/√2, sin60=√3/2, sin90=1 |
| Small angle (θ in rad) | sinθ ≈ θ, tanθ ≈ θ, cosθ ≈ 1 |
| The small-angle approximation is used constantly in optics, SHM and pendulum problems. Memorise it. | |
2. Logarithm & Exponential Formulas
Used in thermodynamics, radioactive decay and any exponential growth or decay problem.
| Rule | Formula |
|---|---|
| Product rule | log(ab) = log a + log b |
| Quotient rule | log(a/b) = log a − log b |
| Power rule | log(aⁿ) = n log a |
| Natural log | ln e = 1, ln 1 = 0 |
| Exponential link | if y = eˣ then ln y = x |
| Radioactive decay N = N₀e^(−λt) and many thermodynamics results rely directly on these rules. | |
3. Differentiation Formulas
The single most used tool in physics. Velocity is the derivative of position, acceleration is the derivative of velocity.
| Function | Derivative |
|---|---|
| Power | d/dx (xⁿ) = n·xⁿ⁻¹ |
| Sine | d/dx (sin x) = cos x |
| Cosine | d/dx (cos x) = −sin x |
| Tangent | d/dx (tan x) = sec²x |
| Exponential | d/dx (eˣ) = eˣ |
| Natural log | d/dx (ln x) = 1/x |
| Product rule | (uv)' = u'v + uv' |
| Quotient rule | (u/v)' = (u'v − uv') / v² |
| Chain rule | dy/dx = (dy/du)(du/dx) |
| Physics use: v = dx/dt, a = dv/dt = d²x/dt². Differentiation turns position into motion. | |
4. Integration Formulas
The reverse of differentiation. Used to find displacement from velocity, work from force, and area under graphs.
| Integral | Result |
|---|---|
| Power (n ≠ −1) | ∫ xⁿ dx = xⁿ⁺¹ / (n+1) + C |
| Reciprocal | ∫ (1/x) dx = ln|x| + C |
| Sine | ∫ sin x dx = −cos x + C |
| Cosine | ∫ cos x dx = sin x + C |
| Exponential | ∫ eˣ dx = eˣ + C |
| Definite integral | ∫ₐᵇ f(x) dx = F(b) − F(a) |
| Physics use: displacement = ∫ v dt, work = ∫ F dx. The area under a v-t graph is displacement. | |
5. Vector Formulas
Physics quantities like force, velocity and field are vectors. These formulas handle them.
| Concept | Formula |
|---|---|
| Magnitude | |A| = √(Aₓ² + Aᵧ² + A_z²) |
| Unit vector | Â = A / |A| |
| Dot product | A·B = |A||B|cosθ = AₓBₓ + AᵧBᵧ + A_zB_z |
| Cross product | |A×B| = |A||B|sinθ |
| Resultant of two | R = √(A² + B² + 2AB cosθ) |
| Dot product gives work (W = F·d), cross product gives torque and magnetic force direction. | |
6. Approximations & Algebra
Small-quantity approximations save huge time in JEE physics. These appear more than students expect.
| Tool | Formula |
|---|---|
| Binomial (small x) | (1 + x)ⁿ ≈ 1 + nx (when x ≪ 1) |
| Quadratic roots | x = [−b ± √(b² − 4ac)] / 2a |
| Componendo (ratios) | used to simplify ratio-based physics equations |
| Straight line | y = mx + c (slope m, intercept c) |
| The binomial approximation appears in gravitation, optics and error analysis. It is a genuine time-saver. | |
Why Mathematical Tools Decide Your JEE Physics Score
- Every chapter uses them: Kinematics, electrostatics, magnetism and modern physics all need these tools
- Calculus is everywhere: Differentiation and integration run through most of physics
- Speed matters: Strong tools mean you solve faster in the exam
- Focus on physics, not maths: When the maths is automatic, you think about the physics
How to Use This Formula Sheet
- Learn, do not just read: Practise each formula on a physics problem
- Revise before tests: Skim the PDF before every physics test or mock
- Link to physics: For each tool, note where it is used (v = dx/dt, W = ∫F dx)
- Keep it handy: Save the PDF on your phone for quick reference
Get the Complete PDF for Free
Download the full Mathematical Tools for Physics formula sheet and revise anytime, anywhere.
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