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For the calculus-based College Board exam, the AP Physics C Mechanics equation sheet is a crucial resource. In contrast to AP Physics 1 and 2, Physics C necessitates derivatives, integrals, and differential equations; therefore, choosing the right equations is essential for resolving kinematics, dynamics, energy, and rotational motion problems.
Only 24% of American students receive a 4 or 5, so what sets top scorers apart is their mastery of the equation sheet and their understanding of when to apply calculus. Effective equation sheet preparation helps students gain $1,500–$4,000 in college credit, develop calculus confidence, and get ready for competitive engineering and physics programs.
| Resource Title | Description | Download |
| Official College Board Equation Sheet (2026) | The precise equation sheet given on the day of the AP Physics C Mechanics exam | Download PDF |
| Annotated Equation Sheet with Calculus Notes | Additional calculus applications and variable definitions on the official sheet | Download PDF |
| Complete Physics C Mechanics Formula Reference | Every equation has calculus derivations and is arranged by topic. | Download PDF |
| Equation Sheet with Worked Examples | Calculus-based problem solutions for each formula | Download PDF |
| Quick Reference Calculus Guide | Calculus formulas (integrals, derivatives) that are crucial for physics | Download PDF |
| Rotational Motion Equation Sheet | Specific torque, angular momentum, and moment of inertia guide | Download PDF |
| Color-Coded Equation Sheet | Algebra and calculus formulas are arranged visually. | Download PDF |
| Equation Sheet Practice Workbook | Issues requiring the selection of strategic equations from the reference sheet | Download PDF |
Beyond the algebra-based AP Physics 1 equations, the College Board equation sheet for AP Physics C Mechanics contains calculus-based formulas. Comprehending the distinction is essential:
| Category | What’s Included | Calculus Required |
| Constants | Gravitational constant (G), acceleration due to gravity (g), Coulomb’s constant (k) | No |
| Kinematics | Position, velocity, acceleration relationships using derivatives and integrals | Yes – v = dx/dt, a = dv/dt |
| Newton’s Laws | F = ma, F = dp/dt (momentum form), force as derivative of momentum | Yes – for variable mass/force |
| Work & Energy | Work as integral of force, kinetic/potential energy, power | Yes – W = ∫F·dx |
| Linear Momentum | p = mv, impulse-momentum theorem, conservation | Yes – for variable forces |
| Rotational Motion | Torque, moment of inertia, angular momentum, rotational kinetic energy | Yes – τ = dL/dt |
| Oscillations | Simple harmonic motion, spring-mass systems, pendulums | Yes – differential equations |
| Gravity | Universal gravitation, gravitational potential energy, orbital mechanics | Sometimes – for elliptical orbits |
Critical Difference from AP Physics 1:
Calculus is used throughout AP Physics C Mechanics. To correctly apply the majority of equations, you must understand how to take derivatives and integrals.
| Relationship | Equation | When to Use |
| Velocity from position | v = dx/dt | Using a position function to determine instantaneous velocity |
| Acceleration from velocity | a = dv/dt = d²x/dt² | Determining the instantaneous acceleration |
| Position from velocity | x(t) = x₀ + ∫v dt | Finding position by integrating velocity |
| Velocity from acceleration | v(t) = v₀ + ∫a dt | Finding velocity by integrating acceleration |
Example Application:
If position is x(t) = 3t² + 2t, find velocity:
| Equation | Calculus Form | Application |
| Newton’s Second Law | F = ma = m(dv/dt) = dp/dt | Variable force or variable mass problems |
| Impulse | J = ∫F dt = Δp | Force varying with time |
| Work | W = ∫F·dx | Force varying with position |
| Power | P = dW/dt = F·v | Instantaneous power |
| Concept | Equation | Calculus Application |
| Work-energy theorem | W = ∫F·dx = ΔKE | Variable force over distance |
| Power | P = dW/dt = F·v | Instantaneous rate of energy transfer |
| Potential energy | U(x) = -∫F dx | Finding PE from conservative force |
| Force from potential | F = -dU/dx | Finding force from potential energy function |
Critical Relationship:
F = -dU/dx means force is the negative derivative of potential energy. This appears frequently on FRQs.
| Constant | Symbol | Value | Units | Primary Use |
| Gravitational constant | G | 6.67 × 10⁻¹¹ | m³/(kg·s²) | Universal gravitation, orbital mechanics |
| Acceleration due to gravity (Earth) | g | 9.8 | m/s² | Near-Earth free fall, weight calculations |
Note: Unlike AP Physics 2, Physics C Mechanics has fewer constants because it focuses primarily on classical mechanics.
The equation sheet provides physics formulas, but you must independently know these calculus techniques:
Essential Derivatives
| Function | Derivative |
| xⁿ | nxⁿ⁻¹ |
| sin(x) | cos(x) |
| cos(x) | -sin(x) |
| eˣ | eˣ |
| ln(x) | 1/x |
| Function | Integral |
| xⁿ | xⁿ⁺¹ / (n + 1) + C |
| 1 / x | ln |
| sin(x) | −cos(x) + C |
| cos(x) | sin(x) + C |
| eˣ | eˣ + C |
Chain rule: d/dx[f(g(x))] = f'(g(x))·g'(x)
Product rule: d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
Integration by parts: ∫u dv = uv – ∫v du
Critical for Physics C: These appear in work integrals, rotational dynamics, and energy problems.
Understanding the test structure helps you prepare strategically:
| Section | Format | Duration | Questions | Calculator? | Equation Sheet? |
| Section I: MCQ | 35 multiple-choice | 45 minutes | 35 | Yes | Yes |
| Section II: FRQ | 3 free-response | 45 minutes | 3 | Yes | Yes |
| Total | Both sections | 90 minutes | 38 questions | Yes | Yes |
Reality for U.S. Students:
Only 24% earn a 4 or 5 – but this is higher than Physics 1 (23%) or Physics 2 (16%). Students taking Physics C tend to be stronger in mathematics, which helps with calculus-based problems.
| Mistake | Why It Costs Points | How to Fix It |
| Using algebra when calculus is required | Wrong answer even with correct physics concept | Use calculus if force, velocity, or position changes over time or space. |
| Not knowing which derivative/integral to use | Can’t set up the problem correctly | Practice: “accumulation” → integral, “rate of change” → derivative |
| Forgetting the chain rule | Incorrect derivatives for composite functions | Identify inner and outer functions at all times. |
| Missing limits of integration | Indefinite integrals when definite are needed | Limits are always necessary for work-related issues (from initial to final position). |
| Confusing linear and rotational equations | Using F = ma when should use τ = Iα | Rotational motion → τ, I, α; linear motion → F, m, a |
| Not knowing moment of inertia formulas | Can’t solve rotational problems | Learn common I formulas by heart (they’re on the sheet, but know which to use). |
| Sign errors in F = -dU/dx | Wrong force direction | The force is pointing in the direction of lower potential energy (negative derivative). |
| Forgetting to use radians | Incorrect angular calculations | Calculus requires that all angular measurements be in radians. |
Download the free resources now.
| Feature | AP Physics 1 | AP Physics C Mechanics |
| Math level | Algebra and trigonometry | Calculus (derivatives and integrals) |
| Equation sheet | Algebra-based formulas | Calculus-based equations |
| Exam length | 3 hours (longer) | 90 minutes (shorter but harder) |
| Topics covered | Broader (10 units including waves, modern physics) | Narrower (limited to classical mechanics) |
| College credit | General physics credit | Physics that is frequently calculus-based I get credit at engineering schools. |
| Difficulty | Conceptual emphasis | Emphasis on mathematical rigor |
| Typical students | All levels | Students in AP Calculus AB/BC |
Bottom Line: Physics C Mechanics covers fewer topics but is more mathematically demanding. This emphasis on solving problems using calculus is reflected in the equation sheet.
Recent College Board data shows the challenge level:
| AP Score | % of Students (2024) | Qualification Level | College Credit |
| 5 | ~16% | Extremely well qualified | Credit at top engineering schools (MIT, Caltech, Stanford) |
| 4 | ~8% | Well qualified | Credit at most universities |
| 3 | ~20% | Qualified | Credit at many schools |
| 2 | ~24% | Possibly qualified | Rarely earns credit |
| 1 | ~32% | No recommendation | No credit |
1. Do I get an equation sheet on the AP Physics C Mechanics exam?
Yes. Calculus formulas, variable definitions, and the appropriate use of derivatives versus integrals are not included.
2. Is the Physics C equation sheet different from Physics 1 and 2?
Yes, entirely different. AP. While Physics 1 and 2 use algebra, Physics C Mechanics uses calculus-based equations (integrals, derivatives). These various mathematical methods are reflected in the equation sheets.
3. Do I need to know calculus for AP Physics C Mechanics?
Absolutely. You need to understand basic differential equations, derivatives, integrals, and the chain rule. Calculus BC is advised, but Calculus AB is usually the minimal prerequisite.
4. What calculus is NOT on the equation sheet that I need to know?
Simple differential equation solutions, integral formulas, integration methods, and derivative rules (power rule, product rule, chain rule). These are presumptive facts.
5. Can I use the equation sheet on both exam sections?
Yes. Both Section I (Multiple Choice) and Section II (Free Response) have equation sheets. You will have access for the full ninety-minute test.
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