Free One-Page Calculus Formula Sheet | Printable PDF

AP Calculus requires you to know and apply a wide range of formulas, and it’s easy to lose track while studying. Having the key rules organized in one place makes practice more effective and review less stressful.

Why Formulas Matter for AP Calculus Success

AP Calculus exams test not only your understanding of concepts but also your ability to quickly apply the right formulas under timed conditions. Having a clear, well-organized formula sheet makes practice and test day much smoother. This guide brings together the most important AP Calculus formulas, tips from our tutors, and a free downloadable PDF for study and revision.

Check out our AP Calculus Resource Hub for more AP tips, or explore our SAT Math Formula Sheet and ACT Math Formula Sheet.

Key AP Calculus Formulas

1. Differentiation Formulas

• Power Rule: d/dx [xⁿ] = n·xⁿ⁻¹

• Product Rule: (fg)’ = f’g + fg’

• Quotient Rule: (f/g)’ = (f’g – fg’)/g²

• Chain Rule: d/dx [f(g(x))] = f’(g(x))·g’(x)

• Trig Derivatives:

  • d/dx [sin x] = cos x

  • d/dx [cos x] = –sin x

  • d/dx [tan x] = sec²x

• Exponential & Logarithmic Derivatives:

  • d/dx [e^x] = e^x

  • d/dx [ln x] = 1/x

2. Integration Formulas

• Basic Rules:

  • ∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C, n ≠ –1

  • ∫ e^x dx = e^x + C

  • ∫ 1/x dx = ln|x| + C

• u-Substitution: ∫ f(g(x))·g’(x) dx → ∫ f(u) du

• Integration by Parts: ∫ u dv = uv – ∫ v du

• Trig Integrals (examples):

  • ∫ sin x dx = –cos x + C

  • ∫ cos x dx = sin x + C

  • ∫ sec²x dx = tan x + C

3. Limits & Continuity

• Standard Limit Laws: lim (f(x) + g(x)) = lim f(x) + lim g(x)

• L’Hôpital’s Rule: If lim f(x)/g(x) is 0/0 or ∞/∞, then lim f/g = lim f’/g’

• Continuity: f(x) is continuous at c if lim x→c f(x) = f(c)

4. Sequences & Series (Quick Formulas)

• Geometric Series: Σ arⁿ = a/(1–r), |r| < 1

• Taylor/Maclaurin Expansion: f(x) ≈ f(a) + f’(a)(x–a) + f’’(a)(x–a)²/2! + …

Tutor Insights: How to Use These Formulas Effectively

Our tutors recommend:

• Practice by category: Don’t just memorize. Work through practice questions using the formulas.

• Know when to apply: For example, chain rule is almost always tested with composite functions.

• Watch for traps: In integration, always double-check if u-substitution or parts is more efficient.

• Timed drills: Simulate exam conditions and practice applying formulas quickly.

Next Steps: Get Expert Support

Formulas are the foundation, but true AP Calculus success comes from applying them to challenging problems. Our Ivy League and 5+ scorers specialize in making calculus strategies simple and effective.

👉 Book a free strategy session with North American Tutors today and get personalized AP Calculus prep.