AP Calculus AB and BC are among the most challenging AP exams, but with the right study plan, they can also be some of the most rewarding. Whether you’re taking AB or BC, mastering the core formulas, theorems, and problem-solving strategies is the fastest route to a top score.
In this RevisionDojo study guide, we’ll cover:
- The essential formulas you must memorize
- The differences in scope between AB and BC
- Strategies for multiple-choice and free-response questions
- Common mistakes to avoid on exam day
📚 Key Formulas for AP Calculus AB & BC
Limits and Continuity
- Limit Definition: limx→af(x)=L\lim_{x \to a} f(x) = L if f(x)f(x) approaches L as xx approaches a.
- Continuity Conditions:
f(a)f(a) is defined, limx→af(x)\lim_{x \to a} f(x) exists, and both are equal.
Derivatives
- Definition of Derivative: f′(x)=limh→0f(x+h)−f(x)hf'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}
- Basic Rules:
- Power Rule: ddxxn=nxn−1\frac{d}{dx}x^n = nx^{n-1}
- Product Rule: (fg)′=f′g+fg′(fg)' = f'g + fg'
- Quotient Rule: (fg)′=f′g−fg′g2\left(\frac{f}{g}\right)' = \frac{f'g - fg'}{g^2}
- Chain Rule: dydx=dydu⋅dudx\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}
Integrals
- Fundamental Theorem of Calculus:
If F′(x)=f(x)F'(x) = f(x), then ∫abf(x)dx=F(b)−F(a)\int_a^b f(x)dx = F(b) - F(a) - Common Integrals:
∫xndx=xn+1n+1+C\int x^n dx = \frac{x^{n+1}}{n+1} + C (n ≠ -1)
∫exdx=ex+C\int e^x dx = e^x + C
∫1xdx=ln∣x∣+C\int \frac{1}{x} dx = \ln|x| + C
BC-Only Topics
- Series Tests: Ratio Test, Root Test, Alternating Series Test
- Parametric Equations: dydx=dydtdxdt\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}
- Polar Coordinates:
Area = 12∫θ1θ2r2dθ\frac{1}{2} \int_{\theta_1}^{\theta_2} r^2 d\theta
🧠 Strategies for Success
- Master the Big 3 Skills: Limits, Derivatives, and Integrals. These are the foundation for almost every question.
- Understand, Don’t Just Memorize: Knowing why a rule works improves recall and adaptability.
- Practice With Real AP Questions: The College Board’s released exams are your best resource.
- Use Your Calculator Wisely: Learn when to switch between exact and decimal answers.
⚠️ Common Mistakes to Avoid
- Forgetting +C in indefinite integrals
- Mixing up chain rule and product rule
- Using calculator syntax incorrectly for definite integrals
- Not checking domain restrictions when solving
📅 RevisionDojo’s Study Plan Framework
- Daily Practice: 3–5 AP-style questions on a mix of topics
- Weekly Review: One full free-response question under timed conditions
- Monthly Mock: Full practice exam to track progress
🧭 Final Advice from RevisionDojo
The AP Calculus AB & BC exams reward conceptual understanding, procedural fluency, and time management. Learn the formulas cold, practice strategically, and approach each problem with a clear method.
With discipline and the right resources, a score of 5 is absolutely within reach.
