AP Exam Review

Part 1 of 7 — Limits & Continuity Review

Essential Limit Techniques

1. Direct substitution — always try first
2. Factoring — cancel common factors
3. Rationalization — multiply by conjugate
4. L'Hopital's Rule — for $0/0$ or $infty/infty$ forms
5. Squeeze Theorem — bound the function

Limits Review 🎯

Review — Part 1 Complete

AP Exam Review

Part 2 of 7 — Derivatives Review

Must-Know Derivative Rules

Plus: Product Rule, Quotient Rule, Chain Rule

Derivatives Review 🎯

Review — Part 2 Complete

AP Exam Review

Part 3 of 7 — Applications of Derivatives Review

Key Applications

1. Related Rates — differentiate equation with respect to time
2. Optimization — find critical points, check endpoints
3. First/Second Derivative Test — classify critical points
4. Concavity — second derivative determines shape

Derivative Applications 🎯

Review — Part 3 Complete

AP Exam Review

Part 4 of 7 — Integration Review

Essential Integrals

$\int x^n\,dx = \frac{x^{n+1}}{n+1} + C \quad (n \neq -1)$

$\int \frac{1}{x}\,dx = \ln|x| + C$

$\int e^x\,dx = e^x + C$

$\int \sin x\,dx = -\cos x + C$

$\int \cos x\,dx = \sin x + C$

$\int \sec^2 x\,dx = \tan x + C$

Integration Review 🎯

Review — Part 4 Complete

AP Exam Review

Part 5 of 7 — FTC, Accumulation, and DEs

FTC Part 1

$\frac{d}{dx}\int_a^x f(t)\,dt = f(x)$

FTC Part 2

$\int_a^b f(x)\,dx = F(b) - F(a)$

Separation of Variables

$\frac{dy}{dx} = f(x)g(y) \implies \frac{dy}{g(y)} = f(x)\,dx$

FTC & DE Review 🎯

Review — Part 5 Complete

AP Exam Review

Part 6 of 7 — Applications of Integration

Key Applications

1. Area between curves: $\int [f - g]\,dx$
2. Volumes (disk/washer): $\pi\int [R^2 - r^2]\,dx$
3. Cross sections: $\int A(x)\,dx$
4. Average value: $\frac{1}{b-a}\int_a^b f\,dx$

Integration Applications Review 🎯

Review — Part 6 Complete

AP Exam Review — Final

Part 7 of 7 — Comprehensive Mixed Review

Comprehensive Review 🎯

AP Exam Review — Complete! 🎓

You have reviewed all major topics for the AP Calculus AB exam:

• ✅ Limits & Continuity
• ✅ Derivatives & Applications
• ✅ Integration & Applications
• ✅ Differential Equations
• ✅ Theorems (IVT, MVT, EVT, FTC)

Good luck on the exam!