AP Calculus AB Monthly Review

AP Calculus AB Monthly Review is a targeted, exam-focused course designed for high school students who want to sharpen their calculus skills and walk into the AP exam with real confidence. Each month, students work through the core pillars of the AB curriculum — limits, derivatives, integrals, and differential equations — tackling actual AP-style multiple-choice and free-response problems with an expert instructor. This isn't passive review: students actively solve problems, uncover the logic behind each technique, and learn to avoid the specific mistakes that cost points on test day. Whether you're catching up, keeping up, or pushing for a 5, this course gives you the structured practice and strategic guidance to make it happen.

What This Course Is — and Who It's For

AP Calculus AB Monthly Review is built for students who are serious about mastering calculus and performing at their best on the AP exam. Whether you're working through the course material for the first time and want extra reinforcement, or you're deep into the school year and need to pull everything together, these monthly sessions give you consistent, high-quality practice with an instructor who knows exactly what the exam demands. Expect an active, problem-solving environment — not a lecture you'll zone out in.

Limits and Continuity: Building the Foundation

The course opens where AP Calculus AB begins: limits. Students practice evaluating limits graphically, numerically, and analytically, including one-sided limits and limits at infinity. You'll apply limit laws to determine when a limit exists and what it equals, and you'll work through the kinds of tricky substitution problems that trip students up on the multiple-choice section. From there, the course connects limits to continuity — including a deep look at the Intermediate Value Theorem and what continuity really means for a function's behavior.

Derivatives: Rules, Applications, and Real Problems

Differentiation is the heart of the AB exam, and this course treats it accordingly. Students build fluency with the power rule, product rule, quotient rule, and chain rule — then push further into implicit differentiation and related rates problems. On the applications side, you'll use the first derivative test to find increasing and decreasing intervals, identify local and global extrema using the Extreme Value Theorem, and analyze concavity and inflection points with the second derivative test. These aren't just formulas to memorize — you'll understand why each technique works and when to reach for it.

Integrals and the Fundamental Theorem of Calculus

Integration gets the same rigorous treatment. Students evaluate definite and indefinite integrals using the power rule and u-substitution, then apply the Fundamental Theorem of Calculus to connect the two branches of the subject. A key focus is calculating the area between curves — a concept that appears frequently on both the multiple-choice and free-response sections. By working through a variety of problem types, students develop the flexibility to handle integrals that don't follow a single obvious pattern.

Differential Equations and Modeling

The course also covers one of the AB exam's most distinctive topic areas: differential equations. Students solve separable differential equations to find general and particular solutions, interpret slope fields to visualize solution behavior, and explore how differential equations model real-world situations in physics, biology, and engineering. This section ties together many of the earlier skills — derivatives, integrals, and function analysis — and shows how calculus operates as a unified tool for understanding change.

Exam Strategy and What You'll Walk Away With

Every session is built around authentic AP Calculus AB problems — the same style, format, and difficulty level you'll see on exam day. Students practice identifying efficient solution paths, avoiding common errors, and pacing themselves across both multiple-choice and free-response sections. By the end of the course, you won't just know the material — you'll know how to perform under pressure, communicate your reasoning clearly, and approach unfamiliar problems with a systematic strategy. This course is your monthly edge in the months leading up to the exam.