AP Calculus BC: 4-Week Exam Review

If the AP Calculus BC exam is weeks away and you want to walk in confident, this four-week intensive review is built exactly for you. Students work through every major topic on the BC exam — limits, derivatives, integration techniques, differential equations, applications of integration, and sequences and series — with a sharp focus on the multiple-choice section where points are won or lost fast. Each session combines targeted concept review with hands-on problem-solving using real AP-style questions, so you're not just refreshing material, you're building the speed and accuracy the exam demands. By the end, you'll have a battle-tested toolkit of calculus techniques and test-taking strategies ready to deploy on exam day.

Built for the Final Push Before the AP Exam

AP Calculus BC covers more ground than almost any other AP course — and the exam tests that material at a level that rewards precision, speed, and deep understanding all at once. This four-week review course is designed for students who have completed BC Calculus and are ready to sharpen everything they know into exam-ready performance. Rather than re-teaching from scratch, each session zeroes in on the concepts and problem types that show up most on the multiple-choice section, giving students focused practice reps with immediate feedback.

Limits, Derivatives, and Their Applications

The course opens by rebuilding confidence on the foundational material. Students revisit limit evaluation — algebraic simplification, L'Hôpital's Rule, the Squeeze Theorem — and clarify the connections between limits, continuity, and the Intermediate Value Theorem. From there, the focus shifts to derivatives: mastering the full rule set (power, product, quotient, chain), differentiating every function type that appears on the BC exam, and recognizing the conditions where a function is not differentiable. Applied derivative topics get serious attention too, including related rates problems and motion analysis (position, velocity, acceleration), which appear regularly in both multiple-choice and free-response contexts.

Integration Techniques and Differential Equations

The middle portion of the course tackles the integration content that separates BC from AB. Students practice u-substitution, integration by parts, partial fractions, and trigonometric substitution — learning not just how to execute each technique but when to recognize which one applies. Approximation methods including left, right, and midpoint Riemann sums and the trapezoidal rule are reviewed alongside improper integrals and average value. Differential equations get dedicated time: students work through separable equations, interpret and sketch slope fields, step through Euler's method, and analyze logistic growth models — all common BC exam targets.

Applications of Integration and Sequences & Series

Students apply integration to calculate areas between curves and set up volumes of solids of revolution using both the disc method and the washer method, as well as volumes with known cross-sections. The course closes with sequences and series — the topic that defines the BC curriculum — covering convergence tests, power series, Taylor and Maclaurin series, and the radius and interval of convergence. This is the content many students find most challenging, and the review is designed to make these concepts feel manageable and testable.

Exam Strategy Woven Throughout

Every session includes AP-style multiple-choice questions worked live, so students get used to the format, pacing, and the specific ways answer choices are designed to mislead. Students learn to identify common distractors, develop a reliable approach for unfamiliar problems, and build the time discipline needed to move through the multiple-choice section efficiently. By the final session, students aren't just reviewing calculus — they're thinking like test-takers who know exactly what to do when the clock starts.