This course is a complete AP Calculus AB review for students currently enrolled in the class, self-studying for the exam, or rebuilding core skills before test day. It begins with a diagnostic assessment and study roadmap, then moves through the full curriculum in a logical sequence: precalculus review, limits and continuity, derivatives and their applications, integration and accumulation, and exam-focused practice.
Lessons emphasize both understanding and execution. Students learn how to read graphs, tables, formulas, and verbal descriptions; compute accurately; justify conclusions with correct notation; and explain results in the style expected on AP free-response questions. The course also teaches calculator use, command words, scoring rubrics, pacing, and error analysis so students can connect content mastery to actual exam performance.
- Start with a diagnostic: identify strengths and weak points in algebra, functions, limits, derivatives, and integrals, then build a targeted study plan.
- Review readiness skills: refresh function notation, algebra manipulation, rates of change, trigonometric facts, and graphing technology needed for calculus.
- Master limits and continuity: evaluate limits from graphs, tables, and equations; handle indeterminate forms; analyze asymptotic behavior; and apply continuity and the Intermediate Value Theorem.
- Build derivative fluency: learn the derivative as a limit, apply differentiation rules, use implicit differentiation, and interpret derivatives in motion and real-world contexts.
- Apply derivatives: analyze increasing and decreasing behavior, extrema, concavity, inflection points, optimization, and related rates with clear justification.
- Learn integration carefully: work with antiderivatives, Riemann sums, definite integrals, the Fundamental Theorem of Calculus, accumulation functions, net change, and motion applications.
- Practice AP-style reasoning: complete worked examples, guided practice, mixed quizzes, and cumulative review that mirror the reasoning demands of multiple-choice and free-response sections.
- Improve exam execution: use mistake logs, timing drills, rubric-based review, and targeted corrections to turn recurring errors into specific action steps.
Throughout the program, students complete original exam-style questions with full answer explanations rather than relying on shortcuts or memorized templates. The result is practical preparation: stronger calculus fundamentals, clearer written reasoning, better calculator judgment, and a more organized approach to timed AP Calculus AB practice.