AP Calculus BC 2025 – Advanced Calculus Course with College Credit Potential

AP Calculus BC is the final calculus course offered at the college level which extends AP Calculus AB with all AB-level material plus other advanced material, such as parametric equations, polar coordinates, and vector-valued functions, and infinite series. This course aims to help students pursue competitive STEM degrees in engineering, mathematics, physics, and computer science.The AP Calculus BC has a demanding course outline, practical learning and exam preparation, making students gain good analytical skills, can be awarded possible college credits, and can be prepared to learn at a prestigious university level.

About the Course

AP Calculus BC goes into more details on the differential and integral calculus and includes more advanced things, not covered in AP Calculus AB. A good background in algebra, trigonometry, and functions is necessary. Students are taught how to use calculus in solving complex mathematical and real life problems.

Course Units:

• Unit 1: Limits and Continuity (4–7%) Study of the concepts of limit, continuity, discontinuity, and asymptotes. Introduces the use of the intermediate value theorem and the LH rule.
• Unit 2: Differentiation – Definition and Fundamental Properties (4–7%) Gives definitions of derivative, differentiability and derivative rules such as power, product, quotient and trigonometric rules.
• Unit 3: Differentiation – Composite, Implicit, and Inverse Functions (4–7%) Emphasis is placed on the chain rule, implicit differentiation, inverse functions, and higher order derivatives.
• Unit 4: Contextual Applications of Differentiation (6–9%) Advances in differentiation of motion, relative rates, and linearization. Applying derivatives to real-life scenarios such as optimization and problem-solving.
• Unit 5: Analytical Applications of Differentiation (8–11%) Introduces Mean Value Theorem, concavity, first and second derivative tests, optimization problems, and graph sketching.
• Unit 6: Integration and Accumulation of Change (17–20%) Builds on definite integrals, Riemann sums, Fundamental Theorem of Calculus, substitution, and BC-only advanced integration methods such as integration by parts, partial fractions, and improper integrals.
• Unit 7: Differential Equations (6–9%) Includes modeling with DEs, slope fields, Euler’s Method (BC only), exponential and logistic models.
• Unit 8: Applications of Integration (6–9%) Applies integration to areas, volumes (disc, washer, and cross-sections), arc length, and particle motion problems.
• Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC Only) (11–12%) Introduces parametric equations, polar curves, vector-valued functions, arc length, and motion in parametric and polar forms.
• Unit 10: Infinite Sequences and Series (BC Only) (17–18%) Covers convergence and divergence tests, Taylor and Maclaurin series, radius and interval of convergence, and representing functions as power series.

Benefits of AP Calculus BC

• Strong STEM Foundation: Build advanced problem-solving skills for engineering, physics, and math-heavy majors.
• Advanced Topics: Learn series, polar, parametric, and vector calculus beyond AB level.
• College Credit: High scores may grant up to a year of college calculus credit.
• Analytical Thinking: Strengthen logical reasoning and mathematical rigor.
• Exam Edge: Practice-based approach prepares students for AP exam success.

What We Offer?

• Comprehensive notes and practice material for each unit.
• Advanced integration and series problem sets.
• Mock AP exams for exam-readiness.
• Individual mentoring and doubt-clearing sessions.
• Progress tracking tools to measure improvement.