Interactive AP Calculus BC lessons with problem-solving approach

The Tutor and Student worked through problems applying the Law of Sines and the Law of Cosines to solve for unknown sides and angles in triangles. They also briefly reviewed the formula for calculating the area of a triangle using two sides and the included angle.

The Student and Tutor reviewed fundamental vector concepts including definition, notation, addition, subtraction, scalar multiplication, and the dot product. They practiced solving problems related to these operations and determining vector orthogonality, with plans to cover the Law of Sines and Cosines in the next session.

The tutor and student reviewed geometric concepts including types of lines (parallel, intersecting, perpendicular) and angles (acute, obtuse, right, straight, complete). They practiced identifying these in alphabets and then transitioned to a game involving fractions to find missing values that sum to one.

The student and tutor reviewed quadratic equations, focusing on calculating the discriminant to determine the nature of the roots and practicing how to plot quadratic equations by calculating points and sketching parabolas. The student worked through various examples for both discriminant calculation and graph plotting.

The Tutor and Student explored the concepts of scalars and vectors, their representation, and operations including the dot product and modulus calculation. They practiced finding the angle between vectors, determining orthogonality, and calculating vector projections using specific formulas and examples. The next steps would involve continuing with related topics and problems.

The tutor and student reviewed key calculus concepts including derivatives and anti-derivatives. They practiced differentiating various function types and integrating functions using different methods like u-substitution and integration by parts. The session served as a final review before the student's exams.