Practical AP Calculus & Statistics lessons with problem solving

The Tutor and Student reviewed differentiation and integration concepts in calculus. They covered various differentiation rules, including the product, quotient, and chain rules, and practiced applying them through examples, with a plan to continue practicing problems.

The tutor and student worked through various differential equation problems, focusing on techniques like separation of variables, integration, and solving for the general solution. They practiced setting up equations from word problems and applying substitution methods. The student identified a need to focus more on setting up initial differential equations from verbal descriptions.

The session covered projectile motion, circular motion, and relative motion. The Student solved problems related to projectile trajectory, centripetal acceleration, and observed velocities from different reference frames. Galilean transformation was introduced, with plans to delve deeper into the concept in the next session.

The student and tutor covered discrete random variables, inclusive/exclusive inequalities, and calculating mean, variance, and standard deviation. They worked through examples to practice these concepts and started discussing binomial distribution. The student was assigned practice problems related to discrete variables.

Nithin and Christa reviewed various probability concepts, including mutually exclusive and inclusive events, Venn diagrams, and both the special and general addition rules. Christa actively practiced probability calculations using card-drawing examples and was introduced to contingency tables. Nithin assigned a practice problem for her to work on, and their next lesson will delve into conditional probability.

Nithin and a student from Mesa Community College reviewed probability, covering sample spaces, events, empirical probability, complements, intersections, unions, and Venn diagrams. The learner worked through examples, including dice rolls and a refrigerator analogy, to illustrate these concepts. Nithin assigned practice questions on the covered sections for completion.