Zoom session Last Minute AP Calculus Exam Review (May 11, 2020)

The speaker emphasizes the importance of final preparations for the upcoming AP exam, encouraging students to review their demo exams and familiarize themselves with the exam process across various devices. They highlight the necessity of having the fall and spring summary sheets, derivative and integral rules, and other resources printed or readily available. The speaker also stresses the importance of reviewing FRQ assignments and mock exams, particularly those covering derivative graph Remis on function tables and differential equations, as these topics are likely to appear on the exam. Additionally, they provide guidance on exam day logistics, such as having e-tickets, PID initials, and numbered paper sheets ready, and remind students to charge their devices and avoid internet searches during the exam to prevent any potential issues.

This paragraph delves into the specifics of the AP exam procedure, including the use of e-tickets, the submission process, and the importance of using black ink and blank printer paper for clarity. The speaker also discusses post-exam activities, such as entering grades into Infinite Campus and the release of AP exam problems for review. They address potential disruptions during the exam and the process for requesting a makeup exam, including the deadlines and the importance of following the correct procedure. The speaker also mentions the possibility of experiencing issues with exam submission and advises students on how to handle such situations, emphasizing the importance of clarity and preparedness.

The speaker provides a comprehensive review of the exam content, focusing on the 'big four' topics: derivative graph, Riemann sum, function table, and differential equation. They also mention additional topics that may appear, such as curve sketching, particle motion, limits, and continuity. The speaker advises students on the importance of understanding common theorems and phrases used by the College Board and suggests that students have all necessary resources readily available during the exam. They also discuss the process of submitting responses and the importance of not taking unnecessary risks with time management during the exam.

The speaker presents a detailed analysis of a derivative graph problem, explaining how to find absolute maxima and minima using the extreme value theorem and the graph of the derivative. They demonstrate the process of calculating the function's value at various points and how to use the graph to determine relative extrema. The speaker then moves on to discuss linear approximation, explaining how to find the equation of the tangent line at a specific point on the graph and how to use this line to approximate the function's value at a nearby point.

This section focuses on Riemann sums and definite integrals, particularly in the context of a sandpit being filled with sand. The speaker explains how to use the given function H of T, which represents the height of the sandpit over time, and its derivative H prime, which represents the rate of change of the height. They guide students through the process of estimating H double prime of 2 using the closest points on the graph and discuss the meaning of the definite integral from 0 to 12 H Prime in terms of the change in height of the sandpit over time.

The speaker continues the discussion on definite integrals, explaining how to evaluate them in the context of the sandpit problem and how to interpret the results. They also cover the process of writing the equation of a tangent line to a function at a specific point, using the given values of the function and its derivative. The speaker emphasizes the importance of understanding whether the tangent line approximation is an over or under approximation, based on the concavity of the function.

This paragraph explores the application of the Mean Value Theorem (MVT) and the Intermediate Value Theorem (IVT) in the context of the sandpit problem. The speaker explains how to guarantee a specific value of H prime and H double prime using these theorems, given the continuous and differentiable nature of the function. They clarify the conditions under which these theorems apply and how they can be used to solve problems involving rates of change and slopes.

The speaker discusses the application of the chain, product, and quotient rules in calculus, using a function table to illustrate how students can find the instantaneous rate of change of a function. They provide a step-by-step guide on how to find derivatives for functions involving composite and multiplicative expressions, emphasizing the importance of correctly identifying the outer and inner functions when applying these rules.

This section focuses on the technique of U-substitution in the context of definite integrals. The speaker explains how to handle a problem with a coefficient that requires substitution, emphasizing the importance of correctly identifying the substitution variable and its derivative. They guide students through the process of solving a definite integral problem involving a function of 3x, demonstrating how to apply U-substitution and the first fundamental theorem of calculus to find the solution.

The speaker introduces the concept of the second derivative and its application in determining the concavity of a function. They explain how to find the second derivative of a function and how it can be used to understand the shape of the function's graph. The speaker also discusses solving differential equations, providing a step-by-step guide on how to isolate the function variable and find the general solution, including the process of identifying the correct solution based on given conditions.

In this final section, the speaker touches on the topic of related rates, providing an example of how to set up and solve a related rates problem. They also discuss the concept of linkage errors, which occur when equal signs are misused to connect expressions that are not equal, potentially leading to points being deducted in exam grading. The speaker advises students to use arrows or no notation at all when showing the progression of their work to avoid such errors.