Multiple Choice Questions ❷ 2011B #5 (BC) – No Calc ❸ 2010B #3 (BC) – Calc OK ❺ 2007 #5 (BC) – No Calc ❻ 2012 #4 (BC) a,b – No Calc AP Calculus BC Saturday Study Session #2: Tabular Data Problems Multiple Choice Solutions 1. B Free Response Solutions ❶ 2012 #1 (BC) – Calc OK – Scoring Guidelines: ❷ 2011B #5 (BC) – No Calc – Scoring Guidelines: ❸ 2010B #3 (BC) – Calc OK – Scoring Guidelines: ❺ 2007 #5 (BC) – No Calc – Scoring Guidelines: ❻ 2012 #4 (BC) a,b – No Calc – Scoring Guidelines: ❼ 2005 #3 (BC) – Calc OK – Scoring Guidelines:Īnswer the questions! This will not earn you any points. One thing not to do: Do not use your graphing calculators to produce a regression equation and use that toĪnswer the questions! This will not earn you any points. In part (a) students were asked to approximate the volume of the tank using a left Riemann sum and indicate the units of measure. Give information about the graph of the function (the function value at a point, increasing/decreasing behavior,Ĭoncavity, local and global extrema, points of inflection) Values of ( )Ah for heights h 0, 2, 5, and 10 are supplied in a table. Intermediate Value Theorem (IVT), the Mean Value Theorem (MVT), or the Fundamental Theorem of Calculus Using a provided table of values for function g, its inverse h, and its derivative g', we unravel the mystery of h' using the chain rule and the concept of inverse functions. Answer theory questions usually related to the “Big Theorems” (i., the Extreme Value Theorem (EVT), the Let's delve into the fascinating realm of inverse functions, exploring how to evaluate the derivative of an inverse function, h', at a specific x-value. Give the units of the answer (unit analysis) Calculate a tangent line approximation (local linear approximation) Explain the meaning of a definite integral in the context of the problem Use a Riemann sum or a trapezoidal approximation to approximate a definite integral Approximate a derivative (slope, rate of change, instantaneous rate of change) at a point by using an average In recent years, at least one of the free-response questions included tabular data. The answers you give are usuallyĪpproximations. Questions about the function, its graph, its derivative, or its definite integral. These are often called “tabular data problems”. The AP Calculus BC exam often includes multiple‐choice and free‐response questions in which the stem of the question I Scored a 1750 before getting Gary’s help and within a four-month span he helped me get a 2200 and a 780 on the Math Level 2 Subject Test.AP Calculus BC Saturday Study Session #2: Tabular Data Problems Gary’s expertise on tacking math problems not only helped me make a strong base in a wide variety of math topics, but this also helped me perform well on the SAT. “I used to be a B student before Gary’s help, but soon after he changed the way I process the material and analyze the problem helping me get an A in the class. Applications to Physics and Engineering.Integration Using Tables and Computer Algebra Systems.Integration of Rational Functions by Partial Fractions.UCHS AP Calculus Review 8: Reasoning from Tabular Data R8. If function u is continuous at x, then u0 as x0. Proof: Differentiability implies continuity. Proof of the derivative of sin (x) Proof of the derivative of cos (x) Product rule proof. Limit of (1-cos (x))/x as x approaches 0. General Logarithmic and Natural Exponential Functions Review 8: Reasoning from Tabular Data R8. Proof of power rule for square root function.Indeterminate Forms and L’Hospital’s Rule.Exponential Functions and Their Derivatives.Linear Approximations and Differentials.Rates of Change in the Natural and Social Sciences.(c) Is the approximation found in part (b) an overestimate or underestimate of the total mass of bacteria in the petri dish Explain your reasoning. Tangents, Velocities, and Other Rates of Change subintervals indicated by the data in the table.Calculating Limits Using the Limit Laws.Mathematical Models: A Catalog of Essential Functions.2008 AP Calculus BC Practice Exam from College Board.2008 AP Calculus AB Practice Exam from College Board.AP Calculus AB and AB Calculus BC Multiple Choice Questions for 1969-1998.AP Calculus AB and AB Calculus BC Free Response Questions by Topic.Summary of Common AP Calculus Derivatives, Integrals and Rules.Here are some excellent AP Calculus resources to get you started along with the worksheets below. There is a difference between knowing the path & walking the path. Free Calculus Worksheets with Solutions (Stewart Calculus):
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