Using correct units, interpret the meaning of H'(6) in the (a) Use the data in the table to estimate H'(6). Selected values of H(t) are given in the table above. The height of a tree at time t is given by a twice-differentiable function H, where H(t)) is measured in meters and t is measured in years.Related rates problem using a new function. Trapezoidal Rule to approximate average value.
#CALCULUS MEMES PLANKTON FREE#
Find the total distance traveled by the boat over the time interval 0 ≤ t ≤ 1.ĪP Calculus BC 2018 Free Response Question 4 Time t is measured in hours, and x(t) and y(t) are At time t ≥' 0, the position of the boat is (x(t),y(t)), where (d) The boat is moving on the surface of the sea. Plankton cells in the column is less than or equal to 2000 million. That gives the number of plankton cells, in millions, in the entire column. Write an expression involving one or more integrals Water in part (b) is K meters deep, where K > 30. (c) There is a function u such that 0 ≤ f(h) ≤ u(h) for all h > 30 and. To the nearest million, how many plankton cells are in this column of water between h = 0 and (b) Consider a vertical column of water in this sea with horizontal cross sections of constant area 3 square Using correct units, interpret the meaning of p'(25) in the context of the problem. The continuous function f is not explicitly given. Plankton cells, in millions of cells per cubic meter, is modeled by Researchers on a boat are investigating plankton cells in a sea.Arc length to find distance traveled for some parametric equations. Using squeeze theorem (comparison test logic) to show that This was a kind of new context but all the same old stuff.Īlso, you had a calculator to do the hard work for you. Justify your answer.ĪP Calculus BC 2018 Free Response Question 2 Number, find the number of people in line at this time.
(d) For 0 ≤ t ≤ 300, at what time t is the number of people in line a minimum? To the nearest whole (c) For t > 300, what is the first time t that there are no people in line for the escalator? (b) During the time interval 0 ≤ t ≤ 300, there are always people in line for the escalator.
(a) How many people enter the line for the escalator during the time interval 0 ≤ t ≤ 300 ? There are 20 people in line at time t = 0. They exit the line at a constant rate of 0.7 person per second. Where r(t) is measured in people per second and t is measured in seconds. People enter a line for an escalator at a rate modeled by the function r given by.Use anĪccumulation function and the Fundamental Theorem of Calculus (FTC). Other activities encourage students to work together, each filling in the blanks on a meme template to represent a concept related to their studies another prompts students to write a text conversation between two characters from history.Questions And Worked Solutions For AP Calculus BC 2018ĪP Calculus BC 2018 Free Response Questions - Complete Paper (pdf)ĪP Calculus BC 2018 Free Response Question 1 So, if an AP Calculus student gets the prompt of “second derivatives,” they could make a meme that reinforces the concept that d^2y/d^2x, a more complex way of denoting a second derivative, which is the same thing as f”(x), a more familiar notation. Then other students guess what the meme is representing. In one activity, for example, students get randomly assigned a prompt, and they have to make a meme about the concept. Teachers can lead their class through group activities that use memes to help students synthesize information. Students can make memes with Antimatter’s built-in meme generation tools on the web and iOS, creating visual jokes about what they’re learning. Tens of thousands of students and teachers are using Antimatter to bring memes into the classroom. The company just closed a $2 million seed round, led by Version One. Though it may sound bizarre, Antimatter is proving its hypothesis about the power of shitposting as an educational tool. “In a sense, shitposting is the highest form of consciousness.” “To be able to shitpost, you have to understand the subject matter really well,” Antimatter founder and CEO Jonathan Libov told TechCrunch last year. Antimatter is an edtech company that operates under a simple, enticing premise: If a student really understands a topic, then they’ll be able to make a meme about it.
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