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AP Calculus AB Page 1 of 6 Test: The Integral and the Fundamental Theorem of Calculus User Name:_______________ Instructor: _________________ Date:__________ (print clearly) Directions for Free Response Section (35 Minutes, 30 points total, 15 per question) • Write your answer inside the boxes provided (do not write in the margins). Do not use extra paper. Use a black or blue pen. • Answer each of the questions fully. Show all your work. Indicate clearly the methods you use; you’ll be graded on the correctness of your methods as well as the accuracy of your final answers. Correct answers without supporting work may not receive credit. Justifications require mathematical (non-calculator, non-computer) reasons. • Most questions will be given in several parts. The answers from one section will often be used in following sections. Missing points in an earlier section does not mean you’ll lose points in following sections. • The test corrector will not assume you used proper set up and methods if you reach the correct answer. It’s up to you to communicate the methods you used. Hints and Tips for Free-Response Portion • Take your time reading the questions. • You have 35 minutes for the free-response questions. Take some time to think about the question. If you don’t understand the question, you’re very unlikely to find the right answer. Scoring As a general rule points are divided as follows: 30% Proper set up of the problem. 30% Proper method employed for solving the problem. 40% Correct answer. The Calculator The calculator can be used for specific tasks, but you must show the setup in standard mathematical notation. For this Test, you may only use your calculator to graph a function and find the roots of an equation. If you’re asked to find the x values of the points of intersection between y = x 2 and y = cos x , you must write x 2 − cos x = 0 before stating that the solution is {x=.82413, -.82413}. What does "Show your Work" Really Mean ?  4 If you’re asked to use limits to find the vertical asymptote for y =    hen you shouldn’t  3 − x  t put x =3 as the answer. You also need to explain that lim  4    = −∞  and lim  4  = ∞  x → 3 +  3 − x  x → 3 −  3 − x  If the question is worth two points, one point is given for a solid explanation and one point for the correct answer. Copyright © 2021 Apex Learning. See Terms of Use for further information. Images of the TI-84 calculator are used with the permission of Texas Instruments Incorporated. Copyright © 2011 Texas Instruments Incorporated.