Teachers and students can use these exam questions and solutions to test the information learned.

Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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## Collection Contents

### Related Rates I Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 1 (and its solution) covers finding the rate at which a particle moving on the x-axis is moving away from a point on the y-axis. Course: 18.01 Single Variable Calculus, Fall 2005 Instructor: Prof. Jason Starr Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Related Rates with Polar Coordinates Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 6 (and its solution) covers finding the rate of change of a particle's distance from the y-axis as it moves around the unit circle. Course: 18.01 Single Variable Calculus, Fall 2005 Instructor: Prof. Jason Starr Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Related Rates II Exam Questions

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Questions 3.3 and 3.4 (and their solutions) cover a melting icicle and a melting block of ice. Course: 18.01 Single Variable Calculus, Fall 2005 Instructor: Prof. Jason Starr Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Related Rates III Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 8 (and its solution) covers finding the rate of change of the radius of a balloon with decreasing volume. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: Prof. David Jerison Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 10 (and its solution) covers finding the time for a substance to decay to one-fourth its original amount, and the rate at which it is decaying at this time. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: Prof. David Jerison Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Related Rates: Searchlight Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 4 (and its solution) covers finding the rate at which a prisoner needs to run to stay ahead of a searchlight. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: Prof. David Jerison Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Viewing Angle for a Launching Rocket Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 4 (and its solution) covers finding the rate of change of the angle at which a person is watching a rocket ten seconds after it takes off. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: Prof. David Jerison Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Related Rates: Christmas Tree Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 5 (and its solution) covers finding the rate at which the shadow of a falling Christmas tree is lengthening. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: Prof. David Jerison Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Related Rates IV Exam Questions

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Questions 5 and 6 (and their solutions) cover the rate of change of the angle of a falling tree and the rate of change of the water level in a cone. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: Prof. David Jerison Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Related Rates V Exam Questions

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Questions 2E-1 through 2E-10 (and their solutions) cover finding the rate of change of a robot's shadow, the rate at which the distance between two boats is increasing, and the rate of change of the thickness of oil in a frying pan. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: Prof. David Jerison Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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