Massachusetts Institute of Technology MIT OpenCoursewareCambridge, Massachusetts, US,

September 5, 2008

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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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- Mathematics > Calculus

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Table of Contents

- First, Second, and Third Derivatives Exam Question
- Computing Derivatives Exam Question
- Derivatives of Trigonometric Functions Exam Question
- Derivative of an Inverse Function Exam Question
- Evaluating Derivatives and Limits Exam Question
- The Inverse Sine Function Exam Question
- Evaluating Derivatives I Exam Questions
- Evaluating Derivatives II Exam Question
- Trigonometric Formulas and Identities Exam Question
- Evaluating Derivatives III Exam Question
- Differentiation Formulas: Polynomials, Products, Quotients Exam Questions
- Higher Derivatives Exam Questions
- Exponentials and Logarithms: Calculus Exam Questions
- Trigonometric Functions Exam Questions
- Differentials and Indefinite Integration Exam Questions
- Inverse Trigonometric and Hyperbolic Functions Exam Questions

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

http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc

http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

Single Variable Calculus Question 2 (and its solution) covers finding the derivatives of an exponential function.

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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Single Variable Calculus Question 6 (and its solution) covers finding the derivatives of exponential and logarithmic functions.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

Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Question 1 (and its solution) covers finding the derivatives of two trigonometric functions.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

Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Question 1.5 (and its solution) covers evaluating the derivative of the inverse of an exponential function.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

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Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Question 1 (and its solution) covers the evaluation of three derivatives and a limit.http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: 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

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Single Variable Calculus Question 4 (and its solution) covers sketching the graph of the inverse sine function and finding its derivative.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Questions 1 and 2 (and their solutions) cover the derivatives of functions.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 2 (and its solution) covers the derivatives of four functions.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 1 (and its solution) covers A list of trigonometric and inverse trigonometric identities and formulas involving integrals and derivatives.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 1 (and its solution) covers three derivatives to be evaluated using a variety of techniques.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 1E-1 through 1E-5 (and their solutions) cover taking derivatives and antiderivatives of polynomials, finding the points on a graph which have horizontal tangent lines, and finding derivatives of rational functions.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 1G-1 through 1G-5 (and their solutions) cover finding second, third, or n^{th} derivatives of functions.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Questions 1I-1 through 1I-5 (and their solutions) cover evaluating derivatives and limits of functions which contain logarithms or exponentials, graphing an exponential function, and calculating interest compounded with different frequencies.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 1J-1 through 1J-4 (and their solutions) cover calculating derivatives of trigonometric functions.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 3A-1 through 3A-3 (and their solutions) cover evaluating five differentials and twenty indefinite integrals using a range of techniques.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 5A-1 through 5A-6 (and their solutions) cover evaluating integrals and derivatives of these functions, as well as graphing them and finding tangent lines or average values.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

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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