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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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Table of Contents

- Solids of Revolution: x- and y-axis Exam Questions
- Miscellaneous Integration Problems Exam Questions
- Solids of Revolution I Exam Question
- Area of a Lune Exam Question
- Area Between Two Curves Exam Questions
- Volume of Solid of Revolution Exam Question
- Arc Length of a Segment of a Curve Exam Question
- Continuously Compounded Interest Exam Question
- Solids of Revolution: Volume of a Vase Exam Question
- Solids of Revolution: Ice Cream Cone Exam Question
- Average Value of a Function Exam Question
- Solids of Revolution: Great Pumpkin Exam Question
- Average Value: SmartHam Exam Question
- Solid of Revolution II Exam Question
- Average Value: Test Scores Exam Question
- Solids of Revolution III Exam Question
- Area Inside a Polar Curve Exam Question
- Arc Length of a Curve I Exam Question
- Estimating the Length of the Sine Curve Exam Question
- Mass of a Metal Disc Exam Question
- Solids of Revolution IV Exam Question
- Arc Length of a Curve II Exam Question
- Integrals in Polar Coordinates: Lunar Eclipse Exam Question
- Arc Length of a Curve III Exam Question
- Polar Coordinates: Spiral Exam Question
- Solids of Revolution: Wine Glass Exam Question
- Average Value: Suspension Bridge Exam Question
- Polar Curves Exam Question

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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Single Variable Calculus Questions 1 and 2 (and their solutions) cover finding the volume of a solid of revolution about the x-axis and finding the volume of a solid of revolution about 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

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Single Variable Calculus Questions I.1 through IV.5 (and their solutions) cover miscellaneous integration.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 8 (and its solution) covers finding the volume of a solid of revolution about the x-axis.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 10 (and its solution) covers finding the area of the region in the 1st and 3rd quadrants between two circles defined in polar coordinates.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 Questions 5.1 and 5.2 (and their solutions) cover finding the area between a curve and a tangent line and the area between two parabolas.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 5.3 (and its solution) covers finding the volume of a solid of revolution about the x-axis.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 5.4 (and its solution) covers finding the arc length of a segment of the graph of the natural logarithm.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 3 (and its solution) covers setting up a definite integral for the amount of money in an account at the end of a year.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 6 (and its solution) covers finding the volume of a glass vase in the shape of a solid of revolutionProf. 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 7 (and its solution) covers finding the volume of ice cream in an overfilled cone defined by a solid of revolution.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 8 (and its solution) covers finding the average value of rectangles inscribed at random in a quarter of a circle.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 finding the volume of candy needed to fill a Great Pumpkin with shape defined in terms of a solid of revolution.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 4 (and its solution) covers finding the average area of slices of a SmartHam defined in terms of a solid of revolution.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 3 (and its solution) covers finding the volume of a solid of revolution about the y-axis.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 4 (and its solution) covers finding the average amount score and average amount of sleep students get the night before a test.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 4 (and its solution) covers finding the volume of a solid of revolution about the y-axis.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 5 (and its solution) covers sketching a curve defined in polar coordinates and finding the area inside it.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 6 (and its solution) covers finding the length of a curve defined parametrically.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 7 (and its solution) covers setting up an integral for the length of one arc of the sine curve, and estimating the value of the integral.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 8 (and its solution) covers setting up and evaluating an integral for the mass of a disc with variable mass density.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 finding the volume of a solid of revolution about the y-axis.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 4 (and its solution) covers setting up and estimating the value of an integral representing the length of a given curve.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 6 (and its solution) covers setting up and evaluating an integral to represent the uncovered area of the two moons involved in a lunar eclipse on another planet.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 4 (and its solution) covers etting up an integral to find the length of a curve given in rectangular coordinates.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 5 (and its solution) covers sketching a spiral defined in polar coordinates, counting the times it crosses the x-axis, and finding the area of specific regions of the spiral.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 8 (and its solution) covers finding the amount of wine that can be held in a glass defined in terms of a solid of revolution about the y-axis.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 11 (and its solution) covers setting up an integral for the length of the main cables in a suspension bridge, and using it to find the average length of the vertical cables connecting to the roadway.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 14 (and its solution) covers sketching a curve given in polar coordinates and finding the area swept by a line segment as one of the endpoints moves along this curve.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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