Calc Problems

BC Calculus Free Response Answers for AP 2004

These answers were typed up and provided by Mr. Calculus.

I think I did pretty well on these problems. Also, I think I did well on the multiple choice. Overall I think I got a 4 or 5.

Advice: Pay attention in class and study! Practice problems at home from the book. Start reviewing as early as possible. I would reccommend about a month of good review time. A study book of some sort is also helpful because it will explain concepts in much easier terms that the text book.

I am going to the University of Michigan College of Engineering. I'm going to be an engineer because I couldn't decide what I wanted to be and I figured that's a good place to start.

Calc site reviews:

Free Doughnuts: A website involving the volume of a box containing FREE DOUGHNUTS. In order to solve the problem, one must know how to set up equations for finding length, width, and height of a figure using variables. The final answer may be obtained using graphical methods or derivatives.

Volume of a Vase: Find the volume of a vase by finding the equation of a line and using solids of revolution to calculate the volume. This relates volume to an equation by integrals.

Calculating the Length of a Plane Curve: Mark coordinate points on the image of a plane curve. Using those points, find a function to represent the plane curve.

Estimating the area of Virginia: Approximate the area of Virginia using rectangles, trapezoids, and Simpson's Rule. Also, links to similar problems for area of other states are included.

Describe the Squirt: Another mark-the-points problem. Approximate a quadratic function that imitates the shape of the water fountain and see it graphed in comparison to the squirt.

Graphing Taylor Polynomials: A graphing device for Taylor polynomials; graphs a function f(x) and the Taylor polynomial approximations to f(x) up to degree 4 for a given c value. The degree one Taylor polynomial (tangent line) will be shown in blue, degree two in red, degree three in green, and degree four in orange. Click on the graph to determine the c value. Overlapping lines may be displayed as a new color!!

Graphing Conic Sections: Use this device to graph conic sections such as parabolas, ellipses, circles, and hyperbolas. Choose the type of general equation and change the values in the equation to graph desired conic section.

Exploration: Exponential Functions and Their Derivatives: A series of applets that allow exploration of exponential functions. Begins with graphs of exponential functions,moves on to calculating their derivatives and tangent lines, further how NOT to calculate the derivative, and a comparison of the graph of the derivative to the original graph.

My math problem.