Hello, my name is Albert Chow. This is the site I must do for Mr. Block's class after taking the Calculus BC AP test. This is my calculus web final project and exam. If you're looking at this, good for you! Herein are the answers to the 2004 Calculus BC free response, form A. Since we're not allowed to copy down the questions, only the answers may be displayed. Below is a link to a site with a copy of the free response questions. Beyond all that, there are links to sites of calculus merit. Some of them are projects Mr. Block assigns to his calculus classes.
Here's the link to Mr. Block's Calculus Website.
Problem 1
Click here for the answers for Problem 1.
This problem was the easiest of all the problems on the 2004 Calculus BC Free Response. I'm quite confident I got most, if not all, the points on this problem.
Problem 2
Click here for the answers for Problem 2.
This problem was more difficult than the first - for me at least. I'm fairly sure I got most of the problem, though I wrote my answer slightly differently than the answer given on the link.
Problem 3
Click here for the answers for Problem 3.
Okay, this problem was difficult for me. I'm not sure how well I did on this one, as I struggled through this.
Problem 4
Click here for the answers for Problem 4.
Another reasonable problem. I'm sure I got all parts but the last, where a computation error probably cost me those last couple points.
Problem 5
Click here for the answers for Problem 5 (part 1).
Click here for the answers for Problem 5 (part 2).
This was the most impossible problem for me. I sat there staring at it for the longest time, not knowing what to do. You could tell who was taking Calculus AB and Calculus BC when people hit this problem. The AB people were just working along, the BC people were looking around and muttering unhappily under their breaths. However, when Mr. Block showed us how to do this problem, it turned out to be much easier than we thought.
Problem 6
Click here for the answers for Problem 6.
This problem was also reasonable. I'm fairly sure I got all parts except part c, where Lagrange's error bound was asked. I couldn't remember what this was, so I didn't answer part c.
Now, let's see . . . I think I did fairly well on the AP, but I probably didn't get a 5, as the 5 seems elusive. I'm hoping for a 4 and trying not to jinx my hope, and get a 2 or 3; but I'm fairly confident I got a 4.
Advice to following years: do everything Mr. Block gives you. The review packets for the tests and the AP problems are a must. Attempting to take notes may help when you go back and review things from the beginning of the year. But be aware that Mr. Block does math at like the "speed of light," so try not to blink (use eyedrops - Mr. Block's suggestion) or you may miss something important.
I'll be attending University of Michigan-Ann Arbor in the fall of 2004. I think I'm going to be a biology major, maybe with a minor in music, economics, or a foreign language. Anyway, I'll go on to medical school (hopefully) and become a pediatrician.
Free Doughnuts This website involves finding the volume of a box of free doughnuts. The problem asks for the maximization of the box to hold the maximum number of free doughnuts. To do this with the limited dimensions of the box, an equation for relating length, width, and highth is needed. The final answer is determined using a graphical method or with derivatives.
Calulating the Volume of a Vase This website involves finding the volume of a given vase. In order to do this, you must find the equation of a curve (the curve of the vase's edge) and use solids of revolution. In this way, the volume of a vase can be determined with integrals.
Calculating the Length of a Plane Curve This website involves finding the length of a plane curve. The tutorial teaches you to plot point coordinates along the edge of the curve, use the points to create a function, and set up a definite integral using the function to find the length of the plane curve. It also shows how to evaluate the answer with a calculator.
Estimating the Area of Virginia This website attempts to find the area of Virginia. To do this, it uses Riemann Sums, utilizing the left rectangle, the right rectangle, the trapezoidal rule, and Simpson's Rule.
Describing the Squirt This website involves describing the arc of a water squirt from a water fountain. To do this, you must plot points like the "Calculating the Length of a Plane Curve" problem and determine a function to describe its parabolic motion. The squirt problem looks fun and easy!
Graphing Taylor Polynomials This website teaches how to find and graph Taylor Polynomials. It's a pretty general graphing site and can graph up to 4 functions on a single graph.
Graphing Conic Sections This website involves graphing the conic sections of parabolas, ellipses, circles, and hyperbolas. All you have to do is choose your desired general function, input your values, and graph your conic section.
Exploration: Exponential Functions and Their Derivatives This website is a conglomeration of several applets that allow a person to explore exponential equations. It starts out with the graphs of exponential functions, then moves on to calculate their derivatives and tangents. It also shows how not to calculate the derivative and, finally, shows a comparison between the graph of the derivative and the original graph.
This is my personal problem (that I made) for the last part of this website. Let's find the area under the curve created by the mcDonald's golden arches. To do this, plot points around the edge of the curve and extrapolate an equation. For the sake of easiness, let's say from the width of the arches is 8 units (x-axis from 0 to 8) and the height is also 8 units (y-axis from 0 to 8). Though the dimensions may not be exact, they may be easier to use. Now, find the definite integral of this equation and you'll have found the area underneath the McDonald's golden arches.