2003 BC Calculus AP Test Solutions
Calculators can be used for the first three problems.. amen.
this problem wasn't too bad.. actually it was really easy.. whatever.
This problem made no sense at all and shouldn't ever be tested on. It was absolutely terrible.
This was fine right until the polar stuff... but even that SHOULD have been easy.. if you can think straight.
Most confusing problem ever.. don't waste your time on the last part.. its kinda crazy.
You can solve this problem just from the information given.. as long as you remember the product rule. They make you solve for stuff that is already known. Joke.
As long as you know the mclaurin series for cosine you should be fine on this problem. If you don't you can still solve the problem right if you're good at math... i think i got it wrong.
My AP Score Prediction:
I think that I did pretty well on the exam. I believe i will get a four or a five because i thought the multiple choice was fairly easy. On the other hand the free response was challenging, but i tried to maximize the points i could get by showing a lot of work. Hopefully i will get a five.
My advice for students next year is to pay attention in the class and don't leave all of your studying until the last night. Study your past tests and go over integrals. The majority of the test is integrals and if you know how to do them well you will most likely get a four or a five. Good luck.
College of Attendance:
Reviews of Math Websites
This website asks how to find the maximum volume of a box created by cutting squares out of the corners of a rectangle and folding the edges to create a box. To solve you should create an equation for volume by defining the height, length, and width in terms of x. Then take the derivative to find the maximum volume because there is a horizontal tangent at that value of x.
Here you are given a vase that is placed on the x-axis in the first quadrant. You can plot points on the edge of the pot to get its equation. Then take the integral rotated about the x-axis to solve for the volume.
Determine the length of this pipe by plotting points to get the equation of the pipe. Then use the integral of the square root of dx/dt^2 plus dy/dt^2 or some other form of ds.
Use Riemman sums to find the area of a graph. You will need to find the area under the left rectangles, then the right rectangles. Add these two up and divide by two to find the average.
This site is very simple. Just find the equation of the water curve by plotting points, and then determine the domain and range. Easy enough.
This page is weird. All you do is put in a function and its derivatives, and the site will give you the graph and taylor series for it. Nice.
If you like graphing things this site is for you. It's not for me. All you do is change the coefficients for a standard function to create parabolas, circles, elipses, or hyperbolas. You can transform them, stretch them, etc.
This website shows you examples of graphs of exponential functions and how to properly take the derivatives of them. Then you can learn how to graph tangent lines to the curves and find their equations. Helpful for beginning of calculus.
My Own Example Problem
Problem: Determine the volume of the cake by using integrals.
Solution: To solve this problem, cut a slice of the cake and set it on the x-axis. Then rotate the slice about the y-axis to create the cake. Approximate the graph of the piece of cake and use integrals with dx slices to solve for the volume of the cake.