TO: Next Year’s AP Calculus BC Students FROM: T. Wernau, AP Calculus BC Teacher As you probably know, the students who take AP Calculus AB and pass the Advanced Placement Test will place out of one semester of college Calculus; those who take AP Calculus BC and pass the Advanced Placement Test will place out of two semesters of college Calculus. Because Calculus BC covers two semesters, you will be learning Calculus twice as fast as the students who take Calculus AB. In order to have enough time to learn the material of two college- level courses, we will start learning Calculus as soon as possible when school begins and will not be able to spend time reviewing the material you learned in Algebra I & II, Geometry, and Precalculus. Attached is a summer homework packet, which will need to be completed by first day of Calculus class in August. The material in the packet should be material you learned in Algebra II and Precalculus. On the fourth day of class, you will take a test on the material in the packet. My recommendation is that you look over the problems in the packet when you receive it but that you wait until the week before school starts to work the problems so that you will remember the material very well when school starts. All of the AP Calculus AB and BC classes at Dulles will be using a graphing calculator. We will, in class be using the TI-Nspire. If you have an earlier calculator, you may need to come in for extra help in learning how to use the calculator for what we need it for. I am looking forward to seeing you in Calculus in August. Sincerely, Mr. Wernau Dulles High School Math Department
CALCULUS BC SUMMER NOTES Some of the material that was briefly covered in Pre-Calculus is knowledge that I need you to know to be able to complete the packet. Here are some notes/examples for you to use: The Limit: 1) Let’s take a look at the function 3 1 ( ) 1 x f x x . What do we know about the graph of this function? __There is a hole at x=1__ Right! Graph it. If we put the point of our pencil on f(0.2) and trace the curve towards f(1) our pencils approaches the y-value of 3. We denote this as : 1 lim ( ) 3 x f x because as we approach f(1) from the left side (the reason for the raise – next to the 1) the value of the graph approaches 3. If we put the point of our pencil on f(1.2) and trace the curve towards f(1) our pencils approaches the y-value of 3. We denote this as: 1 lim ( ) 3 x f x because as we approach f(1) from the right side (the reason for the raised + next to the 1) the value of the graph approaches 3. Because the limit from the left side is equal to the limit from the right side we can use the notation: 1 lim ( ) 3 x f x (notice the lack of a raised + or – ). If this is not the case, we say the limit does not exist.
- Fall '16
- Calculus, lim, Geometric progression, Logarithm