Attention, Mr. Pan's Calculus Class

Mr. Pan's calculus class will be in Computer Room, W101 from Monday, May22 thru Friday, May 26. Power Point Presentation Calculus Project will be done there. Please keep up good work!

P.S. Institute Luncheon will be at 12 pm on June 1, 2006.

"Bye Bye Birdie" performed by New Dorp Students

What a great performance! How talented our New Dorp students are!

My wife and I enjoyed the show very much. We lost control, and laughed throughout the show.

I am extreamly proud of our institute students. They played leading roles and other roles. Their singing, danceing, and conversing were so impressive, expressive, and professional that I almost forgot they were my students. At that moment, I did believe that they are the real characters, Albert, Rosie, parents, Birdie, ... Bravo!

Some of them may soon leave New Dorp H.S. for Colleges to pursue their dreams. I'll miss them badly.

Best wishes to our seniors!

Please don't forget to say "I love you, Mom" today.
Happy Mother's Day!

2006 AB Calculus Exam Section II 5b solution

During the last 3 days, students, and teachers were talking about the solution to free-response question 5b online or in the classroom. Different answers have been presented. which one is the right answer? If you still trust me, read my solution.

Solution to free-response question 5b:

Given dy/dx=(1+y)/x where x ≠ 0
Solve the differential equation. We get,
ln[abs(1+y)] = ln[abs(x)] + C
e^abs(1+y) = e^( ln[abs(x)] + C)
abs(1+y)=e^C* e^ln[abs(x)]
1+y=±e^C * abs(x)
1+y=k *abs(x) where k = ±e^C, and k is a constant.
y=k abs(x) - 1 where x ≠ 0 ( Note: x ≠0 is given)
Using the initial condition f(-1)=1, we get k=2.
So the solution is:
y=2 abs(x) - 1 where x ≠ 0 or the domain is all real numbers except for x=0.
Since the solution is a piecewise function, it can also be expressed as
y= -2x-1 when x<0
y= 2x-1 when x>0

Check the original equation with each piece.
When x<0, y=-2x-1
dy/dx=(1+y)/x
(-2x-1)' = ( 1 + (-2x-1 ))/x
-2 = -2 (True)

When x>0, y=2x-1
dy/dx=(1+y)/x
(2x-1)' = ( 1 + (2x-1 ))/x
2 = 2 (True)

Therefore, The solution is: y=2x - 1 where x ≠ 0.

Do you want to laugh after AP Calculus Exam?

Laugh with the babies, please!

Last Minute Reminders for the A.P. Exam

COPIED FROM THE HANDLEY MATH PAGE

Before the Exam:

Study the Quick Reference Guide on the night before the exam.
This will help keep the formulas fresh in your mind.

Review important concepts.
The exam emphasizes concepts.

Study what you do NOT know.
That may seem obvious, but many people enjoy getting the right answers so much that they only review the stuff they know.

Get a good night's sleep.
Relax. Don't stay up late studying. You need to be able to think during the exam.

On the Day of the Exam:

What to bring:
Several No. 2 pencils, black or dark-blue ballpoint pen, graphing calculator (or two!), a watch, a snack for during the break.

Eat a good breakfast and arrive on time!

Be sure that your calculator is set in RADIAN MODE!


On the Exam:

Be methodical – work neatly and carefully.
You can't get credit if the readers can't read it.


On the Multiple choice Sections:

Read each question carefully and look at the answer
choices.

Do the ones you are sure of.
Don't struggle over one that isn't working out.
remember that you have a limited amount of time.

One type of question may ask you only to set up the problem.
Looking at the answer choices may keep you from doing too much work.

Some questions ask you to choose the one true or false statement form 5 statements.
Be sure you know if you are looking for a true or a false statement.


On the Free Response Sections:
Numerical answers may be left unsimplified and in terms of e, pi, etc.
Avoid simplifying numerical answers (see note below about three-decimal accuracy).

Don't write a long essay.
You may show a number line as your analysis of the sign of the derivative – be sure to label it appropriately , for example y', y'', f ', f '' etc.

Do not explain how to do the problem you cannot do.
A general explanation without work will receive no credit. You must do the problem you are given.

If you work a problem two different ways, choose the best one and put an X
through the other one. If both are left, they will both be scored and the scores will be averaged.

Standard notation must be used – not calculator notation!

Start each problem on the Free Response Section even if you can't do it all.
They are written so that the first parts are easier in order to help you get started.

Do not let the points at the beginning keep you from getting the points at the
end.
If you can do part (c) but don't know how to do part (a) and (b), make a guess for the expression needed.

If you use your calculator to solve an equation, write the equation first.
An answer without an equation might not get full credit, even if it is correct.

If you use your calculator to find a definite integral, write the integral first.
An answer without an integral will not get full credit, even if it is correct.

Do not waste time erasing bad solutions.
Make an X over anything that you don't want the Readers to grade.

Do not use your calculator for anything except:
(a) graph functions, (b) compute numerical derivatives, (c) compute definite integrals, and (d) solve equations.

If a calculation is given as a decimal, it should be correct to three decimal
places after the decimal point.
Do not round in intermediate steps before a final calculation is made.

Some answers, the evaluation of a definite integral for example, must be written as decimals because they are found using a graphing calculator. These answers must be correct to three decimal places past the decimal point. 56.000 may be given as 56.

Too often students may choose to give decimal answers when they are not required. Once a free-response answer is entirely in terms of numbers, there is no need to change the number to a decimal. For example, the answer cos(4) + 7/2 is sufficient. If you decide to change it to a decimal, and it is correct to three decimal places, you will receive credit. However, if you change a correct answer to an incorrect decimal (including one with too few decimals), then you will lose credit.

Some of these ideas are adapted from Dan Kennedy at A.P. Central and from Lin McMullin's Teaching A.P. Calculus