(E)
“Ugh ... too many letters!” you say. We disagree. Solving this problem is no different than solving the
same problem with numbers given. In fact, if the variables bother you, try solving with made-up numbers
first:
Let’s say the height h is 5 meters, and the mass of the bob is 2 kg ... well, we use conservation of
energy. Energy at the top of the swing is all potential, all mgh . So that’s 2 × 10 × 5 = 100 J of
potential energy.
At the bottom, all this energy is kinetic. So 100 . Solving, v = 10 m/s.
Now how did we get that? We set mgh = mv 2 , and solved for v . The masses cancelled, so v
= square root of 2gh . Lo and behold, that’s an answer choice!When Should You Skip a Question?
Never. There is no penalty for guessing, so guess away!Some Final Advice on Multiple-Choice Questions
• Know your pace. Take the practice exams under test conditions (45 minutes for 35 questions, or some
fraction thereof). Are you getting to all the questions? If not, you are going to need to decide your
strengths and weaknesses. Know before the exam which types of problems you want to attempt first.
Then, when you take your exam, FOLLOW YOUR PLAN!
• The multiple-choice questions do not necessarily start easy and get harder, as do SAT questions. So if
you suspect from your practice that you may be pressed for time, know that problems on your strong
topics may be scattered throughout the exam. Problem 35 might be easier for you than problem 5, so
look at the whole test.
• Speaking of time, the AP test authors know the time limit of the exam—you must average a minute and a
half per question in order to answer everything. So they are not going to write a question that really
takes three or four minutes to solve! You must always look for the approach to a problem that will let
you solve quickly. If your approach won’t get you to a solution in less than two minutes, then either
look for another approach or move on.
• One other alternative if you don’t see a reasonable direct approach to a problem: look at the answer
choices. Some might not make any sense; for example, you can eliminate any choice for a speed that is
faster than light, or a couple of answer choices to concept questions might contain obvious errors.
Guess from the remaining choices, and move on.
• Correct your practice exam. For any mistakes, write out an explanation of the correct answer and why
you got it wrong. Pledge to yourself that you will never make the same mistake twice.
How to Approach the Free-Response Section
The best thing about the free-response section of the AP exam is this: you’ve been preparing for it all
year long! “Really?” you ask. “I don’t remember spending much time preparing for it.”