How to Approach the Free-Response Section for AP Physics B & C

Partial Credit

Returning to part (b) from the example problem, it's obvious that you can get lots of partial credit even if you make a mistake or two. For example:

• If you forgot to include friction, and just set the student's force equal to ma and solved, you could still get two out of four points.
• If you solved part (a) wrong but still got a reasonable answer, say 4.5 N for the force of friction, and plugged that in correctly here, you would still get either 3 or 4 points in part (b)! Usually the rubrics are designed not to penalize you twice for a wrong answer. So if you get part of a problem wrong, but if your answer is consistent with your previous work, you'll usually get full or close to full credit.
• That said, if you had come up with a 1000 N force of friction, which is clearly unreasonable, you probably will not get credit for a wrong but consistent answer, unless you clearly indicate the ridiculousness of the situation. You'll still get probably two points, though, for the correct application of principles!
• If you got the right answer using a shortcut—say, doing the calculation of the net force in your head—you would still get full credit. However, if you did the calculation wrong in your head, then you would not get partial credit—AP graders can read what's written on the test, but they're not allowed to read your mind. Moral of the story: Communicate with the readers so you are sure to get all the partial credit you deserve.
• Notice how generous the partial credit is. You can easily get two or three points without getting the right answer and 50–75% is in the 4–5 range when the AP test is scored!

You should also be aware of some things that will NOT get you partial credit:

• You will not get partial credit if you write multiple answers to a single question. If AP graders see that you've written two answers, they will grade the one that's wrong. In other words, you will lose points if you write more than one answer to a question, even if one of the answers you write is correct.
• You will not get partial credit by including unnecessary information. There's no way to get extra credit on a question, and if you write something that's wrong, you could lose points. Answer the question fully, then stop.

The Tools You Can Use

You can use a calculator on the free-response section of the AP exam. Most calculators are acceptable—scientific calculators, programmable calculators, graphing calculators. However, you cannot use a calculator with a QWERTY keyboard, and you'd probably be restricted from using any calculators that make noise or that print their answers onto paper.1 You also cannot share a calculator with anyone during the exam.

The real question, though, is whether a calculator will really help you. The short answer is "Yes": You will be asked questions on the exam that require you to do messy calculations (for example, you might need to divide a number by π, or multiply something by Boltzmann's constant²). The longer answer, though, is "Yes, but it won't help very much." To see what we mean, look back at the hypothetical grading rubric for part (b) of the example problem we discussed earlier. Two of the four possible points are awarded for using the right equations, one point is awarded for finding the magnitude of a force using basic arithmetic, and the last point is awarded for solving a relatively simple equation. So you would get half-credit if you did no math at all, and you would get full credit just by doing some very elementary math. You probably wouldn't need to touch your calculator!

So definitely bring a calculator to the exam but don't expect that you'll be punching away at it constantly.

The other tool you can use on the free-response section is the equations sheet. You will be given a copy of this sheet in your exam booklet. It's a handy reference because it lists all the equations that you're expected to know for the exam.

However, the equations sheet can also be dangerous. Too often, students interpret the equations sheet as an invitation to stop thinking: "Hey, they tell me everything I need to know, so I can just plug-and-chug through the rest of the exam!" Nothing could be further from the truth.

First of all, you've already memorized the equations on the sheet. It might be reassuring to look up an equation during the AP exam, just to make sure that you've remembered it correctly. And maybe you've forgotten a particular equation, but seeing it on the sheet will jog your memory. This is exactly what the equations sheet is for, and in this sense, it's pretty nice to have around. But beware of the following:

• Don't look up an equation unless you know exactly what you're looking for. It might sound obvious, but if you don't know what you're looking for, you won't find it.
• Don't go fishing. If part of a free-response question asks you to find an object's momentum, and you're not sure how to do that, don't just rush to the equations sheet and search for every equation with a "P" in it.

Math and the Physics C Exam

Physics C students often worry about the math they're expected to know for the AP exam, because some of the material covered in the Physics C curriculum involves pretty complicated calculus. Maxwell's equations, for example, involve concepts that are well beyond the scope of most high school calculus classes.

But even though some fancy math shows up in the Physics C curriculum, the math on the AP exam is generally less daunting. Of the 45 points available on each free-response section, it's very rare when more than three or four of these points are awarded for evaluating an integral or derivative. So if you're not a calculus fan, it's okay to pledge to evaluate no integrals on the free-response section, and you can still get a 5 just fine!

The way you succeed without doing much calculus is to have a strong understanding of the physical meaning behind the mathematics. The problems that might seem to involve calculus—those that use an integral or derivative equation from the equations sheet—can usually be approached with algebraic methods. Remember, an integral is just the area under a graph; a derivative is just the slope of a graph. If you have to, set up an integral and don't solve it. Or explain in words what your answer should look like. Also, note that many of the equations that appear on the equations sheet as calculus expressions rarely or never need calculus. For instance, Gauss's law has a nasty integral in it, but when used correctly, Gauss's law rarely requires any calculus. Whatever you do, it is not worth the time and frustration to worry too much about the tough calculus—this isn't a math exam, and the point distribution in the rubrics reflects this fact.

Other Advice About the Free-Response Section

• Always show your work. If you use the correct equation to solve a problem but you plug in the wrong numbers, you will probably get partial credit, but if you just write down an incorrect answer, you will definitely get no partial credit.
• If you don't know precisely how to solve a problem, simply explain your thinking process to the grader. If a problem asks you to find the centripetal acceleration of a satellite orbiting a planet, for example, and you don't know what equations to use, you might write something like this: "The centripetal force points toward the center of the satellite's orbit, and this force is due to gravity. If I knew the centripetal force, I could then calculate the centripetal acceleration using Newton's second law." This answer might earn you several points, even though you didn't do a single calculation.
• However, don't write a book. Keep your answers succinct.
• Let's say that part (b) of a question requires you to use a value calculated in part (a). You didn't know how to solve part (a), but you know how to solve part (b). What should you do? We can suggest two options. First, make up a reasonable answer for part (a), and then use that answer for part (b). Or, set some variable equal to the answer from part (a) (write a note saying something like, "Let v be the velocity found in part (a)"). Then, solve part (b) in terms of that variable. Both of these methods should allow you to get partial or even full credit on part (b).
• If you make a mistake, cross it out. If your work is messy, circle your answer so that it's easy to find. Basically, make sure the AP graders know what you want them to grade and what you want them to ignore.
• If you're stuck on a free-response question, try another one. Question #6 might be easier for you than question #1. Get the easy points first, and then only try to get the harder points if you have time left over.
• Always remember to use units where appropriate.
• It may be helpful to include a drawing or a graph in your answer to a question, but make sure to label your drawings or graphs so that they're easy to understand.
• No free-response question should take you more than 15–17 minutes to solve. They're not designed to be outrageously difficult, so if your answer to a free-response problem is outrageously complicated, you should look for a new way to solve the problem, or just skip it and move on.