SAT  II  Physics  Resources

Introduction to SAT II Physics

The best way to do well on SAT II Physics is to be really good at physics. For that, there is no substitute. But the physics whiz who spends the week before SAT II Physics cramming on Lagrangian mechanics and Dirac notation probably won’t fare any better than the average student who reviews this book carefully. Why? Because SAT II Physics Tests (and first-year university courses) do not cover Lagrangian mechanics or Dirac notation. Take this moment to sigh with relief.

This introduction will tell you precisely what SAT II Physics will test you on, how the test breaks down, and what format the questions will take. You should read this information carefully and base your study plan around it. There’s no use spending hours on end studying for stuff that’s not relevant to the test. Knowing nothing about electromagnetic induction will hurt you on the test, but nowhere near as much as knowing nothing about optics will.

1. Content of SAT II Physics

Math and physics go hand in hand, right? You might be surprised, then, to learn that you aren’t allowed to use a calculator on SAT II Physics. The math required of you never goes beyond simple arithmetic and manipulation of equations. You have, on average, 48 seconds to answer each question, and the people at ETS realize that isn’t enough time to delve into problems involving simultaneous equations or complex trigonometry. They’re more interested in testing your grasp of the basic concepts of physics. If you’ve grasped these concepts, your weakness in math isn’t going to hurt you.

ETS breaks down the concepts you need to know for the test into six categories:

 Here’s some other helpful information:

You need to know: the formulas expressing physical relationships (such as F = ma), how to manipulate equations, how to read a graph

You don’t need to know: trig identities, calculus, three-dimensional vectors and graphs, physical constants (such as G = 6.6710–11 N·m2 ⁄ kg2).

2. Format of SAT II Physics

SAT II Physics is a one-hour-long test composed of 75 questions and divided into two parts. You can answer questions in any order you like, though you’re less likely to accidentally leave a question out if you answer them in the order in which they appear. Part A—classification questions—takes up the first 12 or 13 questions of the test, while Part B—five-choice completion questions—takes up the remaining 62 or 63 questions.

Part A: Classification Questions

Classification questions are the reverse of normal multiple-choice question: they give you the answers first and the questions second. You’ll be presented with five possible answer choices, and then a string of two to four questions to which those answer choices apply. The answer choices are usually either graphs or the names of five related laws or concepts. Because they allow for several questions on the same topic, classification questions will ask you to exhibit a fuller understanding of the topic at hand.

The level of difficulty within any set of questions is generally pretty random: you can’t expect the first question in a set to be easier than the last. However, each set of classification questions is generally a bit harder than the one that came before. You should expect questions 11–13 to be harder than questions 1–4.

Classification Question Example

Directions: Each set of lettered choices below refers to the numbered questions immediately following it. Select the one lettered choice that best answers each question and then blacken the corresponding space on the answer sheet. A choice may be used once, more than once, or not at all in each set.

Questions 1–3

A boy throws a ball straight up in the air and then catches it again.

Explanation

You can usually answer classification questions a bit more quickly than the standard five-choice completion questions, since you only need to review one set of answer choices to answer a series of questions.

The answer to question 1 is B. The ball’s position with respect to time can be expressed by the equation y = –1/2 gt2, where g is the downward, acceleration due to gravity. As we can see, the graph of y against t is an upside-down parabola. In more intuitive terms, we know that, over time, a ball thrown in the air will rise, slow down, stop, and then descend.

The answer to question 2 is E. The acceleration due to gravity means that the velocity of the ball will decrease at a steady rate. On the downward half of the ball’s trajectory, the velocity will be negative, so E, and not A, is the correct graph.

The answer to question 3 is D. The acceleration due to gravity is constant throughout the ball’s trajectory, and since it is in a downward direction, its value is negative.

Don’t worry if the question confused you and the explanations didn’t help. This material and more will be covered in Chapter 2: Kinematics. This was just an exercise to show you how a classification question is formatted.

Part B: Five-Choice Completion Questions

These are the multiple-choice questions we all know and love, and the lifeblood of any multiple-choice exam. You know the drill: they ask a question, give you five possible answer choices, and you pick the best one. Got it? Good. An example appears below.

While you’ll often find two or three questions in a row that deal with the same topic in physics, there is no pattern. You might find a question on modern physics followed by a question on dynamics followed by a question on optics. However, there is a general tendency for the questions to become more difficult as you progress.

Five-Choice Completion Question Example:

Directions: Each of the questions of incomplete statements below is followed by five suggested answers or completions. Select the one that is best in each case and then fill in the corresponding oval on the answer sheet.

Explanation

The answer to this question is C. The key lies in remembering the ideal gas law: PV = nRT. According to this formula, an increase in temperature is accompanied by an increase in pressure. A is wrong, since the average kinetic energy of gas molecules corresponds to their temperature: if the temperature increases, so does the average kinetic energy of the molecules. B is wrong because we’re dealing with a closed container: the mass cannot either increase or decrease. D is wrong because a gas must be cooled, not heated, to change phase into a liquid. Finally, E is wrong because the specific heat of any substance is a constant, and not subject to change. We’ll touch on all this and more in Chapter 9: Thermal Physics.

3. How Your Knowledge Will Be Tested

There are three different levels on which your understanding of physics may be tested. While questions on kinematics often require that you make use of some of the formulas for kinematic motion, questions on quantum physics or atomic structure may often ask just that you remember the name of a particular concept. Knowing the different ways in which your knowledge may be tested should help you better prepare yourself for the exam.

Recall (20–33% of the test)

These are questions of the either-you-know-it-or-you-don’t variety. They test your understanding of the basic concepts of physics. No equations or calculations are necessary for these questions. They’re simply a matter of knowing your stuff.

Single-Concept Problem (40–53% of the test)

These questions expect you to recall, and make use of, one physical relationship, formula, or equation. This might involve plugging numbers into a kinematic equation of motion, or it might involve recalling the equation E = hf and solving for E or f. These questions test to see if you know important formulas and how to apply them.

Multiple-Concept Problem (20–33% of the test)

These questions expect you to bring together two or more different relationships, formulas, or equations. This could involve bringing together two formulas from the same subject—for instance, a problem in linear momentum that requires you to calculate the momentum of an object before a collision so that you can calculate its velocity after the collision—or it may bring together formulas from two different subjects—for instance, a problem that involves an electric point charge moving in circular motion in a magnetic field. These questions test not only your knowledge of physical relationships, but also your ability to integrate more than one in a complex problem.

You’re probably thinking that the recall questions are the easiest, and the multiple-concept problems are the hardest. This isn’t necessarily true. Most people have an easier time bringing together two simple principles of mechanics than recalling the significance of the Rutherford experiment. You’ll find all three types of questions throughout the test, and at different levels of difficulty. Ultimately, every question tests the very same thing: whether you’ve grasped the basic principles of physics.

4. Strategies for Taking SAT II Physics

Physics Hint 1: Know Those Formulas!

You aren’t allowed to bring a calculator into the SAT II, nor are you allowed to bring in a sheet of paper with useful information on it. That means that if you haven’t memorized formulas like F = ma and

you’re going to lose a lot of points. As we said earlier, 67–80% of the test requires that you know your formulas.

This doesn’t mean you have to do a lot of rote memorization. As you become more familiar with the principles of physics, you’ll find that the equations that express these principles will become increasingly intuitive. You’ll find patterns: for instance, the force exerted at any point in a field, be it a gravitational field or an electric field, is inversely proportional to r2. That’s why Coulomb’s Law and Newton’s Law of Gravitation look similar. Knowing your physics will help you know your formulas.

A lot of people feel burdened coming into an exam with lots of formulas and equations in their head. It can feel like your mind is “full,” and there’s no room for the problem solving at hand. If you have trouble remembering formulas, you might want to look them over carefully in the minutes before the test, and then, before you even look at the first question, write down the formulas you have a hard time remembering on the back of the question booklet. That way, you can refer back to them without any painful effort of recollection.

Physics Hint 2: Estimate

Don’t dive blindly into five possible answer choices until you know what you’re looking for. The first way to know what you’re looking for is to understand the question properly. Once you understand the question, get a rough sense of what the correct answer should look like.

Estimation is only useful for questions involving calculation: you can’t “estimate” which Law of Thermodynamics states that the world tends toward increasing disorder. In questions involving a calculation, though, it may save you from foolish errors if you have a sense of the correct order of magnitude. If you’re being asked to calculate the mass of a charging elephant, you can be pretty confident that the answer won’t be 2 kg, which would be far too small, or

kg, which would be far too big. Estimation is a good way to eliminate some wrong answers when you’re making an educated guess.

Physics Hint 3: Put It on Paper

Don’t be afraid to write and draw compulsively. The first thing you should do once you’ve made sure you understand the question is to draw a diagram of what you’re dealing with. Draw in force vectors, velocity vectors, field lines, ray tracing, or whatever else may be appropriate. Not only will a visual representation relieve some of the pressure on your beleaguered mind, it may also help the solution jump right off the page at you.

Drawing graphs can also make a solution appear out of thin air. Even if a problem doesn’t ask you to express anything in graphic terms, you might find that a rough sketch of, say, the velocity of a particle with respect to time will give you a much clearer sense of what you’re dealing with.

And don’t forget to write down those equations! Writing down all the equations you can think of may lead you to a correct answer even if you don’t really understand the question. Suppose you know the problem deals with an electric circuit, and you’re given values for current and electric potential. Write down equations like V = IR and P = IV, plug in values, fiddle around a little, and see if you can come up with an answer that looks right.

Physics Hint 4: Answers Are Not Convoluted

Remember, on SAT II Physics you’re not allowed to use a calculator, and you’re only given, on average, 48 seconds to answer each question. If you’re working on a problem and find yourself writing out lines and lines of simultaneous equations, trying to figure out

or trying to recall your trig identities, you’re probably on the wrong track. These questions are designed in such a way that, if you understand what you’re being asked, you will need at most a couple of simple calculations to get the right answer.

Physics Hint 5: Eliminate Wrong Answers

In General Hint 6: Know How To Guess, we explained the virtues of eliminating answers you know to be wrong and taking a guess. On most questions, there will be at least one or two answer choices you can eliminate. There are also certain styles of questions that lend themselves to particular process-of-elimination methods.

Classification Questions

The weakness of classification questions is that the same five answer choices apply to several questions. Invariably, some of these answer choices will be tempting for some questions but not for others. For instance, you can be pretty sure that kinetic energy isn’t measured in hertz: E may be a tempting answer choice for other questions but not for that one, so you can eliminate it.

Another point that may help you guess in a pinch is that you’ll rarely find that the same answer choice is correct for two different questions. The directions for classification questions explicitly state that an answer choice “may be used once, more than once, or not at all,” but on the whole, the ETS people shy away from the “more than once” possibility. This is by no means a sure bet, but if you’re trying to eliminate answers, you might want to eliminate those choices that you’ve already used on other questions in the same set.

If you’re wondering, the answers to the above questions are 1 A, 2 E, and 3 D.

“EXCEPT” Questions

Questions of the “EXCEPT” variety contain a bunch of right answers and one wrong answer, and it’s generally possible to spot one or two right answers. Even if you can’t answer the question confidently, you might remember that alpha particles have a positive charge and that they are identical to the nucleus of a helium atom. Already, you’ve eliminated two possible answers, and can make a pretty good guess from there.

If you’re interested, the answer is D: Rutherford’s gold foil experiment showed that alpha particles would occasionally deflect off the gold foil at extreme angles, thus proving that atoms have nuclei.

“I, II, and III” Questions

In this style of multiple-choice question, the “I, II, and III” questions provide you with three possible answers, and the five answer choices list different combinations of those three. There’s an upside and a downside to questions like these. Suppose you know that a concave mirror has f > 0 and a convex mirror doesn’t, but you’re not sure about a converging lens. The downside is that you can’t get the right answer for sure. The upside is that you can eliminate B, D, and E, and have a 50% chance of guessing the right answer. As long as you’re not afraid to guess—and you should never be afraid to guess if you’ve eliminated an answer—these questions shouldn’t be daunting.

The value of f for a converging lens is positive, so the answer is C.

Physics Hint 6: Be Flexible

Knowing your physics formulas is a must, but they’re useless if you don’t know how to apply them. You will probably never be asked to calculate the force acting on an object given its mass and acceleration. Far more likely, you will be asked for the acceleration given its mass and the force acting on it. Knowing that F = ma is useless unless you can also sort out that a = F⁄m.

The ETS people don’t want to test your ability to memorize formulas; they want to test your understanding of formulas and your ability to use formulas. To this end, they will word questions in unfamiliar ways and expect you to manipulate familiar equations in order to get the right answer. Let’s look at an example.

A satellite orbits the Earth at a speed of 1000 m⁄s. Given that the mass of the Earth is

kg and the universal gravitational constant is N · m2 ⁄ kg2, what is the best approximation for the radius of the satellite’s orbit?

m

m

m

m

m

What’s the universal gravitational constant? Some people will know that this is the G in the equation for Newton’s Law of Gravitation: . Other people won’t know that G is called the “universal gravitational constant,” and ETS will have successfully separated the wheat from the chaff. It’s not good enough to know some formulas: you have to know what they mean as well.

Given that we know what the universal gravitational constant is, how do we solve this problem? Well, we know the satellite is moving in a circular orbit, and we know that the force holding it in this circular orbit is the force of gravity. If we not only know our formulas, but also understand them, we will know that the gravitational force must be equal to the formula for centripetal force,

. If we know to equate these two formulas, it’s a simple matter of plugging in numbers and solving for r.

Knowing formulas, however, is a small part of getting the right answer. More important, you need to know how to put these two equations together and solve for r. On their own, without understanding how to use them, the equations are useless.

But there are two slightly underhanded ways of getting close to an answer without knowing any physics equations. These aren’t foolproof methods, but they might help in a pinch.

Slightly Underhanded Way #1: Elimination through Logic

By scanning the possible answer choices, you can see that the answer will begin either with a 4 or a 2.5. There are three options beginning with 4 and only two beginning with 2.5. Odds are, the correct answer begins with 4. The test makers want to give you answer choices that are close to the correct answer so that, even if you’re on the right track, you might still get caught in a miscalculation.

Second, make a rough estimate. At what sorts of distances might a satellite orbit? We can eliminate A immediately: that answer has our satellite orbiting at 4 cm from the center of the Earth! That leaves us with a choice between B and C. Those aren’t bad odds for guessing.

Slightly Underhanded Way #2: Work with the Letters

This is a method for those of you who like manipulating equations. From looking at the answer choices, you know the answer will be in meters. You’ve been given three quantities, one expressed in m/s, one expressed in kg, and one expressed in N·m2/kg2. These are the only three quantities you’ll be asked to draw upon in order to get your answer. Because F = ma, you know you can substitute kg·m/s2 for N. So a quantity expressed in N·m2/kg2 can equally be expressed in m3/kg·s2.

The trick, then, is to combine a quantity expressed in these terms with a quantity expressed in meters per second and a quantity expressed in kilograms, and wind up with a quantity expressed solely in meters. To do that, you need to get rid of the “kg” and the “s” by canceling them out. Start by canceling out the “kg”: