Strategies for SAT II Physics

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 2 × 10⁶ kg, which would be far too big. Estimation is a good way to eliminate some wrong answers when you’re making an educated guess.

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.

Remember, on subject test 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.

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

Questions 1–3 relate to the following quantities:

• A. Frequency
• B. Amplitude
• C. Period
• D. Wavelength
• E. Kinetic Energy

1. Which is measured in hertz?
2. For a mass on a spring, which is maximized when the displacement of the mass from its equilibrium position is zero?
3. Which quantity is not applied to pendulum motion?

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 ₁A,₂E, and₃D.

All of the following are true about an α-particle EXCEPT

(A) It has an atomic mass of 4

(B) It carries a positive charge

(C) It is identical to the nucleus of a helium atom

(D) It will always pass right through a thin sheet of gold foil

(E) It contains two neutrons

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.

For which of the following is f > 0:
I. Concave mirror
II. Convex mirror
III. Converging lens

(A) I only

(B) II only

(C) I and III only

(D) II and III only

(E) I, II, and III

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.

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 6.0 × 10 ²⁴kg and the universal gravitational constant is 6.67 × 10^-11

N · m² ⁄ kg²,what is the best approximation for the radius of the satellite’s orbit?

(A) 4 ×10^-2m

(B) 4 ×10⁸m

(C) 4 ×10¹²m

(D) 2.25 ×10⁴m

(E) 2.25 ×10¹⁰m

What’s the universal gravitational constant? Some people will know that this is the G in the equation for Newton’s Law of Gravitation:F=G(m₁)G(m₂)/r². 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,F=mv²/r. 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.

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.

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”:

Now you need to cancel out the “s2” in the denominator. Let’s divide by the square of our “m/s” quantity:

There you have it. You didn’t need to use a single formula to get the answer. You just had to be aware of the terms in which your answer needed to be expressed, and manipulate the quantities you were given in the question.

Word to the wise: don’t use this method unless you’re absolutely stumped. It can backfire, and is of course no substitute for careful reasoning.