端木·宇 2008-6-19 20:46
SAT II Physics Test-Taking Strategies
All the strategies discussed above can be applied equally to SAT IIPhysics and SAT II Modern Hebrew. That’s why they’re called “generalhints.” However, as you may have noticed, there are a number ofdifferences between the study of physics and the study of modernHebrew. Because physics is unlike modern Hebrew, and even unlike mathand chemistry, there are a number of strategies that apply uniquely toSAT II Physics. Some of these strategies will help you out in physicsgenerally, while some are suited to the unique idiosyncrasies of theSAT II format.
[b] Physics Hint 1: Know Those Formulas![/b]
You aren’t allowed to bring a calculatorinto the SAT II, nor are you allowed to bring in a sheet of paper withuseful information on it. That means that if you haven’t memorizedformulas like [i]F = ma[/i] and [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/89f16a3eae0881d7a41b52a2aa4926b3.gif[/img] 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 ofrote memorization. As you become more familiar with the principles ofphysics, you’ll find that the equations that express these principleswill become increasingly intuitive. You’ll find patterns: for instance,the force exerted at any point in a field, be it a gravitational fieldor an electric field, is inversely proportional to [i]r[/i]2. 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 anexam with lots of formulas and equations in their head. It can feellike your mind is “full,” and there’s no room for the problem solvingat hand. If you have trouble remembering formulas, you might want tolook them over carefully in the minutes before the test, and then,before you even look at the first question, write down the formulas youhave a hard time remembering on the back of the question booklet. Thatway, you can refer back to them without any painful effort ofrecollection.
[b] Physics Hint 2: Estimate[/b]
This hint goes hand in hand with [b]General Hint 5: Know What You’re Being Asked[/b].Don’t dive blindly into five possible answer choices until you knowwhat you’re looking for. The first way to know what you’re looking foris to understand the question properly. Once you understand thequestion, get a rough sense of what the correct answer should look like.
Estimation is only useful for questionsinvolving calculation: you can’t “estimate” which Law of Thermodynamicsstates that the world tends toward increasing disorder. In questionsinvolving a calculation, though, it may save you from foolish errors ifyou have a sense of the correct order of magnitude. If you’re beingasked to calculate the mass of a charging elephant, you can be prettyconfident that the answer won’t be 2 kg, which would be far too small, or [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/8ab6175c051ba06fd1e3ec2b1f2cecaa.gif[/img]kg, which would be far too big. Estimation is a good way to eliminate some wrong answers when you’re making an educated guess.
[b] Physics Hint 3: Put It on Paper[/b]
Don’t be afraid to write and drawcompulsively. The first thing you should do once you’ve made sure youunderstand the question is to draw a diagram of what you’re dealingwith. Draw in force vectors, velocity vectors, field lines, raytracing, or whatever else may be appropriate. Not only will a visualrepresentation 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 solutionappear out of thin air. Even if a problem doesn’t ask you to expressanything 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 muchclearer sense of what you’re dealing with.
And don’t forget to write down thoseequations! Writing down all the equations you can think of may lead youto a correct answer even if you don’t really understand the question.Suppose you know the problem deals with an electric circuit, and you’regiven values for current and electric potential. Write down equationslike [i]V = IR[/i] and [i]P = IV[/i], plug in values, fiddle around a little, and see if you can come up with an answer that looks right.
[b] Physics Hint 4: Answers Are Not Convoluted[/b]
Remember, on SAT II Physics you’re not allowed to use a calculator, and you’re only given, on average, 48seconds to answer each question. If you’re working on a problem andfind yourself writing out lines and lines of simultaneous equations,trying to figure out [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/0dcc6d14cf6446fe90221fe81eb83dc6.gif[/img]or trying to recall your trig identities, you’re probably on the wrongtrack. These questions are designed in such a way that, if youunderstand what you’re being asked, you will need at most a couple ofsimple calculations to get the right answer.
[b] Physics Hint 5: Eliminate Wrong Answers[/b]
In [b]General Hint 6: Know How To Guess[/b],we explained the virtues of eliminating answers you know to be wrongand taking a guess. On most questions, there will be at least one ortwo answer choices you can eliminate. There are also certain styles ofquestions that lend themselves to particular process-of-eliminationmethods.
Classification Questions
[u]Questions 1–3[/u] 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?Which quantity is not applied to pendulum motion?
3.
The weakness of classification questions isthat the same five answer choices apply to several questions.Invariably, some of these answer choices will be tempting for somequestions but not for others. For instance, you can be pretty sure thatkinetic energy isn’t measured in hertz: [b]E[/b] 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 apinch is that you’ll rarely find that the same answer choice is correctfor two different questions. The directions for classificationquestions explicitly state that an answer choice “may be used once,more than once, or not at all,” but on the whole, the ETS people shyaway from the “more than once” possibility. This is by no means a surebet, but if you’re trying to eliminate answers, you might want toeliminate those choices that you’ve already used on other questions inthe same set.
If you’re wondering, the answers to the above questions are 1 [b]A[/b], 2 [b]E[/b], and 3 [b]D[/b].
“EXCEPT” Questions
All of the following are true about an [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/2cb28a944df97a78e6453eea972f70bc.gif[/img]-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 abunch of right answers and one wrong answer, and it’s generallypossible to spot one or two right answers. Even if you can’t answer thequestion confidently, you might remember that alpha particles have apositive charge and that they are identical to the nucleus of a heliumatom. Already, you’ve eliminated two possible answers, and can make apretty good guess from there.
If you’re interested, the answer is [b]D[/b]:Rutherford’s gold foil experiment showed that alpha particles wouldoccasionally deflect off the gold foil at extreme angles, thus provingthat atoms have nuclei.
“I, II, and III” Questions
For which of the following is [i]f[/i] > 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 youknow that a concave mirror has [i]f[/i] > 0and a convex mirror doesn’t, but you’re not sure about a converginglens. The downside is that you can’t get the right answer for sure. Theupside is that you can eliminate [b]B[/b], [b]D[/b], and [b]E[/b], andhave a 50% chance of guessing the right answer. As long as you’re notafraid to guess—and you should never be afraid to guess if you’veeliminated an answer—these questions shouldn’t be daunting.
The value of [i]f[/i] for a converging lens is positive, so the answer is [b]C[/b].
[b] Physics Hint 6: Be Flexible[/b]
Knowing your physics formulas is a must, butthey’re useless if you don’t know how to apply them. You will probablynever be asked to calculate the force acting on an object given itsmass and acceleration. Far more likely, you will be asked for theacceleration given its mass and the force acting on it. Knowing that [i]F = ma[/i] is useless unless you can also sort out that [i]a = F⁄m[/i].
The ETS people don’t want to test yourability to memorize formulas; they want to test your understanding offormulas and your ability to use formulas. To this end, they will wordquestions in unfamiliar ways and expect you to manipulate familiarequations in order to get the right answer. Let’s look at an example.
[size=2]A satellite orbits the Earth at a speed of 1000 m⁄s. Given that the mass of the Earth is [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/07c6cc2c055b10e189d78682c72f6775.gif[/img]kg and the universal gravitational constant is [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/bdc68ee4ee1ea9fbc558b5031d9db428.gif[/img]N · m2 ⁄ kg2, what is the best approximation for the radius of the satellite’s orbit?[/size]
(A)[img]http://www.51sat.net/Article/UploadFiles/200709/20070906110927269.gif[/img]m
(B)[img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/aae3c440a3375d5f34615e1c18635c9c.gif[/img]m
(C)[img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/dac16975a0f745f0f97d9644a01f95cd.gif[/img]m
(D)[img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/31a27cf4505ed12e458993bf43cc0528.gif[/img]m
(E)[img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/f4087a9a5ee986b681c1d56c4491ac87.gif[/img]m
What’s the universal gravitational constant? Some people will know that this is the [i]G[/i] in the equation for Newton’s Law of Gravitation: [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/f071c4392a3284c5ad2bcc1a4e5dc77e.gif[/img]. Other people won’t know that [i]G[/i]is called the “universal gravitational constant,” and ETS will havesuccessfully separated the wheat from the chaff. It’s not good enoughto know some formulas: you have to know what they mean as well.
Given that we know what the universalgravitational constant is, how do we solve this problem? Well, we knowthe satellite is moving in a circular orbit, and we know that the forceholding it in this circular orbit is the force of gravity. If we notonly know our formulas, but also [i]understand[/i] them, we will know that the gravitational force must be equal to the formula for centripetal force, [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/1d8c491316408a134669873058b39509.gif[/img]. If we know to equate these two formulas, it’s a simple matter of plugging in numbers and solving for [i]r[/i].
Knowing formulas, however, is a small partof getting the right answer. More important, you need to know how toput these two equations together and solve for[i] r[/i]. On their own, without understanding how to use them, the equations are useless.
But there are two slightly underhanded waysof getting close to an answer without knowing any physics equations.These aren’t foolproof methods, but they might help in a pinch.
[b]Slightly Underhanded Way #1: Elimination through Logic[/b]
By scanning the possible answer choices, youcan see that the answer will begin either with a 4 or a 2.5. There arethree options beginning with 4 and only two beginning with 2.5. Oddsare, the correct answer begins with 4. The test makers want to give youanswer choices that are close to the correct answer so that, even ifyou’re on the right track, you might still get caught in amiscalculation.
Second, make a rough estimate. At what sorts of distances might a satellite orbit? We can eliminate [b]A[/b] immediately: that answer has our satellite orbiting at 4 cm from the center of the Earth! That leaves us with a choice between [b]B[/b] and [b]C[/b]. Those aren’t bad odds for guessing.
[b] Slightly Underhanded Way #2: Work with the Letters[/b]
This is a method for those of you who likemanipulating equations. From looking at the answer choices, you knowthe answer will be in meters. You’ve been given three quantities, oneexpressed 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 [i]F = ma[/i], 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 quantityexpressed in these terms with a quantity expressed in meters per secondand a quantity expressed in kilograms, and wind up with a quantityexpressed 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”:
[align=center][img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/7078423cd409331d2980254c8c6d56e5.gif[/img][/align]
Now you need to cancel out the “s2” in the denominator. Let’s divide by the square of our “m/s” quantity:
[align=center][img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/b3452f0e3ff9e5d43041ef828676cccd.gif[/img][/align]
There you have it. You didn’t need to use asingle formula to get the answer. You just had to be aware of the termsin which your answer needed to be expressed, and manipulate thequantities you were given in the question.
Word to the wise: don’t use this methodunless you’re absolutely stumped. It can backfire, and is of course nosubstitute for careful reasoning.
[[i] 本帖最后由 端木·宇 于 2008-6-19 20:51 编辑 [/i]]
