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What math do I need to know for the Physics GRE?

Posted: Wed Aug 12, 2009 4:05 am
by cooper
I was working on practice test 0177, problem 51. It is easy to solve using Malus's law. However, one step in the solution requires knowing the cosine of 45 degrees. This is easy enough with a calculator, but calculators aren't allowed on the exam (unless I am SERIOUSLY misinformed). So what do I have to do? Do I have to spend time memorizing the signs and cosines of different values so I can get questions like problem 51 correct on the exam?

While we are on the subject, another problem on test 0177 (I forget which problem) required a knowledge of the value of ln 4, or something like that. In my Physics courses, whenever I had to solve something like that I would use a calculator, which, again, isn't allowed on the exam. I can't solve it without a calculator. So what should I do? Do I have to spend time memorizing the values of different ln values for the Physics GRE? What else about math should I teach myself (or memorize)? Is there a better way to go about solving problems like 51 other than memorizing the values of different cosines? Thanks.

Re: What math do I need to know for the Physics GRE?

Posted: Wed Aug 12, 2009 10:28 am
by physics_auth
I would recommend you learn by heart some arithmetical values, since it is the quickest way to save time. For example, it is ok if you learn the sine and cosine of 30, 45, 60, 0 and 90 degrees by heart. Learn also by heart that SqrtP{2} = 1.41 and Sqrt{3} = 1.73. As for logarithms you need to know some basic knowledge on how to handle the logarithms with 10 as a base, how to handle sums and differences of logarithms (which turn to products and ratios of their arguments respectively), and it would be advisable to learn the values of lne = 1, ln2 = 0.69 and ln1 = 0. Learn also by heart some useful combinations of physics constants: Take for example, hc = 12.4 keV * A {A = 10^-10 m} or (kT)room = (1/40) eV. Knowing such combinations by heart can help sb manipulate the various formulas with greater convenience and more confidently! If, in the real test, you meet some other calculation like the one you mentioned then: ln4 = 2ln2 = 2* 0.7 = 1.4, roughly, and that's it. Remember also, some basic propeties of logarithms like ln(x^y) = y*lnx, x>0. Sometimes, in the real test, when the answer to one question contains strange calculations like for example the cos(15), then it is also probable to see this factor appeared as it is in the quoted answers {since it is difficult for sb to know by heart cos(15)}, but it is not always such that ... . Under different circumstances you could act like this: cos0 > cos15 > cos30 or 1 > cos15 > Sqrt{3} / 2 = 1.7 /2 = 0.85, thus you immediately know where cos(15) is confined and check the possible answers to see which fits with the result you found (even approximately).

... and as a final piece of advice: get rid of your calculator as soon as possible since it takes some time to start doing calculations "by hand". Do not defer this till the final days! When working by hand do not hesitate to make approximations (but do not overdo it, for instance do not make an approximation that would lead to a speed greater than c and so on).

Re: What math do I need to know for the Physics GRE?

Posted: Wed Aug 12, 2009 10:37 am
by grae313
These are things that you absolutely have to know, and are things that every physics major knows like the days of the week.

Memorize sin, cos, and tan of 0, 30, 45, 60, and 90 degrees and of course know their equivalents in radians.

Also memorize the basic triangles, like a 45,45,90 triange is x, x, x root(2), a 30,60,90 triange is x, 2x, x root(3)

and physics_auth is absolutely right, make sure you are not using a calculator for ANY practice problems, even if they are non-PGRE problems that are a bit harder, just practice estimating and doing back-of-the-envelope calculations.

Re: What math do I need to know for the Physics GRE?

Posted: Sat Aug 15, 2009 7:33 am
by cooper
Thanks for the very detailed answer phys_auth, you were very helpful. Thanks for the follow up answer Jessie.