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DON'T PANIC! How To Study for a Physical Science Final When You Didn't Learn Anything!

Now that finals have passed for most of the college students on the semester schedule, I'd like to reflect on the panic that arises when students in required introductory physical science classes come to the end of a course and realize that they haven't retained anything! What is the correct approach to triaging such situations?

Of course, the best way to engage with material is by answering questions that are similar to those that will be on the examination, and most professors will be kind enough to tell you what the format and types of questions will be. Generally, there are two types of questions you will find: qualitative and quantitative. I'll deal with the best way to study for each type of question in turn.
 
Qualitative Questions
The tendency here is to think that cramming and memorizing facts is the best way to go to answer such multiple choice, free response, or essay questions on qualitative subjects. However, this is not often the case. There are generally some underlying principles, patterns, or conceptual frameworks that, once understood, can lead you to the correct answer without memorization required. I'll give two examples below.
 
Chemistry
In introductory chemistry courses, often the periodic table of elements will be given as an allowed resource on the examination. Students tend to think of this as a kind of "cheat sheet", but instead they really ought to think carefully about the organizing principles of the table as a starting point for answering chemistry questions. Of particular import are understanding the differences between the rows (periods) and columns (groups or families) and why this organization scheme is chosen.

Typically, the easiest way to approach a conceptual framework of chemistry is one that treats the electron clouds of atoms as the most important feature of the element. The atomic numbers and valences follow distinct patterns in the table and related directly to the particular way that electrons fill orbitals. Students should remember that charges need to balance, that atomic numbers are associated with immutable (except in the case of nuclear reactions and radioactive decay) number of protons, that the number of electrons in a neutral atom or molecule will equal the number of protons, and that filled valence shells around nuclei are how the least reactive (and therefore most stable) materials form. These simple frameworks apply for things as simple as noble gas elements all the way to the most complicated organic molecules, and a remarkable amount of information can be gained by remembering these principles and applying them to the questions being asked.

It is important to realize that what I'm talking about here is triage-studying. There are exceptions to many of these simplistic rules and trends associated with the periodic table. But at the point when you've become convinced that you "know nothing" about a subject, it is not useful to focus on the exceptions to the rules. There may very well be questions on the test about these exceptions, but trying to get those questions right is not your job at this point. Those questions are meant to distinguish the good and the very best students in the course. Presumably, this is not the level you are at: you are simply hoping to pass the course and do well enough on the final exam so as to not be placed in academic jeopardy. So don't get hung up on the exceptions to rules. Get the basic concepts down so that you can work out responses to every practice question. If and when you've gotten to the point that there are no more questions that you "have no idea how to start", then you can start to dig deeper. But if it's last minute, you unfortunately will probably not have the time.
 
Wave Mechanics
Almost everybody has at least a rudimentary understanding of a wave as an undulating, oscillating disturbance moving through space. Most people when asked to draw waves have no problem, but the key is understanding the differences between the different features you can measure in a wave. One way to approach the subject is to think of three separate features of waves 1) extending through space, 2) repeating in time, and 3) carrying energy and momentum from one place to another. Generally, we can separate each of these features out and there are different measurable quantities associated with each feature. For 1) we can measure wavelengths as being the distance (SPACE) between successive crests or troughs of a wave. For 2) we can measure the period of the wave as being the number of successive crests or troughs that "wash over" a stationary observer while the frequency of the wave is just the reciprocal of the period. For 3) we note that the "strength" of a wave is related to a quantity called the amplitude: a measurement of the maximum amount of disturbance that takes place from when there is no wave to when there is a wave, a quantity known as the amplitude. Note that this means that when we consider the amplitude of a wave, it is not the difference between the value of whatever is "waving" at the crest and the trough, but rather half of that difference since we are really interested in the disturbance from a resting "non-wave" state.

From these simple ideas, essentially all of wave mechanics proceeds. For example, waves of constant speed will have a direct relationship between features 1) and 2) set by how fast the wave travels. Additionally, the Doppler Effect can be easily conceptualized by understanding the approaching or receding from an object creating waves will affect both the 1) and 2) features of the wave but not feature 3). These ideas tend to develop naturally from this simple conceptual picture. There are, of course, many subtleties as waves become more complicated and you allow for different waves to travel through the same locations and the same times, but once the basic ideas are understood, much of the strange and wonderful implications can be reasoned out from this simple picture.

Quantitative Questions
Students tend to me much more afraid of quantitative questions than they are of qualitative questions. However, instructors know this is true for introductory science classes and, consequently, quantitative questions are often easier than qualitative ones! Different classes will emphasize different quantitative reasoning skills, but generally introductory classes will try to focus on the following important features:
 
Consider Abandoning Your Calculator
There is often a benefit to not using your calculator. The best introductory science instructors will not allow calculators on their exams, and if this happens, you should be grateful because it means they had to put thought into their exams in order to make the questions. Even if they do allow calculators it is often useful to try to do as much as you can without. Chemistry tends to lend itself a bit more to calculator use owing to the need to calculate molecular weights that may require a certain laborious amount of arithmetic, but physics, astronomy, and earth sciences that are not focused on chemistry will often present quantitative problems that not only can be done without a calculator but are often more meaningful when done without since the questions that can be asked at the introductory level tend to be only rough estimates, to with an order of magnitude. This leads naturally to the next idea:
 
Scientific Notation
It is generally worthwhile to use scientific notation completely. The mathematics of scientific notation make doing everything but taking logarithms and peculiar exponents a piece of cake. If you find a need to take a logarithm or a peculiar exponent (such as 2/3 or 1/4) in a problem and there are no calculators on the examination, it is likely that the instructor designed the question to be compatible with doing such a thing. For example, (10 000)^(1/4) = 10 or 8^(2/3) = 4.
 
Unit Conversion
A remarkable amount of science can be done simply by understanding how units convert between each other. Students often make the mistake of not thinking carefully about this subject before a final exam since they think it to be trivial, but attention to detail when dealing with units and conversion factors are more often than not the best way to guarantee that you will not go down unnecessary rabbit holes or be distracted by calculations that are meaningless. Know what the metric prefixes mean and how to use them (they are essentially orders of magnitude) are especially important. Looking at compound units that are exponentiated is an additional clue, and should be paid close attention to when, for example, converting a length to a volume or vice versa. If you have only an hour to study before the exam, you could do worse than practicing unit conversions. For example, how many cm^3 in one m^3? How many seconds in a year? What is the density of water in kg/m^3 if its density is 1 g/cm^3?

Proportionality and Scaling
In the physical sciences, especially for quantitative questions where no calculators are allowed, a typical question will  involve not making a direct calculation of a quantity but rather seeing how changing certain characteristics of a situation will affect other characteristics of the situation. The simplest case is when a = b. If you double a, you double b. If a = 1/b, if you double a you will halve b. Or if a^2 = b/c, if you double a and keep c the same, you will quadruple b. Becoming familiar with these kinds of scaling and proportionality questions is incredibly powerful, and many physical science courses will lean heavily on these kinds of questions. Sometimes students will try to do the full calculation when all that is required is a scaling. Don't fall into this trap!

Conclusion
I hope these last-minute tips are helpful when you are studying for your final exams. Of course, nothing is better than studying over the course of the semester, but hindsight is 20/20 and there are still many things you can do to improve that grade and keep yourself from failing that required course. Remember, don't panic, take a deep breath, and work things out carefully. You'll probably find you know more than you thought you did!