OAT Equations
Today I will be going over the common equations found on the OAT. One of the most important aspects of the OAT is figuring out what equations are the most important to study. This is especially true for Physics and Quantitative Reasoning, but equations will be found in Biology and General Chemistry as well.
Note: I have created several free practice problems for this article!
For Biology, you need to know that p squared plus 2 pq plus q squared (p^2 + 2pq + q^2) gives the fraction of a population that is homozygous dominant, heterozygous, and homozygous recessive. This is the single most important equation of the section, however, you must also know how to compute genetics probabilities in reproduction situations. Here’s an example of this:
If the father has a sex-linked recessive trait (on the X chromosome, as almost all of them are), and the mother is phenotypically normal, and the allele frequency of the recessive trait in the population is .01 then what are the odds that a male child will exhibit the recessive phenotype (barring mutations)? The correct answer is .01, because he just gets a Y chromosome from the father, and his one X chromosome comes from the mother, and the probability of this chromosome containing the recessive allele is essentially equal to .01, or it’s allele frequency in the population. It’s actually a very tiny amount less, but I’m not getting into that mathematical technicality. What about the odds of a female child exhibiting the recessive phenotype? The odds are the SAME (.01) because she has to get a recessive X from the father, and then the odds of a recessive allele coming from the mother is again, essentially .01.
For General Chemistry, the most important equation is the combined gas law pv=nRt where p is pressure, v is volume, n is number of moles, R is the gas constant (be sure its units match with the units from the other variables!) and t is temperature in kelvins. You should know stoichiometry cold! You must understand how to work with molarity, molality, gram formula mass, how to balance oxidation-reduction reactions, etc.
Here is another practice problem:
If I dissolve 117 grams of NaCl in 4 liters of H2O then what is the molarity of the solution? First, we find out how many moles of NaCl are being dissolved. To do this we divide 117 grams by the gram formula mass for NaCl, which is 58.5 (found by adding the atomic mass of Na and Cl). This gives us 117/58.5 equals 2 moles NaCl is being dissolved. Molarity is a measurement of moles of solute per liter of solution. The solute is the thing being dissolved, the NaCl. The solvent is the thing dissolving it, or the water. We will ignore the volume of the NaCl as it isn’t relevant to the problem. So our total volume is 4 liters of solution, and we have 2 moles of solute, so 2/4 gives us 0.5 moles per liter, which is a molarity of 0.5
Another important concept is enthalpy.
A simple enthalpy example: How much energy, in calories (although they’d more likely ask in joules), does it take to heat 3 grams of ice from -8 Celsius to 142 degrees Celsius? The answer is 3 x .5 x 8 plus 3 x 80 plus 3 x 1 x 100 plus 3 x 540 plus 3 x .5 x 42 And to find it in joules, multiply that whole answer by roughly 4.18 In the first step, we are finding the amount of energy to heat three grams of ice from -8 Celsius to 0 Celsius. In the next step, we find how much energy it takes to melt the ice. Then we find out how much it takes to heat the now liquid water to 100 Celsius. Next, we find out how much energy it takes to boil the water to steam. Finally, we calculate how much energy is needed to heat the steam from 100 Celsius to 142 Celsius. Our final answer is just the sum of all of these steps.
For Quantitative Reasoning, know all about the various trig. setups (including arc functions), and know the values for the trig. functions of the following angles (in degrees): 0, 30, 45, 60, 90, 180, 270, 360, and understand how to inter-convert between degrees and radians, know the different right triangle ratios (such as 3, 4, 5, or 5, 12, 13) and the multiples of those, etc. The rest of it is more or less just applying algebra. There are also plenty of shortcuts that can save you precious time throughout this section; I’ll go over some of those in future articles.
Here’s a quick example of a Quantitative Reasoning problem: sin of 11 pi over 12 is equal to which of the following: arcsin of pi over six (absurd choice) sin of 13 pi over 12 (close, except the sine function is negative in quadrant 3) or sin of pi over 12 (correct answer). Note the inherent symmetry of the various trig. functions, because if you can visualize the curves, it will help you avoid blatantly wrong answers.
For Physics, there’s so many equations that it will be getting its own article! However, I’ll give you a quick overview here. Know the equations for projectile motion, work, energy (potential and kinetic energy), momentum including angular momentum, friction, density, pressure, spring equations (for energy, frequency and period as well), know how to interconvert pretty much all the various units, know the equations for electricity, magnetism, and circuits (only bother with DC circuits, not AC circuits) and know the lensmaker’s equation. That’s a lot, which is why I’ll be writing a separate article just for Physics.
Thanks for reading!
Sincerely,
Dale Paynter
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