It’s 2015, there is now the new MCAT, good luck to all of the new generation taking it. It’s something we all go through, so no matter how you do it’s a feat that you’re taking it. A lot of people start off as premeds, and then perhaps find something else that suits them better. But, people who take the MCAT have pretty much signed the premed contract with their blood. It’s a surreal experience when it eventually hits you that you’re be sitting for the exam a few weeks, and it will literally help shape your destiny. I took mine a few years back, a two years before I applied to medical school so I was one of the last to have the essays included. They eventually removed the essay portion, it was a pain to interpret if it even meant anything. Besides that, there are different forms of communication, and perhaps speed writing essays isn’t the most useful metric for who’ll make a good doctor. Personally, I liked the essay portion because it was a nice intermission between more rigorous sections. At the time, I was a paid contributing writer, so I didn’t practice essays for the MCAT. So, because I’ve never attempted them before it felt less draconian and repetitive as reading passages and clicking answer selections.
Though, I remember having a terrible week coming into the MCAT, including the night before the exam. Somehow, I had angered the MCAT gods that week, that night before dogs across my neighborhood barked from about 3:30-6 AM. So, instead of sleeping in for the MCAT, I was watching the History channel (this was way back when the history channel actually showed history, and MTV already had lost interest in music etc). During my exam, I was tired, delirious, and just ready to plow through the MCAT so I could go to a bar and celebrate my last day seeing the MCAT. If I think back about one of my essays, I was so giddy, I recall I wrote about hamburgers. When I finished the exam, for a brief second, I thought about not sending my score as you have that option. But, I thought, “NEVER AGAIN!”, and I pressed submit. I always feel lousy after exams, even if I’m prepared. A month later, I found out my independent dual readers at the AMCAS liked my hamburger rhetoric and I received a reasonable ‘matriculating score’, and I’m very proud I wrote about hamburgers. You’ll have your own experience, including some bad days and good days.
The old MCAT was around for over 20-years, and this allowed for the AAMC to gather a lot of data about correlation (but not necessarily causation) of the data. The old MCAT had a maximum score of 45, with 3 sections each worth 15 points, and for most of the exam’s shelf-life an essay. For all people who take the MCAT, the national average was about 24 points. The average matriculant for US MD programs had gradual creep up, from about 29 to 31 towards the end of the exam when message boards, tutors, and prep companies had the MCAT down to a science (no pun intended). Please note that because we’re talking only of averages we’re throwing out a lot of higher or lower scores that go into medical school and did just fine, an average score and a person’s score are not the same thing. We survived the MCAT, I can only imagine how those before felt with their paper test (I like paper tests). But, one thing is certain you’ll survive the new one, good luck and do your best!
At the end of the day, it’s just part of your application. So a bad score won’t doom you but a great score won’t buy you an acceptance either.
I’ve been browsing the search terms people use to find my blog, and I decided to answer some common questions that seem to come up through people’s search or stuff people ask me a lot. This will be a quick rapid fire Q & A, this time I’ll focus on the MCAT. Though bear in mind the scoring system and the subjects will be changed on the new MCAT, in general the test represents the same idea i.e. part of your application to enter medical school:
1. [Is there a difference] between the AAMC practice tests vs the real MCAT?
Yes and no, but mostly no. The AAMC practice tests are representative of what you should expect on the MCAT. If you’ve taken enough practice AAMC tests you’ve probably noticed there’s some relative variability in perceived difficulty — some tests you’ll think are easy, some you’ll think are less so. In general, the core material doesn’t change much, instead it’s how they ask you that may stump you on a particular test. For myself, while self studying my practice scores varied in the last month from 32-36 and I was averaging about a 33 on practice exams (my first practice score was about a 22). But, I ended up with a 30P on the real exam which I suppose isn’t that bad considering how bad my personal life was on test week (family issues) and the night before the exam was. The key to these practice tests is to establish a range, and know that you may either score within that range or about 2-points below it. Why 2-points? Well, that’s within the confidence interval stated by the AAMC, if you score a 29 then a 27 or a 31 were in your range in theory. I can’t promise you that every school is open to the AAMC interpretation of scores, but that’s actually why the new MCAT is coming out with a new scale to further enforce this point and make it easier to interpret. This may also be why applicants who underperformed on their MCAT with a 28 or so are surprised to find that the bulk of their interview (if invited) isn’t spent on defending their MCAT score, this is probably especially true if everything else in the applicants file suggests they could have done better.
The biggest difference however will be in how anxious you feel about the exam, or at least it was that way for me. The good news it’s a good feeling to think that with each question you attempt the closer you potentially are to not seeing the MCAT ever again (hopefully).
2. Is it bad to take a MCAT practice test twice?
There are two skills you pick up while studying for the MCAT:
– 2.1. Getting better at the content on the MCAT
– 2.2 Getting better at taking the MCAT
You’ll definitely get the most value the first time you take the test to see how well you know the content. However, reviewing your past exams is part of the process of getting better at taking the MCAT. The first pass through the test is the easiest, you just take the test and do your best. But, reviewing the exam is a skill all in itself. For that part you want to ask yourself the following questions:
A. Why did I get this question wrong, or why am I getting these types of questions wrong? — separate the material into: 1) I had no idea how to even approach it, 2) I sort of knew it, and 3) I should of gotten it but misread etc. The last one, 3, is the easiest to fix as you just need to start annotating things better to make sure it doesn’t happen again. The first part, 1, is probably the most time consuming as you’d likely need to do a targeted content review on that subject (or that subject’s foundation). The middle one, 2, is the trickiest because it’s easy to fall into false comfort of classifying things as “I sort of knew it” and not dedicated enough time to these issues. In other words, you either know it (3) or you didn’t (1,2).
B. If I got this question right, was there another way to arrive to the same answer? — knowing alternative ways to answer a question is not only good conceptually, it may save you on the next exam. For example, if you’re given the answer choice of:
a. 9.21 E-23
b. 4.21 E-26
c 9.21 E-18
d. 4.21 E-34
You might have arrived to the right answer, let’s say it’s C, by crunching the numbers. But, likely in these types of math problems you could have arrived to the same answer by just evaluating the powers without doing any of the math that made the 9.21 part. This is because as long as you do the powers correctly, the max you can be off without fully evaluating the problem is by a factor of 10 (i.e. you’ll either come up with E-17 or E-19). So, sure, if you had answers within a factor of 10 you’d then need to do more math, but in this case you likely wouldn’t and it ends up being a very quick calculation.
C. Make a plan of how to NOT miss these types of problems again, though except for discrete questions never expect to see the duplicate permutation of the same question again.
3. Are there miracles on the MCAT?
Probably not, in fact you should expect just the opposite. This is why you need to practice and attempt to overshoot during practice because on the real test, for various reasons, it may not go so well. One person I interviewed with told me on their test day there was obnoxious construction going on across the street, another talked of an equally annoying fellow test taker, mine had a character that apparently was into keyboard S&M. Though, I do know a person who felt the test they received was everything they happened to be strong at, and she did better than any of her practice exams. However, realistically don’t expect a match made in heaven for your exam.
The biggest mistake you can make on the MCAT is expecting a miracle, you’ll probably score somewhere around your practice scores — maybe you’ll do a little better, maybe you’ll do a little worse. The practice tests aren’t trying to scare you into studying, if you find the practice AAMC impossibly difficult then there are no miracles to be had on test day.
Certainty — there is such an irony in the word “certainty”, as few things in life are ever certain.
Though, there is some overarching truths inherent to every premeds journey, or certainties: prerequisites, volunteering, and some type of leadership and/or some other types of enrichment experience. And, again we edge closer to certainty as we mature along our premed journeys’, after all there’s a lot less certainty of a freshman premed continuing on into medical school than a premed senior/post graduate. The reasons are pretty blatant, and don’t need much exploration: the premed journey whittles down a lot of people, regardless of your beautiful mind and/or heart, and by the time you reach the end you’re probably a ‘decent’ applicant if you stuck with it and life didn’t molest you too obtrusively. A lot of great people never make it to taking Organic Chemistry, the gnarled and tattered survivors go onto take the MCAT. The socially emaciated, #MCATPTSD desiccated husks of people, formerly known as a premed, then goes onto enter the must brutal game of musical chairs i.e. the AMCAS. At that time, if you chose to apply then you are now an applicant — this nebulous “friend” zone where you’re still a premed, but you are “certainly” a premed after you’ve pressed the SUBMIT button on the AMCAS.
Before pressing the submit button, early in a premed’s career the title “premed” is one often wore in honor. For the medical school applicant premed, this is probably the most fearful time in their life, and the title suddenly bears great weight. In fact, there’s likely a strong correlation to how many people expect you to become a doctor your perceived Atlas boulder on your neck. Indeed, I’d argue there’s even some type of transcendental comradery that is threaded between applicants and accepted medical students (and even doctors), a mutual respect borne through similar experience regardless of outcome.
Let me assuage your concerns, it’s perfectly normal to be apprehensive about applying to medical school, there is no shame in it. Indeed, it’s better to have every doubt you can conjure up prior to being accepted into medical school — and even then the doubts probably won’t stop stirring. This is probably especially true if your parents have geared you up to be a premed since you were a fetus because this is likely the first time you realized the destination of your train tracks. There was little certainty when you started your career as a premed that you’d end your undergraduate career as one (if traditional), and there is little certainty that when you press submit you’ll get in. And really, there is a maturity involved in re-evaluating your life, after all the true path to medicine forged you own way.
But, there is one sure way to be certain you won’t get in, by sabotaging yourself (perhaps unconsciously) by putting in a low grade application effort on the AMCAS or self-selecting out. And its fine to decide to do something else, this is in no way a failure, the most important thing is that you consciously choose and don’t let the sands of fate do as they may.
Though know there is one certainty: the only way to get into medical school is to apply to medical school.
If you haven’t heard already, the MCAT is hard. I struggled for a couple of weeks to come up with a succinct way to explain why it’s so hard, besides the reasons people might already have imagined. In vain I’ve kicked around a draft or two, those never made it past conception. And fruitless mulling now gives birth to this entry. Today’s post will focus on what an MCAT PS passage problem is like, the article is somewhat of a continuation of MCAT math entry I posted a while back. I wanted to show who the math and problem solving plays out during a passage. If you want more information about what’s on the current MCAT it’s best to keep up with the AAMC site, because the test is changing in 2015.
After you take enough practice test (you might even take all of them) you tend to pick up on the MCAT language, the MCAT feel. This is analogous to taking the same professor for the same serious, their testing style no matter how hard will eventually become familiar to you, no matter the subject. The AAMC tests are the only tests that actually measure your growth, the rest are assessments that try their best to emulate the MCAT. Some better do a better job than others. However, it can not be understated how hard the AAMC tries to make the one MCAT more or less equivalent to another MCAT (normalized for evolving prerequisites and recommended courses). I found that some MCAT exams seemed to be more “for me” than others, but again I can’t stress it enough, the MCAT is pretty consisted on what’s tested. It’s just that how you are asked will be different each time, sometimes it feels so different that it might take you a few weeks to understand why an answer is correct, even if you instinctively always get those questions correct. Everyone who sits for the real MCAT eventually falls victim to a cycle of realizing “Maybe, the answer was C, now that I think about it…”, viscous cycle.
It’s very difficult to talk about the MCAT PS passages, the subject of this post, without showing you the MCAT. But, with all the material being copyrighted (and with me avoiding arrests) we’ll have to compromise. I’ll make up an example of a passage, to give you a feel taste of what I mean without blowing a passage or me being put in padlocks.
I probably wouldn’t understand the passage entirely until the very end, or until I’ve answered all of the questions. This is very odd you might think, but this is because the MCAT is heuristic. In other words, the exam rewards test takers who can use their past experience to problem solve, learn as they go, and discovery a “best case” solution on the fly on new problems they’ve never seen before. MCAT passages are not as algorithmic as college course exams tended to be, that is you could probably give you a 20 page cheat sheet and a calculator on the MCAT and you’d likely either do the same or worse because you’d waste time on strategies that aren’t rewarded on the MCAT. The is the essence of the passages for the physical science section, in contrast the discrete questions reward people for their memory of MCAT fundamentals — the discrete questions should be the “free points” part of the test, but be aware most of the points will come from the passage as there’s more passage questions than discrete ones. Here’s the brief outline of the passage, I wrote a brief version, so you could skip over the superfluous explanation marked off by dotted lines:
Physical Science Universal Structure
1. Introduction to what is being measured or discussed.
2. Premises introduced.
3. Evidence presented possibly for or against the premises.
4. Conclusion of passage, typically ending abruptly, and flings you straight int the question stems*. It’s important that you don’t think of the question stems as just stand alone questions, they are entangled with the passage in some way. No matter how you feel, the passage is always right — unless it’s wrong, but in that case the MCAT is still right.
The test is great at shock and awe, assaulting your nerves from the first sentence — there’s a slight chance the sound of your heart beat will drown out all of your memory of the first sentence. But, the main goal is to keep a calm head, and jump straight into MCAT mode, and think “What is this passage about?”.
- The beginning of the passage was the hardest part. It’s very easy to get three or four sentences in before I actually started focusing. You’ll likely go through all the 5 stages of grief while reading the passage, my best advice is to skip to acceptance before you start reading the first sentence.
2. Premises introduced and 3. Evidence presented possibly for or against the premises: Be an objective reader, note details, have confidence that you might understand the passage at some point in your life.
- The focus should be objective, you are on a fact finding mission and nothing else — all I need to care about is where I could find the explanation later if I needed it. There’s a good chance you’ll learn a lot about the passage by going through the questions, because the questions are sometimes more informative than the passage. So, don’t be sad if you feel like a college drop out after browsing through a passage, I don’t think they were expecting anyone to say “Ah, what an easy passage”.
- Don’t bother thinking “Why the hell do I have to know about gauge pressure and deep under mining operation?” or “What does answering a passage about the effects of sulfur leeching into ground water in Indonesia have to do with becoming world’s best ___ doctor?”, it’s a waste of time. Just accept that it’s happening, you can eat a carton of Ben & Jerry’s later, don’t bother wasting test time or study time thinking about “why this passage?”. With that being said, on the real MCAT, my first thoughts were “Hell with this passage,, then I remembered it was the real test” haha. I buckled down from there, and never lapsed after that. Arguably, the most important task at the beginning of the passage is to first calm own, then to note what the subject of the passage is.
- I would note where the explanations of the equations were in the passage or process I didn’t get. I wouldn’t actually care if I got it or not, I was confident at some point I might.
- I would highlight numbers as I read them (this can be done on the computer with the real MCAT), maybe they would be important maybe the wouldn’t be. They often weren’t important, but knowing where they were made me feel better.
4. Conclusion of passage, typically ending abruptly.
- I probably wouldn’t understand the passage entirely until the very end, or until I’ve answered all of the questions. This is very odd you might think, but this is because the MCAT is heuristic. In other words, the exam rewards test takers who can use their past experience to problem solve, learn as they go, and discover a “best case” solution on the fly on to new problems they’ve never seen before. MCAT passages are not as algorithmic as college course exams tended to be, that is you could probably give you a 20 page cheat sheet and a calculator on the MCAT and you’d likely either do the same or worse because you’d waste time on strategies that aren’t rewarded on the MCAT. The is the essence of the passages for the physical science section, in contrast the discrete questions reward people for their memory of MCAT fundamentals — the discrete questions should be the “free points” part of the test, but be aware most of the points will come from the passage as there’s more passage questions than discrete ones.
The best way to demonstrate what I mean is to give you a fake passage I just made up. I was inspired by some TV shows lately. The next paragraph will jump straight into the passage, brace for it, the MCAT will just throw you in with the lions after each passage:
Mock Physical Science Passage — This is what it feels like. But, before you begin I have to apologize for using the scientific notation system where 1×10^2 = 1E2, I was lazy and it looks better when typed without a math writing program. Good luck, and don’t lose focus!
Schwarzchild radius (rs) is defined as the radius at which any body of mass (mo) must be compressed to create an event horizon, creating a black hole. The event horizon describes the boundary between rs, and the edge of spacetime where Netwonian physics still apply.
The first rigorous idea of a black hole came about from a solution to one of Einstein’s equations, and seen as nothing more than a mathematical “fluke” at the time. Another consequence of Einsteins theories was the melding of space with time, into the concept of unified space-time. Einstein had theorized that gravity was not so much a force as Newton had envisioned, but rather an effect of the warping of spacetime by mass. The more the mass the more the warping in space time. Black holes can contort space to such an extent that they can act like lens as described below.
theta = 4Gm/rc2 = 2rs/r
r = radius between observer and object creating gravitational lens
Now, we are aware that black holes are almost found ubiquitously throughout the universe, even our own galaxy has a super massive black hole at its center. On earth, it is theorized that the Large Hadron Collider (LHC) generates enough power to create microscopic black holes. Before the LHC was unveiled it was feared by some layman observers that, scientists would inadvertently create microscope black holes that could eventually engorge on Earth, devouring our entire solar system in what would be the largest scientific blunder in history. But, people need not fear, because the black holes would be so small and would evaporate almost instantly, all black holes are believed to evaporate at the rate described by t(ev)
t(ev)= 5120 pi G^2*M^3/hc^4
G = universe gravitational constant = 6.67E-11m^3*kg^-1* s^-2
h = Planck’s Constant = 6.626E-34 J*s
c = speed of light = 2.99E8
1. The final radius of a black hole is related to its mass, given Earth’s Schwartzchild’s radius what is Earths approximate weight?
A. 6E30 kg
B. 6,300,000 kg
C. 6E24 kg
D. 6E21 kg
2. Before ultimately colliding, black holes have been seen orbiting each other. If there are two black holes orbiting each other at distance r, and the radius is halved, how much does the force change between the two black holes? And what if the mass of one black hole is reduced to a 1/4th of it’s original value?
A. The force between black hole 1 and black hole two are equal and opposite. Because of the reduction in mass, the forces exerted between the two black holes would reduce by a 1/4th.
B. The force would be greater on the smaller black hole than the larger one. Because of the reduction in mass,The forces exerted between the two black holes would increase by a 1/4th on the large black hole, and double on the large black hole.
C. The force would be four times as great on the smaller black hole. Because of the reduction in mass, the forces exerted between the two black holes would reduce by a 1/4th.
D. The force would be half as much as before. The mass of the black holes no longer matter.
3. If a star is obscured slightly be the sun, and it is visible during a total solar eclipse on the Earth. If the light rays are bent towards Earth (towards the normal) what type of lens does gravity act as? Which wavelengths would be bent the most towards the normal?
A. Diverging lens, longer wave lengths like red would be bent harder.
B. Converging lens, shorter wave lengths will be bent harder.
C. Diverging lens, shorter wave lengths will be bent harder.
D. Converging lens, longer wave lengths will be bent harder.
4. Astronomers call black holes messy eaters, it is thought that perhaps half of the mass that is pulled into a black hole never makes it into the black hole itself due to various forms of turbulence. Eventually, this mass that never makes it can form an accretion disk. Some matter actually escapes the black hole, after being converted into pure energy is than remitted as gamma and X – rays. What if one solar mass (1.998E30 kg) is engulfed by a black hole, and 1 part per million of it’s mass is converted into pure energy how much energy would that be in joules ? (Updated!)
A. 2E133 joules
B. 2E 10 joules
C. 2E 34 joules
D. 2E41 joules
Get the idea? Scroll down for answers.
Answer 1: C
Using the first equation, it’s just plug and chug. I’m going to estimate, because I’m lazy and it’s almost 2 AM. rs = 2Gm/c^2
I’ll just take care of 2G/c^2 at once, to make life easier = 2*6.626E-11/(3E8)^2 =
There’s no calculor on the MCAT so let’s say that is actually equal to
= 2*7E-11/(3E8)^2 = ~1.5E-27
Now,w it’s easy just take the equation rs = 2Gm/c^2, and isolate the m =
mass = 9E-3/1.5E-27 = ~6E24 kg
Answer 2: A
I made this question easier, because on the MCAT there’s always a trick to it. And the question was too calculation heavy. Anyways, the forces are always opposite and equal for the MCAT, especially this is a cardinal rule for conservative forces. And mass is directly proportional to the force of gravity, as F = Gm1*m2/r^2. That second clause either helped you or hurt you. But, learn how to use all of the clauses of the questions to your advantage. Also notice that the clauses repeat every, the stem are repetitive — practice keeping track of the differences.
Answer 3: B
Converging lens, converging lens converge light. You didn’t have to read the passage to understand this, and the question stem did pretty much provide enough detail to figure it out without knowing about black holes as well. Next, you just ought to know shorter wavelengths get refracted more than longer wavelengths. If you couldn’t figure out the answer toe the first clause then you could of tried to make sense of the second clause first, or vice versa — that’s the lesson here.
Answer 4: D
Quick math really, just use E = mc^2, make Einstein proud. The hardest part, just like the real MCAT is remembering to do all the steps. If a solar mass is around 2E30 kg, 1 millionth of that would be 2E24 kg, this would be around the mass of Mars. Then E = mc^2 (expect a ridiculously huge number because usually we use this formula for small values), so that ends up being:
E = 2E30 kg *1E-6* (3E8)^2 m/s = ~18E41 = ~1.8E41 joules = ~2.0E41 joules. If you could harness that power to a 100 watt light bulb it would run for longer than the current age of the universe =x. In reality, the answers were so far apart that keeping track of the 2 and the 3 was pretty pointless. So, you could of done everything with 1E30 and (1E8)^2 and got an answer reasonable enough for the MCAT. If you see the ones place repeat in the answer, then the devils in the scientific notation. *This is a revision, a reader pointed out a typo, thank you!
The upside about MCAT passages is that you always walk away learning more than when you came in, whether you like it or not.
Thanks for reading, and thanks for the warm response about the MCAT math posting. Admittedly, I was a little worried when I wrote that last article, boredom forcing my readers into mass exodus was a sure risk. But, then I remembered how intimated I was as a premed, non traditional at that. I remember taking my first MCAT practice exam, I think I felt nauseous afterwards. My thoughts were racing, “How could I ever pull this off…by myself?”, I panicked internally to myself. Every traditional premed I knew had taken a course, and it seemed rather par for course. Some premeds can afford them, some premeds have a game plan and get scholarships, some couldn’t afford them and were ignorant of potential scholarships (me, me ,me). At the time, I was defecating proverbial bricks, though the panic did wake me up — I revamped my strategy entirely, and did just fine on the real exam. With that in mind, good luck all you premeds gearing up to take the MCAT this season; keep in mind there is a light at the end of the tunnel, but then there’s another tunnel =D)
Fast forward to yesterday, I was sprinting around my old university, where I now work until June (then off to Boston). One of my jobs was to participate on an organization committee for a Southern California Research Conference. With a under staffed team, we held a very successful event with over 100 presenters of various disciplines oral and poster. A grant was established in order to send the best 10 presenters to another regional conference. At award ceremony, there was a keynote speaker, an MD and also Olympic gold medalist key note speaker from UCSF. She gave a terrific speech, lots of premeds and budding scientists scored experience and CV points, everything was flung together but it all worked out.
To reward myself for helping to make the impossible possible for this conference I bought two bottles of wine. For the weekend?
- Someone from SDN sent me their Personal Statement (PS), I’ll be giving them feed back tomorrow. So far, a few people have sent me quite a few PS messages, from Twitter here, and SDN. Fortunately, I apparently didn’t causes insufferable damage to their application because they did get accepted. They were already excellent applicants, they just needed a critical eye to bring it out in their PS.
- Draft something about how to design a personal statement.
- Finish another entry about the MCAT, specifically about passages on the PS section and MCAT math — the fun! It may be some of my last posts about the MCAT, as soon I’ll be panicking about medical student problems in August.
- Wind down one of my jobs — less responsibility equals more tom-foolery!
Good luck everyone, remember the MCAT doesn’t define who you are and if you’re capable of being a doctor. It’s just a test, everyone takes it, we all felt the pain, we all squirmed in our seats. But, we all eventually conquer it in their own way, that’s what unites everyone who dawns the white coat.
Aside Posted on Updated on
Find me on twitter https://twitter.com/doctorORbust
The most important rule is speed. The math isn’t hard, you just don’t have time to let it be part of your test schedule. So, being able to power through the math in a quick way is important. This is hard to have faith in if you haven’t been practicing math lately, or rigorously, as most people just spend time reading over review materials to study for the MCAT. The problem is only compounded by the fact that most premeds are biology majors, and have jettisoned all math skills out of their minds once it was no longer a requirement. Devote time to math skills every day while you’re studying for the MCAT, divorce yourself from your cellphone calculator:
1. Most on the MCAT are simple problems of multiplication and division and nothing more. The power of this concept shouldn’t be underestimated, because the rules that work for multiplication and division that you already know work for unit analysis. (See physics example below, because it’s a long example)
2. Learn to believe in estimation (science labs, ball park, then go for it, usually the ball park is good enough do to uncertainty). All values are calculable, but not all calculations have value. Keep in mind that each round of estimation will introduction error, just keep track of the direction of the error if you need a more accurate estimation — or you can just introduce less rounds of estimation.
3. You don’t need to master differential equations (or anything remotely close to that level), but all math concepts help. The most important thing you will take away from calculus are slopes and areas under the curve. But, you don’t need calculus to ever find a slope or area under the curve on the MCAT, it’s just useful if you’ve been introduced to these ideas already.
4. Become familiar with the log scale base 10, enough to estimate pH values within error of 1 pH point. (See Chemistry example below)
5. Any numbers written down larger than 10 should be written in scientific notation, if the number has pi, leave it till the end. Usually the problem will rely merely on basic math and scientific notation rules. You should become a scientific notation guru — don’t be over confident, devote practice to this. Getting this down is essential to being able to estimate, or ball park huge/tiny numbers. Do your groceries in scientific notation, just make it part of your life.
6. See relationships without doing that calculation (see 9). For example you have to have inverse and direct proportionality down cold, as well as inverse squares.
7. Natural decay (Aexp-t/T), half lives, be able to estimate them. How much there is now is based on how much there just was but a moment ago. Patterns appear a lot in the universe, pi reflects some type of geometric relationship (or rate), Euler’s number (e) in general demonstrates another rate of growth or decline, but instead of geometries, it shows growth (or decline) compounding on itself.
For example: if an experiment is done, and it shows that the cooling of a pool of blood on the cement from a particular crime scene can be described with regard to time with the equation Aexp-t/T. If it takes the blood 10 minutes to cool to half of it’s original temperature (98F), after 20 more minutes what is the closest approximation to the temperature of the blood if left to cool? (assume the temperature obeys exponential decay)
The trick to this is understanding what a half life means. A half life is simply the time it takes for some value to be half of what it was before. So, if it takes 10 minutes to have one half life, 30 minutes would be 3 half lives. First half life 98F/2 = 49F, then the second half life was 49F/2 or 25F, the third would be 25F/2 or 12F. This idea goes for anything that follows exponential decay (Euler’s number based powers).
8. Understand how to use (x)cos*theta or (y)sin*theta in a problem. These show up any time there’s a vector, i.e. a magnitude and an directional. Typically, the MCAT will tell you what the cos or sin of whatever angle you need, except the typical ones you should know, so don’t spend too much time worrying about the math. If you’re not sure if you should use cos or sin for a vector question, just use this rule of thumb:
If the vector is maximum at 0 degrees (to the normal) than it’s ought to be cosine, for example work performed while pushing a block at angle theta would use cos, because the maximum value would manifest from you pushing directly on the block. While the rule doesn’t always work, it works well enough for the stuff on the MCAT. Understanding this principle will take you very far, from the MCAT, to understanding the vestibular and auditory hair system and their relationship to action potentials in medical school.
Examples and Explanations
Example Mock Problem for Physics – Reference Number 1
Estimate the amount of time it takes to get to mars (Proving Idea’s 1 & 5)
It has long been said that in order for humans to survive inevitable extinction we will have to travel like our forefathers. But, instead of transcribing around the Earth, we will need to eventually move the human race to other planets. At the moment, the most promising planet is Mars. The photons of light originating from the sun only take approximately 4 minutes and 40 seconds to reach Mars after passing Earth. Mars, has a much thinner atmosphere than Earth, in fact it’s atmosphere is only 0.6% that of Earth’s. Mars is frigid heavenly body, with the mean temperature hovering around -60 C. Combined with the fact that Mars has an ozone layer that is 300 times thinner than Earth’s, and has no active magnetic field, future explorers who roam the planet would be bombarded by ultra violet rays and other high energy particles we are usually shielded from on Earth.
1. There are plans to launch a probe to to orbit Mars, however the probe will only travel at 1 million times slower than light, assuming the probe has a constant velocity, how long would it take for the probe to reach Mars? (the speed of light 3 x 10^8 m/s)
You can see this question in another of ways: unit analysis, or calculate, or estimate because the answer choices are so far apart. Let’s try the first way, unit analysis:
A unit analysis problem usually looks like this. It’ll have a bunch of numbers, and you’ll have to figure out what the numbers represent, and that’s usually good enough to answer the problem. As you won’t get a calculator on the real test, it’s a typical question as there’s only so many math questions that are fair game. Let’s brush off our unit analysis:
The rules of unit analysis are the same for mult/div, that’s all you need to know.
First let’s recognize what each number was representing, 300,000,000 was the speed of light, with units of m/s because it’s a velocity. The question stem told us that the speed of light is 1,000,000 times faster than our speed, so that was just scientific notation. That is, since 300,000,000/x = 1,000,000, is that equals (3 x 10^8)/(3 x10^2) = 1 x 10^6, i.e 3 x 10^2 is “x”. Our 300 number is another velocity, so the units are m/s. The last bit is 260, I’ll save that for the last. Let’s see what we have so far:
3,000,000 number will have m/s
300 will have m/s
The final answer will be in seconds, and the m will magically disappear so if we take our units (I bolded it so its easier to track):
(m/s)/(m/s) = (m/s) x (s/m) = everything cancels
Yay, our units canceled out, but what about that 260 number? Remember the answer was asking about time, so as everything else canceled out we know 260 has to have the units of time, and since the answer is X secs, we know that 260 most be on top:
((m/s)/(m/s))(s) = seconds
In this problem it was enough to know this much because the answer has to be B according to unit analysis. If the answer choices were more similar, then you’ only need to go one step further and remember that (m/s)/(m/s) doesn’t equal (m/s)(m/s). In other words don’t let unit analysis make you think that 300,000,000/300 is equal to 300/300,000,000. So, you would simply have to pick which goes on the top or the bottom. Alternatively, you could of sat down and calculated the real number, but that would of taken longer, and wouldn’t be a choice selection anyways. Physics and chemistry problems are generally solvable with unit analysis and basic math. On the actual MCAT it’s more likely that they’ll ask you to convert the seconds into days, just to torture you, but the work is the same.
Example of Chemistry Problem – Reference Number 4
In human blood the pH is buffered by the interaction of carbonic acid with carbon dioxide. The hydration of CO2 with H2O is the rate limiting step, and the reaction can be described as:
[CO2] + [H20 ] <-> [H2CO3] <-> [H+] + [HCO3-]
[CO2] + [H2O] <-> [H+] +[HCO3-] (mediated by the enzyme carbonic anhydrase)
The buffer system will try to maintain an equilibrium described by:
K = [H+][HCO3-]/[CO2]
In logarithmic form it becomes:
pH = pKa + log [HCO3-]/[CO2]
Assuming if the pKA of HCO3- is shifted to 6.1 because of enzyme activity and if the concentration of HCO3- is 24 mM and the soluble amount of CO2 in the blood is 1 mM, what is the blood pH?
Now, the proper way to get to the answer would be to pick up a calculator. Type in…6.1 + log(24) = something. Of course you don’t get a calculator. Is this a memory question, should you remember the exact pH of blood (probably not, but knowing the range would be helpful, but let’s ignore that fact)? The question is actually a lot easier than it looks, you have to first understand logs, and be okay with estimating. First, we are dealing with log base 10, so every factor of 10 represents a change in one pH value:
log (.01) = -2
log (.1) = -1
log(0) = meaningless
log (10) = 1
log (100) = 2
log (1000) = 3
Looking back at the original problem, 6.1 + log (24), well we have a problem, because you an I both don’t know what the log of 24 is according to log values above. But, let’s just estimate for now, we’ll prove way this was okay later. So, let’s use a number we know from our values I listed, 10. So, if we put in 6.1 + log (10) we get 7.1, this is much easier than figuring out what the log of 24 was. Now, we just have to think logically, 7.1 can’t be the answer because the concentration was actually 24 mM and not 10 mM. So, that eliminates B, an the answer can’t be A, because that answer is even lower than B. The answer can’t be D either, because 6.1 and 8.1 would mean that there is a 100 times more carbonic acid conguate [HCO3-] than acid [CO2]. In other words, 6.1 + log (100) = 8.1, so this is a gross overshoot. The answer can only be C.
We can use calculus to prove that the pH will change in minute amounts with the equation:
dpH = 0.4343/[initial acid concentration] x d[H+]
What this means is that small fluctuations in the concentration of the protons added to solution will change the pH at a rate of (0.4343/initial concentration). So, let’s say we had an initial concentration of 1M, an you added .01M more of [H+ ]you expect the pH to chance to .004343. So, don’t expect the pH change from point to point to be intuitive, instead know how to use a less refined estimation for the MCAT.
Here’s the math behind that, which you’ ll never need to know. Just take it as a lesson that you should remember the log rule base 10, as opposed to expect to calculate it exactly on the MCAT:
[*correction 2/24: the last value in the pic above should be dy = dpH, I’ll fix it later * fixed 2/26]
Well, that’s all I have for now. I made up the questions, so if you see any mistakes let me know! Anyways, good luck and study hard, the math skills you pick up now will stick with you!