Arithmetic TRICKS, take two

[BerkReviewTeach]

Reposting the thread

Hey Guys,

I was wondering what ARITHMETIC tricks you could implement int he MCAT...im just confused because there are a lot (ignoring the ones in EK), but I need to know if you have a list compiled after extensive practice that you would recommend knowing.

Rounding, no seriously rounding really helps.

I seriously went to the library and checked out a 5th grade text book. It has lots of stuff on unit conversions, rounding, fractions, and exponentials. I felt stupid doing problems out of it...but it helps you to do them fast and gives you practice. I hate how I've was so dependent on calculators! I couldn't even add fractions without the calculator until I looked at the text book. Just practice problems because you don't want to spend a lot of time on them on the test or to make stupid math errors. Good luck!

I so 100% agree with your comment. It's funny you mention fifth grade, because in class we discuss the highly advanced method of having no shame and doing it like a fifth grader.

Key things that I have found hurt people are:

Powers of ten: This is helped by decimal hopping and labeling numbers with "increased by factor of 10" or "decreased by factor of 100". It comes down to paying attention really.

Ratios: These are made easiest by making denominators easy to deal with. Also, if a ratio is hard to calculate as written, flip it and see if it is easier the other way. We somehow emotionally deal with bigger-over-smaller ratios better than smaller-over-bigger ratios.

Fractions and Equivalent Decimal-based Value: Learn the correlation between fractions and decimals 1/4 = .25, 1/5 = .2, etc... These can prove EXTREMELY useful on the exam.

There are many more strategies and techniques, but these are generally the big three for most people. A little practice goes a long, long way.

The funny thing I've found is that the supposedly more difficult math skills like logs, square roots of complex numbers, and exponential decay/growth are typically easier for people than basic division, fractions, and multiplication.

Learn how to estimate log calculations:

-log (1E-5) = pH 5
-log (1E-4) = pH 4

And -log(3E-5) =~ pH 4.5

If you remember that a '3' in front of the 10^-X, corresponds to the halfway point between two pH values then you can estimate whether all H+ (or OH-) concentration values will give a pH between X and X.5, X.5 or X+1, etc...

What textbook or SAT-like book could I use that would get these fundamentals into becoming a second language. I love ur advice Vihsdas, and its little bitty tricks like those I was wondering if you had a list of after taking the MCAT, I am pretty sure u may have had like 20-30 tricks in ur bag to tackle physics problems...other than that I really need book titles to do in a couple of days.

thanks

Wow, what a great little tidbit! Thanks much for this stuff!
"My log has a magic number. It's three."
A silly way to put it, but instantly memorable.

One of my favorite tricks is Left Add Right Subtract. This refers to exponents, for example, if you move the decimal point to the left one, you need to add one to the exponent. If you move the decimal point to the right one, you need to subtract one from the exponent.

1 x 10^5, move left one decimal point to the left and you got .1 x 10^6

I hope this helps.

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[drbull]

I just had to bump this thread.

There are some real pearls for MCAT studying here that need to be taken advantage of!

 

[yellowbird12]

This website may be helpful too
http://calculustricks.com/tricks/multiplication/

 

[SSerenity]

If you have the time to invest (15-20 minutes) to get comfortable with the Major System http://en.wikipedia.org/wiki/Mnemonic_major_system

Turns numbers into words

this will pay off greatly.

Heres how I memorized Sin/Cos values:
I rounded these values off, to make them easier to work with:

Cos(0) = 1 (Tie)
Cos (30) = 0.85 (Vile)
Cos (45) = 0.71 (God)
Cos (60) = 0.50 (Lice)
Cos (90) = 0 (Saw)

To permanently memorize these, pick a room with 5 objects (chair, lamp, window, etc).
Assign Place the image of "God" in the middle. So when you walk in the room, immediately on your right you will see a Tie on the chair, followed by a vile, somewhere in the room, etc.

Walking counter clockwise will give you all the COS values. Now walk counterclockwise to get all the SIN values.


I use the same trick for memorizing fractions = > decimals. This system is infinitely expandable.

Example:
0.75 = 3/4
0.75 = Kyle (my friend who is a firefighter)
3/4 = Mayor (M=3, R=4)
The image of Kayle putting out my burning Mayor always reminds me of this relationship. Ignore all decimals.


Another example, to memorize all the wavelengths of colors in ROYGBV (nobody cares about indigo, I question its existence).

Kisses | Shank | Leppar | Legit | Rakehog | Remove | Roses

These translate to:
700 | 627 | 594 | 561 | 477 | 438 | 400
which captures the visible spectrum

Once again you can throw these into a memory palace (method of loci) for long term storage.

There are some very creative applications to this method, its worth investing in!

 

[malaika]

This thread is amaXing!!! Def bookmarking this. Thank you all

 

[AdamMc]

This is not one of those OMG greatest trick ever type of things, but it has helped me become a little quicker with certain problems.

If you are trying to find the time it takes for an object to fall a certain height (air resistance negligible) and you will be using y= vt+1/2at^2 so y=(-5)t^2

I noticed instead of dividing by 5 which takes a little bit of time, not much you can just take it and multiply by 2 and place a decimal point in the final answer.

Ex. 178/5= 35.6 or 178x2= 356 place the decimal after the last number to get 35.6

98/5=19.6 98x2=196=19.6
99,876/5=19,975.2 99,876x2=199,752=19,975.2

Might help some people and it might not, I just find it easier to multiply in my head by 2 rather than divide by 5.

 

[molecularmolly]

this a biology textbook companion website site---registration is free. After you do that, scroll down below the contents, and there's a bunch of resources. The "math for life" pdf and the experiment links are helpful for the whole mcat, not just biology...there's helpful stuff on logs for chem. I used to be good at math, but got rusty after graduating a year ago, so I relate to the math stuff. This is helpful b/c it's written in a really down to earth way.

Hey that's cool I didn't even have to register! Thanks for sharing

 

[niharmehta]

Hi guys, all those who feel long calculations- multiplication, division, square roots, cubes etc are very time consuming in competitive exams should check out my blog:
http://vedicmathsrocks.blogspot.in/
It has amazing and astonishing TRICKS for all.. It also reflects the knowledge of Great Indian scholars.

 

[dodo22]

I like the triangles a lot, it's so fast. I always used to do the tables, but this saves me time, thanks !

 

[MCAT-MVP]

Here is something really helpful for finding the negative log from our MCAT Tips
.