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MCAT Tutorial: Math Review

3 months ago
Moon:

most of this stuff is p. obvious but since you can't use a calculator on the mcat it doesn't hurt to review the basics and practice doing calculations by hand

3 months ago
Moon:

$${\bf{Scientific~Notation:}}$$ writing numbers in the format X * 10^n where X is a number w/ an absolute value from 1 to 10 (not including 10), and n is an exponent when adding/subtracting #'s in scientific notation watch your exponents; convert them to the same exponent first, then convert back into scientific as needed when multiplying/dividing, remember your exponent rules, and again, convert back to scientific notation as needed $${\bf{Significant~Figures:}}$$ - identify the first nonzero digit and the last nonzero digit, and include all the digits in between, inclusive ex. 00105.4 has only 4 significant digits (the leading zero's do not count) - leading zero's are not significant - trailing zero's are not significant in a whole # but are significant in decimal #'s ex. 10540 only has 4 significant digits (the trailing zero does not count) but 1054.0 has 5 significant digits (the trailing zero after a decimal pt. does count). 1050 has 3 significant figures while 1050. has 4 (notice the decimal point after the last 0)

3 months ago
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$${\bf{Estimation:}}$$ - when multiplying try to round some #'s up and some #'s down to "even" things out. rounding to the nearest whole #, or even one decimal place, is usually acceptable - when dividing try to round both #'s in the same direction (both up or both down) - when the answer choices are numerically far apart, more rounding may be acceptable, but be mindful of rounding when the choices are close together $${\bf{Logarithm~Rules:}}$$ |dw:1531625665128:dw| converting between base 10 and natural log: log(x) is about ln(x)/2.303 estimating logarithms: log(n * 10^m) = log(n) + log(10^m) = m + log(n) which is approximately m + 0.n

3 months ago
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$${\bf{Trigonometry:}}$$ know your sin cos and tan ratios (soh cah toa) and the values on the UC (it's easier to start by constructing quadrant I and then reflecting across the axes to get the other values) |dw:1531625894357:dw| |dw:1531625906761:dw|

3 months ago
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$${\bf{Inverse~and~Direct:}}$$ inverse: one variable increases the other decreases direct: both variables change in the same direction $${\bf{Units~and~Conversions:}}$$ know your latin prefixes and their representative symbols between exponents -12 and 12 |dw:1531626153202:dw| know how to do dimensional analysis and make sure the units of your answer are consistent with the units of the answer choices $${\bf{Solving~Systems:}}$$ substitution and elimination are your best bets here

3 months ago
Moon:

Anyway, that's the end of my tutorial, I hope it was a helpful resource. Source material is the Third Edition Kaplan Physics & Mathematics Prep Book for the new MCAT

3 months ago