Question

MCAT Tutorial: Math Review

Answer 1

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

Answer 2

\({\bf{Scientific~Notation:}}\)

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)

Answer 3

\({\bf{Estimation:}}\)
- 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

\({\bf{Logarithm~Rules:}}\)



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

Answer 4

\({\bf{Trigonometry:}}\) 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)

Answer 5

\({\bf{Inverse~and~Direct:}}\) 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



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

Answer 6

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