MATH BITS
From EK:
Directly proportional
Exponential
Inversely proportional
Logarithmic relationship
& exponential
So long as the value of n is within the given parameters, the general shape of the graph will not
change even with a (+b)
Sigmoidal (ex. cooperative mechanisms, ex. Hb binding affinity, protein unfolding, DNA
melting/unwinding, etc.)
Parabolic
Hyperbolic (ex. Michaelis-mention with [S] vs Vmax) or (ex. negative cooperative binding)
Statistics:
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Regression
o One or more variables are used to predict an outcome.
o All variables examined are continuous
o Linear regression – degree of dependence between one variable and another. Data
is on scatter plot, one-way influence of one variable on another.
Correlation - all variables examined are continuous.
o Variables have equal status and are not considered independent or dependent
variables.
o Unlike regression, correlation makes no assumptions about which variable is
influencing the other.
o Correlation coefficient indicates the strength of a correlation:
 1, perfect.
 0-1, positive correlation (as one increases, the other increases)
 0, random.
 -1-0, negative correlation (as one increases the other decreases, & v.v.)
 -1, opposite
Chi-square – when all variables are categorical, looks at if 2 distributions of categorical
data differ from each other.
o Null hypothesis vs. alternative hypothesis.
o Helps us make decisions about whether the observed outcome differs significantly
from the expected outcome.
T-test – compares mean values of a dependent variable and an independent variable that
has 2 category/groups, ex. is there a significant difference between the height (dependent
variable) of boys and girls (independent variable with 2 categories) in high school?
o Two-tailed = possibility of relationship in both directions, one-tailed = one
direction.
ANOVA – similar to t-test, compare distributions of dependent variable between groups
of categorical (independent) variable, but can be used for independent variables that have
3+ categories/groups.
o If value doubles, 100% increase
The median is less susceptible to variation than the mode (mode can be completely changed just
by the changing one value in the sequence – v. susceptible to variation)
Multiplying with scientific notation:
ex. (9x109)(5x10–3)(1x10–1)
Multiply the coefficients, add/subtract the exponents, simplify:
= (9x5x1)x109–3–1
= 45x105
= 4.5x106
ex. 4.5x106 x 4
Put everything in scientific notation and then follow the steps above
= (4.5x106)(4x100)
= 18x106+0
= 1.8x107
Logarithmic approximations:
3 things to know (2 rules, 1 pattern)
Rules:
log(ab) = log(a) + log(b)
log(xy) = log(x) * y
Pattern:
Notice the pattern of sequential odd numbers
Example: approximate log(0.0073)
log(0.0073) = log(7.3 x 10-3) = log(7.3) + (log(10) * -3) ≈ 0.9 + (1 * -3) = 0.9 – 3 = -2.1
Example: approximate log(55)
log(55) = log(5.5 x 101) = log(5.5) + log(10) ≈ 0.7 + 1 = 1.7
Converting between ln(x) and log(x)
ln(x) ≈ 2.3 log(x)
Negative exponents
ex.:
Fractional exponents
Physics:
soh cah toa
s = sine
c = cosine
t = tangent
a = adjacent
h = hypotenuse
o = opposite
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In a 45-45-90 (angles) triangle, the edge length ratio is 1:1: √2 (a:o:h)
o a&o=x
o h = x√2
o So in a situation where h=10, x√2 = 10… solve for x
o x√2 = 10
o x = 10/√2
o x = 10/√2 * √2/√2
o x = 10√2 / 2
o x = 5√2
o We have solved for the length of our adjacent and
opposite sides.
o From http://tinyurl.com/m44558f
Vectors
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Cross-products are done with sine (cross-sign at cross-roads)
o (a→ x b→)sinθ
Dot-products are done with cosine
o (a→ + b→)cosθ
Chemistry:
GETTING RID OF LOG
Simply remove log from one side, take the anti-log of the other side.
Log base is 10 unless otherwise noted.
Example:
pKa = -log (Ka)
Ka = 10–pKa
Example:
Estimating pH:
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If you see a number that looks like 1.0 x 10x (e.g. 1.0 x 10-4 as an example), the
pH is simply the exponent without the negative sign (e.g. pH 4 in our example).
If the first number isn't 1.0 (e.g. 2.4 x 10-6), there is a trick:
o The exponent is 6, but that is NOT your pH.
o The rule is that you subtract 0.5 from the exponent when you have a number
other than 1.0 before the x 10x
o So in our example of 2.4 x 10-6, we calculate 6 - 0.5 to be 5.5.
o The pH will be somewhere between 5.5 and 6.0
o Check the MC choices on the MCAT to see what answer falls within that
range.
o This works because the MCAT will NOT have answers looking like 5.5, 5.7,
5.8, etc. They will be more wide spread than that (2.0, 4.3, 5.7, 8.0, etc.)