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MATH BITS From EK:

Directly proportional

Exponential

Inversely proportional & exponential

Logarithmic relationship

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  

Cross-products are done with sine o (a→ x b→)sinθ Dot-products are done with cosine o (a→ + b→)cosθ

(cross-sign at cross-roads)

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:  

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.)...