Episode 25 recAPs the understandings behind the equations and formula sheet.
Episode 25 recAPs the understandings behind the equations and formula sheet. Topics for discussion are: surface area to volume ratio (1:00), water and solute potential (2:02), laws of probability (3:30), standard deviation and standard error of the mean (4:20), and chi square (5:20). Always make your math have meaning through analysis, biological application, and units!
The Question of the Day asks (7:10) “What is the greek letter for summation?”
Thank you for listening to The APsolute RecAP: Biology Edition!
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Hi and welcome to the APsolute Recap: Biology Edition. Today’s episode will recap Math Reminders
Lets Zoom out:
Math? I thought this was Science? The AP Biology Equations and Formulas sheet is not only readily available online but also 100% allowed as a reference during the test. Grab your numbers, plug them in and get your answers. But numbers will only get you so far. Interpretation and application of the numbers is where understanding comes in. And please, from me and all of your science teachers, always include units with your answers!
Lets Zoom in:
First up - Surface area to volume ratio. This correlates to Topic 2.3 - Cell size. This ratio affects the ability for a biological system to obtain resources, get rid of wastes, release thermal energy etc. The challenge is that volume increases at a faster rate than surface area. Organisms must efficiently exchange chemicals and energy with their environment to maintain homeostasis. This concept also applies to cell compartmentalization - consider the inner folds of a mitochondrial membrane. The more folds, the more opportunities to build up that electrochemical gradient of hydrogen ions. Surface area to volume ratio is dependent upon the shape of the cell - yes, not all cells are spheres. This math sheet contains the formulas for shers, rectangles, cylinders and cubes. Plug and play, then apply your numbers to the biological concept (most likely a cell transport question).
Next, Water and Solute Potential. This matches topic 2.8 on tonicity and osmoregulation. Ok, so this is the potential to do what exactly? Water potential equals the pressure potential plus the solute potential. Water Potential is indicated by the Greek letter psi and looks like a trident. Remember, your numbers need to have meaning. Your numbers help to explain how concentration gradients affect the movement of molecules across membranes. The greatest value that water potential can be is zero, with pure water. Therefore, any solution that has solutes in it, will have a negative value.
The solute potential of a solution is equal to -iCRT. i, the ionization constant, is equal to the number of particles the solute will make, or ionize into, in water. For NaCl this would be 2 whereas for glucose, which doesn’t ionize, this number is 1. C = the molar concentration (this is often from experimental data; where the line of best fit crosses the x-axis). R is the pressure constant and is always equal to 0.0831 liter bar/mole K. And lastly, T = Temperature in degrees Kelvin, which is 273 + °C of solution. Do not memorize this, it will all be in the math sheet. You may have to first solve for solute potential before solving for water potential in a given problem.
Moving onto the Laws of Probability. This is relevant to Topic 5.3 with Mendelian genetics. Pop quiz - what are the chances you will get a 5 on the AP Bio test? The grading scale is out of five, there for a 1 out of 5 is 20%. Thankfully, AP scoring doesn’t work this way, and you’ve been listening to the APsolute Recap - so the odds are more in your favor. The rules of probability can be applied to follow the passing of single gene traits from parent to offspring. If A and B are mutually exclusive, then add their probabilities together. If A and B are independent, then multiply their probabilities. So what is the probability of flipping a coin and it lands on two heads in a row? Or two heterozygous parents have an offspring that is homozygous recessive, consecutively? Punnett Squares model the probability of alleles recombining during fertilization.
The remaining math recaps for this episode have applications in more than one unit of study as they are used to statistically analyze data. Standard Deviation is a measurement of how spread out data points are. In standard Error of the mean, the standard deviation value is divided by the square root of the sample size (or n). For the purposes of the AP Exam, students will not be required to perform calculations using the standard deviation or standard error of the mean equation. However, you must understand the underlying concepts and applications. When graphing error bars in AP Biology, they must indicate +/- 2X the SEM. So if my standard error of the mean is 1.5, then I need to graph my error bars as 3 above and 3 below the average. If two error bars are overlapping, then there is no statistical difference between the variable groups. Essentially, the data is too spread out from the average to say that the groups are distinct.
Closing out with Chi Square. This statistical test compares your observed experimental data with an expected calculated outcome, determining if differences are just due to chance or another influencing variable. In statistics a “significant” difference means there is less than 5% chance that the variation in the data is due to random events. Therefore, the variation is most likely due to an environ-mental factor. A common scenario is to be given observed phenotypic traits and where you must figure out the expected through a punnett square. Observed, expected - sounds like chi square. Once your value is calculated (again, check the math sheet - and remember your PEMDAS rules), compare your value to the Chi-square table of critical values. You will find the column of your degree of freedom and the p value row of 0.05, or 95% confidence. Your degree of freedom is equal to the number of distinct possible outcomes minus one (so if there is an option of heads or tails in a coin flip, then the degree of freedom is 1). Chi square values are often used to reject or fail to reject a null hypothesis. If the calculated Chi-Square value is smaller than the critical value, we fail to reject our null hypothesis because our data is consistent with what we would expect—any slight difference is due to chance. If the calculated Chi Square is larger than the critical value, we reject our null hypothesis because our data is too different from what was expected to explain the differences by chance—there must be some other explanation.
Other math topics like Hardy-Weinberg Equilibrium and Simpson’s Diversity Index will not be included in the 2020 exam, as these apply to Evolution and Ecology respectively.
To recap….
Yes, there is math in AP Biology. Have your calculator handy and check your equations and formulas sheet. Always make your math have meaning through analysis, biological application and units.
Today’s Question of the day is about symbols.
Question: What is the Greek letter for summation?