AP Biology · Exam guide
AP Biology Math Skills: Rates, Percent Change, Surface Area to Volume, and Water Potential
The calculations on the AP Biology exam are short. They use formulas from the equation sheet and ask for a number with units and a short interpretation. This guide works the four most common ones.
Percent change
Percent change = (final - initial) / initial x 100. Mean seedling height rose from 8.0 cm to 13.0 cm. The percent change is (13.0 - 8.0) / 8.0 x 100 = 62.5 percent.
Surface area to volume ratio
A cube with a side of 2 cm has a surface area of 6 x 2^2 = 24 cm^2 and a volume of 2^3 = 8 cm^3, so the ratio is 3 to 1. A cube with a side of 4 cm has a surface area of 96 cm^2 and a volume of 64 cm^3, so the ratio is 1.5 to 1. As an object grows, volume grows faster than surface area, so the ratio falls. That is why large cells have trouble exchanging materials, and why many are small or have folded membranes.
Rate
Rate = change in the quantity / change in time. Always include units, such as mL of oxygen per minute or grams per hour. When a graph is given, use two points on the line, not points that are not on it.
Water potential
Water potential is the sum of the solute potential and the pressure potential. The solute potential is -iCRT, where i is the ionization constant, C is the molar concentration, R is the pressure constant, 0.0831 liter bar per mole kelvin, and T is the temperature in kelvin.
Example: a 0.3 M sucrose solution at 25 degrees Celsius, which is 298 K. Sucrose does not ionize, so i = 1. The solute potential is -(1)(0.3)(0.0831)(298) = -7.43 bars. In an open beaker, the pressure potential is zero, so the water potential is -7.43 bars. Water moves from higher (less negative) water potential to lower (more negative) water potential.
It leaves out the negative sign. Solute potential is always negative or zero.
It shows the formula, the values, and the sign and units.
Common mistakes
- Dividing by the final value instead of the initial value in percent change.
- Using degrees Celsius instead of kelvin in the water potential formula.
- Leaving out units or a negative sign.
- Computing a rate with points that are not on the line of the graph.
Frequently asked questions
Are the formulas given on the exam?
Yes. An equation sheet is provided, but you need to know how to use each formula.
Can I use a calculator?
Yes, a calculator is allowed. Check the current rules for which types.
How many decimal places should I give?
Follow the question. If it does not say, two or three significant figures is usually safe.
Which way does water move?
From a higher water potential to a lower water potential.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every unit in the AP Biology course ends with a quiz of multiple-choice and short free-response questions, with a writing space that scores against the four-point rubric and a model response to compare against. These free lessons also build the skills the free-response section tests:
See the AP Biology course Free lessons and lesson list
More AP Biology guides (8)
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Free-response and writing
- AP Biology Long Free-Response Question Explained: Interpreting and Evaluating Experimental Results
- AP Biology Graphing Question Explained: How to Construct a Graph and Interpret the Data
- AP Biology Short Free-Response Questions Explained: The Four Types and the 4-Point Rubric
- AP Biology Statistics and Data Analysis: Chi-Square, Error Bars, and Conclusions
- AP Biology Hardy-Weinberg Problems: Allele Frequencies Step by Step
- AP Biology Experimental Design: Variables, Controls, and Predictions
Multiple choice
AP is a registered trademark of the College Board, which is not affiliated with and does not endorse this site. This guide is our own explanation of the question types and scoring. For the official scoring guidelines, see the College Board.