AP Biology Formula Sheet

The same content as the sheet you get on the exam, in our own layout. Every value in it is worked out by our math engine. The practice exams show this sheet under their Reference button.

AP Biology formula sheet

The equations and formulas you may look up on the AP Biology exam, gathered in one place: statistics and probability, rates and growth, water potential, diversity, and surface area and volume. The exam gives you a sheet with the same content; knowing what each symbol means, and when each formula applies, saves time when you need it.

Statistical analysis and probability

Formula	Name
$\bar{x} = \dfrac{1}{n}\sum_{i=1}^{n} x_i$	mean
$s = \sqrt{\dfrac{\sum (x_i - \bar{x})^2}{n - 1}}$	sample standard deviation
$SE_{\bar{x}} = \dfrac{s}{\sqrt{n}}$	standard error of the mean
$\chi^2 = \sum \dfrac{(o - e)^2}{e}$	chi-square

$\bar{x}$ is the sample mean, $n$ the sample size, $s$ the sample standard deviation (the estimate, from the sample, of the population's standard deviation), $o$ the observed results, $e$ the expected results and $\sum$ the sum of all. The degrees of freedom are the number of distinct possible outcomes minus one.

Chi-square table

The critical values: if $\chi^2$ is larger than the value for the degrees of freedom and the $p$ value chosen, the difference between observed and expected results is significant.

$p$ value	1	2	3	4	5	6	7	8
0.05	$3.84$	$5.99$	$7.81$	$9.49$	$11.07$	$12.59$	$14.07$	$15.51$
0.01	$6.63$	$9.21$	$11.34$	$13.28$	$15.09$	$16.81$	$18.48$	$20.09$

The columns are the degrees of freedom.

Laws of probability

When	Then
A and B are mutually exclusive	$P(\text{A or B}) = P(\text{A}) + P(\text{B})$
A and B are independent	$P(\text{A and B}) = P(\text{A}) \times P(\text{B})$

Hardy-Weinberg equations

Equation	Symbols
$p^2 + 2pq + q^2 = 1$	$p$ is the frequency of allele 1 in a population
$p + q = 1$	$q$ is the frequency of allele 2 in a population

Mode, median, mean and range

Mode: the value that occurs most often in a data set.
Median: the middle value, which separates the greater and the lesser halves of a data set.
Mean: the sum of all the data points divided by the number of data points.
Range: the greatest value (the sample maximum) minus the smallest (the sample minimum).

Metric prefixes

Factor	Prefix	Symbol
$10^{9}$	giga	G
$10^{6}$	mega	M
$10^{3}$	kilo	k
$10^{-1}$	deci	d
$10^{-2}$	centi	c
$10^{-3}$	milli	m
$10^{-6}$	micro	μ
$10^{-9}$	nano	n
$10^{-12}$	pico	p

Rate and growth

Formula	Name
$\dfrac{dY}{dt}$	rate
$\dfrac{dN}{dt} = B - D$	population growth
$\dfrac{dN}{dt} = r_{max}N$	exponential growth
$\dfrac{dN}{dt} = r_{max}N\left(\dfrac{K - N}{K}\right)$	logistic growth

$dY$ is the amount of change, $dt$ the change in time, $dN$ the change in population size, $B$ the birth rate, $D$ the death rate, $N$ the population size, $K$ the carrying capacity and $r_{max}$ the maximum per capita growth rate of the population.

Simpson's diversity index

Formula	Symbols
$\text{Diversity index} = 1 - \sum\left(\dfrac{n}{N}\right)^2$	$n$ is the total number of organisms of one species, $N$ the total number of organisms of all species

Water potential

Formula	Symbols
$\Psi = \Psi_P + \Psi_S$	$\Psi_P$ is the pressure potential, $\Psi_S$ the solute potential
$\Psi_S = -iCRT$	the solute potential of a solution

The water potential of a solution in an open container equals its solute potential, because the pressure potential of a solution in an open container is zero. In $\Psi_S = -iCRT$ , $i$ is the ionization constant (1.0 for sucrose, which does not ionize in water), $C$ the molar concentration, $R$ the pressure constant, $R$ = $0.0831\,\mathrm{L{\cdot}bar/(mol{\cdot}K)}$ , and $T$ the temperature in kelvins (°C + 273).

Surface area and volume

Shape	Surface area	Volume
Sphere	$SA = 4\pi r^2$	$V = \frac{4}{3}\pi r^3$
Rectangular solid	$SA = 2lh + 2lw + 2wh$	$V = lwh$
Cylinder	$SA = 2\pi rh + 2\pi r^2$	$V = \pi r^2 h$
Cube	$SA = 6s^2$	$V = s^{3}$

$r$ is the radius, $l$ the length, $h$ the height, $w$ the width, $s$ the length of one side of a cube, $SA$ the surface area and $V$ the volume.