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Appendix A A
Appendix A
AP BIOLOGY EQUATIONS AND
FORMULAS
Statistical Analysis and Probability x = sample mean
n = size of the sample
s = sample standard deviation (i.e., the sample-based estimate of the standard deviation of the population)
o = observed results
e = expected results
Degrees of freedom are equal to the number of distinct possible outcomes minus one.
Mean Standard Deviation*
x n xi i
n
=
1 S
x x n
i
∑(^ )^
2
1
Standard Error of the Mean Chi-Square*
SE (^) x
s
n
= χ 2
2
( o e ) e Chi-Square Table p value
Degrees of Freedom 1 2 3 4 5 6 7 8 0.05 3.84 5.99 7.82 9.49 11.07 12.59 14.07 15. 0.01 6.64 9.21 11.34 13.28 15.09 16.81 18.48 20.
Laws of Probability If A and B are mutually exclusive, then: P (A or B) = P (A) + P (B) If A and B are independent, then: P (A and B) = P (A) × P (B)
Hardy-Weinberg Equations p^2 + 2 pq + q^2 = 1 p = frequency of the dominant allele in a population p + q = 1 q = frequency of the recessive allele in a population
Metric Prefixes
Factor Prefix Symbol 109 giga G 106 mega M 103 kilo k 10 -2^ centi c 10 -3^ milli m 10 -6^ micro μ 10 -9^ nano n 10 -12^ pico p
Mode = value that occurs most frequently in a data set
Median = middle value that separates the greater and lesser halves of a data set
Mean = sum of all data points divided by number of data points
Range = value obtained by subtracting the smallest observation (sample minimum) from the greatest (sample maximum)
- For the purposes of the AP Exam, students will not be required to perform calculations using this equation; however, they must understand the underlying concepts and applications.
A2 Appendix A
Rate and Growth (^) dY = amount of change
dt = change in time
B = birth rate
D = death rate
N = population size
K = carrying capacity
rmax = maximum per capita growth rate of population
Water Potential ( Ψ )
Ψ = ΨP + ΨS
ΨP = pressure potential
ΨS = solute potential
The water potential will be equal to the solute potential of a solution in an open container because the pressure potential of the solution in an open container is zero.
The Solute Potential of a Solution ΨS = –iCRT
i = ionization constant (this is 1.0 for sucrose because sucrose does not ionize in water)
C = molar concentration
R = pressure constant (R = 0.0831 liter bars/mole K)
T = temperature in Kelvin (ºC + 273)
Rate dY dt
Population Growth dN dt =^ B^ –^ D
Exponential Growth dN dt
= r max N
Logistic Growth
dN dt
r N K^ N K
= (^) max −
Temperature Coefficient Q (^10) †
Primary Productivity Calculation mg O L
0.698 mL mg = mL O L
(^2) × 2
mL O L
0.536 mg C fixed mL O = mg C fixed L
2 2
×
(at standard temperature and pressure)
T 2 = higher temperature
T 1 = lower temperature
k 2 = reaction rate at T 2
k 1 = reaction rate at T 1
Q 10 = the factor by which the reaction rate increases when the temperature is raised by ten degrees
Surface Area and Volume
Volume of a Sphere
V = 4 3 πr^3 Volume of a Rectangular Solid V = lwh Volume of a Right Cylinder V = πr^2 h Surface Area of a Sphere A = 4πr^2 Surface Area of a Cube A = 6s^2 Surface Area of a Rectangular Solid A = (^) Σ surface area of each side
r = radius
l = length
h = height
w = width
s = length of one side of a cube
A = surface area
V = volume
Σ = sum of all
Dilution (used to create a dilute solution from a concentrated stock solution) CiVi = CfVf
i = initial (starting) C = concentration of solute f = final (desired) V = volume of solution
Gibbs Free Energy ΔG = ΔH – TΔS ΔG = change in Gibbs free energy ΔS = change in entropy ΔH = change in enthalpy T = absolute temperature (in Kelvin) pH* = – log 10 [H+^ ]
- For the purposes of the AP Exam, students will not be required to perform calculations using this equation; however, they must understand the underlying concepts and applications.
† (^) For use with labs only (optional).
