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Appendix A A
Appendix A
AP BIOLOGY EQUATIONS AND
FORMULAS
StAtiSticAl AnAlySiS And ProbAbility (^) s = sample standard deviation (i.e., the sample based estimate of the standard deviation of the population) x = mean n = size of the sample o = observed individuals with observed genotype e = expected individuals with observed genotype
Degrees of freedom equals the number of distinct possible outcomes minus one.
Standard Error Mean
Standard Deviation Chi-Square
chi-SquAre tAble Degrees of Freedom p 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 9.32 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) x P(B) hArdy-weinberg equAtionS
p^2 + 2pq + 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 10 9 giga G 10 6 mega M 10 3 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)
A2 Appendix A
rAte And growth 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, since the pressure potential of the solution in an open container is zero. the Solute Potential of the Solution
Ψs = – iCRT
i = ionization constant (For sucrose this is 1.0 because sucrose does not ionize in water.) C = molar concentration R = pressure constant (R = 0.0831 liter bars/mole K) T = temperature in Kelvin (273 + ºC)
rate dY/dt Population growth dN/dt=B-D exponential growth
logistic growth
dY= amount of change t = time B = birth rate D = death rate N = population size K = carrying capacity rmax = maximum per capita growth rate of population
temperature coefficient q 10
Primary Productivity calculation
mg O 2 /L x 0.698 = mL O 2 /L
mL O 2 /L x 0.536 = mg carbon fixed/L
t 2 = higher temperature t 1 = lower temperature k 2 = metabolic rate at t 2 k 1 = metabolic 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 (^) 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
Volume of a Sphere
V = 4/3 π r^3
Volume of a cube (or Square column)
V = l w h
Volume of a column
V = π r^2 h
Surface Area of a Sphere
A = 4 π r^2
Surface Area of a cube
A = 6 a
Surface Area of a rectangular Solid
A = Σ (surface area of each side)
r = radius l = length h = height w = width A = surface area V = volume
Σ = Sum of all
a = surface area of one side of the cube 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 [H+]
