Waqar - Gatewaytobiology
Uploaded by
Atta Ul Mustafa ZainWaqar - Gatewaytobiology
Uploaded by
Atta Ul Mustafa Zain2023
Gate way to Biology
Free-Response Questions
GW BIOLOGY EQUATIONS AND FORMULAS
Statistical Analysis and Probability
Mean Standard Deviation x = sample mean
n
1 Â(xi - x )2 n = sample size
x =
n Âxi s=
n -1
i=1 s = sample standard deviation (i.e., the sample-based
Standard Error of the Mean Chi-Square estimate of the standard deviation of the
population)
SE = s 2 o e2
x
n e o = observed results
Chi-Square Table e = expected results
p Degrees of Freedom
value 1 2 3 4 5 6 7 8 = sum of all
0.05 3.84 5.99 7.81 9.49 11.07 12.59 14.07 15.51
Degrees of freedom are equal to the number of
0.01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09
distinct possible outcomes minus one.
Laws of Probability Metric Prefixes
If A and B are mutually exclusive, then:
Factor Prefix Symbol
P (A or B) = P (A) + P (B)
109 giga G
If A and B are independent, then:
106 mega M
P (A and B) = P (A) P (B) 103 kilo k
10–1 deci d
Hardy-Weinberg Equations
10–2 centi c
p2 + 2pq + q2 = 1 p = frequency of allele 1 in a
10–3 milli m
population
p+q=1 10–6 micro μ
q = frequency of allele 2 in a 10–9 nano n
population 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)
Rate and Growth Water Potential ( Y )
Rate dY = amount of change Y = YP + YS
dY dt = change in time
dt YP = pressure potential
B = birth rate
Population Growth
dN D = death rate YS = solute potential
= B- D
dt N = population size The water potential will be equal to the
Exponential Growth K = carrying capacity solute potential of a solution in an open
container because the pressure potential of
rmax = maximum per capita
dN the solution in an open container is zero.
= rmax N growth rate of population
dt
The Solute Potential of a Solution
Logistic Growth
YS = -iCRT
dt max K (
dN = r N K - N
) i = ionization constant (1.0 for sucrose
because sucrose does not ionize in
water)
Simpson’s Diversity Index
2
Diversity Index = 1 - Â( )n
N
C = molar concentration
R = pressure constant
n = total number of organisms of a particular species ( R = 0.0831 liter bars/mole K)
N = total number of organisms of all species T = temperature in Kelvin (ºC + 273)
pH = – log[ H+]
Surface Area and Volume
Surface Area of a Sphere Volume of a Sphere r = radius
SA 4 r 2 V 4 r3 l = length
3
Surface Area of a Rectangular Volume of a Rectangular Solid h = height
Solid V lwh
w = width
SA 2lh 2lw 2wh
Volume of a Cylinder s = length of one
Surface Area of a Cylinder V r h 2 side of a
SA 2 rh 2 r 2 cube
Volume of a Cube SA = surface area
Surface Area of a Cube V s 3
SA 6s2 V = volume