# AP Biology Necessary Graphing and Quantitative Skills

This note will go over all the necessary graphing and quantitative skills and mathematical concepts a student should know for AP Biology. They will be using everything that is in this note across all units.

Variables apart of the Experimental Design:

Independent Variable: The Variable that is being manipulated

Dependent Variable: The variable that is being measured of tested

Control group: this is used to compare the different groups of the experiment and whether there was a significant difference.

Negative control group: something that is known to have no effect

Positive control group: is known to have an affect

Control Variables: the variables apart of the experiment that are kept constant

Alternative hypothesis: a hypothesis that determines a negative result or a positive result( A will have an affect on B if…)

Null hypothesis: there will be no effect on the dependent variable (A will have no effect on B). For example:

• Placebo (N)

• No treatment(N)

Types of Graphs:

Pie Graph:

• Can show the frequencies of data

• Can show out of a total amount of individuals

• Or in a percentage form

Bar Graph:

• Parametric

• Can show data between two groups

• Usually has error bars

Scatterplot:

• Shows points on a graph with a correlation line extrapolated

Histogram:

• Great for nonparametric data shows the outliers

Bar and Whisker plot:

• Also used for nonparametric data and shows the ranges of data in a more conformed way

Line Graph:

• These can show time course experiments

• Can have several lines

• Can also have error bars on the points

This is a helpful video that explains the different types of graphs:

Error/SEM bars:

What do error bars represent

• Error bars represent the standard error of the mean

How would you graph SEM bars

• To graph these you must add the number to the maxim point then subtract from the maximum point

If the error bars do overlap then…

• There is no statistical difference or significance that we cannot be 95% sure with our data

If the error bars don’t overlap then…

• There is a statistical significance in the data and we are 95% confident that there is

With this you then can?

• reject the null hypothesis

or

• Accept the null hypothesis

• Accept the alternative hypothesis

or

• Reject the alternative hypothesis

Chi square:

Null hypothesis- there is no difference that...will effect…(can also be an alternative hypothesis)

Degrees of freedom: #of choices-1

P-value: 0.05 for AP Bio goes into the idea of 95% confidence interval

Critical Value: degree of freedom at the P-value.

Chi square equation and chart will be given in the test along with any formulas you may need to know for AP Biology.

1. No mutation

2. No natural selection

3.  Random mating

4. Large population

5.  No gene flow

Hardy-Weinberg:

p - frequency of the dominant allele.

• p + q = 1
• Usually has error bars

• can be given and if so use the equation above

q - frequency of the recessive allele.

• p + q = 1
• always solve for q or use q first

q2 - individuals that are recessive for the trait.

• p2+2pq+q2=1
• if given, radical 2 it to get q value

p2 - individuals that are dominant for the trait.

• p2+2pq+q2=1
• if given, divide to get p and then do p - 1 to get q

2pq - heterozygous individuals.

• p2+2pq+q2=1
• most likely won't be given first
• could multiply by 2 to get allele total

Surface Area to Volume Problems:

• This goes into the topic of compartmentalization of cells!

• The greater the surface area to volume ratio is the more efficient the cell can work when processing things

• Try and maybe imagine a big deep pool vs a small shallow pool. Which one could you travel faster in?

Water Potential/Osmosis Problems:

• Water potential is a calculation that determines the likelihood of water leaving a certain location

• The higher the water potential the more likely water will leave

• Water potential can be affected by the concentration of solute and the pressure

• When one bar is a greater bar then the other then that one has the higher water potential

• The highest water potential is 0

• Water potential values are negative so the greater the negative value the more likely water will move.

• Watch this video to understand better:

Ecology Formula: to interpret and represent population dynamics in ecosystems

•   Rate Population Growth Exponential Growth Logistic Growth dY/dt dN = B – Ddt dN = rmaxNdt dN= rmaxN( K – N)dt                     K dY = amount of change              B = birth rate                D = death rate               N = population sizeK = carrying capacity                rmax = maximum per capita growth rate of population NotesdN  = ∆N = Change in population size  = population growth rate dt      ∆t          change in time