This AP Biology reference sheet brings together the equations and concepts students use most often when solving data-based biology problems. It supports quick review for labs, free-response questions, and multiple-choice practice. Students need it because AP Biology often tests whether they can choose the correct model, substitute values correctly, and explain biological meaning from a calculation.
Key Facts
- Mean is calculated as x-bar = sum of all values / n, where n is the number of data points.
- Standard deviation measures spread around the mean and is commonly used to compare variation among biological samples.
- Chi-square is calculated as X2 = sum of (observed - expected)^2 / expected, and a larger value means a larger difference between observed and expected results.
- Hardy-Weinberg allele frequencies follow p + q = 1, and genotype frequencies follow p^2 + 2pq + q^2 = 1.
- Population growth can be modeled as dN/dt = rN for exponential growth, where N is population size and r is the per capita growth rate.
- Logistic growth can be modeled as dN/dt = rN((K - N) / K), where K is carrying capacity.
- Water potential is calculated as psi = psi_s + psi_p, where psi_s is solute potential and psi_p is pressure potential.
- Free energy change is calculated as delta G = delta H - T delta S, and a negative delta G indicates an energetically favorable process.
Vocabulary
- Chi-square test
- A statistical test used to compare observed data with expected data and decide whether differences are likely due to chance.
- Hardy-Weinberg equilibrium
- A model describing a population in which allele and genotype frequencies stay constant across generations when no evolutionary forces act.
- Carrying capacity
- The maximum population size an environment can support with its available resources.
- Water potential
- A measure of the tendency of water to move from one area to another, usually from higher potential to lower potential.
- Free energy
- The usable energy in a system that can do work during a biological or chemical process.
- Allele frequency
- The proportion of a specific allele among all alleles for a gene in a population.
Common Mistakes to Avoid
- Using genotype frequency as allele frequency is wrong because p and q represent alleles, not whole genotypes.
- Forgetting to square the difference in a chi-square calculation is wrong because X2 requires (observed - expected)^2 for each category.
- Treating standard deviation as standard error is wrong because standard deviation describes variation in data, while standard error estimates uncertainty in the sample mean.
- Ignoring units in water potential problems is wrong because pressure potential and solute potential must use the same units before they are added.
- Assuming exponential growth continues forever is wrong because real populations often face limited resources and may shift toward logistic growth.
Practice Questions
- 1 In a population at Hardy-Weinberg equilibrium, the frequency of the recessive phenotype is 0.16. Find q, p, and the heterozygote frequency 2pq.
- 2 A chi-square test has observed counts of 42 and 58, while expected counts are 50 and 50. Calculate X2.
- 3 A population has N = 500 and r = 0.04. Using exponential growth, calculate dN/dt = rN.
- 4 Explain why a population that is not evolving must meet multiple Hardy-Weinberg conditions, including random mating and no natural selection.
Understanding AP Biology Reference Sheet
Statistics become useful when they help you judge whether a pattern is likely to be meaningful. A mean gives one central value, but it can hide important differences. Two groups can have the same mean while one group has much wider variation.
Standard deviation helps reveal that spread. In a lab graph, error bars often show standard deviation. Large overlapping error bars do not automatically prove that groups are the same.
They do signal that individual results varied a lot. Check the sample size too. A small sample can give an unreliable picture of a population.
Chi-square is used when results fall into separate categories, such as flower colors, offspring phenotypes, or numbers of pill bugs choosing each side of a chamber. First, make an expected outcome from a biological model. Then compare it with the observed counts.
The calculation does not prove that a hypothesis is true. It estimates whether the differences could reasonably result from random chance. You must use counts rather than percentages unless you convert percentages back into counts.
Each expected category should have enough individuals for the test to be reliable. On AP Biology questions, the final conclusion should connect the result to the null hypothesis instead of merely reporting a number.
Hardy-Weinberg calculations work best as a snapshot of a population. They let biologists estimate hidden genotype frequencies from visible trait data. A recessive phenotype can reveal the frequency of individuals with two recessive alleles, which can then be used to estimate carriers.
Real populations rarely meet every Hardy-Weinberg condition for long. Mutation creates new alleles. Migration moves alleles between populations.
Natural selection changes reproductive success. Genetic drift has strong effects in small populations.
Nonrandom mating changes genotype frequencies. When a population differs from the model, think about which evolutionary mechanism could explain the change.
Population models are simplified descriptions, not promises about what nature will do. Exponential growth can occur briefly when resources are abundant, such as bacteria growing in fresh nutrient broth. Logistic growth includes limits from food, space, disease, predation, or waste buildup.
Carrying capacity can shift after drought, habitat loss, seasonal change, or a new food source. Population graphs may rise above carrying capacity before falling because environmental feedback is often delayed. Water potential explains why plant cells gain or lose water.
Water moves toward lower water potential. Solutes lower water potential, while pressure inside a firm plant cell raises it.
Free energy helps explain why some reactions release usable energy and others need energy input. Cells often couple an unfavorable reaction to ATP breakdown, making the combined process energetically favorable.