AP Biology equations in practice — water potential, growth models, Simpson index and Hardy–Weinberg

The AP Biology exam gives every student an equations and formulas sheet, but having a formula in front of you is not the same as using it quickly and correctly under time pressure. Calculation questions appear in both the multiple-choice and the free-response sections, and they are usually lost to the same handful of slips: temperature left in degrees Celsius, the ionization constant forgotten for a salt, a minus sign dropped, an exponential formula used where the question describes a carrying capacity, or a proportion left unsquared. This material drills the equations from the sheet that students use least often, with every number given inside the question.

The first group of questions works with water. You calculate the solute potential of sucrose and sodium chloride solutions with −iCRT, converting to kelvin and choosing the right ionization constant; add pressure potential and solute potential to get the water potential of a plant cell; predict the direction of net water movement between a cell and its surroundings; and estimate the water potential of potato cells from the sucrose concentration at which they neither gain nor lose mass.

The second group covers population growth: births minus deaths, exponential growth with the maximum per capita growth rate, logistic growth with a carrying capacity, and the population size at which logistic growth is fastest. The third group uses Simpson's diversity index, first on a single plot and then to compare two plots with the same species but very different evenness. The last questions apply the Hardy–Weinberg equations to genotype counts: finding allele frequencies by counting alleles, comparing the observed number of heterozygotes with the number expected at equilibrium, and working out the frequency of unaffected carriers from the frequency of a recessive condition.

Every distractor is the result of a real mistake, and each explanation shows the full substitution and names the mistake behind the tempting wrong answers, so a wrong choice tells you exactly what to fix.

The material offers a quiz and a flashcard deck. The flashcards review each equation with the meaning of every symbol: solute and water potential, the three growth models, Simpson's index, the Hardy–Weinberg equations, the ionization constant and carrying capacity. Work through it with a calculator, as you would on exam day, where a calculator is permitted.

• Calculate solute potential with −iCRT, including the ionization constant and kelvin temperature
• Combine pressure and solute potential and predict the direction of water movement
• Apply the exponential and logistic growth equations and find where logistic growth is fastest
• Calculate and compare Simpson's diversity index for two communities
• Use Hardy–Weinberg equations on genotype counts, expected heterozygotes and carrier frequency

Practice material written by Zestly, based on the College Board AP Biology course framework (topics 2.7, 7.5, 8.3, 8.4 and 8.5) and the AP Biology equations and formulas sheet (2026 exam reference information).