AP Biology Formula Sheet – Key Equations, Processes & Must-Know Facts (College Board CED)
This sheet gathers the equations and ideas that come up again and again across AP Biology, organised in the same order as the College Board Course and Exam Description (CED), effective Fall 2025. It is built for quick revision: find your unit, check the equation, then test yourself on the facts underneath it. Equations marked as from the official CED formula sheet are the ones printed in the appendix of the CED itself; other equations are core course equations that you are still expected to understand and use.
How to use this sheet: Do not just read the boxes. Cover the right-hand explanation, say what each symbol means out loud, and work one small example for every equation before moving on. When a unit has no new equation, that is useful information too — the marks there come from explaining processes clearly, not from plugging numbers into a formula. For related revision, see the Biology MCQs hub, and the companion sheets for GCSE Biology, IGCSE Biology and A-Level Biology.
Unit 1: Chemistry of Life (8–11% of the multiple-choice section)
Key equations — from the official CED formula sheet
Water potential: Ψ = Ψp + Ψs
Solute potential: Ψs = −iCRT
Here Ψp is pressure potential and Ψs is solute potential. In the solute-potential equation, i is the ionisation constant (1.0 for sucrose, which does not ionise in water), C is molar concentration, R is the pressure constant 0.0831 litre bars per mole per kelvin, and T is temperature in kelvin (degrees Celsius + 273). Water moves from a region of higher (less negative) water potential to a region of lower (more negative) water potential. In an open container, pressure potential is zero, so water potential equals solute potential.
Core processes and must-know facts:
- Water is polar: the oxygen end carries a partial negative charge and the hydrogen ends carry partial positive charges. Hydrogen bonds between water molecules explain cohesion, adhesion, a high specific heat, and the way water acts as a solvent for many substances.
- Living things are built mainly from carbon, hydrogen, oxygen, nitrogen, phosphorus and sulfur, and carbon’s ability to form four bonds makes large, varied organic molecules possible.
- Carbohydrates, lipids, proteins and nucleic acids are the four main macromolecule groups. Small monomer units join into long polymers, and breaking a polymer apart is the reverse process.
- Carbohydrates supply quick energy and structural material; lipids store energy, build membranes and act as signals; proteins do most of the work in a cell, from speeding up reactions to moving substances and sending signals; nucleic acids store and carry genetic instructions.
- A protein’s shape decides what it can do. Heat, pH changes or other harsh conditions can unfold a protein, and an unfolded protein usually stops working properly.
- DNA is double-stranded and stores hereditary information, while RNA is usually single-stranded and takes part in building proteins. Both are built from nucleotide monomers, each with a sugar, a phosphate group and a nitrogen-containing base.
Unit 2: Cells (10–13% of the multiple-choice section)
Key equations — from the official CED formula sheet
Surface area and volume of a sphere: SA = 4πr2, V = (4/3)πr3
Surface area and volume of a cube: SA = 6s2, V = s3
Surface area and volume of a rectangular solid: SA = 2lh + 2lw + 2wh, V = lwh
Surface area and volume of a cylinder: SA = 2πrh + 2πr2, V = πr2h
Here r is radius, s is the side of a cube, and l, w and h are length, width and height. The surface-area-to-volume ratio matters because exchange with the surroundings happens across a surface, while demand grows with volume: as a cell grows, its ratio falls, which limits how large a single cell can usefully become.
Magnification (general microscopy relationship, not printed on the CED formula sheet): magnification = image size ÷ actual size, with both sizes in the same units.
Core processes and must-know facts:
- Prokaryotic cells have no membrane-bound nucleus and no membrane-bound organelles, while eukaryotic cells keep their DNA in a nucleus and divide their work among specialised compartments.
- The nucleus holds genetic material; mitochondria release usable energy from food molecules; chloroplasts capture light energy in plant cells; ribosomes build proteins; the endomembrane system modifies, packages and moves proteins and lipids; vacuoles store substances; and the cytoskeleton gives shape and moves material inside the cell.
- The plasma membrane is a fluid bilayer with proteins embedded in it. It controls what enters and leaves, and its selective permeability depends on both the lipid layer and its proteins.
- Passive transport, including simple diffusion and facilitated diffusion through channel or carrier proteins, needs no energy input from the cell. Active transport moves substances against their gradient and costs energy, usually from ATP.
- Osmosis is the movement of water across a selectively permeable membrane. In a hypotonic surroundings a cell gains water, in a hypertonic surroundings it loses water, and in an isotonic surroundings there is no net gain or loss.
- Cells compartmentalise their work: keeping different reactions in different spaces lets incompatible processes run side by side and lets each space keep its own conditions.
Unit 3: Cellular Energetics (12–16% of the multiple-choice section)
Key equations — core course equations (not in the CED formula-sheet appendix)
Photosynthesis: 6CO2 + 6H2O → C6H12O6 + 6O2
Cellular respiration (overall): C6H12O6 + 6O2 → 6CO2 + 6H2O + energy (captured as ATP)
Rate (from the official CED formula sheet): rate = dY ÷ dt, where dY is the amount of change and dt is the change in time.
Note: the CED states that the equation for Gibbs free energy is beyond the scope of the AP Exam, so it is deliberately left off this sheet. Learn the idea that energy flows and that usable energy is captured or released, without memorising that equation.
Core processes and must-know facts:
- Enzymes speed up reactions by lowering the energy barrier that must be crossed, without being used up themselves. Each enzyme works best in a narrow range of temperature and pH, and its shape fits its substrate.
- Competitive inhibitors block the active site, while non-competitive inhibitors bind elsewhere and change the enzyme’s shape. Both slow a reaction down, but in different ways.
- ATP is the cell’s short-term energy currency: energy is stored when ATP is built and released when it is broken down, and the cell constantly recycles it.
- In photosynthesis, light-dependent reactions in the thylakoids split water, release oxygen, and produce energy carriers. The Calvin cycle then uses those carriers to fix carbon dioxide into sugar.
- In cellular respiration, glycolysis in the cytoplasm splits glucose into two smaller molecules, the Krebs cycle completes the breakdown of carbon compounds, and the electron transport chain produces most of the ATP. Oxygen acts as the final electron acceptor in aerobic respiration.
- When oxygen is missing, fermentation recycles the electron carrier needed for glycolysis to continue, so a small amount of ATP can still be made, but far less than in aerobic respiration.
- Photosynthesis and respiration are linked: the products of one are largely the starting materials of the other, which is why energy flows through living systems rather than cycling like matter.
Unit 4: Cell Communication and Cell Cycle (10–15% of the multiple-choice section)
Key equations: No new equation is introduced for this unit on the official CED formula sheet. The skill tested here is explaining a sequence and predicting what happens when one step changes, so revise the pathways below as step-by-step stories, not as calculations.
Core processes and must-know facts:
- Cell signalling follows three stages: reception, when a signal molecule binds a receptor; transduction, when the signal is relayed and often amplified inside the cell; and response, when the cell changes its activity.
- Signals can act on the same cell, on nearby cells, or at a distance through the bloodstream. Whether a cell responds depends on whether it carries the matching receptor, not just on whether the signal is present.
- Second messengers and enzyme cascades amplify a signal, so a small number of signal molecules can produce a large response inside the cell.
- Feedback keeps systems steady: negative feedback reverses a change and returns a system toward its set point, while positive feedback strengthens a change and drives a process to completion.
- The cell cycle runs through growth and preparation, DNA copying, further growth, and mitosis followed by division of the cytoplasm. Checkpoints pause the cycle when DNA is damaged or copying is incomplete.
- Mitosis produces two genetically identical daughter cells and is used for growth, repair and asexual reproduction. Uncontrolled division, when checkpoints fail, can lead to tumours.
- Apoptosis is programmed cell death: an orderly, controlled removal of damaged or unneeded cells that protects the organism as a whole.
Unit 5: Heredity (8–11% of the multiple-choice section)
Key equations — from the official CED formula sheet
Chi-square: χ2 = Σ((O − E)2 ÷ E), where O is the observed result and E is the expected result, summed over all categories.
Degrees of freedom: number of distinct possible outcomes minus one. Compare the chi-square value with the critical value at p = 0.05: a larger value means the difference from the expected result is unlikely to be due to chance alone.
Laws of probability: if A and B are mutually exclusive, P(A or B) = P(A) + P(B). If A and B are independent, P(A and B) = P(A) × P(B).
Mean and standard error: mean, x̄ = Σx ÷ n, where n is sample size; standard error of the mean, SE = s ÷ √n, where s is the sample standard deviation.
Core processes and must-know facts:
- Meiosis halves the chromosome number and shuffles genetic material, producing genetically varied gametes. Fertilisation then restores the full chromosome number in the offspring.
- Crossing over during prophase I and the independent assortment of chromosomes during metaphase I are the two main sources of new gene combinations in meiosis.
- In a cross between two heterozygous parents for one gene, the expected genotype ratio is 1:2:1 and the expected phenotype ratio is 3:1 when one allele is fully dominant.
- Linked genes on the same chromosome tend to be inherited together, but crossing over can separate them. The farther apart two genes are, the more often they are separated.
- Not all inheritance is simple dominance: incomplete dominance gives an intermediate phenotype, codominance shows both alleles, multiple alleles and polygenic traits add further variety, and some traits are carried on sex chromosomes.
- The environment can change how genes are expressed, so the same genotype can produce different phenotypes in different conditions. Pedigrees and test crosses are used to work out inheritance patterns from family data.
- Use chi-square to judge whether observed offspring numbers fit an expected ratio. State the expected numbers first, show the calculation, and then explain what the result means for the hypothesis.
Unit 6: Gene Expression and Regulation (12–16% of the multiple-choice section)
Key equations: No new equation is introduced for this unit on the official CED formula sheet. The marks here come from tracing information accurately from DNA to RNA to protein, and from explaining how that flow is controlled.
Core processes and must-know facts:
- DNA replication is semi-conservative: each new double helix keeps one original strand and one newly built strand. Replication starts at origins, unwinds the helix, and builds each new strand in the 5′ to 3′ direction.
- Transcription copies a gene into RNA using one DNA strand as a template. In eukaryotes the RNA is processed before leaving the nucleus, including removal of non-coding sections and addition of a cap and a tail.
- Translation reads messenger RNA in three-base codons at the ribosome, and each codon matches a transfer RNA carrying one amino acid. The chain folds into a protein as it is built.
- Gene expression is regulated at several points: whether a gene is switched on, how its RNA is processed, and how long its protein lasts. Bacteria often control groups of related genes together, while eukaryotes use transcription factors and changes to chromosome structure.
- Different cell types in one organism carry the same DNA but express different genes, which is how specialised cells arise from a single fertilised egg.
- Mutations change DNA sequence. Some have no effect, some change one amino acid, and insertions or deletions that shift the reading frame usually change many amino acids after the mutation point.
- Biotechnology tools include gel electrophoresis, which separates DNA fragments by size; polymerase chain reaction, which copies a chosen DNA section many times; and bacterial transformation, which introduces new DNA into cells. Gene editing tools can change a targeted DNA sequence.
Unit 7: Natural Selection (13–20% of the multiple-choice section)
Key equations — from the official CED formula sheet (Hardy–Weinberg)
Allele frequencies: p + q = 1
Genotype frequencies: p2 + 2pq + q2 = 1
Here p is the frequency of allele 1 and q is the frequency of allele 2 in the population. In the genotype equation, p2 is the frequency of one homozygote, 2pq is the frequency of heterozygotes, and q2 is the frequency of the other homozygote. These equations describe a population that is not evolving; if observed frequencies differ from the prediction, something is changing allele frequencies.
Core processes and must-know facts:
- Natural selection acts on variation that already exists in a population. Individuals with traits that suit their environment tend to survive and reproduce more, so those traits become more common over generations.
- Hardy–Weinberg equilibrium assumes a large population with random mating and no mutation, migration, genetic drift or selection. Real populations usually break at least one of these conditions.
- Genetic drift changes allele frequencies by chance and has the strongest effect in small populations. A bottleneck or a founder event can sharply reduce variation in a population.
- Evidence for evolution comes from fossils, anatomical similarities and differences, embryology, biogeography, and comparisons of DNA and protein sequences. The more similar two species’ sequences are, the more recently they usually shared a common ancestor.
- Speciation happens when populations stop exchanging genes, often after geographic separation or after reproductive barriers build up. Over time, accumulated differences can make interbreeding impossible.
- Phylogenetic trees show proposed evolutionary relationships. Shared derived traits group species together, and the branching pattern, not the left-to-right order of the tips, carries the meaning.
- Evolution continues today: antibiotic resistance in bacteria and pesticide resistance in pests are current, observable examples of selection changing populations.
Unit 8: Ecology (10–15% of the multiple-choice section)
Key equations — from the official CED formula sheet
Population growth: dN ÷ dt = B − D, where dN is the change in population size, B is birth rate and D is death rate.
Exponential growth: dN ÷ dt = rmaxN, where N is population size and rmax is the maximum per capita growth rate.
Logistic growth: dN ÷ dt = rmaxN(K − N) ÷ K, where K is carrying capacity.
Simpson’s Diversity Index: Diversity Index = 1 − Σ(n ÷ N)2, where n is the total number of organisms of one species and N is the total number of organisms of all species.
Core processes and must-know facts:
- Organisms respond to their environment through behaviour and physiology, and the same species can show different responses in different conditions.
- Energy flows through ecosystems in one direction, from producers to consumers, and much of it is lost at each transfer, so food chains stay short. Matter, by contrast, is recycled through biogeochemical cycles such as the carbon, water, nitrogen and phosphorus cycles.
- Population growth is exponential when resources are unlimited, but in real habitats density-dependent factors such as competition, predation and disease slow growth as the population approaches carrying capacity, giving logistic growth.
- Density-independent factors, such as storms or drought, affect a population regardless of its size. Both kinds of factor shape the population curves you are asked to interpret.
- Communities are shaped by competition, predation, herbivory, symbiosis and keystone species, whose loss changes the community far more than their numbers alone would suggest.
- Biodiversity can be described by species richness and by how evenly individuals are spread among species. Simpson’s Diversity Index combines both ideas: a community dominated by one species scores lower than a community with many evenly represented species.
- Human activity disrupts ecosystems through habitat loss, introduced species, pollution and climate change. Excess nutrients can trigger algal growth and oxygen depletion in water, and harmful substances can build up to higher concentrations at higher trophic levels.
Keep Revising
Work through this sheet unit by unit rather than reading it end to end. For each unit, write the equations from memory, explain one process without looking, and then check yourself against the sheet. Spend extra time on the units with the largest exam share — natural selection, cellular energetics and gene expression — but do not skip the smaller units, because a confident answer there is often the easiest mark on the paper. Finally, practise with data: describe a graph in words, carry out a chi-square or Hardy–Weinberg calculation step by step, and always finish by saying what the number means for the biology, not just what the number is.
AP Biology Section MCQs
Unit-wise practice questions for AP Biology (College Board CED) — 30 MCQs per unit with answers and explanations.
