Biology
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AP Biology — Cheatsheet

Formulas, exam-day tips, and key terms on one page.

Formulas & relationships

Hydrogen bond
δ⁺H···O δ⁻
The dotted line is the hydrogen bond (an intermolecular attraction), not the covalent O–H bond within a molecule.
Dehydration synthesis / hydrolysis
monomer–OH + H–monomer ⇌ monomer–monomer + H₂O
Left-to-right removes water to bond (dehydration synthesis); right-to-left adds water to break (hydrolysis).
Peptide bond formation
–COOH + H₂N– → –CO–NH– + H₂O
A peptide bond joins the carboxyl carbon of one amino acid to the amino nitrogen of the next, releasing water.
Complementary base pairing (DNA)
A–T · G–C
Adenine pairs with thymine (2 hydrogen bonds); guanine pairs with cytosine (3 hydrogen bonds). In RNA, uracil replaces thymine, so A pairs with U.
Surface-area-to-volume ratio (cube)
SA:V = 6s² / s³ = 6 / s
For a cube of side length s, surface area is 6s² and volume is s³. As s increases, the ratio 6/s falls — bigger cells have relatively less membrane per unit of contents.
The secretory pathway
ribosome/rough ER → transport vesicle → Golgi → secretory vesicle → plasma membrane
The path a protein follows from synthesis to export. Each arrow is a vesicle budding off one compartment and fusing with the next.
Transport at a glance
passive: high → low (no ATP) · active: low → high (ATP)
The direction relative to the concentration gradient tells you whether energy is needed. "Down" the gradient is free; "up" the gradient costs ATP.
Water potential
Ψ = Ψp + Ψs
Ψ is water potential; Ψp is pressure potential and Ψs is solute potential. Water always moves from higher Ψ to lower Ψ. Pure water at atmospheric pressure has Ψ = 0; adding solute makes Ψs (and thus Ψ) negative.
Enzyme catalysis
enzyme + substrate ⇌ enzyme·substrate → enzyme + product
The enzyme binds substrate, forms an enzyme–substrate complex, releases product, and is regenerated — never used up.
Overall photosynthesis
6 CO₂ + 6 H₂O + light → C₆H₁₂O₆ + 6 O₂
Inputs: carbon dioxide, water, and light energy. Outputs: glucose and oxygen. This is the exact reverse of cellular respiration.
Overall aerobic respiration
C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O + energy (ATP)
Inputs: glucose and oxygen. Outputs: carbon dioxide, water, and ATP. The reverse of photosynthesis.
ATP cycle
ATP + H₂O ⇌ ADP + Pᵢ + energy
Left-to-right (hydrolysis) releases energy for cellular work; right-to-left (regeneration) requires energy from catabolism.
Signal amplification cascade
1 ligand → few receptors → many kinases → millions of products
Each step multiplies the number of active molecules, so a small signal yields a large response.
The one-line test
response opposes change ⇒ negative · response amplifies change ⇒ positive
Ask only: does the loop push the variable back toward the set point, or further away?
Cell cycle at a glance
G1 → S → G2 → [ Prophase → Metaphase → Anaphase → Telophase ] → Cytokinesis
G1 · S · G2 make up interphase; PMAT is mitosis; cytokinesis splits the cytoplasm into two cells.
What drives a checkpoint transition
cyclin (rising) + Cdk (constant) → active cyclin-Cdk complex → advance
Cdk levels stay roughly constant; it is the cyclic rise and fall of cyclins that turns the complexes on and off.
Independent assortment combinations
2ⁿ possible gamete types
n is the haploid chromosome number. For humans (n = 23) this is 2²³ ≈ 8.4 million combinations — before crossing over adds even more.
Probability rules
P(A and B) = P(A) × P(B) · P(A or B) = P(A) + P(B)
Multiply for independent events happening together; add for mutually exclusive outcomes. Independent assortment is what licenses the multiplication rule across genes.
Incomplete dominance vs. codominance
Incomplete: Aᴿ + Aᵂ → blended intermediate · Codominant: Iᴬ + Iᴮ → both shown at once
The heterozygote is the giveaway: an in-between phenotype (pink) is incomplete dominance; two full phenotypes displayed together (type AB) is codominance.
Recombination frequency
RF = (recombinant offspring ÷ total offspring) × 100%
A recombination frequency of 1% corresponds to roughly 1 map unit (centimorgan). The maximum is 50%, at which point genes assort as if unlinked.
Direction of synthesis
DNA polymerase builds 5′ → 3′ only
New nucleotides can only be added to a free 3′ end, so the new strand grows 5′→3′ while it is read off a 3′→5′ template.
Transcription base pairing
DNA A → RNA U · DNA T → RNA A · DNA G → RNA C · DNA C → RNA G
RNA has no thymine — wherever the DNA template has adenine, the new mRNA carries uracil (U), not thymine (T).
Codon → anticodon pairing
mRNA codon 5′–A U G–3′ pairs with tRNA anticodon 3′–U A C–5′
The anticodon is antiparallel and complementary to the codon (A–U, G–C), just like the two strands of DNA.
Mutation effects at a glance
silent = same aa · missense = different aa · nonsense = premature stop · frameshift = whole downstream frame altered
Substitutions cause silent/missense/nonsense; insertions and deletions cause frameshifts.
PCR amplification
copies after n cycles = starting copies × 2ⁿ
Each cycle doubles the DNA, so growth is exponential — 30 cycles turns one molecule into roughly a billion.
Relative fitness (w)
w = (offspring of a genotype) ÷ (offspring of the most successful genotype)
The fittest genotype is set to w = 1; every other genotype is scored relative to it. Fitness is always comparative, never an absolute number.
Molecular similarity and relatedness
more shared DNA/protein sequence → more recent common ancestor
Sequence differences accumulate over time, so the degree of molecular difference estimates how long ago two lineages diverged.
Allele frequencies
p + q = 1
For a gene with two alleles, p is the frequency of the dominant allele and q the frequency of the recessive allele; together they must account for 100% of the alleles.
Genotype frequencies
p² + 2pq + q² = 1
p² = homozygous dominant, 2pq = heterozygous, q² = homozygous recessive. This is just (p + q)² expanded, and the three genotype frequencies must sum to 1.
The engine of speciation
reduced gene flow + divergence (mutation, selection, drift) → reproductive isolation
Cut off gene flow long enough and independently accumulating genetic differences eventually make interbreeding impossible — that is a new species.
Relatedness on a tree
more recent shared node → more closely related
Closeness is judged by how recently two lineages share a common ancestor (branch point), not by physical resemblance or by how far apart the tips are drawn.
The 10% rule
energy at next level ≈ 0.10 × energy at current level
Roughly 90% of the energy at each trophic level is lost as heat (respiration), waste, and uneaten parts; only ~10% is stored as biomass the next level can eat.
Exponential growth
dN/dt = rN
dN/dt is the population’s growth rate (individuals per unit time); r is the per-capita rate of increase; N is the current population size. Bigger N → faster growth, with no upper limit.
Logistic growth
dN/dt = rN((K − N)/K)
The (K − N)/K factor slows growth as N approaches carrying capacity K. When N = K, the factor is 0 and growth stops; when N is small, the factor ≈ 1 and growth is nearly exponential.
Symbiosis by outcome
mutualism +/+ · commensalism +/0 · parasitism +/−
Read each pair as the effect on partner 1 / partner 2. Predation and herbivory are +/− interactions too, but they are brief feeding events, not long-term symbioses.
Heat transfer
q = m·c·ΔT
q = heat (J), m = mass (g), c = specific heat (4.18 J/g·°C for liquid water), ΔT = change in temperature (°C). Water’s large c means a large q is needed for a small ΔT.
Dehydration synthesis ⇌ hydrolysis
n monomers → (n − 1) bonds → (n − 1) H₂O released
Forming each bond in a linear chain removes one water (dehydration synthesis); breaking each bond consumes one water (hydrolysis). For n monomers linked into one chain there are (n − 1) bonds — the same rule for sugars, amino acids, and nucleotides.
Protein structure hierarchy
primary → secondary → tertiary → quaternary
Sequence → local backbone folds (H-bonds) → whole-chain 3-D shape (R-group interactions) → assembly of multiple chains. Denaturation unravels secondary–quaternary levels but leaves primary (peptide bonds) intact.
The endosymbiotic sequence
free-living aerobic prokaryote → engulfed by host cell → retained, undigested endosymbiont → modern organelle (double membrane · circular DNA · 70S ribosomes · binary fission)
Mitochondria trace to an aerobic bacterium; chloroplasts to a later-engulfed cyanobacterium. The nucleus and ER, by contrast, arose autogenously by infolding of the host membrane — not by engulfment.
Water potential
Ψ = Ψp + Ψs
Ψ is water potential, Ψp is pressure potential, Ψs is solute potential (all in MPa). Water always moves toward lower (more negative) Ψ. Pure water at atmospheric pressure has Ψ = 0.
Solute potential
Ψs = −iCRT
i = ionization constant (1 for sucrose/glucose, 2 for NaCl); C = molarity; R = 0.00831 L·MPa·mol⁻¹·K⁻¹; T = temperature in kelvin (°C + 273). Ψs is always 0 or negative — solutes lower water potential.
Calvin cycle per net G3P
3 CO₂ + 9 ATP + 6 NADPH → 1 G3P + 9 ADP + 8 Pᵢ + 6 NADP⁺
Three turns per G3P; double everything (6 CO₂, 18 ATP, 12 NADPH) for one glucose. ATP > NADPH because RuBP regeneration costs extra ATP.
Carriers delivered to the ETC (per glucose)
10 NADH + 2 FADH₂ → ETC → ~26–28 ATP
Approx. 2.5 ATP per NADH and 1.5 ATP per FADH₂: (10 × 2.5) + (2 × 1.5) = 25 + 3 = 28, trimmed by shuttle costs to ~26–28.
Amplification factor of a catalytic cascade
total amplification ≈ (product molecules per enzyme)^(number of catalytic steps)
Amplification compounds *multiplicatively* — each catalytic step multiplies the previous total, so factors grow as a power of the step count, not a sum.
The G1 → S decision, in one line
growth signal → cyclin D-Cdk4/6 → Rb phosphorylated → E2F released → S-phase genes ON
Rb *restrains* the cycle when unphosphorylated; phosphorylating it *removes* the brake. Losing Rb removes the brake permanently.
Chi-square goodness-of-fit statistic
χ² = Σ (O − E)² / E
O = observed count, E = expected count. Sum the term (O − E)² / E over every phenotype category. Use raw counts, never percentages.
Degrees of freedom
df = (number of categories) − 1
A 9:3:3:1 cross has 4 categories → df = 3. A monohybrid 3:1 cross has 2 categories → df = 1. Degrees of freedom depend on the categories, NOT on the sample size.
Recombination frequency
RF = (recombinant offspring ÷ total offspring) × 100%
Count both recombinant classes. 1% RF ≈ 1 map unit (centimorgan). Maximum RF is 50%, at which point linked genes assort as if independent.
Additivity of map distances
For gene order A — B — C: distance(A,C) ≈ distance(A,B) + distance(B,C)
The largest pairwise distance spans the two outer genes. Double crossovers make the measured outer distance slightly less than the exact sum, so short intervals give the most accurate maps.
lac operon: two switches, one output
strong transcription ⇔ (lactose present → repressor OFF) AND (glucose absent → cAMP-CAP ON)
Negative control = the repressor senses lactose; positive control = CAP senses glucose (via cAMP). Fail either switch and expression is low.
PCR amplification
copies after n cycles = starting copies × 2ⁿ
Each cycle doubles the target, so growth is exponential. Examples: 2³ = 8, 2⁴ = 16, 2⁸ = 256, 2¹⁰ = 1024, 2²⁰ ≈ 1 million.
Allele frequencies
p + q = 1
p is the frequency of the dominant allele, q the frequency of the recessive allele. By gene-counting, p = (2·AA + Aa) ÷ (2N).
Genotype frequencies
p² + 2pq + q² = 1
p² = homozygous dominant, 2pq = heterozygous, q² = homozygous recessive. Only a population at equilibrium is expected to match these three values.
Maximum parsimony
preferred tree = the tree requiring the fewest character-state changes
Fewer changes means less assumed homoplasy (convergence or reversal). Among competing trees, the simplest explanation is favored.
Molecular clock
sequence divergence ≈ rate × time → time = divergence ÷ rate
Calibrate the rate using a node whose age is known from the fossil record, then apply it to date other divergences.
Exponential growth
dN/dt = rN
Whole-population growth rate = per-capita rate r × current size N. The per-capita rate itself, (1/N)(dN/dt), is simply the constant r — it never changes no matter how large N gets.
Logistic growth
dN/dt = rN((K − N)/K)
The (K − N)/K term is the density-dependent brake. The per-capita rate here is (1/N)(dN/dt) = r((K − N)/K), which shrinks toward 0 as N → K. This is the equation form of "competition intensifies with crowding."
Maximum growth rate
peak dN/dt = rK/4, at N = K/2
Substituting N = K/2 into the logistic equation: r(K/2)((K − K/2)/K) = r(K/2)(1/2) = rK/4. This is the maximum sustainable yield point exploited in fisheries and wildlife management.
Interaction outcomes
competition −/− · predation +/− · mutualism +/+ · commensalism +/0
Read each pair as the effect on species 1 / species 2. Competitive exclusion applies specifically to the −/− case when two species share one limiting resource with fully overlapping niches.
Simpson’s Diversity Index
D = 1 − Σ(n/N)²
n = number of individuals of one species; N = total individuals of all species; Σ sums the squared proportions across every species. D ranges from 0 (one species dominates, no diversity) to nearly 1 (many equally abundant species). Higher D = greater diversity.

On the exam

How to get a 5

Key terms

Hardy–Weinberg equationsp + q = 1 and p² + 2pq + q² = 1. p² = homozygous dominant, 2pq = heterozygous, q² = homozygous recessive.
Five conditions for Hardy–Weinberg equilibriumNo mutation, no natural selection, no gene flow, random mating, and large population (no genetic drift).
Net products of glycolysis (per glucose)2 pyruvate, 2 net ATP, 2 NADH. Occurs in the cytoplasm; does not require oxygen.
Where does the ETC occur, and the final electron acceptor?Inner mitochondrial membrane (cristae); O₂ is the final acceptor, forming H₂O. Produces most ATP (~26–28).
Light reactions vs Calvin cycleLight reactions: thylakoid membrane, make ATP + NADPH + O₂. Calvin cycle: stroma, uses ATP/NADPH + CO₂ to make G3P/sugar.
Fluid mosaic membranePhospholipid bilayer with embedded proteins; hydrophilic heads out, hydrophobic tails in. Semi-permeable; regulates transport.
Osmosis and tonicityWater moves from high to low water potential. Hypertonic → cell shrinks; hypotonic → swells/bursts; isotonic → no net movement.
Feedback (negative) inhibitionEnd product binds an early enzyme's allosteric site, shutting the pathway off — maintains homeostasis.
Central dogmaDNA → (transcription) → mRNA → (translation) → protein. Transcription in nucleus; translation at ribosomes.
Signal transduction stepsReception (signal binds receptor) → Transduction (relay cascade, often phosphorylation) → Response (cellular change).
Mitosis vs Meiosis outcomeMitosis: 1 division → 2 diploid identical cells. Meiosis: 2 divisions → 4 haploid varied gametes.
Sources of genetic variation in meiosisCrossing over (prophase I), independent assortment (metaphase I), and random fertilization.