OAT cheat sheet

Cell theory: all organisms are composed of one or more cells; the cell is the basic unit of life; all cells arise from pre-existing cells by division.

Mitosis phases in order: prophase, metaphase, anaphase, telophase; cytokinesis follows. Meiosis has two divisions and produces four haploid cells.

DNA base pairing: adenine pairs with thymine (two hydrogen bonds), guanine pairs with cytosine (three hydrogen bonds); in RNA, uracil replaces thymine.

Mendelian genetics: monohybrid cross of heterozygotes yields a 3:1 phenotype ratio and 1:2:1 genotype ratio; dihybrid cross yields 9:3:3:1 for unlinked genes.

Hardy-Weinberg equilibrium requires no mutation, no migration, no selection, random mating, and a large population; allele frequencies p + q = 1 and genotype frequencies p² + 2pq + q² = 1.

Enzymes lower activation energy without altering the reaction's equilibrium; they are not consumed and are sensitive to temperature and pH.

Photosynthesis: light reactions in the thylakoid membrane produce ATP and NADPH; the Calvin cycle in the stroma fixes CO₂ using RuBisCO.

Cellular respiration: glycolysis in the cytoplasm yields 2 ATP and 2 pyruvate; the Krebs cycle and oxidative phosphorylation in mitochondria yield most of the ATP.

Blood flow through the heart: right atrium → right ventricle → pulmonary artery → lungs → pulmonary vein → left atrium → left ventricle → aorta.

Ideal gas law: PV = nRT, with R = 0.0821 L·atm/(mol·K); at STP one mole of an ideal gas occupies 22.4 L.

Molarity = moles of solute / liters of solution; dilution follows M₁V₁ = M₂V₂.

pH = −log[H⁺]; pOH = −log[OH⁻]; at 25 °C, pH + pOH = 14 and Kw = 1.0 × 10⁻¹⁴.

Henderson–Hasselbalch equation: pH = pKa + log([A⁻]/[HA]); a buffer is most effective when pH is within about one unit of pKa.

Le Chatelier's principle: increasing reactant concentration or pressure (for gases) shifts equilibrium toward products; increasing temperature favors the endothermic direction.

Oxidation is loss of electrons; reduction is gain of electrons. In a redox reaction, the reducing agent is oxidized and the oxidizing agent is reduced.

Quantum numbers: n (principal, ≥1), l (0 to n−1), ml (−l to +l), ms (±½); no two electrons in an atom may share all four quantum numbers.

Periodic trends: atomic radius decreases across a period and increases down a group; electronegativity and ionization energy generally increase across a period and decrease down a group.

Hybridization: four electron domains give sp³ (tetrahedral, ~109.5°), three give sp² (trigonal planar, ~120°), two give sp (linear, 180°).

IUPAC naming: identify the longest carbon chain, number to give the lowest locants to substituents, and name substituents alphabetically.

SN1 proceeds via a carbocation intermediate, is favored by tertiary substrates and polar protic solvents, and shows racemization; SN2 is a one-step backside attack favored by primary substrates and polar aprotic solvents.

Markovnikov's rule: in HX addition to an alkene, the hydrogen adds to the carbon with more hydrogens, placing the halogen on the more substituted carbon.

Oxidation states in organic molecules: primary alcohols oxidize to aldehydes then carboxylic acids; secondary alcohols oxidize to ketones; tertiary alcohols resist oxidation.

Carboxylic acid derivatives in decreasing reactivity: acid chloride > anhydride > ester > amide; hydrolysis converts them back to the carboxylic acid.

Chirality: a carbon with four different substituents is a stereocenter; a molecule with one stereocenter is chiral, and enantiomers rotate plane-polarized light in opposite directions.

Aromaticity (Hückel's rule): a planar, cyclic, fully conjugated system with 4n + 2 π electrons is aromatic; 4n π electrons is antiaromatic.

Main-idea questions ask what the passage is primarily about; the correct answer covers the whole passage, not a single supporting detail.

Detail questions require locating a specific statement in the passage; the correct answer is directly supported by the text, not by outside knowledge.

Inference questions ask what can be reasonably concluded; the correct answer must follow logically from the passage without adding new assumptions.

Tone and attitude questions require identifying the author's stance from word choice; extreme words such as "never" or "always" often signal an incorrect answer.

Vocabulary-in-context questions require using surrounding sentences to determine the meaning of a word as used in the passage, not its most common dictionary meaning.

EXCEPT and NOT questions ask which choice is not supported; evaluate each choice against the passage and eliminate the three that are supported.

Passage structure questions ask how the author organizes ideas (cause–effect, comparison, chronology); identifying transition words helps determine the structure.

When two answers seem correct, choose the one that is most directly supported by the passage and avoids unsupported qualifications or exaggerations.

Kinematics: v = v₀ + at; Δx = v₀t + ½at²; v² = v₀² + 2aΔx; these apply only when acceleration is constant.

Newton's second law: ΣF = ma; weight is W = mg, and normal force equals mg only on a horizontal surface with no other vertical forces.

Work and energy: W = Fd cos θ; kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; conservation of mechanical energy applies when only conservative forces act.

Momentum: p = mv; impulse J = FΔt = Δp; in an isolated system, total momentum is conserved in all collisions.

Ohm's law: V = IR; power P = IV = I²R = V²/R; resistors in series add (R_eq = R₁ + R₂), while in parallel 1/R_eq = 1/R₁ + 1/R₂.

Waves: speed v = fλ; for a wave on a string, v = √(T/μ), where T is tension and μ is linear mass density.

Snell's law: n₁ sin θ₁ = n₂ sin θ₂; light bends toward the normal when entering a medium with a higher index of refraction.

Thermodynamics: ΔU = Q − W; the first law expresses conservation of energy, and the second law states that entropy of an isolated system never decreases.

Percent change = (new − old) / old × 100; a 20% increase followed by a 20% decrease yields a net 4% decrease, not zero.

Ratios and proportions: set up a proportion a/b = c/d and cross-multiply; keep units consistent on both sides.

Averages: mean = sum / count; if a set of n numbers has mean m, the sum is nm; adding a value equal to the mean does not change the mean.

Probability of independent events: P(A and B) = P(A) × P(B); P(A or B) = P(A) + P(B) − P(A and B).

Combinations and permutations: nCr = n! / [r!(n−r)!] counts unordered selections; nPr = n! / (n−r)! counts ordered arrangements.

Exponent rules: xᵃ · xᵇ = xᵃ⁺ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁻ᵃ = 1/xᵃ; x⁰ = 1 for x ≠ 0.

Slope of a line through (x₁, y₁) and (x₂, y₂) is (y₂ − y₁)/(x₂ − x₁); parallel lines have equal slopes and perpendicular lines have slopes whose product is −1.

Quadratic formula: x = [−b ± √(b² − 4ac)] / (2a); the discriminant b² − 4ac determines the number of real roots.