DAT cheat sheet

Hardy-Weinberg: p + q = 1 and p² + 2pq + q² = 1; deviations indicate selection, drift, migration, mutation, or nonrandom mating.

Michaelis-Menten: V = Vmax[S]/(Km + [S]); Km is the substrate concentration at ½Vmax; competitive inhibitors raise Km, while pure noncompetitive inhibitors lower Vmax.

Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA]); buffer capacity is greatest when pH = pKa.

Gibbs free energy: ΔG = ΔH − TΔS; ΔG < 0 is spontaneous, ΔG = 0 is equilibrium, and ΔG > 0 is nonspontaneous.

SN2 is one step with backside attack and inversion; SN1 proceeds through a carbocation and gives racemization.

DNA base pairing: A–T has two hydrogen bonds; G–C has three; a purine always pairs with a pyrimidine.

Ideal gas law: PV = nRT; one mole of ideal gas occupies 22.4 L at STP; temperature must be in kelvin.

Redox: oxidation is loss of electrons and reduction is gain; the oxidizing agent is reduced and the reducing agent is oxidized.

Hole punching: each unfold reflects the current hole pattern across the crease; a hole centered on a crease does not duplicate.

Cube counting: count only exposed painted faces; each shared face between two cubes removes two exposed faces from the total.

Aperture passing: the shape must pass through the opening without rotation or reflection; match notches and proportions exactly.

Angle ranking: judge the opening between the two sides; longer sides do not necessarily indicate a larger angle.

Paper folding: each fold doubles layers only in the folded region; a cut through all layers creates mirror-image holes on unfolding.

3D form development: faces sharing an edge in the net become adjacent in the solid; opposite faces never share an edge or vertex.

Orthographic projection: front and top views share width; front and end views share height; top and end views share depth.

Pattern folding: match edge lengths and orientation; a face rotated in the net may appear rotated in the correct answer.

Main idea: the correct answer covers the whole passage; a true but narrow detail is not the main idea.

EXCEPT questions: three choices are supported by the passage; locate evidence for each and eliminate those three.

Inference: accept only conclusions that must follow from stated information; outside knowledge is not permitted.

Tone: identify attitude from adjectives and qualifiers; extreme language is usually wrong unless the passage is equally extreme.

Vocabulary in context: determine meaning from the immediate sentence and surrounding sentences, not from a memorized common definition.

Paragraph function: label each paragraph as claim, evidence, counterexample, or conclusion to locate details quickly.

Contrast signals such as however, although, yet, and nevertheless often introduce the author's qualified or main point.

A choice can be supported by the passage yet fail to answer the specific question stem; reread the stem before selecting.

Percent change = (new − old)/old × 100%; percent increase and decrease use the original value as the denominator.

Combinations: nCr = n!/[r!(n−r)!]; permutations: nPr = n!/(n−r)!; use permutations when order matters.

Independent events: P(A and B) = P(A)P(B); mutually exclusive events: P(A or B) = P(A) + P(B).

Combined work rate = 1/t₁ + 1/t₂ + …; total time is the reciprocal of the combined rate.

Compound interest: A = P(1 + r/n)^(nt); simple interest: I = Prt.

Distance = rate × time; average speed = total distance ÷ total time, not the average of separate speeds.

Circle: A = πr² and C = 2πr; triangle: A = ½bh; Pythagorean theorem: a² + b² = c².

Line: y = mx + b; slope m = (y₂ − y₁)/(x₂ − x₁); perpendicular slopes are negative reciprocals.