DAT Quantitative Reasoning cheat sheet

Biology: DNA replication is semiconservative; helicase unwinds, primase lays RNA primers, DNA polymerase III extends 5'→3', and ligase seals Okazaki fragments on the lagging strand.

Biology: In a dihybrid cross of heterozygotes (AaBb × AaBb) with independent assortment, the 9:3:3:1 phenotype ratio reflects 9/16 dominant-dominant, 3/16 each mixed class, 1/16 double recessive.

Biology: Enzyme kinetics - Michaelis-Menten v = Vmax[S]/(Km+[S]); Km equals the substrate concentration at half-maximal velocity and is inversely related to enzyme affinity.

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

Chemistry: pH = −log[H+]; strong acid fully dissociates, weak acid uses Ka, and pH + pOH = 14 at 25 °C.

Chemistry: Le Chatelier's principle - adding reactant or removing product shifts equilibrium right; raising temperature favors the endothermic direction.

Physics: Newton's second law F = ma; on an incline the component of gravity along the plane is mg·sinθ and the normal force is mg·cosθ (frictionless).

Physics: Kinematics - v = v₀ + at, x = v₀t + ½at², v² = v₀² + 2ax; free-fall acceleration is g ≈ 9.8 m/s² downward.

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

Angle ranking: compare by opening width, not by leg length; a short-legged wide angle can be larger than a long-legged narrow one.

Cube counting: count only painted exterior faces; track total cubes per stack, then sum exposed faces across all visible sides, top, and front/back/left/right.

Paper folding: the number of holes equals the number of punch marks unless a punch lands on a fold line or overlaps an existing hole; unfold by reflecting across each crease in reverse order.

Hole punching with symmetry: a punch on a fold line produces a single merged hole, while a punch off the fold produces two mirror-image holes.

Top-front-end views: the top view gives width and depth, the front view gives width and height, and the end view gives depth and height; match shared edges between adjacent views.

Aperture passing: a shape passes through an opening only if its silhouette in the direction of travel fits entirely within the opening's outline.

Pattern folding: identify a distinctive face (unique marking) and trace adjacent faces by shared edges; opposite faces on a cube never share an edge.

Form development (2D net to 3D): count edges and verify that every fold line in the net becomes a shared edge; mismatched edge lengths indicate an incorrect net.

Spatial relations: mental rotation preserves distances and angles; mirror images reverse chirality and cannot be superimposed by rotation alone.

Passage structure: identify the thesis (usually in the first or last paragraph), supporting evidence, and any counterargument or concession.

Tone questions: match the author's attitude to the passage's diction; words like 'unfortunately' or 'remarkably' signal evaluative stance.

Inference questions: the correct answer must follow necessarily from stated evidence; an answer that is merely plausible but unsupported is a distractor.

EXCEPT/LEAST questions: three choices are supported by the passage and one is not; verify each supported choice against a specific line.

Scope traps: answers that are too broad ('all scientists'), too narrow, or introduce outside information are typically wrong.

Cause-effect vs. correlation: the passage may describe an association without claiming causation; do not upgrade correlation to causation in the answer.

Vocabulary-in-context: substitute each answer choice into the sentence and select the one that preserves the sentence's original meaning.

Main-idea vs. detail: the main idea summarizes the whole passage; a detail answer is true but too specific to capture the author's point.

Time management: skim for structure first, then read the questions and return to the passage for line-specific evidence.

Percent change = (new − old)/old × 100; successive percent changes multiply: a 20% increase then 25% decrease gives 1.20 × 0.75 = 0.90, a net 10% decrease.

Averages: sum = average × count; if a set is symmetric, the mean equals the median, and adding a value equal to the mean leaves the mean unchanged.

Ratios and proportions: set up cross-multiplication a/b = c/d → ad = bc; for part-to-whole, part = ratio fraction × total.

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

Combinatorics: permutations nPr = n!/(n−r)!; combinations nCr = n!/(r!(n−r)!); 'at least one' = 1 − P(none).

Geometry: area of triangle = ½bh; circle area = πr², circumference = 2πr; Pythagorean theorem a² + b² = c² for right triangles.

Algebra: quadratic formula x = [−b ± √(b² − 4ac)]/(2a); discriminant b² − 4ac > 0 gives two real roots, = 0 one root, < 0 no real roots.

Rates: distance = rate × time; combined work rate = 1/t₁ + 1/t₂ = 1/t_total; average speed = total distance / total time (not the average of speeds).

Exponents and logs: xᵃ·xᵇ = xᵃ⁺ᵇ, (xᵃ)ᵇ = xᵃᵇ, log(ab) = log a + log b, and log_b(x) = ln x / ln b.