DAT Natural Sciences cheat sheet

Hardy-Weinberg equilibrium requires no mutation, no migration, random mating, infinite population size, and no selection; deviations signal that an assumption is violated.

Mendelian ratios: monohybrid F2 phenotype ratio 3:1, dihybrid 9:3:3:1; testcross with a homozygous recessive reveals an unknown genotype.

Enzyme kinetics: Michaelis-Menten v = Vmax[S]/(Km+[S]); Km is the substrate concentration at half-maximal velocity, and a competitive inhibitor raises apparent Km without changing Vmax.

Gas exchange: oxygen-hemoglobin dissociation curve shifts right (Bohr effect) with increased CO2, decreased pH, or increased temperature, lowering hemoglobin affinity for O2.

Membrane transport: simple diffusion follows the concentration gradient without energy; primary active transport (Na+/K+ ATPase) moves ions against gradients using ATP.

Cell cycle checkpoints: G1/S checks DNA integrity and cell size; G2/M verifies replication completion; metaphase checkpoint confirms spindle attachment before anaphase.

Thermodynamics: ΔG = ΔH − TΔS; a reaction is spontaneous when ΔG is negative, and enzymes lower activation energy without altering ΔG.

Acid-base: pH = −log[H+]; a buffer resists pH change best when its pKa is within one pH unit of the target pH (Henderson-Hasselbalch: pH = pKa + log[A−]/[HA]).

Newtonian mechanics for biology problems: F = ma, work = Fd cosθ, and conservation of energy (KE + PE = constant) in the absence of nonconservative forces.

Angle ranking: compare aperture width, not line length; longer lines appear to make smaller angles, so mentally rotate to match orientation.

Cube counting: count visible faces only, then add hidden cubes supporting any cube above ground level; a stack of height n contributes n cubes to that column.

Hole punching: work backward from the final fold; each fold doubles the number of holes, and holes reflected across a crease line produce mirror-image positions.

Paper folding: a fold along a line reflects every hole across that crease; unfold in reverse order and mirror each hole across the most recent crease.

Cube folding (net to cube): opposite faces on a net are separated by exactly one face in a straight line or by the net's alternating pattern; adjacent faces share an edge.

Aperture/3D form development: front, top, and side views must agree; a hidden line in one view corresponds to an edge not visible from that direction.

Pattern folding: locate a distinctive mark and check whether its orientation on the folded object matches the net after folding; marks cannot cross fold lines.

Orthographic projection: the top view sits above the front view, and the right-side view sits to the right; lines of projection align features across views.

Main-idea questions: the correct answer must cover the whole passage scope; choices that are too narrow or too broad are wrong.

Tone and attitude: identify evaluative adjectives and qualifiers (e.g., 'arguably', 'unfortunately') because they reveal the author's stance.

Inference questions: the answer must be supported by the text, not by outside knowledge; eliminate choices that require assumptions absent from the passage.

EXCEPT/LEAST questions: three choices are supported; find the one that contradicts or is unmentioned, and verify each against a specific line.

Detail questions: return to the passage and match the exact wording; paraphrase traps change a key qualifier such as 'all' versus 'some'.

Passage structure: note transitions (however, therefore, for example) to map argument flow; contrast signals often precede the author's main point.

Vocabulary in context: substitute each answer choice into the sentence and check whether the surrounding sentence's logic still holds.

Comparison passages: track which author holds which claim; answers that attribute a view to the wrong author are the most common distractor.

Percent change = (new − old)/old × 100; successive percent changes multiply, so a 20% increase then a 20% decrease yields a net 4% decrease.

Average (arithmetic mean) = sum/count; for evenly spaced sets the mean equals the median, and the sum equals mean × count.

Probability of independent events multiplies; probability of either of two mutually exclusive events adds; P(A or B) = P(A) + P(B) − P(A and B).

Ratios: set up a proportion a/b = c/d and cross-multiply; keep units consistent before solving.

Work-rate problems: combined rate = 1/t1 + 1/t2; time together = 1/(1/t1 + 1/t2).

Distance = rate × time; for round trips with different speeds, average speed = total distance/total time, not the arithmetic mean of speeds.

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

Exponent and radical rules: x^a · x^b = x^(a+b), (x^a)^b = x^(ab), and √(ab) = √a · √b for nonnegative a and b.

Data interpretation: read axis scales and units carefully; a graph's visual slope can mislead if the axes are not drawn to the same scale.