ROCN cheat sheet

Analogies: classify the relationship first (part-to-whole, cause-effect, degree, function, category), then apply it in the same direction and same grammatical form.

Antonym items with a negating prefix: strip the prefix, define the base word, then reverse the meaning - 'inimical' → hostile → friendly.

Word roots that recur: bene/bon = good, mal = bad, ver = truth, cred = believe, spec = look, dict = say, port = carry, mit/miss = send.

A word's connotation can be positive, negative, or neutral; answer choices sharing denotation are separated by connotation and intensity.

In sentence equivalence, both correct answers must produce sentences with the same meaning; a single plausible word is not enough.

Eliminate answer choices that are the wrong part of speech before judging meaning; a noun cannot fill a verb blank.

Double-definition words (cleave, sanction, table, clip) must be resolved from context, not from the most familiar sense.

Restate the sentence in plain words before looking at the choices; predicting the blank reduces attraction to near-miss distractors.

Percent change = (new − old) ÷ old × 100; successive changes of a% then b% give a net factor of (1 + a/100)(1 + b/100), not a + b.

Average speed for equal distances = 2ab/(a + b); average speed = total distance ÷ total time, never the mean of the speeds.

Work rates add: combined time = 1 ÷ (1/a + 1/b); two workers together always finish faster than the faster one alone.

Probability of independent events = product of individual probabilities; P(at least one) = 1 − P(none).

Circle: area = πr², circumference = 2πr; a central angle of θ degrees cuts an arc of (θ/360)(2πr).

Triangle: angles sum to 180°; area = ½bh; the 3-4-5 and 5-12-13 triples are right triangles, as are any multiples of them.

Slope = (y₂ − y₁)/(x₂ − x₁); parallel lines share a slope, perpendicular slopes multiply to −1.

Ratios scale by a common multiplier k: a 3:5 ratio means 3k and 5k, and the total is 8k.

Absolute value inequalities: |x| < a means −a < x < a; |x| > a means x > a or x < −a.

Mechanical advantage of a lever = effort arm ÷ resistance arm; a longer effort arm lowers the force needed.

First-class lever: fulcrum between load and effort (seesaw); second-class: load between fulcrum and effort (wheelbarrow); third-class: effort between fulcrum and load (tongs).

Fixed pulleys change direction only (MA = 1); movable pulleys roughly halve the effort, and MA equals the number of rope segments supporting the load.

Inclined plane: less force is needed but it acts over a greater distance; work input is unchanged in an ideal machine.

Gear trains: meshed gears turn in opposite directions; the smaller gear turns faster, and speed ratio is inversely proportional to tooth count.

Hydraulics follow Pascal's principle: pressure is equal throughout, so F₁/A₁ = F₂/A₂ and a small piston moves farther than a large one.

Density determines flotation: an object floats in a fluid denser than itself and sinks when its density is greater.

Heat flows from higher to lower temperature; metals conduct heat well, and trapped air is a good insulator.

Net folding: opposite faces of a cube net never share an edge and are separated by exactly one face in a straight row.

Rotation preserves shape and size; reflection reverses orientation (handedness), so a rotated letter cannot become its mirror image.

A cube has 6 faces, 12 edges, and 8 vertices; cutting a corner off adds one face and three edges.

Count blocks in a stack by columns: visible top faces give the footprint, and hidden blocks equal the height beneath each visible top.

When unfolded, a pattern on a cube face keeps its adjacency: faces touching in the net touch on the cube.

Paper folding and punching: each fold doubles the number of holes, and unfolding mirrors holes across each fold line.

Map/compass orientation: a 90° clockwise turn takes north to east, east to south, south to west, west to north.

Two objects that appear different only by scaling are similar, not congruent; congruence requires identical size.

Newton's second law: F = ma; weight = mg, and mass is unchanged while weight varies with local gravity.

Water freezes at 0 °C / 32 °F and boils at 100 °C / 212 °F at standard sea-level pressure.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂; chlorophyll in chloroplasts captures the light.

The pH scale runs 0–14: below 7 is acidic, 7 neutral, above 7 basic; each unit is a tenfold change in hydrogen ion concentration.

Series circuit: one path, current is the same everywhere, and one break stops all flow; parallel circuit: separate branches keep working.

Ohm's law: V = IR, so current rises with voltage and falls with resistance.

The water cycle steps are evaporation, condensation, precipitation, and collection/runoff.

Sound needs a medium and travels faster in solids than in gases; light travels faster than sound, so lightning is seen before thunder.

Main idea = the author's central claim; a supporting detail can be true and still be the wrong answer to a main-idea question.

Tone words signal attitude: 'unfortunately', 'remarkably', and 'arguably' each shift the author's stance.

'According to the passage' questions require textual support; 'inferred' questions require a small, necessary step beyond the text.

Watch for scope shifts: an answer that is broader or narrower than the passage's claim is wrong even if plausible.

Contrast markers (however, although, yet, despite) usually introduce the author's real point.

Cause-and-effect answers must match the passage's direction; reversing cause and effect is a common distractor.

Extreme wording (always, never, all, none) is usually unsupported unless the passage itself is absolute.

Vocabulary-in-context questions are answered by substituting each option back into the sentence and testing fit.

Ship directions: bow is forward, stern is aft, port is left facing forward, starboard is right facing forward.

Relative bearings use the ship as the reference: dead ahead is 000°, dead astern 180°, broad on the starboard beam 090°.

Speed at sea is measured in knots; one knot = one nautical mile per hour ≈ 1.15 statute miles per hour.

One nautical mile ≈ 1,852 meters, and one minute of latitude equals one nautical mile.

Latitude lines (parallels) run east–west and measure north–south position; longitude (meridians) runs north–south and measures east–west position.

The equator is 0° latitude; the prime meridian is 0° longitude; latitude ranges 0–90° and longitude 0–180° east or west.

Compass north differs from true north by magnetic variation; true bearing = magnetic bearing + variation (east variation added).

Order of rank (junior to senior): seaman, petty officer, chief petty officer, warrant officer, ensign, lieutenant, commander, captain, admiral.

Mission first, then people: accomplish the task while protecting the welfare and safety of the team.

Integrity is non-negotiable: report your own errors and others' misconduct through the chain of command rather than concealing them.

Escalation rule: handle routine issues at the lowest level; immediately report safety, legal, or ethical violations upward.

Delegation requires clear task, standard, and deadline, plus the authority and resources to complete it.

Correct a subordinate privately, praise publicly; public correction damages trust and unit cohesion.

When two rules conflict, follow the lawful order that protects life and safety, and document the decision.

A new leader should observe and ask questions before changing established procedures.

Feedback is specific and behavioral ('the report was two hours late'), not personal ('you are unreliable').