NG Navy Exam cheat sheet

Percent change = (new − old) ÷ old × 100; a 20% increase then a 20% decrease leaves 96% of the original, a net 4% loss.

Work-rate formula: combined time = (a × b) ÷ (a + b) for two workers; rates add, times do not.

Distance = rate × time; for two objects moving toward each other, add speeds; moving apart in the same direction, subtract speeds.

Average = sum ÷ count, so sum = average × count; to raise an average, the new value must exceed the current average.

Simple interest = principal × rate × time; total repayment adds principal back to the interest.

Mixture rule: amount of pure substance = concentration × volume; set initial pure amount equal to final pure amount when adding solvent.

Ratio problems: convert to parts, find the value of one part by dividing the total by the number of parts, then multiply.

Markup and discount are taken on different bases: markup on cost, discount on list price, so the final price is not symmetric.

Profit = revenue − cost; profit percent is normally computed on cost, not on selling price.

Quadratic formula: x = [−b ± √(b² − 4ac)] ÷ 2a for ax² + bx + c = 0; discriminant b² − 4ac < 0 means no real roots.

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

Circle: area = πr², circumference = 2πr; sphere volume = (4/3)πr³, cylinder volume = πr²h.

Triangle area = ½ × base × height; the Pythagorean theorem a² + b² = c² applies only to right triangles.

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

Factoring: x² − y² = (x − y)(x + y); x² + 2xy + y² = (x + y)².

Sum of interior angles of a polygon = (n − 2) × 180°; each exterior angle of a regular n-gon = 360° ÷ n.

Absolute value |x| equals distance from zero, so |x| = k gives two solutions x = k and x = −k when k > 0.

Probability of an event = favorable outcomes ÷ total equally likely outcomes; independent events multiply.

Synonyms share meaning; antonyms oppose it. Use the sentence's context to decide which relation the stem requires.

Prefixes: bene- good, mal- bad, ante- before, post- after, circum- around, contra- against, hyper- over, hypo- under.

Roots: -cred- believe, -dict- say, -duc- lead, -ject- throw, -mit- send, -port- carry, -spec- look, -voc- call.

Suffixes: -ous full of, -ify to make, -ism doctrine, -ity state of, -less without, -able capable of.

A word with a positive connotation can still be the wrong answer if the sentence's tone is neutral or negative.

Eliminate choices that are too broad or too narrow; the correct synonym matches the part of speech and intensity of the stem.

Words with similar spellings often differ sharply: eminent (famous) vs. imminent (about to happen); affect (verb) vs. effect (noun).

Homophones: their/there/they're, principal/principle, stationary/stationery - meaning depends on spelling.

Main idea = topic + author's point about it; it must cover the whole passage, not one supporting detail.

Supporting details answer who, what, when, where, why, or how; they never state the main idea by themselves.

Inference answers must be logically forced by the text; a plausible guess not supported by stated evidence is wrong.

Tone words: objective, critical, nostalgic, ironic, persuasive - match the author's attitude, not the subject's.

Sequence questions: track signal words such as first, then, after, finally, and note cause-effect pairs like because, therefore, as a result.

A passage's purpose (to inform, persuade, describe, or entertain) is often signaled by the first and last sentences.

Vocabulary in context: substitute each choice into the sentence and keep only the one that preserves the passage's meaning.

Beware absolute words (always, never, all) in answer choices; passages usually support qualified claims.

Newton's laws: F = ma; an object at rest stays at rest unless a net force acts; every action has an equal and opposite reaction.

Water freezes at 0 °C (32 °F) and boils at 100 °C (212 °F) at standard pressure; density peaks near 4 °C.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂; occurs in chloroplasts using chlorophyll.

Cell basics: mitochondria release energy (ATP), ribosomes build proteins, the nucleus holds DNA, the cell membrane controls entry.

Atomic structure: protons (+) and neutrons (0) in the nucleus, electrons (−) in shells; atomic number = protons.

pH below 7 is acidic, 7 neutral, above 7 basic; each whole step is a tenfold change in hydrogen ion concentration.

Blood flow: arteries carry blood away from the heart, veins return it, capillaries exchange gases and nutrients.

The rock cycle: igneous forms from cooled magma, sedimentary from compacted deposits, metamorphic from heat and pressure.

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

Pulley systems: a single fixed pulley changes direction only (MA = 1); movable pulleys add MA roughly equal to the supporting rope segments.

Inclined plane: less force is needed over a longer distance; ideal MA = length of incline ÷ height.

Gear ratio = driven teeth ÷ driving teeth; meshed gears turn in opposite directions, and the larger gear turns slower.

Hydraulic systems transmit pressure equally (Pascal's principle); force = pressure × area, so a larger piston gives more force.

Torque = force × perpendicular distance from the pivot; balance occurs when clockwise torque equals counterclockwise torque.

Friction opposes motion, converts energy to heat, and increases with rougher surfaces and greater normal force.

A wheel and axle acts as a lever: MA = radius of wheel ÷ radius of axle.

Density = mass ÷ volume; an object floats if its density is less than the fluid's.

Ohm's law: V = IR; power P = VI = I²R = V² ÷ R.

Series circuit: current is the same everywhere, resistances add, voltage divides; total R = R₁ + R₂ + …

Parallel circuit: voltage is the same across branches, current divides, and 1/R = 1/R₁ + 1/R₂ + … so total resistance is less than the smallest branch.

Resistor color code: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9; gold and silver mark tolerance.

A capacitor stores charge in an electric field and blocks DC while passing AC; a resistor limits current and drops voltage.

A diode conducts in one direction only (anode to cathode); an LED is a diode that emits light when forward biased.

AC reverses direction periodically (60 Hz in the US); DC flows one way, as from a battery.

Semiconductors such as silicon and germanium conduct poorly when pure; doping creates n-type (extra electrons) and p-type (holes).

A transformer changes AC voltage by the turns ratio: V₂ ÷ V₁ = N₂ ÷ N₁; it does not work on steady DC.

Percent change = (new − old) ÷ old × 100; a 20% increase then a 20% decrease leaves 96% of the original, a net 4% loss.

Work-rate formula: combined time = (a × b) ÷ (a + b) for two workers; rates add, times do not.

Distance = rate × time; for two objects moving toward each other, add speeds; moving apart in the same direction, subtract speeds.

Average = sum ÷ count, so sum = average × count; to raise an average, the new value must exceed the current average.

Simple interest = principal × rate × time; total repayment adds principal back to the interest.

Mixture rule: amount of pure substance = concentration × volume; set initial pure amount equal to final pure amount when adding solvent.

Ratio problems: convert to parts, find the value of one part by dividing the total by the number of parts, then multiply.

Markup and discount are taken on different bases: markup on cost, discount on list price, so the final price is not symmetric.

Profit = revenue − cost; profit percent is normally computed on cost, not on selling price.

Quadratic formula: x = [−b ± √(b² − 4ac)] ÷ 2a for ax² + bx + c = 0; discriminant b² − 4ac < 0 means no real roots.

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

Circle: area = πr², circumference = 2πr; sphere volume = (4/3)πr³, cylinder volume = πr²h.

Triangle area = ½ × base × height; the Pythagorean theorem a² + b² = c² applies only to right triangles.

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

Factoring: x² − y² = (x − y)(x + y); x² + 2xy + y² = (x + y)².

Sum of interior angles of a polygon = (n − 2) × 180°; each exterior angle of a regular n-gon = 360° ÷ n.

Absolute value |x| equals distance from zero, so |x| = k gives two solutions x = k and x = −k when k > 0.

Probability of an event = favorable outcomes ÷ total equally likely outcomes; independent events multiply.

Synonyms share meaning; antonyms oppose it. Use the sentence's context to decide which relation the stem requires.

Prefixes: bene- good, mal- bad, ante- before, post- after, circum- around, contra- against, hyper- over, hypo- under.

Roots: -cred- believe, -dict- say, -duc- lead, -ject- throw, -mit- send, -port- carry, -spec- look, -voc- call.

Suffixes: -ous full of, -ify to make, -ism doctrine, -ity state of, -less without, -able capable of.

A word with a positive connotation can still be the wrong answer if the sentence's tone is neutral or negative.

Eliminate choices that are too broad or too narrow; the correct synonym matches the part of speech and intensity of the stem.

Words with similar spellings often differ sharply: eminent (famous) vs. imminent (about to happen); affect (verb) vs. effect (noun).

Homophones: their/there/they're, principal/principle, stationary/stationery - meaning depends on spelling.

Main idea = topic + author's point about it; it must cover the whole passage, not one supporting detail.

Supporting details answer who, what, when, where, why, or how; they never state the main idea by themselves.

Inference answers must be logically forced by the text; a plausible guess not supported by stated evidence is wrong.

Tone words: objective, critical, nostalgic, ironic, persuasive - match the author's attitude, not the subject's.

Sequence questions: track signal words such as first, then, after, finally, and note cause-effect pairs like because, therefore, as a result.

A passage's purpose (to inform, persuade, describe, or entertain) is often signaled by the first and last sentences.

Vocabulary in context: substitute each choice into the sentence and keep only the one that preserves the passage's meaning.

Beware absolute words (always, never, all) in answer choices; passages usually support qualified claims.

Newton's laws: F = ma; an object at rest stays at rest unless a net force acts; every action has an equal and opposite reaction.

Water freezes at 0 °C (32 °F) and boils at 100 °C (212 °F) at standard pressure; density peaks near 4 °C.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂; occurs in chloroplasts using chlorophyll.

Cell basics: mitochondria release energy (ATP), ribosomes build proteins, the nucleus holds DNA, the cell membrane controls entry.

Atomic structure: protons (+) and neutrons (0) in the nucleus, electrons (−) in shells; atomic number = protons.

pH below 7 is acidic, 7 neutral, above 7 basic; each whole step is a tenfold change in hydrogen ion concentration.

Blood flow: arteries carry blood away from the heart, veins return it, capillaries exchange gases and nutrients.

The rock cycle: igneous forms from cooled magma, sedimentary from compacted deposits, metamorphic from heat and pressure.

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

Pulley systems: a single fixed pulley changes direction only (MA = 1); movable pulleys add MA roughly equal to the supporting rope segments.

Inclined plane: less force is needed over a longer distance; ideal MA = length of incline ÷ height.

Gear ratio = driven teeth ÷ driving teeth; meshed gears turn in opposite directions, and the larger gear turns slower.

Hydraulic systems transmit pressure equally (Pascal's principle); force = pressure × area, so a larger piston gives more force.

Torque = force × perpendicular distance from the pivot; balance occurs when clockwise torque equals counterclockwise torque.

Friction opposes motion, converts energy to heat, and increases with rougher surfaces and greater normal force.

A wheel and axle acts as a lever: MA = radius of wheel ÷ radius of axle.

Density = mass ÷ volume; an object floats if its density is less than the fluid's.

Ohm's law: V = IR; power P = VI = I²R = V² ÷ R.

Series circuit: current is the same everywhere, resistances add, voltage divides; total R = R₁ + R₂ + …

Parallel circuit: voltage is the same across branches, current divides, and 1/R = 1/R₁ + 1/R₂ + … so total resistance is less than the smallest branch.

Resistor color code: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9; gold and silver mark tolerance.

A capacitor stores charge in an electric field and blocks DC while passing AC; a resistor limits current and drops voltage.

A diode conducts in one direction only (anode to cathode); an LED is a diode that emits light when forward biased.

AC reverses direction periodically (60 Hz in the US); DC flows one way, as from a battery.

Semiconductors such as silicon and germanium conduct poorly when pure; doping creates n-type (extra electrons) and p-type (holes).

A transformer changes AC voltage by the turns ratio: V₂ ÷ V₁ = N₂ ÷ N₁; it does not work on steady DC.

Percent change = (new − old) ÷ old × 100; a 20% increase then a 20% decrease leaves 96% of the original, a net 4% loss.

Work-rate formula: combined time = (a × b) ÷ (a + b) for two workers; rates add, times do not.

Distance = rate × time; for two objects moving toward each other, add speeds; moving apart in the same direction, subtract speeds.

Average = sum ÷ count, so sum = average × count; to raise an average, the new value must exceed the current average.

Simple interest = principal × rate × time; total repayment adds principal back to the interest.

Mixture rule: amount of pure substance = concentration × volume; set initial pure amount equal to final pure amount when adding solvent.

Ratio problems: convert to parts, find the value of one part by dividing the total by the number of parts, then multiply.

Markup and discount are taken on different bases: markup on cost, discount on list price, so the final price is not symmetric.

Profit = revenue − cost; profit percent is normally computed on cost, not on selling price.

Quadratic formula: x = [−b ± √(b² − 4ac)] ÷ 2a for ax² + bx + c = 0; discriminant b² − 4ac < 0 means no real roots.

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

Circle: area = πr², circumference = 2πr; sphere volume = (4/3)πr³, cylinder volume = πr²h.

Triangle area = ½ × base × height; the Pythagorean theorem a² + b² = c² applies only to right triangles.

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

Factoring: x² − y² = (x − y)(x + y); x² + 2xy + y² = (x + y)².

Sum of interior angles of a polygon = (n − 2) × 180°; each exterior angle of a regular n-gon = 360° ÷ n.

Absolute value |x| equals distance from zero, so |x| = k gives two solutions x = k and x = −k when k > 0.

Probability of an event = favorable outcomes ÷ total equally likely outcomes; independent events multiply.

Synonyms share meaning; antonyms oppose it. Use the sentence's context to decide which relation the stem requires.

Prefixes: bene- good, mal- bad, ante- before, post- after, circum- around, contra- against, hyper- over, hypo- under.

Roots: -cred- believe, -dict- say, -duc- lead, -ject- throw, -mit- send, -port- carry, -spec- look, -voc- call.

Suffixes: -ous full of, -ify to make, -ism doctrine, -ity state of, -less without, -able capable of.

A word with a positive connotation can still be the wrong answer if the sentence's tone is neutral or negative.

Eliminate choices that are too broad or too narrow; the correct synonym matches the part of speech and intensity of the stem.

Words with similar spellings often differ sharply: eminent (famous) vs. imminent (about to happen); affect (verb) vs. effect (noun).

Homophones: their/there/they're, principal/principle, stationary/stationery - meaning depends on spelling.

Main idea = topic + author's point about it; it must cover the whole passage, not one supporting detail.

Supporting details answer who, what, when, where, why, or how; they never state the main idea by themselves.

Inference answers must be logically forced by the text; a plausible guess not supported by stated evidence is wrong.

Tone words: objective, critical, nostalgic, ironic, persuasive - match the author's attitude, not the subject's.

Sequence questions: track signal words such as first, then, after, finally, and note cause-effect pairs like because, therefore, as a result.

A passage's purpose (to inform, persuade, describe, or entertain) is often signaled by the first and last sentences.

Vocabulary in context: substitute each choice into the sentence and keep only the one that preserves the passage's meaning.

Beware absolute words (always, never, all) in answer choices; passages usually support qualified claims.

Newton's laws: F = ma; an object at rest stays at rest unless a net force acts; every action has an equal and opposite reaction.

Water freezes at 0 °C (32 °F) and boils at 100 °C (212 °F) at standard pressure; density peaks near 4 °C.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂; occurs in chloroplasts using chlorophyll.

Cell basics: mitochondria release energy (ATP), ribosomes build proteins, the nucleus holds DNA, the cell membrane controls entry.

Atomic structure: protons (+) and neutrons (0) in the nucleus, electrons (−) in shells; atomic number = protons.

pH below 7 is acidic, 7 neutral, above 7 basic; each whole step is a tenfold change in hydrogen ion concentration.

Blood flow: arteries carry blood away from the heart, veins return it, capillaries exchange gases and nutrients.

The rock cycle: igneous forms from cooled magma, sedimentary from compacted deposits, metamorphic from heat and pressure.

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

Pulley systems: a single fixed pulley changes direction only (MA = 1); movable pulleys add MA roughly equal to the supporting rope segments.

Inclined plane: less force is needed over a longer distance; ideal MA = length of incline ÷ height.

Gear ratio = driven teeth ÷ driving teeth; meshed gears turn in opposite directions, and the larger gear turns slower.

Hydraulic systems transmit pressure equally (Pascal's principle); force = pressure × area, so a larger piston gives more force.

Torque = force × perpendicular distance from the pivot; balance occurs when clockwise torque equals counterclockwise torque.

Friction opposes motion, converts energy to heat, and increases with rougher surfaces and greater normal force.

A wheel and axle acts as a lever: MA = radius of wheel ÷ radius of axle.

Density = mass ÷ volume; an object floats if its density is less than the fluid's.

Ohm's law: V = IR; power P = VI = I²R = V² ÷ R.

Series circuit: current is the same everywhere, resistances add, voltage divides; total R = R₁ + R₂ + …

Parallel circuit: voltage is the same across branches, current divides, and 1/R = 1/R₁ + 1/R₂ + … so total resistance is less than the smallest branch.

Resistor color code: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9; gold and silver mark tolerance.

A capacitor stores charge in an electric field and blocks DC while passing AC; a resistor limits current and drops voltage.

A diode conducts in one direction only (anode to cathode); an LED is a diode that emits light when forward biased.

AC reverses direction periodically (60 Hz in the US); DC flows one way, as from a battery.

Semiconductors such as silicon and germanium conduct poorly when pure; doping creates n-type (extra electrons) and p-type (holes).

A transformer changes AC voltage by the turns ratio: V₂ ÷ V₁ = N₂ ÷ N₁; it does not work on steady DC.