PN Sailor Initial Test cheat sheet

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

Work rate: combined rate = 1/a + 1/b; time together = ab ÷ (a + b) for two workers.

Distance = rate × time; for average speed over equal distances, average = 2xy ÷ (x + y) (harmonic mean), not the arithmetic mean.

Simple interest = P × r × t; compound amount = P(1 + r/n)^(nt).

Arithmetic sequence: aₙ = a₁ + (n − 1)d; sum = n(a₁ + aₙ) ÷ 2. Geometric: aₙ = a₁r^(n−1).

Ratio and proportion: if a:b = c:d then ad = bc; scale problems use the same unit before multiplying.

Area formulas: triangle ½bh, circle πr², trapezoid ½(b₁+b₂)h; volume of cylinder πr²h, of a rectangular solid lwh.

Probability of an event = favorable outcomes ÷ total outcomes; for independent events multiply, for mutually exclusive events add.

Newton's laws: inertia (no net force, no change in motion); F = ma; every action has an equal and opposite reaction.

Speed of light in vacuum ≈ 3 × 10⁸ m/s; speed of sound in air ≈ 343 m/s at 20 °C and rises with temperature.

Water freezes at 0 °C and boils at 100 °C at 1 atm; density of fresh water is 1 g/cm³ and seawater is about 1.025 g/cm³, so objects float higher in seawater.

pH below 7 is acidic, 7 neutral, above 7 basic; a strong acid plus a strong base yields salt and water (neutralization).

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts.

Human blood circulation: oxygenated blood leaves the left ventricle through the aorta; deoxygenated blood returns via the vena cava to the right atrium.

Solar system order from the Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune; Jupiter is the largest planet.

Earth's layers: crust, mantle, outer core (liquid), inner core (solid); tectonic plate movement causes earthquakes and volcanoes.

Number series: check differences first, then ratios, then alternating or two interleaved sequences, then squares/cubes ± constant.

Letter series: convert letters to positions (A=1 … Z=26) and apply the same difference pattern to spot the rule.

Syllogism rule: a valid conclusion must be true in every model satisfying the premises; "some A are B" does not imply "some B are A" unless stated.

Contrapositive is always valid: from "If P then Q" infer "If not Q then not P"; the converse "If Q then P" is not valid.

Analogy items: state the relationship in words (part-to-whole, cause-effect, function) before choosing the matching pair.

Odd-one-out: test each option against a single property (number of sides, symmetry, closed vs open shape) and find the one that fails.

Abstract matrices: track each attribute separately - rotation direction, shading, count of elements - across rows and columns.

Ordering problems: draw a line or table and place items using the most restrictive clue first, then eliminate.

Mechanical advantage of a lever = effort arm ÷ load arm; a class-1 lever with the fulcrum near the load lifts more weight with less effort.

Pulley systems: a single fixed pulley changes direction only (MA = 1); movable pulleys sharing the load give MA equal to the number of supporting rope segments.

Inclined plane: MA = length ÷ height; the trade-off is that force decreases while distance increases.

Gear trains: meshed gears turn in opposite directions; the smaller gear turns faster, and speed ratio = teeth of driven ÷ teeth of driver.

Hydraulic press follows Pascal's principle: F₁/A₁ = F₂/A₂, so a larger piston produces a larger force.

Density and buoyancy: an object floats if its density is less than the fluid's; it displaces a weight of fluid equal to its own weight.

Spatial folding: count the faces adjacent to a given face; opposite faces on a cube never share an edge and appear once each in a net.

Mirror and rotation items: a mirror reverses left-right; a 90° turn moves a top feature to the side, so track one marked point through the transformation.

1896: Katipunan revolution begins; 1898: Declaration of Independence in Kawit, Cavite on 12 June; 1899: First Philippine Republic at Malolos.

The 1987 Constitution is the current charter, ratified in a plebiscite on 2 February 1987, and restored a presidential, bicameral system.

Bill of Rights (Article III) guarantees due process, equal protection, freedom of speech and assembly, and protection against unreasonable searches.

Three branches: Executive (President, elected to a 6-year term with no reelection), Legislative (Senate 24 members, 6-year terms; House of Representatives, 3-year terms), Judicial (Supreme Court and lower courts).

Article II declares the Philippines a democratic and republican state, renounces war as an instrument of national policy, and affirms civilian supremacy over the military.

Citizenship: those who are citizens at the time of adoption, by birth (jus sanguinis), or by naturalization; dual allegiance is dealt with by law.

Suffrage: Filipino citizens at least 18 years old, resident in the Philippines for at least one year and in the voting place for at least six months.

National symbols and dates: flag and anthem under RA 8491; Araw ng Kagitingan 9 April; Independence Day 12 June; National Heroes Day last Monday of August.

Ranks: officer ranks run from Ensign (O-1) through Lieutenant Junior Grade, Lieutenant, Lieutenant Commander, Commander, Captain, then flag ranks Rear Admiral, Vice Admiral, Admiral.

Enlisted ranks begin with Seaman Third Class and rise through Petty Officer Third, Second and First Class, then Chief Petty Officer and Master Chief Petty Officer.

Ship directions: bow is forward, stern aft, port is left facing the bow, starboard is right; athwartships means across the beam.

Bearings are measured clockwise from north in degrees (000°–360°); relative bearing is measured from the ship's heading.

Speed at sea is measured in knots (1 knot = 1 nautical mile per hour ≈ 1.852 km/h); depth in fathoms (1 fathom = 6 feet).

Watch organization divides the day into watches; the traditional at-sea watch rotation is four hours, with the dog watches (1600–1800 and 1800–2000) splitting the evening.

General orders for a sentry include taking charge of the post and all government property in view, and walking the post in a military manner.

Core values and conduct: chain of command flows upward through the petty officer and officer structure; salutes are rendered to officers and the national flag, and honors are rendered to the colors at 0800 and sunset.