AFM Enlistment (English) cheat sheet

Subject–verb agreement: a singular subject takes a singular verb; intervening phrases do not change the subject's number (The box of tools is heavy).

Pronoun case: use subject pronouns for subjects (he and I went) and object pronouns for objects (between you and me).

Comma splice: two independent clauses need a conjunction, semicolon, or period; a comma alone is insufficient.

Dangling modifier: an introductory participial phrase must modify the sentence subject (Walking home, I saw the rain - not Walking home, the rain began).

Affect is usually a verb meaning to influence; effect is usually a noun meaning a result.

Reading comprehension: a main-idea answer must cover the whole passage, not one supporting detail.

An inference must be supported by textual evidence and logic; it is not speculation beyond the passage.

Vocabulary in context: choose the meaning that fits the sentence, not simply the most common dictionary sense.

Percent change = (new value − old value) ÷ old value × 100%.

Part = whole × rate; whole = part ÷ rate; rate = part ÷ whole.

For a ratio a:b, the total has a + b parts; the share for a = total × a/(a + b).

Average = sum of values ÷ count; sum = average × count.

Speed = distance ÷ time; time = distance ÷ speed; distance = speed × time.

Unit conversions: 1 km = 1,000 m; 1 hour = 3,600 s; 1 kg = 1,000 g.

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

Data interpretation: match all values to the same unit and read axis labels, including multipliers such as thousands.

A syllogism is valid when its conclusion follows necessarily from its premises; validity does not require the premises to be true.

All A are B and all B are C implies all A are C.

Some A are B implies some B are A; it does not imply some B are not A.

If P then Q is equivalent to its contrapositive: if not Q then not P.

The converse, if Q then P, is not equivalent to if P then Q.

Number series: test successive differences, ratios, alternating sequences, squares, primes, and combined patterns.

Deduction: from all X are Y and Z is X, conclude Z is Y.

P is sufficient for Q when P → Q; P is necessary for Q when Q → P.

Lever balance: effort × effort arm = load × load arm, using perpendicular distances from the pivot.

Mechanical advantage = load ÷ effort; for an ideal lever it also equals effort arm ÷ load arm.

Fixed pulley: changes force direction with ideal mechanical advantage 1; movable pulley: ideal mechanical advantage about 2.

Inclined plane: ideal mechanical advantage = length ÷ height when friction is ignored.

Gear ratio = driven gear teeth ÷ driving gear teeth; a larger driven gear turns slower with more torque.

Pressure = force ÷ area; the same force over a smaller area produces higher pressure.

Work = force × distance moved in the force's direction; power = work ÷ time.

Friction opposes relative motion and increases with normal force and surface roughness.

Stability: an object is stable if the vertical line through its center of gravity falls within its base.

Mental rotation preserves handedness; a rotated shape is not the same as its mirror image.

Cube nets: faces separated by exactly one face in a straight line become opposite faces when folded.

Map scale: actual distance = map distance × scale factor; convert both measurements to the same unit first.

Scale 1:50,000 means 1 cm on the map represents 500 m on the ground; 1:25,000 means 1 cm represents 250 m.

Contour lines closer together indicate a steeper slope; widely spaced lines indicate gentler terrain.

Closed contour loops with hachures indicate a depression.

Diagram reading: legends define symbols and orientation arrows define direction.

A fold line becomes an edge; overlapping layers can hide patterns on folded paper.

The United Nations has 193 member states; its headquarters is in New York City.

The Holy See and Palestine are permanent observer states at the United Nations.

NATO has 32 member states as of 2024, after Sweden joined; Article 5 is its collective-defense clause.

The European Union has 27 member states; the euro is the official currency of 20 EU member states as of 2024.

The African Union has 55 member states and is headquartered in Addis Ababa.

Earth's atmosphere is about 78% nitrogen and 21% oxygen by volume.

The speed of light in a vacuum is approximately 300,000 km/s.

In a parliamentary system, the executive is drawn from the legislature and is accountable to it.