AJA Officer Academies Entrance Examination cheat sheet

Negating prefixes reverse meaning: un-, in-/im-/il-/ir-, dis-, non-, a-/an-; im- precedes p, b, m (impossible), il- precedes l (illegal), ir- precedes r (irregular).

Common roots: bene- good, mal- bad, cred- believe, dict- say, spec-/spect- look, chron- time, aud- hear, path- feeling.

Analogy relationships are named before choosing: part-to-whole (wheel : car), cause-to-effect (fire : ash), function (knife : cut), degree (warm : hot), category (oak : tree).

Sentence completion: contrast markers (although, however, despite, but, yet) signal that the missing word opposes another idea; continuation markers (and, because, therefore) signal agreement.

Syllogistic inference: a conclusion is valid only if it must be true whenever the premises are true; two 'some' premises cannot support an 'all' conclusion.

Odd-one-out: state the property shared by the majority (word class, topic, root, number of syllables), then select the single option lacking it.

Reading comprehension: the credited option is supported by stated or directly implied passage content; outside knowledge and plausible-but-unstated assumptions are wrong.

Spelling traps: accommodate (two c, two m), necessary (one c, two s), separate (par-a), definitely (no a in the middle), occurred (two r, one c).

Connotation differs from denotation: 'thrifty' and 'stingy' share meaning but differ in approval; answer options often fail on tone rather than on sense.

Speed = distance ÷ time; average speed = total distance ÷ total time, and equals the arithmetic mean of the speeds only when equal times are spent at each speed.

Percentage change = (new value − original value) ÷ original value × 100; an increase from 50 to 60 is a 20% rise, and a fall back from 60 to 50 is a 16.7% drop.

Simple interest I = PRT ÷ 100; compound amount A = P(1 + r/n)^(nt), where n is compounding periods per year and r is the decimal rate.

Ratio shares: for a split in ratio a : b, each part = total × a ÷ (a + b); convert three-part ratios to fractions with denominator equal to the ratio sum.

Work rates add: if two actors take a and b hours alone, combined time = ab ÷ (a + b); general form 1/T = 1/t1 + 1/t2 + …

Profit% = (SP − CP) ÷ CP × 100, always on cost price; mark-up is on cost, margin is on selling price, so the two percentages differ for the same transaction.

Probability of independent events multiplies; for mutually exclusive events it adds; P(not E) = 1 − P(E).

Divisibility: 3 by digit sum; 4 by last two digits; 8 by last three digits; 9 by digit sum; 11 by alternating digit sum equal to 0 or a multiple of 11.

Number series: test first differences, then second differences, then constant ratios, then alternating or paired subsequences before assuming a polynomial rule.

The United Nations was founded on 24 October 1945, has 193 member states and is headquartered in New York; the Secretariat is led by the Secretary-General.

The UN Security Council has 15 members: five permanent members with veto power (China, France, Russia, United Kingdom, United States) and ten elected for two-year terms.

The African Union, founded in 2002 to replace the Organisation of African Unity of 1963, is headquartered in Addis Ababa, Ethiopia.

ECOWAS was established in 1975 by the Treaty of Lagos to promote West African economic integration; its headquarters are in Abuja, Nigeria.

Nigeria gained independence on 1 October 1960, became a republic in 1963, and is a federation of 36 states plus the Federal Capital Territory under the 1999 Constitution.

The Commonwealth is a voluntary association of states, most formerly British-ruled; its Secretariat is in London and the British monarch is its symbolic Head.

The four Geneva Conventions of 1949, with the 1977 Additional Protocols, protect the wounded, shipwrecked, prisoners of war and civilians; grave breaches constitute war crimes.

The Sustainable Development Goals are 17 goals adopted by the UN in 2015 with a 2030 target, succeeding the eight Millennium Development Goals.

The International Court of Justice settles disputes between states at The Hague; the International Criminal Court tries individuals for genocide, war crimes, crimes against humanity and aggression.

Conditional equivalence: 'if A then B' equals 'if not B then not A' (contrapositive); the converse 'if B then A' and the inverse 'if not A then not B' are not equivalent to it.

'A only if B' means A → B, making B necessary; 'A if B' means B → A; 'A if and only if B' means both directions hold.

'A unless B' translates as 'if not B then A', equivalently 'if not A then B'.

Syllogism rules: two negative premises give no valid conclusion; two particular premises give no valid conclusion; a term distributed in the conclusion must be distributed in a premise.

The negation of 'all A are B' is 'some A are not B'; the negation of 'some A are B' is 'no A are B'.

Alphabet series: letter positions run A = 1 to Z = 26, so differences of +2 or −3 map directly to shifts; watch for reversed, alternating and interleaved sequences.

Figure series analysis order: count sides or elements, then check rotation (45°, 90°, 180°), then reflection, then shading alternation, then closed regions and intersections.

On a cube net, faces separated by exactly one face in a straight line are opposite and never share an edge once folded.

Seating and ordering puzzles: draw the line or circle, place the most constrained clue first, then propagate fixed positions before testing alternatives.

Priority ordering for response options: preservation of life and safety first, then legality and ethics, then mission completion, then team welfare and efficiency, then personal convenience.

Escalate a decision when it involves risk of injury, illegality, a breach of policy, or demands authority or resources beyond your level.

Integrity rule: an unlawful order must be refused and reported; superior rank does not make an unlawful instruction binding.

Choose the lowest-level action that fully resolves the problem; bypassing the chain of command is justified only where the immediate supervisor is the source of the problem.

Situational leadership: directing fits low competence and high commitment, coaching fits developing skill, supporting fits capable but reluctant members, delegating fits confident experts.

Feedback structure: describe the situation, the specific observed behaviour, its impact, then the expected standard; avoid attributing personality or motive.

Briefing content: mission and intent, situation, task and roles, resources, timeline, contingencies and confirmation of understanding.

Autocratic style suits time-critical or safety-critical decisions; democratic style suits complex issues needing buy-in; consultative participation improves commitment but slows response.

Fatigue, dehydration and information overload measurably degrade judgement; the standard countermeasures are rest rotation, checklists and independent cross-checking.

Newton's second law F = ma; weight is W = mg with g ≈ 9.8 m/s², so 10 kg weighs about 98 N.

Ohm's law V = IR; electrical power P = VI = I²R = V²/R; energy consumed = power × time.

Standard units: force in newtons (N), energy in joules (J), power in watts (W), pressure in pascals (Pa), frequency in hertz (Hz).

Density = mass ÷ volume; pure water is about 1,000 kg/m³, so one litre of water has a mass of about 1 kg.

In dry air at 20 °C sound travels at about 343 m/s; light in vacuum travels at about 3 × 10⁸ m/s.

Water boils at 100 °C at one atmosphere but at a lower temperature at high altitude, where atmospheric pressure is reduced.

The pH scale runs 0–14 and is logarithmic; each unit is a tenfold change in hydrogen ion concentration, with 7 neutral at 25 °C.

Radioactive decay: after n half-lives the fraction of nuclei remaining is (1/2)^n, and activity falls by the same proportion.

Combustion requires fuel, oxygen and heat; removing any one side of the fire triangle stops burning, which is why cooling, smothering or fuel removal all extinguish fire.