AP ICET cheat sheet

Series: check differences, then ratios, then alternating sub-series (odd/even positions) before assuming a single rule.

Coding-decoding: map letter positions A=1…Z=26; for shift codes compute the offset from two known pairs, then apply it uniformly.

Blood relations: draw a node graph; vertical lines = generations, horizontal = siblings/spouse; 'X's son's sister' resolves to X's daughter.

Direction sense: use axes with N=+y, E=+x; final displacement = sqrt(x^2 + y^2); Pythagoras applies to right-angle turns only.

Syllogism: a conclusion follows only if true in every Venn arrangement; 'some A are B' does not imply 'some B are A' is false - it converts validly.

Seating arrangement: fix the confirmed position first, then place definite neighbours; circular arrangements have (n-1)! distinct orders, not n!.

Data interpretation: percentage change = (new - old)/old × 100; average = total/sum of items; read units (lakh/crore) before computing.

Odd-one-out: test a property common to all but one (prime vs composite, perfect squares, divisibility) rather than surface meaning.

Profit and loss: profit% is computed on cost price unless stated; SP = CP(1 + p/100); successive discounts of a% and b% give net (1 - a/100)(1 - b/100).

Simple interest SI = PRT/100; compound interest CI = P(1 + R/100)^T - P; for 2 years CI - SI = P(R/100)^2.

Time-speed-distance: distance = speed × time; convert km/h to m/s by multiplying by 5/18; average speed = total distance / total time, not mean of speeds.

Work: if A alone takes a days and B alone b days, together they take ab/(a+b) days; rates add.

Ratio and proportion: if a:b = c:d then ad = bc; in a mixture replaced n times from quantity Q, remaining = Q(1 - x/Q)^n.

Averages: adding a value equal to the mean leaves the mean unchanged; if every value is multiplied by k, the mean is multiplied by k.

Permutation and combination: nPr = n!/(n-r)!; nCr = n!/(r!(n-r)!); arrangements of a word with repeats = n!/(p!q!…).

Mensuration: circle area πr^2, circumference 2πr; cylinder volume πr^2h; sphere volume (4/3)πr^3; cone volume (1/3)πr^2h.

Number system: a number is divisible by 3 (or 9) if its digit sum is; by 8 if its last three digits are; LCM × HCF = product of the two numbers.

Subject-verb agreement: singular subject takes singular verb; 'each, every, either, neither, everyone' are singular; 'news, mathematics' are singular despite the -s.

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university); 'the' for unique or already-mentioned nouns.

Tenses: present perfect (has/have + past participle) for past action with present relevance; past perfect for the earlier of two past events.

Prepositions collocate: 'composed of', 'consist of', 'capable of', 'afraid of', 'good at', 'married to', 'different from'.

Error spotting order: check subject-verb agreement, then tense consistency, then pronoun reference, then preposition, then articles.

One-word substitutions: 'philanthropist' (lover of mankind), 'misanthrope' (hater of mankind), 'ephemeral' (short-lived), 'ubiquitous' (present everywhere).

Idioms: 'to let the cat out of the bag' = reveal a secret; 'a blessing in disguise' = apparent misfortune that turns out good; 'to beat about the bush' = avoid the point.

Reading comprehension: main-idea answers must cover the whole passage; options that are true but narrow or too extreme are distractors.

Active to passive: object becomes subject, verb becomes be + past participle, agent introduced by 'by'; tense of the original is preserved.

Computer generations: 1st vacuum tubes, 2nd transistors, 3rd integrated circuits, 4th microprocessors, 5th AI/ULSI.

Memory hierarchy fastest to slowest: registers, cache, RAM, secondary storage; 1 KB = 1024 bytes, 1 MB = 1024 KB.

OSI has 7 layers (Physical, Data Link, Network, Transport, Session, Presentation, Application); TCP is connection-oriented, UDP is connectionless.

Software types: system software (OS, utilities, drivers) vs application software (word processors, browsers, ERPs).

Business forms: sole proprietorship (unlimited liability), partnership (Indian Partnership Act 1932), company (separate legal entity, limited liability).

Accounting equation: Assets = Liabilities + Capital; every transaction keeps it balanced by double entry.

Financial statements: balance sheet is a position statement at a date; profit and loss account reports performance over a period.

Management functions: planning, organising, staffing, directing, controlling; 'span of control' is the number of subordinates one manager supervises.

Economics basics: law of demand - other things equal, quantity demanded falls as price rises; elasticity = % change in quantity / % change in price.