NUST Mature Age Entry cheat sheet

Percentage change formula: change = (new − old) ÷ old × 100%; a rise from 40 to 50 is +25%, while a fall from 50 to 40 is −20% - the base is always the original value.

Ratio scaling rule: if a:b = 3:5 and a + b = 64, one part = 64 ÷ 8 = 8, so a = 24 and b = 40; total quantity is divided by the sum of ratio parts, not by either part alone.

Work-rate rule: rates add when working together, so 1/T = 1/t₁ + 1/t₂; two workers at 6 h and 12 h finish in 4 h because 1/6 + 1/12 = 1/4.

Average speed for equal distances is the harmonic mean: v = 2v₁v₂ ÷ (v₁ + v₂); 60 km/h and 40 km/h over equal distances give 48 km/h, not 50 km/h.

Simple interest I = PRT ÷ 100 and compound amount A = P(1 + r)^n; compound interest exceeds simple interest from the second period onward.

Probability of independent events multiplies: P(A and B) = P(A) × P(B); P(A or B) = P(A) + P(B) − P(A and B) for overlapping events.

Area and volume set: circle πr², triangle ½bh, trapezium ½(a + b)h, cylinder πr²h, sphere (4/3)πr³; Pythagoras c² = a² + b² identifies right triangles.

Logical-inference decision rule: a conclusion follows only if every premise-compatible case satisfies it; a single counterexample invalidates an 'all' or 'must' claim.

Data-interpretation rule: read axis scales and units before comparing; a bar twice as tall represents twice the value only when the axis starts at zero.

Subject–verb agreement: the verb agrees with the head noun, not an intervening phrase - 'The list of items is long'; indefinite pronouns (everyone, each, nobody) take singular verbs.

Tense sequencing rule: use past perfect (had + past participle) for the earlier of two past actions, and present perfect for past action with present relevance ('has lived here since 2019').

Conditional pattern: zero/general (if + present, present), first (if + present, will), second (if + past, would), third (if + had + past participle, would have + past participle).

Relative-pronoun rule: use 'who' for people, 'which' for things, 'whose' for possession, and 'that' in defining clauses; omit the comma in defining clauses.

Misplaced-modifier rule: an introductory participial phrase must describe the subject of the main clause - 'Walking home, she saw the rain' is correct; 'Walking home, the rain was seen' is not.

Vocabulary strategy: use surrounding contrast and cause–effect signals (however, therefore, despite) to infer an unfamiliar word's meaning before checking options.

Reading-comprehension rule: the answer must be supported by the passage text, not by outside knowledge; eliminate options that are true in general but unstated.

Parallelism rule: items joined by and, or, not only…but also must share grammatical form - 'reading, writing and speaking', not 'reading, to write and speaking'.

Punctuation rule: a semicolon joins two independent clauses; a colon introduces a list or explanation; a comma alone cannot join two full sentences (comma splice).