FPSC TGT cheat sheet

Quadratic formula: the roots of ax² + bx + c = 0 (a ≠ 0) are x = (−b ± √(b² − 4ac)) / 2a; the discriminant b² − 4ac gives two distinct real roots if positive, one repeated root if zero, and complex roots if negative.

Circle: area = πr², circumference = 2πr; sphere: volume = (4/3)πr³, surface area = 4πr².

Sum of interior angles of an n-sided polygon = (n − 2) × 180°; each exterior angle of a regular n-gon = 360°/n.

Newton's second law F = ma; weight W = mg with g ≈ 9.8 m/s²; the SI unit of force is the newton (kg·m/s²).

Speed of light in vacuum c ≈ 3 × 10⁸ m/s; sound travels about 343 m/s in air at 20 °C and requires a material medium.

pH = −log₁₀[H⁺]: below 7 acidic, exactly 7 neutral, above 7 basic; one pH unit equals a tenfold change in hydrogen-ion concentration.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, driven by light energy absorbed by chlorophyll in chloroplasts.

Atomic number = number of protons and defines the element; mass number = protons + neutrons; isotopes share the atomic number but differ in neutron count.

Mitosis yields two genetically identical diploid cells for growth and repair; meiosis yields four haploid gametes and creates variation through crossing over.

Revised Bloom's taxonomy order (low to high): Remember → Understand → Apply → Analyse → Evaluate → Create.

Piaget's stages: sensorimotor (0–2), preoperational (2–7), concrete operational (7–11), formal operational (11 and above).

Vygotsky's zone of proximal development is the gap between unaided performance and performance with guidance; scaffolding is support placed inside that zone and faded as competence grows.

Formative assessment occurs during learning and informs teaching; summative assessment occurs at the end of a unit or course and certifies achievement.

Criterion-referenced tests compare a learner with fixed standards; norm-referenced tests compare a learner with a peer group using mean and standard deviation.

Herbartian five lesson-plan steps: preparation, presentation, comparison/association, generalisation, application.

Thorndike's laws: readiness (learning occurs when the learner is ready), exercise (repetition strengthens bonds), effect (satisfying outcomes strengthen responses).

Kolb's experiential learning cycle: concrete experience → reflective observation → abstract conceptualisation → active experimentation.

Maslow's hierarchy order: physiological, safety, belonging, esteem, self-actualisation - lower needs are usually met before higher ones.

Eight parts of speech: noun, pronoun, verb, adjective, adverb, preposition, conjunction, interjection.

Active → passive: the object becomes subject, the verb becomes a form of be + past participle, and the original subject moves to a by-phrase or is omitted.

Conditionals: first (if + present, will + base), second (if + past, would + base), third (if + past perfect, would have + past participle).

Present perfect = has/have + past participle; it links a past action to the present and co-occurs with for, since, already, yet, just, ever, never.

Direct → indirect speech: a past reporting verb shifts the reported verb one tense back; today → that day, tomorrow → the next day, here → there.

Shakespearean sonnet: 14 lines of iambic pentameter, rhyme abab cdcd efef gg; Petrarchan sonnet: octave (abbaabba) plus sestet (cdecde).

Figures of speech: simile compares using like/as; metaphor asserts identity; personification gives human traits to non-human things; hyperbole is deliberate exaggeration.

A gerund is verb + -ing functioning as a noun (subject, object, complement); a participle modifies a noun; an infinitive is to + base verb.

Punctuation rules: a semicolon joins independent clauses; a colon introduces a list or explanation; an apostrophe marks possession or contraction, not a plural.

Pakistan's constitutions: 1956 (first), 1962 (presidential), 1973 (current, parliamentary, adopted 14 August 1973).

The Objectives Resolution was passed in March 1949 by the Constituent Assembly and became a substantive part of the 1973 Constitution through Article 2A.

Pakistan's legislature: National Assembly has 336 seats (266 general, 60 women, 10 non-Muslims); the Senate has 96 seats after the 2018 FATA merger.

Pakistan joined the UN on 30 September 1947; the UN was founded in 1945 with headquarters in New York, and its Security Council has 5 permanent and 10 elected members.

SAARC was founded in 1985 with headquarters in Kathmandu; the OIC is headquartered in Jeddah and ASEAN in Jakarta.

K2 (8,611 m, Karakoram) is Pakistan's highest peak and the world's second highest; Nanga Parbat (8,126 m) ranks ninth globally.

The Indus is Pakistan's longest river and drains into the Arabian Sea; Tarbela Dam is on the Indus and Mangla Dam on the Jhelum.

Nobel laureates linked to Pakistan: Abdus Salam (Physics, 1979, electroweak unification); Malala Yousafzai (Peace, 2014, the youngest-ever laureate).

Pakistan's provinces: Punjab, Sindh, Khyber Pakhtunkhwa, Balochistan, plus Islamabad Capital Territory, Gilgit-Baltistan and Azad Jammu and Kashmir.