EMRS PGT cheat sheet

English literature chronology anchors: Elizabethan drama (Marlowe, Shakespeare, c. 1585–1615), Metaphysical poets (Donne, c. 1600–1630), Restoration comedy (Dryden, Congreve, 1660–1700), Romanticism (1798 Lyrical Ballads to c. 1832), Victorian (1832–1901), Modernism (c. 1910–1940).

Grammar decision rule: use 'who/whom' by case - 'who' as subject, 'whom' after preposition or as object; 'which' for non-restrictive clauses after commas, 'that' for restrictive clauses.

Hindi grammar: संज्ञा के भेद - जातिवाचक, व्यक्तिवाचक, भाववाचक, समूहवाचक, द्रव्यवाचक; संधि के प्रकार - स्वर संधि, व्यंजन संधि, विसर्ग संधि।

Mathematics formula set for PGT: quadratic roots x = [−b ± √(b²−4ac)]/2a; sum of roots = −b/a; product = c/a; discriminant b²−4ac determines nature of roots.

Calculus core: d/dx(xⁿ)=nxⁿ⁻¹; ∫xⁿdx = xⁿ⁺¹/(n+1)+C (n≠−1); product rule (uv)' = u'v + uv'; chain rule dy/dx = dy/du · du/dx.

Physics constants and laws: g ≈ 9.8 m/s²; F = ma; work-energy theorem W = ΔKE; Ohm's law V = IR; lens/mirror formula 1/f = 1/v − 1/u (lens) and 1/f = 1/v + 1/u (mirror).

Chemistry: mole concept - 1 mol = 6.022×10²³ particles = molar mass in grams; pH = −log[H⁺]; Le Chatelier's principle predicts shift direction on concentration, pressure, temperature change.

Biology: mitosis produces two diploid daughter cells, meiosis produces four haploid cells with crossing over in prophase I; DNA base pairing A–T, G–C with two and three hydrogen bonds respectively.

History/Geography markers: Indian National Congress founded 1885; Jallianwala Bagh 1919; Quit India 1942; Tropic of Cancer passes through 8 Indian states; monsoon onset over Kerala around 1 June.

Number series rule: check successive differences first, then ratios, then alternating/prime-square patterns before assuming a complex rule.

Coding-decoding: convert letters to positions (A=1 … Z=26); reverse alphabet value = 27 − position; apply shift consistently across all letters.

Blood relation: draw a tree - vertical lines for generations, horizontal for siblings/marriage; never infer gender from a name alone.

Direction sense: fix north at top, track net displacement with vectors; final distance = √(x² + y²) for perpendicular moves.

Percentage and profit: profit% = (SP − CP)/CP × 100; successive discounts of a% and b% equal a single discount of a + b − ab/100 percent.

Time-speed-distance: convert km/h to m/s by multiplying 5/18; relative speed adds for opposite directions, subtracts for same direction.

Average and mixtures: average = sum/count; alligation ratio = (mean − cheaper) : (dearer − mean).

Static GK anchors: Indian Constitution adopted 26 November 1949, in force 26 January 1950; first President Dr Rajendra Prasad; RBI established 1935; ISRO founded 1969.

Syllogism rule: a conclusion follows only if true in every possible Venn diagram of the premises; 'some' statements are reversible, 'all' are not.

Bloom's revised taxonomy order (low to high): Remember, Understand, Apply, Analyse, Evaluate, Create - verbs in objectives must match the intended level.

Piaget's stages: sensorimotor (0–2), preoperational (2–7), concrete operational (7–11), formal operational (11+) - conservation appears in concrete operational.

Vygotsky: Zone of Proximal Development is the gap between independent performance and assisted performance; scaffolding sits inside that gap.

Kohlberg's moral development: preconventional (obedience, self-interest), conventional (approval, law and order), postconventional (social contract, universal principles).

Erikson's school-relevant stages: industry vs inferiority (6–12) and identity vs role confusion (adolescence).

NEP 2020 structure: 5+3+3+4 replacing 10+2, covering ages 3–18; NCF 2023 and NCF-SE 2023 operationalise it.

RTE Act 2009: free and compulsory education for ages 6–14, no detention and no board exam until class VIII completion, pupil-teacher ratio 30:1 at primary.

Assessment types: formative is ongoing and diagnostic; summative is end-of-course; CCE blends scholastic and co-scholastic evaluation.

Inclusive education principle: adaptation of curriculum and environment to the learner, not segregation of the learner from the classroom.

Active to passive: object becomes subject, verb becomes 'be + past participle', agent introduced by 'by'; only transitive verbs passivise.

Direct to indirect speech: shift tense back one step, change pronouns by person rule (1st person follows speaker, 2nd follows listener, 3rd unchanged), adjust time/place words.

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

Common error traps: 'each/every/either' take singular verbs; 'one of the' takes a plural noun with singular verb; 'since' marks a point, 'for' a duration.

Idiom and one-word substitution practice: 'to bite the dust' = to fail; 'altruist' = one who works for others' welfare; 'ephemeral' = short-lived.

Hindi वाक्य शुद्धि: लिंग-वचन-काल का अन्वय, कारक चिह्न (ने, को, से, में) का सही प्रयोग, अनावश्यक पुनरुक्ति का त्याग।

Hindi मुहावरे: 'अंधे की लाठी' = एकमात्र सहारा; 'नौ दो ग्यारह होना' = भाग जाना; 'आँख का तारा' = अत्यंत प्रिय।

Hindi समास पहचान: तत्पुरुष में उत्तर पद प्रधान, द्वंद्व में दोनों पद प्रधान, बहुव्रीहि में कोई भी पद प्रधान नहीं, अव्ययीभाव में पूर्व पद अव्यय।

Vocabulary precision: distinguish 'affect' (verb) from 'effect' (noun), 'complement' (completes) from 'compliment' (praises), 'principal' (chief) from 'principle' (rule).