UTET Paper 2 cheat sheet

Piaget's stages: sensorimotor (0–2 years, object permanence), preoperational (2–7, egocentrism, no conservation), concrete operational (7–11, conservation, classification, reversibility), formal operational (11+, abstract and hypothetical reasoning).

Vygotsky: learning is social; the ZPD is the distance between independent and assisted performance; scaffolding is withdrawn as competence grows; egocentric speech becomes inner speech.

Kohlberg's six stages in three levels: pre-conventional (punishment-obedience, instrumental exchange), conventional (good boy/girl, law and order), post-conventional (social contract, universal ethical principle).

IQ = (mental age ÷ chronological age) × 100; 90–110 is average; Binet and Simon produced the first practical intelligence scale in 1905; the Stanford–Binet reports ratio and deviation IQ.

Gardner's eight intelligences: linguistic, logical-mathematical, spatial, bodily-kinaesthetic, musical, interpersonal, intrapersonal, naturalistic - ability is plural, so assessment should use more than one mode.

RTE Act 2009 rules: free and compulsory education for ages 6–14; no detention or expulsion until elementary completion; no board examination before class VIII; PTR 30:1 at primary and 35:1 at upper primary; 25% seats in private unaided schools for disadvantaged groups.

Learning disabilities are specific, not intellectual disability: dyslexia (decoding and reading), dysgraphia (writing and spelling), dyscalculia (number), dyspraxia (motor coordination); the child usually has average or above-average IQ.

Assessment types: formative (during learning, feedback, low stakes), summative (end of term, grading), diagnostic (before teaching or after persistent failure, locates specific gaps); CCE combines scholastic and co-scholastic areas.

Bruner: knowledge is represented enactively (action), iconically (image) and symbolically (language); a spiral curriculum revisits concepts at greater depth; discovery learning lets the learner structure material.

Natural order of language skills: listening, speaking, reading, writing; oracy precedes literacy, and reading and writing depend on oral competence.

Skimming gives the gist quickly; scanning locates a specific detail such as a date or name; intensive reading is close and language-focused; extensive reading is wide and fluency-focused.

Chomsky: a Language Acquisition Device and universal grammar explain rapid first-language acquisition; deep structure is converted into surface structure by transformations.

Krashen: acquisition is subconscious, learning is conscious; comprehensible input at i+1, low affective filter and a silent period support acquisition; the monitor is a limited conscious editor.

Structural approach: select and grade sentence patterns, present them in a situation, drill orally, then introduce reading and writing; it is behaviourist and accuracy-first.

Communicative approach: the aim is communicative competence, not only correct form; tasks carry real information gaps, fluency is encouraged and errors are treated as natural steps in learning.

Figures of speech rules: simile compares using like/as; metaphor states one thing as another; personification gives human traits to non-human things; alliteration repeats initial consonants; onomatopoeia imitates sound; oxymoron joins opposites.

Remedial teaching cycle: give a diagnostic test → identify the specific errored sub-skill → reteach with simpler material and more practice → retest to confirm the gap has closed.

Bloom's revised taxonomy from low to high: remembering, understanding, applying, analysing, evaluating, creating; question papers should sample all levels, not only recall.

English has about 44 phonemes in RP: 24 consonants and 20 vowels (12 pure vowels plus 8 diphthongs); spelling and sound are not in one-to-one correspondence.

A morpheme is the smallest meaningful unit; free morphemes stand alone (book), bound morphemes must attach (re-, -ing); a phoneme distinguishes meaning (/p/ versus /b/).

Eight parts of speech: noun, pronoun, verb, adjective, adverb, preposition, conjunction, interjection; a phrase has no finite verb and no subject, a clause has both.

Tense rule: simple past for a finished time (yesterday, in 1990); present perfect for a past action with present relevance or unspecified time (since, for, already, yet).

Passive transformation: object → subject, verb → be + past participle, subject → by-phrase; only transitive verbs can be passivised.

Reported speech: shift the tense one step back, change pronouns to the reporter's viewpoint, and adjust time and place words (now → then, today → that day).

Composition types: narrative (events), descriptive (senses), expository (explains), argumentative (persuades with reasons and evidence); formal letters avoid contractions and use a salutation and complimentary close.

Test quality: validity is measuring what is claimed; reliability is consistency across occasions and raters; a test can be reliable yet invalid, but never valid without reliability.

Teaching aids: audio (radio, tape), visual (charts, models, flashcards), audio-visual (video, language laboratory); concrete aids suit the lower stage, symbolic aids the higher stage.

Circle: area = πr², circumference = 2πr; triangle = ½ × base × height; parallelogram = base × height; trapezium = ½(a + b)h.

Volume: cuboid l×b×h, cube a³, cylinder πr²h, sphere (4/3)πr³; total surface area of a cylinder = 2πr(r + h), of a sphere = 4πr².

For two positive integers, HCF × LCM = product of the numbers; the HCF divides the LCM; compute HCF by prime factorisation or Euclid's division lemma.

Simple interest = PRT/100; compound amount = P(1 + R/100)^n; profit% = (SP − CP)/CP × 100, taken on cost price unless the question says otherwise.

Polygon: interior angle sum = (n − 2) × 180°; exterior angle sum = 360° for every convex polygon; each exterior angle of a regular n-gon = 360°/n.

Polya's four steps: understand the problem, devise a plan, carry out the plan, look back; Van Hiele levels run visualisation → analysis → informal deduction → formal deduction → rigour.

Newton's laws: a body keeps its state of rest or motion unless a net force acts (F = ma); every action has an equal and opposite reaction; balanced forces cause no change in motion.

Ohm's law V = IR; resistors in series add directly; in parallel 1/R = 1/R₁ + 1/R₂; power P = VI = I²R; a fuse is connected in series in the live wire.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ in the presence of chlorophyll and sunlight; light energy becomes chemical energy stored in glucose, and oxygen is released.

Indus Valley: Harappa and Mohenjodaro on the Indus, the Lothal dockyard in Gujarat, the Great Bath at Mohenjodaro, grid-planned streets and covered drains; the script remains undeciphered.

Heterodox sects: Buddhism - Buddha born 563 BCE at Lumbini, Four Noble Truths, Eightfold Path; Jainism - Mahavira, ahimsa and strict asceticism; both used Prakrit and rejected Vedic ritual.

Mauryas: Chandragupta founded the empire with Kautilya's Arthashastra; Ashoka's Kalinga war (261 BCE) turned him to dhamma, recorded in Prakrit edicts on pillars and rocks.

Delhi Sultanate: five dynasties - Slave, Khalji, Tughlaq, Sayyid, Lodi (1206–1526); the Mughal empire began with Babur's victory at the First Battle of Panipat in 1526; Akbar introduced mansabdari and Din-i-Ilahi.

Freedom movement dates: INC founded 1885 (A. O. Hume); Partition of Bengal 1905; Jallianwala Bagh 1919; Non-cooperation 1920; Dandi March 1930; Quit India 1942.

Constitution: adopted 26 November 1949, enforced 26 January 1950; Fundamental Rights in Part III, Directive Principles in Part IV, Fundamental Duties in Part IVA added by the 42nd Amendment (1976).

Latitude and longitude: the Tropic of Cancer (23.5° N) crosses eight Indian states; India's standard meridian is 82.5° E, giving IST = GMT + 5:30.

Monsoon: the south-west monsoon brings rain from June to September; the retreating monsoon affects the Coromandel coast in October–November; Mawsynram records the highest average rainfall.

Uttarakhand: formed on 9 November 2000 with 13 districts; Nanda Devi is the highest peak; the Ganga and Yamuna rise from the Gangotri and Yamunotri glaciers; the Valley of Flowers is a UNESCO site.