APTET Paper 2 cheat sheet

Piaget's four stages: sensorimotor (0–2, object permanence), preoperational (2–7, egocentrism, animism, irreversibility), concrete operational (7–11, conservation, classification, seriation), formal operational (11+, abstract and hypothetico-deductive reasoning).

Vygotsky: development is social before it is individual; the Zone of Proximal Development is the gap between independent and assisted performance; scaffolding is temporary support withdrawn as competence grows; egocentric speech becomes inner speech.

Kohlberg's six stages in three levels: pre-conventional (punishment avoidance; instrumental exchange), conventional (good boy–nice girl; law and order), post-conventional (social contract; universal ethical principles).

Erikson's psychosocial crises up to adolescence: trust vs mistrust (0–1), autonomy vs shame and doubt (1–3), initiative vs guilt (3–6), industry vs inferiority (6–12), identity vs role confusion (adolescence).

Bloom's revised taxonomy (2001), lowest to highest: Remember, Understand, Apply, Analyse, Evaluate, Create; the first three are lower-order objectives, the last three higher-order.

IQ = (mental age ÷ chronological age) × 100 (Stern); intelligence theories: Spearman's general factor g, Thurstone's primary mental abilities, Gardner's eight multiple intelligences, Sternberg's triarchic componential–experiential–contextual model.

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

Learning disabilities: dyslexia affects reading and decoding, dysgraphia affects writing and spelling, dyscalculia affects number and calculation, dyspraxia affects motor coordination; ADHD is an attention disorder and is not classified as a learning disability.

Assessment for learning uses formative tools (observation, oral questioning, portfolios, rubrics, peer and self assessment); summative tools (term tests, projects) judge achievement at the end of a unit; CCE combines both and records scholastic and co-scholastic areas continuously.

Language skills follow the receptive-to-productive order LSRW - listening, speaking, reading, writing; listening and reading are receptive skills, speaking and writing are productive skills.

Telugu varnamala in the school classification: 16 అచ్చులు (vowels) and 36 హల్లులు (consonants); consonants are arranged in వర్గాలు of five (క, చ, ట, త, ప వర్గాలు) plus non-vargiya letters.

సంధి is the joining of two sounds where a vowel follows a vowel; main types: సవర్ణదీర్ఘ (రామ + ఆలయం = రామాలయం), గుణ (సూర్య + ఉదయం = సూర్యోదయం), వృద్ధి, యణాదేశ (అతి + అంత = అత్యంత), త్రిక, ద్విత్వ, అమ్రేదిత.

సమాసాలు: తత్పురుష (case relation dominates), కర్మధారయ (qualifier + qualified), ద్విగు (numeral + noun), ద్వంద్వ (both members coordinate), బహువ్రీహి (compound denotes a third entity), అవ్యయీభావ (first member indeclinable).

అలంకారాలు: ఉపమ (explicit comparison), రూపక (identification of one thing with another), అతిశయోక్తి (exaggeration), శ్లేష (double meaning), యమక (repetition of a syllable group), ఉత్ప్రేక్ష (as-if imagination).

ఛందస్సు: గురువు = 2 మాత్రలు, లఘువు = 1 మాత్ర; నగణం = three laghus, మగణం = three gurus; మాత్రాఛందస్సు includes కంద, ఆటవెలది, తేటగీతి, సీసం, ద్విపద; అక్షరఛందస్సు వృత్తాలు include ఉత్పలమాల, చంపకమాల, శార్దూలం, మత్తేభం.

First-language acquisition is natural, unconscious and rule-generating, so learner errors are developmental; teaching proceeds through authentic material - stories, rhymes, drama, newspaper, language games - before formal grammar nomenclature.

Evaluation tools for Language I: dictation, reading aloud scored on a fluency rubric, cloze tests, comprehension questions at literal, inferential and evaluative levels, guided composition and project work; objective items test recall, open items test expression.

RP English has 44 phonemes: 12 pure vowels (monophthongs), 8 diphthongs and 24 consonants; /θ/ and /ð/ are dental fricatives absent from Indian languages and are the commonest pronunciation problem.

Twelve tense forms exist: each of present, past and future has simple, continuous, perfect and perfect continuous; the present perfect links a past action to a present result, not to a finished past time.

Passive voice: object becomes subject + correct form of be + past participle + by + original subject, with tense preserved - 'They build houses' becomes 'Houses are built by them'.

Reported speech backshift: present to past, will to would, can to could; time and place words shift (now to then, today to that day, here to there); questions take if/whether and statement word order.

Figures of speech: simile (like/as), metaphor (direct identification), personification, alliteration (initial consonant repetition), onomatopoeia, hyperbole, irony, oxymoron.

Methods: Grammar-Translation (rules plus translation), Direct Method (target language only, inductive grammar), Audio-lingual (behaviourist drills and habit formation), Communicative Language Teaching (meaningful interaction), TBLT (task-based learning).

Krashen's five hypotheses: acquisition–learning distinction, monitor, natural order, comprehensible input (i + 1), affective filter; Cummins separates BICS (conversational fluency) from CALP (academic proficiency).

Testing terms: discrete-point items test one element at a time; integrative items (cloze, dictation, essay) test language in use; reliability is consistency of scores, validity is measuring the intended construct.

Divisibility: by 3 and 9 via digit sum, by 4 via last two digits, by 8 via last three digits, by 11 via difference of alternating digit sums; for any two numbers HCF × LCM = product of the numbers.

Commercial arithmetic: profit% = (SP − CP)/CP × 100, loss% is taken on CP, discount is taken on MP; SI = PRT/100; CI amount = P(1 + R/100)^n; successive discounts a% and b% equal a + b − ab/100.

Rate problems: work rates add (1/a + 1/b = 1/t); speed = distance/time; downstream = boat + stream, upstream = boat − stream; average speed over equal distances = 2xy/(x + y).

Mensuration: circle 2πr and πr²; triangle ½ × base × height or Heron's formula; cylinder 2πrh and πr²h; cone curved surface πrl with l = √(r² + h²), volume ⅓πr²h; sphere 4πr² and 4/3πr³.

Algebra: (a + b)² = a² + 2ab + b²; a² − b² = (a + b)(a − b); quadratic roots x = [−b ± √(b² − 4ac)]/2a; AP nth term a + (n − 1)d, sum n/2[2a + (n − 1)d].

Geometry: angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles; similarity by AA, SAS, SSS; the angle in a semicircle is 90°; a tangent is perpendicular to the radius at the point of contact.

Physics: Newton's laws with F = ma; work = force × displacement, power = work/time; Ohm's law V = IR, series R = R₁ + R₂, parallel 1/R = 1/R₁ + 1/R₂; Joule's law H = I²Rt.

Chemistry: atomic number = protons, mass number = protons + neutrons; pH below 7 acidic, 7 neutral, above 7 basic; one mole = 6.022 × 10²³ particles; the reactivity series orders metals; balancing an equation conserves atoms.

Biology: chloroplast carries out photosynthesis (6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ in light); mitochondria release energy by respiration; xylem carries water upward, phloem translocates food; Mendel's laws are segregation and independent assortment.

Indus Valley Civilisation (c. 2500–1500 BCE): Harappa and Mohenjo-daro, grid streets and covered drainage, the Great Bath, Lothal dockyard, an undeciphered script; decline set in around 1500 BCE.

Ancient India: Mauryan empire founded by Chandragupta with Kautilya's Arthashastra; Ashoka's Kalinga war in 261 BCE produced the policy of dhamma; the Gupta period is called the golden age; Sangam literature records Chera, Chola and Pandya kingdoms.

Medieval India: five Delhi Sultanate dynasties (Slave, Khilji, Tughlaq, Sayyid, Lodi); Vijayanagara at Hampi under Krishnadevaraya fell at Talikota in 1565; Babur won the First Battle of Panipat in 1526 and Akbar built the mansabdari system.

Freedom movement: Revolt of 1857; Indian National Congress founded 1885; Partition of Bengal 1905 and the Swadeshi movement; Champaran 1917, Non-cooperation 1920, Dandi March 1930, Quit India 1942; independence and partition in 1947.

Indian geography: the Tropic of Cancer crosses eight states; the southwest monsoon reaches Kerala in early June; the Western and Eastern Ghats flank the Deccan plateau; major soils are alluvial, black (regur), red, laterite and desert.

Himalayan rivers (Indus, Ganga, Brahmaputra) are snow-fed and perennial; peninsular rivers (Godavari, Krishna, Kaveri, Narmada, Tapti) are rain-fed; the Godavari is the longest peninsular river and is called Dakshina Ganga.

Constitution: adopted 26 November 1949, enforced 26 January 1950; Part III Fundamental Rights, Part IV Directive Principles, Article 51A Fundamental Duties added by the 42nd Amendment 1976; the 73rd and 74th Amendments (1992) gave panchayats and municipalities constitutional status.

Economy: primary (agriculture, mining), secondary (manufacturing), tertiary (services); GDP measures output inside borders while GNP adds net factor income from abroad; NITI Aayog replaced the Planning Commission in 2015; MGNREGA was enacted in 2005.

Social studies pedagogy: inquiry and source-based methods use inscriptions, coins, monuments, maps and oral history; assessed skills include map reading, timeline construction, cause–effect reasoning and project or field-work reporting.