REET Level 2 cheat sheet

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

Vygotsky: Zone of Proximal Development is the gap between independent performance and assisted performance; scaffolding is temporary, gradually withdrawn support; inner speech follows egocentric speech.

Kohlberg's moral levels: preconventional (punishment/obedience, instrumental exchange), conventional (good boy–nice girl, law and order), postconventional (social contract, universal ethical principles).

Erikson's school-relevant crises: industry vs inferiority (6–12, mastery and competence in school tasks) and identity vs role confusion (adolescence, peer and self-definition).

Classical conditioning (Pavlov): neutral stimulus paired with unconditioned stimulus becomes conditioned stimulus. Operant conditioning (Skinner): behaviour shaped by reinforcement schedules; variable-ratio schedules resist extinction best.

Inclusive education principle: adapt task, material, method, and assessment (curriculum differentiation) rather than segregating the learner; a barrier is located in the environment, not in the child.

Assessment terms: formative = ongoing, diagnostic feedback; summative = end-of-term judgement; norm-referenced compares learners, criterion-referenced compares against stated learning outcomes.

Learning disability markers: dyslexia (decoding and spelling), dysgraphia (writing and motor output), dyscalculia (number sense and calculation), dyspraxia (motor coordination); normal intelligence is assumed.

Hindi varnamala: 11 स्वर (अ आ इ ई उ ऊ ऋ ए ऐ ओ औ), 2 अयोगवाह (अं अनुनासिक, अः विसर्ग), 33 व्यंजन in वर्ग (क-वर्ग to प-वर्ग) plus अन्तःस्थ and ऊष्म; total 45 letters.

Hindi संधि types: स्वर संधि (दो स्वर मिलकर परिवर्तन), व्यंजन संधि, विसर्ग संधि; examples: विद्या + आलय = विद्यालय (स्वर), निः + चय = निश्चय (विसर्ग).

Hindi समास: तत्पुरुष (उत्तर पद प्रधान, जैसे राजपुत्र), द्वंद्व (दोनों पद प्रधान, माता-पिता), बहुव्रीहि (अन्य पद प्रधान, दशानन), द्विगु (संख्यावाची, त्रिलोक), अव्ययीभाव (पूर्व पद अव्यय, प्रतिदिन).

Sanskrit cases (vibhakti): प्रथमा कर्ता, द्वितीया कर्म, तृतीया करण, चतुर्थी सम्प्रदान, पञ्चमी अपादान, षष्ठी सम्बन्ध, सप्तमी अधिकरण.

Hindi काल: वर्तमान, भूत (सामान्य, पूर्ण, अपूर्ण), भविष्यत्; क्रिया पक्ष: पूर्ण (perfective) vs अपूर्ण (imperfective) distinguishes करता है from कर रहा है and किया from करता था.

Phonology terms: phoneme = smallest meaning-distinguishing sound unit; allophone = positional variant; minimal pair (e.g., /p/ vs /b/ in पल/बल) proves phoneme status.

Language acquisition vs learning (Krashen): acquisition is subconscious and meaning-focused; learning is conscious rule study; the affective filter (anxiety, low motivation) blocks intake.

Figures of speech: उपमा (comparison with वह/सा), रूपक (direct identification), अनुप्रास (repeated consonant), यमक (same word, different meaning), श्लेष (one word, multiple senses).

English tense-aspect grid: simple (habit/fact), continuous (in progress), perfect (completed with present relevance), perfect continuous (duration up to now); stative verbs (know, believe, own) normally reject continuous.

Conditionals: zero (if + present, present - general truth), first (if + present, will), second (if + past, would - unreal present), third (if + had + V3, would have + V3 - unreal past).

Reported speech backshift: present → past, past → past perfect, will → would, can → could; time markers shift now→then, today→that day, tomorrow→the next day.

Passive formation: object becomes subject + be (in the tense of the original) + past participle; only transitive verbs passivise; agent introduced by by.

Determiners and articles: a/an for first mention and countable singular; the for shared or unique reference; zero article for generic plurals and abstract nouns (Honesty is valued).

English phonemes: 44 sounds (24 consonants, 12 pure vowels, 8 diphthongs); voiced/voiceless pairs /p–b/, /t–d/, /k–g/, /f–v/, /s–z/, /ʃ–ʒ/, /tʃ–dʒ/, /θ–ð/.

Cohesive devices: reference (pronouns), substitution (one/do), ellipsis, conjunction (however, therefore), lexical cohesion (synonym, repetition); coherence is global logical unity.

Clauses: finite clause has a tensed verb; non-finite are infinitive (to go), gerund (going), participle (gone/going); a relative clause modifies a noun and may be restrictive or non-restrictive.

Fractions and decimals: a/b ÷ c/d = a/b × d/c; a decimal terminates only if the reduced denominator has no prime factors other than 2 and 5.

Percentage and profit-loss: percentage change = (change/original) × 100; SP = CP × (100 + profit%)/100; successive discounts of a% and b% equal a + b − ab/100 percent.

Simple vs compound interest: SI = PRT/100; CI amount = P(1 + R/100)^T; for T = 2, CI − SI = P(R/100)².

Geometry: sum of interior angles of an n-gon = (n − 2) × 180°; Pythagoras a² + b² = c²; area of circle = πr², circumference = 2πr; volume of cylinder = πr²h.

Mensuration: cube volume a³, surface area 6a²; cuboid volume lbh, surface area 2(lb + bh + hl); cone volume = ⅓πr²h.

Mean, median, mode: mean = sum/count; median is the middle value of ordered data (average of two middles for even n); mode is the most frequent value; the mean is pulled by outliers.

Science: Newton's laws - inertia (first), F = ma (second), equal and opposite reaction (third); weight = mg and differs from mass, which is constant.

Cell and life processes: mitochondria = respiration/ATP, chloroplast = photosynthesis, ribosome = protein synthesis; photosynthesis equation 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ in light.

Electricity and light: Ohm's law V = IR; power P = VI = I²R; series current is common, parallel voltage is common; light travels in straight lines, and reflection angle i = angle r.

Indian Constitution: adopted 26 November 1949, came into force 26 January 1950; Fundamental Rights in Part III (Articles 12–35), Directive Principles in Part IV (Articles 36–51), Fundamental Duties in Part IVA (Article 51A, added by the 42nd Amendment, 1976).

Latitudes and longitudes: Tropic of Cancer 23½°N, Tropic of Capricorn 23½°S, Arctic/Antarctic Circles 66½°; 1° of latitude ≈ 111 km; IST is based on 82½°E.

Indian geography: western coastal plains narrow, eastern coastal plains wide; Western Ghats continuous with the Palghat gap, Eastern Ghats discontinuous; monsoon arrives in Kerala around early June.

Freedom movement sequence: Revolt of 1857, INC founded 1885, Partition of Bengal 1905, Jallianwala Bagh 1919, Non-Cooperation 1920, Civil Disobedience 1930 (Dandi March), Quit India 1942.

Ancient India: Indus Valley sites Harappa and Mohenjo-daro (urban planning, drainage); Mauryan administration under Chandragupta with Kautilya's Arthashastra; Ashoka's dhamma after Kalinga (261 BCE).

Governance: a bill becomes law after passage by both Houses and presidential assent; Money Bill is introduced only in Lok Sabha with prior presidential recommendation; a no-confidence motion can be moved only in Lok Sabha.

Economics basics: GDP measures final goods and services produced within a country's borders; inflation is a sustained rise in the general price level; a repo rate is the rate at which RBI lends to banks.

If a learner's error is systematic and rule-governed (e.g., overgeneralising past tense to goed), treat it as an interlanguage stage, not carelessness; correct by contrast, not repetition drills alone.

If a task is achievable only with assistance, place it in the ZPD and scaffold; if achievable alone, raise the challenge to avoid boredom.

Use concrete manipulatives when the learner has not yet attained conservation; move to symbolic work only after concrete operational reasoning is demonstrated.

Match assessment to purpose: diagnostic before a unit, formative during, summative at the end; use criterion-referenced items to report mastery of stated outcomes.

For multilingual classrooms, allow the home language as a cognitive resource for concept formation, then bridge to the target language; do not treat code-switching as a deficit.

Feedback rule: specific, task-focused feedback on the process outperforms person-focused praise ("you are clever"), which can reduce persistence after failure.

Reliability = consistency of scores across occasions and raters; validity = the test measures what it claims; a test can be reliable but invalid, not the reverse for high-stakes use.

Item analysis: difficulty index p = proportion correct (0.30–0.70 is a useful working band); discrimination index D = p(upper) − p(lower); negative D flags a flawed key or item.

Continuous and Comprehensive Evaluation (CCE) covers scholastic plus co-scholastic areas and uses both formative and summative tools; it is not synonymous with frequent testing.

RTE Act 2009: free and compulsory education for ages 6–14, no detention or expulsion until completion of elementary education, no board examination until Class VIII, and a defined pupil–teacher ratio.

Universal Design for Learning: provide multiple means of representation, of action and expression, and of engagement; accommodation changes the conditions, modification changes the content standard.

Ethics: keep learner data confidential, avoid labelling, obtain informed consent from guardians for research or publication of learner work, and disclose assessment criteria in advance.

Food chain: producer → primary consumer → secondary consumer; energy transfer is roughly 10% per trophic level, so food chains rarely exceed four or five links.

Biogeochemical cycles: carbon (photosynthesis, respiration, combustion), nitrogen (fixation by Rhizobium and lightning, nitrification, denitrification), water (evaporation, condensation, precipitation).

Human body: blood circulation is double (pulmonary and systemic); the nephron is the kidney's functional unit; alveoli are the gas-exchange surface of the lungs.

Health and disease: deficiency of vitamin A causes night blindness, B1 beriberi, C scurvy, D rickets; iodine deficiency causes goitre.

Pollution indicators: BOD rises with organic load in water; particulate matter PM2.5 penetrates deep into the alveoli; ozone in the troposphere is a pollutant, while stratospheric ozone is protective.

Renewable vs non-renewable: solar, wind, hydro, biomass are renewable; coal, petroleum, natural gas are fossil and non-renewable; biogas is mainly methane.

LSRW sequence: listening and speaking precede reading and writing in natural acquisition; reading has sub-skills skimming (gist), scanning (specific detail), and intensive reading (close analysis).

Communicative Language Teaching prioritises meaning, interaction, and authentic tasks; the grammar-translation method prioritises rules and translation and underdevelops oral fluency.

Top-down reading uses schema and prediction; bottom-up decoding uses letters, sounds, and words; fluent readers integrate both.

Process writing: planning, drafting, revising, editing, publishing; product writing emphasises the finished text and model imitation.

Phonics teaches grapheme–phoneme correspondences; the whole-language approach immerses learners in meaningful text; the best-evidenced early reading instruction combines systematic phonics with rich language exposure.

Error correction rule: correct errors that block meaning immediately; delay correction of fluency-focused speaking to a feedback slot so that accuracy work does not inhibit production.

Van Hiele levels of geometric thought: visualisation, analysis, informal deduction, formal deduction, rigour; instruction should match the learner's level.

Concrete → pictorial → abstract (CPA) sequence is the standard bridge from manipulatives to symbols for number operations.

NCF 2005 position: mathematics should be mathematised - the child's own strategies and informal algorithms are the starting point, not a deviation to be erased.

Common misconception: treating the decimal with more digits as larger (0.9 vs 0.25) or assuming multiplication always makes larger; both trace to overgeneralising whole-number rules.

Problem-solving heuristic (Polya): understand the problem, devise a plan, carry out the plan, look back and verify.

Diagnostic value: an error pattern (e.g., always subtracting the smaller digit from the larger in borrowing) reveals a rule the child is applying, which must be confronted directly.

Source criticism: primary sources (inscriptions, coins, contemporary records) are produced in the period; secondary sources interpret them; both need contextual reading.

Chronology and change-over-time reasoning require periodisation plus cause-and-effect chains; avoid presentism (judging the past by present norms).

Map skills: scale, direction, legend, and grid reference; latitude lines run east–west but measure north–south distance, and longitude lines run north–south but measure east–west distance.

Inquiry cycle in social science: question → collect evidence → interpret → construct an argument → communicate; fieldwork and local history make abstract civic concepts concrete.

Controversial issues are handled by presenting multiple perspectives with evidence and reasoning, not by imposing one conclusion.

Concept mapping of terms (democracy, federalism, secularism) with Indian constitutional articles anchors abstract civics content to specific provisions.

Process skills ladder: observing, classifying, measuring, inferring, predicting, hypothesising, controlling variables, experimenting, concluding.

A fair test changes one variable, holds others constant, and includes a control; without a control, causal claims are unsupported.

Constructivism: learners' alternative conceptions (e.g., heavier objects fall faster) persist unless directly elicited and confronted with discrepant evidence.

5E model: Engage, Explore, Explain, Elaborate, Evaluate; explanation follows exploration so that the concept is grounded in the learner's own data.

Laboratory safety rule: dilute acid by adding acid to water, never water to acid; heat test tubes at an angle away from people; wear eye protection with chemicals.

Assessment of practical work should credit design, observation records, and reasoning, not only the final numerical answer.

Intrinsic motivation arises from interest, autonomy, and competence; extrinsic rewards can undermine intrinsic motivation when the task was already interesting (overjustification effect).

Maslow's order: physiological, safety, belonging, esteem, self-actualisation; unmet lower needs depress academic engagement.

Growth mindset (Dweck): ability is malleable; praising effort and strategy sustains persistence, while praising fixed traits fosters helplessness after failure.

Attention and memory: working memory is limited, so chunking and spaced practice beat massed repetition; distributed practice improves long-term retention.

Individual differences: intelligence is multidimensional (Gardner's multiple intelligences, Guilford's structure of intellect); no single score captures a learner's capability.

Test anxiety is reduced by predictable routines, practice under similar conditions, and teaching retrieval strategies rather than by lowering standards.

संज्ञा के भेद: व्यक्तिवाचक, जातिवाचक, भाववाचक; सर्वनाम के भेद: पुरुषवाचक, निजवाचक, निश्चयवाचक, अनिश्चयवाचक, प्रश्नवाचक, सम्बन्धवाचक।

विशेषण के भेद: गुणवाचक, संख्यावाचक, परिमाणवाचक, सार्वनामिक; क्रिया के भेद: सकर्मक/अकर्मक, सामान्य/संयुक्त/नामधातु।

वाच्य: कर्तृवाच्य (कर्ता प्रधान), कर्मवाच्य (कर्म प्रधान), भाववाच्य (अकर्मक क्रिया, जैसे उससे चला नहीं जाता)।

काल और पक्ष: पूर्ण क्रिया (किया, गया) कार्य की समाप्ति बताती है; अपूर्ण (करता था, जा रहा है) जारी या अभ्यस्त कार्य बताती है।

मुहावरा अर्थ-प्रधान होता है और वाक्य में क्रिया की तरह प्रयुक्त होता है; लोकोक्ति पूर्ण वाक्य होती है और अनुभव-सिद्ध कथन बताती है।

वर्तनी नियम: 'इ' और 'ई' का प्रयोग, अनुस्वार व चन्द्रबिन्दु का अन्तर, श/ष/स का स्थान; तत्सम शब्दों में मूल रूप बना रहता है।

Subject–verb agreement: each/every/either/neither take singular verbs; none and collective nouns may take singular when acting as one unit; 'a number of' takes plural, 'the number of' takes singular.

Pronoun case: after a preposition or as object use me/him/her (between you and me); as subject use I/he/she; who is subject, whom is object.

Modals: must (obligation), should (advice), may (permission/possibility), can (ability), could/might (remote possibility), need not (absence of necessity) versus must not (prohibition).

Preposition rules: since with a point in time, for with duration; in/on/at for place from large to small; depend on, consist of, prefer to, married to.

Punctuation: comma for non-restrictive clauses, semicolon between independent clauses, apostrophe for possession and contractions, colon before an explanation or list.

Sentence types: simple (one clause), compound (coordinated), complex (subordinated), compound-complex; fragments and run-ons are the most common structural errors.

Divisibility: by 3 or 9 if digit sum is divisible; by 4 if last two digits are; by 8 if last three digits are; by 11 if alternating digit sum difference is 0 or a multiple of 11.

HCF × LCM = product of the two numbers; LCM of fractions = LCM of numerators / HCF of denominators.

Squares 1–30 and cubes 1–15 should be recalled; a² − b² = (a + b)(a − b); (a + b)² = a² + 2ab + b².

Average speed for equal distances = 2xy/(x + y); for equal times it is the simple mean (x + y)/2.

Ratio and proportion: if a : b = c : d then ad = bc; dividing a quantity Q in ratio a : b gives Qa/(a + b) and Qb/(a + b).

Time and work: if A finishes in x days and B in y days, together they take xy/(x + y) days; efficiency is inversely proportional to time.

Newton's second law F = ma; momentum p = mv is conserved in the absence of external force; impulse = change in momentum = F × t.

Work = force × displacement in the direction of force; power = work/time; kinetic energy = ½mv²; potential energy = mgh; energy is conserved but degraded in form.

Heat: Q = mcΔT; latent heat Q = mL; conduction needs a medium, convection is bulk fluid movement, radiation needs none and travels at light speed.

Acids and bases: pH below 7 acidic, 7 neutral, above 7 basic; acid + base → salt + water (neutralisation); litmus red in acid, blue in base.

Atomic structure: atomic number Z = protons; mass number A = protons + neutrons; isotopes differ in neutrons, isobars differ in protons and have the same mass number.

Chemical reactions: combination, decomposition, displacement, double displacement, redox; balancing conserves atoms of each element.

Resource classification: renewable vs non-renewable, potential vs actual, biotic vs abiotic; sustainable use means consumption within regeneration rates.

Soil types in India: alluvial (most extensive, fertile), black (cotton soil, moisture-retentive), red (iron-rich), laterite (leached, heavy rainfall areas), arid and mountain soils.

Agriculture: kharif crops sown with the monsoon (rice, cotton, maize), rabi in winter (wheat, gram, mustard), zaid in the short summer season.

Industries: agro-based (sugar, textile), mineral-based (iron and steel, cement), and knowledge-based; location depends on raw material, power, transport, market, and labour.

Census and population terms: density = population/area; sex ratio = females per 1000 males; literacy rate excludes children below 7 in the standard calculation.

Disaster management cycle: mitigation and preparedness before, response during, recovery and reconstruction after an event.

A cloze test measures contextual reading and grammar by deleting words at regular intervals; an open cloze requires production, a multiple-choice cloze requires recognition.

Rubrics for writing should name criteria (content, organisation, grammar, vocabulary) and describe performance levels; analytic scoring gives a profile, holistic scoring a single impression.

Remedial teaching cycle: diagnose the specific error, reteach the underlying rule with contrasting examples, practise in context, then reassess the same skill.

Dictation tests spelling and listening simultaneously; it should not be the sole measure of writing ability.

Portfolio assessment documents drafts and reflections over time and reveals progress that a single test cannot show.

Oral assessment criteria: fluency, accuracy, pronunciation, and interaction; rate separately so that one weakness does not depress the whole score.

Place value is the foundational concept for all written algorithms; without it, borrowing and carrying become arbitrary rules.

Number sense includes estimation and benchmarking (e.g., is 7/8 closer to 0, ½, or 1?); it should be assessed alongside exact computation.

Multiplication models: repeated addition, array/area, and scaling; the array model best explains the commutative property.

Division has two meanings - partitive (sharing into groups) and quotative (measurement, how many groups of size n); word problems must be matched to the intended meaning.

Fractions as part-whole, as division, as ratio, and as measure: teaching only part-whole causes later difficulty with multiplication and division of fractions.

Mental mathematics strategies (compensation, doubling, near-doubles, bridging through ten) should be taught explicitly before formal algorithms are drilled.

EVS integrates science, social science, and environmental education around the child's immediate environment; themes progress from self and family to community and beyond.

Observation-based learning: learners record, compare, and question real phenomena (plants, water, waste) rather than memorise definitions.

Local knowledge and community resources are valid curriculum content; surveys and interviews build both data skills and civic understanding.

Project work in EVS should include a question, a plan, data collection, presentation, and reflection; the process, not only the display, is assessed.

Environmental values are formed through participation (waste segregation, water audits) more than through moral instruction alone.

Safety and ethics in EVS activities: avoid harming living things during observation; return specimens; seek permission before photographing people.

Behaviourism (Thorndike): law of effect - responses followed by satisfaction are strengthened; law of exercise and law of readiness accompany it.

Gestalt learning: the whole is more than the sum of parts; insight learning (Kohler) occurs suddenly after restructuring the perceptual field.

Tolman's latent learning: learning can occur without reinforcement and remain unexpressed until performance is required.

Bandura's social learning: attention, retention, reproduction, motivation; modelling transmits aggression and prosocial behaviour alike.

Information processing: sensory register → short-term/working memory (limited capacity, about 7 ± 2 chunks) → long-term memory; rehearsal and elaboration aid transfer.

Transfer of learning: positive transfer aids a new task, negative transfer interferes; near transfer is easier than far transfer.

भाषा शिक्षण के चार कौशल: सुनना, बोलना, पढ़ना, लिखना; सुनना और बोलना पहले, पढ़ना-लिखना बाद में।

पठन कौशल के प्रकार: सरसरी दृष्टि से पढ़ना (skimming), विशिष्ट सूचना ढूँढ़ना (scanning), गहन पठन; मौन पठन गति और समझ बढ़ाता है।

व्याकरण शिक्षण आगमन (inductive) विधि से प्रभावी होता है: उदाहरण पहले, नियम बाद में; निगमन विधि नियम पहले देती है।

भाषा और बोली में अन्तर: बोली स्थानीय और अपेक्षाकृत सरल होती है, भाषा व्यापक, मानकीकृत और साहित्यिक रूप धारण करती है।

मूल्यांकन के साधन: निबन्ध, पत्र, संवाद, कविता पाठ, श्रुतलेख; केवल वस्तुनिष्ठ प्रश्न भाषा-प्रयोग की क्षमता नहीं मापते।

त्रुटि और अशुद्धि: त्रुटि विकासशील अवस्था का संकेत है, अशुद्धि असावधानी; त्रुटि-विश्लेषण से शिक्षण की दिशा तय होती है।

Preamble declares India a sovereign, socialist, secular, democratic republic; the words socialist and secular were added by the 42nd Amendment (1976).

Fundamental Rights include equality (Art. 14–18), freedom (19–22), against exploitation (23–24), religion (25–28), cultural and educational rights (29–30), and constitutional remedies (32).

Article 32 (right to constitutional remedies) is called the heart and soul of the Constitution by Ambedkar; writs include habeas corpus, mandamus, prohibition, certiorari, quo warranto.

Directive Principles (Part IV) are non-justiciable guidelines for policy; they include uniform civil code, village panchayats, and living wage.

Union executive: President is head of state and supreme commander; the Prime Minister leads the Council of Ministers, which advises the President.

Panchayati Raj: 73rd Amendment (1992) gave constitutional status to panchayats, with a three-tier structure and reservation for women and SC/ST.

Practical assessment criteria: hypothesis quality, variable control, accuracy of measurement, recording, interpretation, and safety compliance.

Formative probing in science uses predict–observe–explain tasks; the prediction reveals the learner's existing conception before instruction.

Concept cartoons and annotated diagrams assess understanding without depending heavily on writing fluency.

Numerical problems should be assessed for setup and reasoning, not only the final value; partial credit for a correct method with an arithmetic slip is defensible.

Laboratory records should include date, aim, apparatus, procedure, observations, and conclusion; reproducibility requires recording conditions.

Safety audit: locate the first-aid box, eyewash, and fire extinguisher; know the disposal route for broken glass and chemical waste.

Measures of central tendency: mean (sensitive to extreme scores), median (robust to outliers), mode (categorical data).

Measures of dispersion: range, quartile deviation, mean deviation, standard deviation; SD is the square root of variance and uses every score.

Normal distribution: about 68% of scores fall within ±1 SD, 95% within ±2 SD, 99% within ±3 SD of the mean.

Percentile rank gives the percentage of the group scoring at or below a score; it is not the percentage of marks obtained.

Correlation coefficient r ranges from −1 to +1; r = 0 means no linear relationship, not no relationship.

Standard scores: z = (X − mean)/SD; T-score = 50 + 10z; both express a raw score relative to the group.

Gifted learners need enrichment and acceleration; under-challenge produces boredom and behavioural issues that can be mistaken for disorder.

Hearing impairment affects phonological development and hence reading; visual impairment requires tactile and auditory substitutes and orientation training.

Autism spectrum: difficulties in social communication and restricted, repetitive behaviour; visual schedules and predictable routines reduce anxiety.

ADHD markers: inattention, hyperactivity, impulsivity across settings; diagnosis requires impairment in more than one setting, not classroom observation alone.

Guidance is developmental and preventive (study skills, career information); counselling is remedial and addresses specific personal difficulties.

Referral rule: when a difficulty persists despite good-quality classroom adaptation, involve parents and a specialist rather than attributing it to the child's attitude.

Linear equation: ax + b = 0 gives x = −b/a; a pair a₁x + b₁y = c₁ and a₂x + b₂y = c₂ has a unique solution if a₁/a₂ ≠ b₁/b₂, none if equal but not equal to c₁/c₂, infinite if all three ratios are equal.

Quadratic: roots of ax² + bx + c = 0 are [−b ± √(b² − 4ac)]/2a; discriminant D > 0 real distinct, D = 0 equal, D < 0 complex.

Sum of roots = −b/a, product = c/a; a quadratic can be written x² − (sum)x + (product) = 0.

Algebraic identities: (a + b)³ = a³ + b³ + 3ab(a + b); a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²).

Circle: angle in a semicircle is 90°; the angle at the centre is twice the angle at the circumference; tangents from an external point are equal.

Similar triangles: corresponding angles equal and sides proportional; area ratio equals the square of the side ratio.

River valley civilisations: Mesopotamian (Tigris–Euphrates), Egyptian (Nile), Indus (Indus), Chinese (Hwang Ho); all depended on flood agriculture and urban planning.

Renaissance began in Italian city-states, emphasising humanism and classical learning; the printing press (Gutenberg, 15th century) accelerated its spread.

Industrial Revolution began in Britain in the late 18th century with textile machinery and steam power; it shifted production from the household to the factory.

French Revolution (1789) ideals - liberty, equality, fraternity - influenced nationalist movements worldwide, including India's.

World Wars: First (1914–18) triggered by the Sarajevo assassination within an alliance system; Second (1939–45) ended with the Axis defeat and the founding of the UN (1945).

Map projections distort area, shape, distance, or direction; the Mercator preserves direction and distorts polar area.

Lesson plan components: learning outcomes, prior knowledge, teaching aids, introduction, presentation, practice, assessment, and closure.

Learning outcomes should be observable and measurable ("classifies quadrilaterals by property"), not vague ("knows quadrilaterals").

Questioning: closed questions check recall, open questions probe reasoning; wait time of three or more seconds increases response length and quality.

Group work should have individual accountability and a defined role for each member; unstructured groups allow social loafing.

Classroom management rule: preventive strategies (clear routines, proximity, engaging tasks) are more effective than reactive punishment.

Homework should consolidate or extend, be differentiated, and receive feedback; unmarked homework teaches that it does not matter.

Morphology: free morphemes stand alone (book), bound morphemes attach (un-, -ness); prefixes change meaning, suffixes often change word class.

Word formation processes: affixation, compounding, conversion (zero derivation), blending (smog), clipping (exam), acronym (UNESCO), borrowing.

Synonyms share core meaning but differ in connotation and collocation (house/home, cheap/inexpensive); teaching collocation prevents unnatural usage.

Idioms are non-compositional (kick the bucket); phrasal verbs combine verb + particle with a new meaning (give up, put off) and may be separable or inseparable.

Context clues for unknown words: definition, example, contrast, and general sense of the sentence; teaching these raises independent reading.

Hindi शब्द-भंडार: तत्सम (संस्कृत से), तद्भव (परिवर्तित रूप), देशज (स्थानीय), विदेशी (आगत) शब्दों का वर्गीकरण।

Cell organelles: nucleus controls activity, mitochondria release energy, ribosomes synthesise protein, chloroplast carries out photosynthesis, vacuole stores and maintains turgor.

Plant vs animal cell: cellulose cell wall, chloroplasts, and a large central vacuole are typical of plant cells; centrioles are typical of animal cells.

Photosynthesis needs light, chlorophyll, CO₂, and water; respiration releases energy from glucose and occurs in all living cells, day and night.

Human systems: digestive enzymes (amylase in saliva, pepsin in stomach, trypsin in small intestine); breathing rate and heart rate rise with activity.

Reproduction: pollination transfers pollen to stigma; fertilisation forms the zygote; in humans the placenta mediates exchange between mother and embryo.

Classification: binomial nomenclature gives genus and species; five kingdoms are Monera, Protista, Fungi, Plantae, Animalia.

Multiple-choice item rules: one clearly correct key, plausible distractors, no grammatical cue linking stem to key, avoid 'all of the above' and negatives in the stem.

Objective items sample widely but test recognition; essay items test organisation and argument but have lower scoring reliability unless a rubric is used.

Bloom's revised taxonomy: remember, understand, apply, analyse, evaluate, create; the verb in the outcome determines the cognitive level.

Table of specifications (blueprint) balances content areas against cognitive levels so that a test is not skewed to recall.

Item difficulty and discrimination should be computed after a pilot; items with negative discrimination are revised or discarded.

Fairness check: items must avoid cultural and gender bias and must not depend on vocabulary unrelated to the construct being tested.

Multilingualism as a resource: the NCF 2005 and NEP 2020 recommend using the home language as a bridge in early years and gradually transitioning to the school language.

BICS (basic interpersonal communicative skills) develops in about two years; CALP (cognitive academic language proficiency) takes five to seven years, so academic underperformance may reflect language load, not ability.

Accommodations for visual impairment: braille, large print, audio description, tactile diagrams, extra time, and a scribe where writing is not the construct tested.

Accommodations for learning disability: reader, extra time, reduced copying from the board, oral responses; the standard being assessed stays unchanged.

Gender-responsive classroom: balanced examples, equitable participation, and challenging stereotyped textbook images.

Barrier-free access includes ramps, accessible sanitation, and seating that allows a wheelchair user to participate in group work.

Attachment (Bowlby, Ainsworth): secure, avoidant, ambivalent, disorganised; secure attachment predicts better school adjustment and peer competence.

Piaget's moral development: heteronomous morality (rules fixed by authority) shifts to autonomous morality (rules as agreements) around 10 years.

Peer relations: sociometric status categories - popular, rejected, neglected, controversial; rejected-aggressive children are at highest risk of later difficulty.

Adolescent development: puberty onset varies widely; egocentrism appears as imaginary audience and personal fable, which explain risk-taking and self-consciousness.

Emotional regulation develops through co-regulation with adults, then internalisation; labelling emotions verbally supports regulation.

Bullying intervention works best as a whole-school approach with clear reporting routes, not as punishment of individual incidents alone.

Mean of grouped data uses class midpoints: mean = Σfᵢxᵢ / Σfᵢ; the median class is the class where cumulative frequency reaches n/2.

Probability of an event = favourable outcomes / total equally likely outcomes; P(A) + P(not A) = 1 and 0 ≤ P(A) ≤ 1.

For two independent events, P(A and B) = P(A) × P(B); for mutually exclusive events, P(A or B) = P(A) + P(B).

Bar graphs compare categories, histograms show frequency distribution of continuous data, pie charts show parts of a whole, and line graphs show change over time.

Mode of grouped data lies in the modal class; the empirical relation is mode ≈ 3 median − 2 mean for moderately skewed data.

Sampling bias: a sample drawn only from a convenient group (e.g., one class) cannot support a claim about the whole school population.

Sectors: primary (agriculture, mining), secondary (manufacturing), tertiary (services); the share of the tertiary sector in India's GDP is the largest.

Poverty line in India is estimated from consumption expenditure; the Multidimensional Poverty Index adds health, education, and standard of living.

Human Development Index combines life expectancy, education (mean and expected years of schooling), and per capita income.

Money and banking: RBI issues currency and controls credit; CRR and repo rate are tools of monetary policy; inflation reduces purchasing power.

Public finance: direct taxes (income, corporate) fall on the same person; indirect taxes (GST) can be shifted to the consumer.

Sustainable development balances economic growth, social equity, and environmental protection; the SDGs set 17 global goals to 2030.

Earth's rotation causes day and night; revolution plus axial tilt (23½°) causes seasons; the equator receives more direct insolation than the poles.

Solar system order: Mercury, Venus, Earth, Mars, asteroid belt, Jupiter, Saturn, Uranus, Neptune; inner planets are rocky, outer are gas/ice giants.

Moon phases follow the synodic month of about 29.5 days; a solar eclipse occurs at new moon, a lunar eclipse at full moon.

Water cycle: evaporation, transpiration, condensation, precipitation, runoff, infiltration; groundwater recharge depends on infiltration rate.

Greenhouse gases (CO₂, CH₄, N₂O, water vapour) trap outgoing infrared radiation; the ozone layer absorbs ultraviolet radiation.

Natural hazards: earthquakes occur at plate boundaries, volcanoes at subduction zones and hotspots, and cyclones form over warm oceans above about 27 °C.

Action research cycle: identify the problem, plan an intervention, act, observe, reflect, then revise; it is cyclical and local.

Reflective practice tools: teaching journal, peer observation with a protocol, learner feedback, and lesson video review.

A teaching hypothesis should be testable ("if I add worked examples, error rate in word problems will drop"), not a general wish.

Evidence for improvement should include pre/post comparison and work samples, not only impressions of a lesson's success.

Collaborative professional learning (lesson study) improves instruction when teachers jointly plan, observe, and revise a single research lesson.

Ethical reflection: examine one's own assumptions and biases about learners' home background and language before interpreting performance.

वाक्य के भेद अर्थ के आधार पर: विधानवाचक, निषेधवाचक, प्रश्नवाचक, आज्ञावाचक, विस्मयादिबोधक; रचना के आधार पर सरल, संयुक्त, मिश्र।

संधि और संधि-विच्छेद: स्वर संधि में दीर्घ, गुण, वृद्धि, यण, अयादि भेद; जैसे सूर्य + उदय = सूर्योदय (गुण संधि)।

अलंकार: अनुप्रास (व्यंजन की आवृत्ति), उपमा (वह/सा/सम से तुलना), रूपक (अभेद आरोप), उत्प्रेक्षा (मानो/जनु), मानवीकरण।

रस के नौ भेद: शृंगार, हास्य, करुण, रौद्र, वीर, भयानक, बीभत्स, अद्भुत, शांत; रस की उत्पत्ति स्थायी भाव से होती है।

छन्द: चौपाई (4 चरण, 16 मात्रा प्रति चरण), दोहा (13 + 11 मात्रा), सोरठा (11 + 13 मात्रा), रोला (24 मात्रा प्रति चरण)।

काल-वाच्य प्रयोग: 'राम ने पत्र लिखा' कर्तृवाच्य है, 'राम से पत्र लिखा गया' कर्मवाच्य, 'राम से चला नहीं जाता' भाववाच्य।