PCET cheat sheet

Piaget's stages: sensorimotor (0-2, object permanence), preoperational (2-7, egocentrism, symbolic play), concrete operational (7-11, conservation, reversibility), formal operational (11+, abstract logic).

Vygotsky's ZPD is the gap between independent performance and assisted performance; scaffolding is temporary support within that zone; private speech becomes inner speech.

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

Erikson's psychosocial crises: trust vs mistrust (infancy), autonomy vs shame (1-3), initiative vs guilt (3-6), industry vs inferiority (6-12), identity vs role confusion (adolescence).

Classical conditioning (Pavlov): neutral stimulus paired with unconditioned stimulus becomes conditioned stimulus; operant conditioning (Skinner): reinforcement increases behaviour, punishment decreases it; positive adds a stimulus, negative removes one.

Inclusive education principle: children with disabilities learn best in the least restrictive environment with necessary accommodations; the RPWD Act 2016 lists 21 disability categories and mandates inclusive schooling.

Continuous and Comprehensive Evaluation (CCE) assesses scholastic (curricular) and co-scholastic (attitudes, values, sports, arts) areas using formative and summative tools, not only term-end exams.

Learning is a continuous, active construction of knowledge; errors are diagnostic windows into a child's thinking, not evidence of failure.

Punjabi has 10 vowel letters (ਅ ਆ ਇ ਈ ਉ ਊ ਏ ਐ ਓ ਔ) and 32 consonants (ਕ ਖ ਗ ਘ ਙ ਚ ਛ ਜ ਝ ਞ ਟ ਠ ਡ ਢ ਣ ਤ ਥ ਦ ਧ ਨ ਪ ਫ ਬ ਭ ਮ ਯ ਰ ਲ ਵ ੜ ਸ ਹ).

The Gurmukhi script is written left to right; all letters hang from a common top line (ਸਿਰਲੇਖ); ੳ, ੲ, ਸ are vowel carriers, not full consonants.

Tone (ਸੁਰ) is phonemic in Punjabi: low, mid, high tone; written h (ਹ) after a consonant often marks low tone (e.g., ਕਹਿਣਾ).

Nasalisation is marked by ਟਿੱਪੀ (ਂ) over short vowels and ਬਿੰਦੀ (ੰ) over long vowels; ਅੱਧਕ (ੱ) doubles the following consonant.

Punjabi word order is Subject-Object-Verb; postpositions follow the noun; gender is masculine/feminine; adjectives agree with the noun in gender and number.

Language acquisition vs learning (Krashen): acquisition is subconscious and meaning-focused; learning is conscious and rule-focused; the affective filter can block input.

L1 and L2 skills transfer: strong oral competence and vocabulary in the home language support reading comprehension in the second language (Cummins' interdependence hypothesis).

Assessment should test listening, speaking, reading and writing separately; dictation tests spelling and sound-symbol mapping, not comprehension.

The English phoneme inventory includes 24 consonants and about 20 vowels (12 monophthongs + 8 diphthongs in RP); English spelling is not phonemic, so sight-word and phonics instruction must both be used.

The five components of reading: phonemic awareness, phonics, fluency, vocabulary and comprehension; fluency = accuracy × rate × prosody.

Grammar rule: subject-verb agreement in number and person; indefinite pronouns (everyone, each) take singular verbs; collective nouns usually take singular verbs in Indian English.

Tense-aspect system: simple, continuous, perfect, perfect continuous across present, past and future; stative verbs (know, believe, own) rarely take continuous forms.

Direct to indirect speech: shift tense one step back, change pronouns to the reporter's perspective, and adjust time/place words (now→then, here→there, tomorrow→the next day).

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

Communicative Language Teaching prioritises meaning, interaction and authentic tasks over isolated grammar drills; the teacher acts as facilitator.

Assessment of writing uses analytic rubrics: content, organisation, grammar, vocabulary and mechanics; holistic scoring gives a single overall impression.

Place value: each position is 10 times the one to its right; the value of a digit = digit × 10^position (e.g., 7 in 4,703 = 700).

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

LCM × HCF = product of the two numbers (for two positive integers); use prime factorisation or the Euclidean algorithm to find HCF.

Area and perimeter: rectangle A = l×b, P = 2(l+b); triangle A = ½×b×h; circle A = πr², C = 2πr; parallelogram A = b×h; trapezium A = ½(a+b)h.

Volume: cuboid V = l×b×h; cube V = a³; cylinder V = πr²h; total surface area of cuboid = 2(lb+bh+hl).

Percentage and profit/loss: profit% = (SP−CP)/CP × 100; discount% = (MP−SP)/MP × 100; simple interest SI = PRT/100; compound amount A = P(1+R/100)^T.

Fractions: a/b + c/d = (ad+bc)/bd; division by a fraction equals multiplication by its reciprocal; a decimal terminates only if the denominator in lowest terms has factors 2 and 5 only.

Angle facts: sum of angles in a triangle = 180°; exterior angle = sum of the two opposite interior angles; sum of interior angles of an n-gon = (n−2)×180°.

Food chain: producer → primary consumer → secondary consumer → decomposer; energy transfer is about 10% per trophic level (10% law), so food chains rarely exceed 4-5 links.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂; chlorophyll in chloroplasts absorbs light; oxygen is released as a by-product.

Water cycle processes: evaporation, transpiration, condensation, precipitation, infiltration and runoff; groundwater recharge depends on permeable soil and vegetation cover.

Air composition: about 78% nitrogen, 21% oxygen, 0.93% argon, 0.04% carbon dioxide; CO₂ and methane are major greenhouse gases.

Pollution indicators: BOD measures organic water pollution; lichens are sensitive air-pollution indicators; ozone (O₃) in the stratosphere shields UV, while ground-level ozone is a pollutant.

Human body systems: digestive (mouth to anus), circulatory (heart, arteries, veins), respiratory (lungs, alveoli), excretory (kidneys, nephrons); the small intestine absorbs most nutrients.

Adaptations: cactus has spines (modified leaves) and a thick stem for water storage; camel stores fat in the hump; fish have gills for dissolved oxygen.

Natural resources: renewable (solar, wind, biomass) vs non-renewable (coal, petroleum, natural gas); soil erosion is checked by contour ploughing, terracing and shelter belts.

Indian Constitution: adopted 26 November 1949, came into force 26 January 1950; it declares India a sovereign, socialist, secular, democratic republic with a parliamentary system.

Fundamental Rights (Part III, Articles 12-35) include equality, freedom, against exploitation, religion, cultural and educational rights, and constitutional remedies; Fundamental Duties were added by the 42nd Amendment (1976).

The Preamble's objectives are justice, liberty, equality and fraternity; the Directive Principles of State Policy (Part IV) are non-justiciable guidelines for governance.

Three tiers of government: Union, State and local (73rd and 74th Amendments, 1992, gave constitutional status to panchayats and municipalities).

Indian geography: the Tropic of Cancer (23.5°N) passes through eight states; the Himalayas are young fold mountains; the Deccan Plateau is made of old igneous basalt.

Monsoon: the southwest monsoon (June-September) brings most rainfall; the Western Ghats' windward side gets heavy rain and the leeward side is a rain shadow.

Freedom movement milestones: Revolt of 1857, Indian National Congress founded 1885, Partition of Bengal 1905, Jallianwala Bagh 1919, Non-Cooperation 1920, Dandi March 1930, Quit India 1942, Independence 1947.

Map skills: latitude lines run east-west and measure north-south position; longitude lines run north-south; IST is based on 82.5°E, and 1° of longitude equals 4 minutes of time difference.

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

Work, energy and power: W = F·d·cosθ; kinetic energy KE = ½mv²; potential energy PE = mgh; power P = W/t; SI units are joule and watt.

Electricity: Ohm's law V = IR; series resistance R = R₁+R₂+R₃; parallel 1/R = 1/R₁+1/R₂+1/R₃; power P = VI = I²R = V²/R.

Light: reflection angle of incidence = angle of reflection; refraction bends light toward the normal when entering a denser medium; concave mirrors converge, convex diverge; focal length f = R/2.

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

Periodic table: groups are vertical columns with similar valence electrons; periods are horizontal rows; metals are on the left, non-metals on the right, metalloids along the zig-zag line.

Cell: the basic structural and functional unit of life; plant cells have a cell wall, chloroplasts and a large vacuole; animal cells lack a cell wall and have centrioles.

Human systems: blood groups A, B, AB, O with Rh factor; the heart has four chambers; nephrons filter blood in the kidneys; neurons transmit electrical impulses.