SPSC Subject Specialist cheat sheet

Newton's second law: F = ma; one newton is the force that gives a 1 kg mass an acceleration of 1 m/s².

For ax² + bx + c = 0 (a ≠ 0), x = (−b ± √(b² − 4ac)) / 2a; the discriminant b² − 4ac gives two real roots (> 0), one repeated root (= 0) or complex roots (< 0).

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂; light reactions occur on the thylakoid membranes and the Calvin cycle in the stroma.

Ohm's law: V = IR; resistors in series add (R = R₁ + R₂), while in parallel 1/R = 1/R₁ + 1/R₂.

DNA base pairing is A–T (two hydrogen bonds) and G–C (three hydrogen bonds); human somatic cells have 46 chromosomes (23 pairs), gametes have 23.

One mole = 6.022 × 10²³ particles (Avogadro constant); the mass of one mole in grams equals the relative molecular mass.

Pythagoras' theorem, a² + b² = c², holds only for right-angled triangles, with c the side opposite the 90° angle.

Speed of light in vacuum c ≈ 3.0 × 10⁸ m/s; weight W = mg, with g ≈ 9.8 m/s² near Earth's surface.

pH = −log₁₀[H⁺]; at 25 °C a pH below 7 is acidic, 7 is neutral and above 7 is basic.

Bloom's revised taxonomy, lowest to highest: Remember → Understand → Apply → Analyse → Evaluate → Create.

Bloom's three domains: cognitive (mental skills), affective (attitudes and values, Krathwohl) and psychomotor (physical skills, Simpson).

Piaget's stages: sensorimotor (0–2), preoperational (2–7), concrete operational (7–11), formal operational (11 and above).

Vygotsky: learning happens within the Zone of Proximal Development, and scaffolding is the support given inside that zone and then withdrawn.

Formative assessment is ongoing and feedback-oriented; summative assessment comes at the end of a unit and is grading-oriented.

Validity means a test measures what it claims; reliability means consistency across occasions, forms or raters. A test can be reliable but invalid, never valid without reliability.

Herbart's five lesson steps: preparation, presentation, association (comparison), generalisation, application.

Thorndike's laws are readiness, exercise and effect; Skinner is associated with operant conditioning and Pavlov with classical conditioning.

The eight parts of speech are noun, pronoun, verb, adjective, adverb, preposition, conjunction and interjection.

Twelve tenses arise from 3 times (present, past, future) × 4 aspects (simple, continuous, perfect, perfect continuous).

Conditionals: first = if + present, will + base; second = if + past, would + base; third = if + past perfect, would have + past participle.

Passive voice is a form of be + past participle; only transitive verbs (verbs with an object) can be made passive.

Agreement rule: 'one of + plural noun' takes a singular verb; each, every, either and neither are grammatically singular.

Reported speech backshift: present→past, present perfect→past perfect, will→would, can→could; now→then, tomorrow→the following day.

Gerund = -ing form used as a noun ('Swimming is healthy'); present participle = -ing form used as an adjective ('the crying baby'); infinitive = to + base verb.

Figures of speech: simile uses like/as, metaphor implies the comparison, personification gives human traits, alliteration repeats initial consonants, hyperbole exaggerates.

Prepositions of time: at + clock time or night, on + day or date, in + month, year or season.

Pakistan became independent on 14 August 1947; Quaid-e-Azam Muhammad Ali Jinnah was the first Governor-General and Liaquat Ali Khan the first Prime Minister.

Constitutional sequence: Objectives Resolution (March 1949), Constitution of 1956 (Islamic Republic, parliamentary), 1962 (presidential), 1973 (present, parliamentary and federal).

Pakistan's four provinces are Punjab, Sindh, Khyber Pakhtunkhwa and Balochistan, in addition to Islamabad Capital Territory, Gilgit-Baltistan and Azad Jammu and Kashmir.

Indus Waters Treaty (1960, brokered by the World Bank): India received the eastern rivers Ravi, Beas and Sutlej; Pakistan received the western rivers Indus, Jhelum and Chenab.

United Nations: founded 1945, headquarters in New York; the Security Council has 5 permanent veto-holding members and 10 members elected for two-year terms.

SAARC was founded in 1985 with its secretariat in Kathmandu and eight members; the OIC was founded in 1969 with headquarters in Jeddah and 57 members.

K2, at 8,611 m, is the world's second-highest mountain and lies in the Karakoram range of Gilgit-Baltistan.

Karachi is the capital of Sindh; the Indus is the province's principal river and forms a delta where it meets the Arabian Sea.