Afghanistan Kankor cheat sheet

Quadratic formula: roots of ax²+bx+c=0 are x = (−b ± √(b²−4ac)) / 2a; discriminant D = b²−4ac gives two real roots if D>0, one if D=0, none real if D<0.

Sum and product of roots: x₁+x₂ = −b/a and x₁x₂ = c/a for ax²+bx+c=0.

Pythagorean identity: sin²θ + cos²θ = 1; also tanθ = sinθ/cosθ and 1 + tan²θ = sec²θ.

Law of sines: a/sinA = b/sinB = c/sinC = 2R; law of cosines: a² = b² + c² − 2bc·cosA.

Arithmetic sequence: aₙ = a₁ + (n−1)d, Sₙ = n(a₁+aₙ)/2; geometric: aₙ = a₁rⁿ⁻¹, Sₙ = a₁(rⁿ−1)/(r−1) for r≠1.

Area formulas: triangle = ½·base·height, circle = πr², trapezoid = ½(a+b)h; volume of sphere = (4/3)πr³.

Logarithm rules: log(xy) = log x + log y, log(x/y) = log x − log y, log(xⁿ) = n·log x, log_b b = 1.

Distance between points = √((x₂−x₁)² + (y₂−y₁)²); slope m = (y₂−y₁)/(x₂−x₁); parallel lines have equal slopes, perpendicular slopes multiply to −1.

Newton's second law: F = ma; weight W = mg, with g ≈ 9.8 m/s² near Earth's surface.

Kinematics: v = u + at, s = ut + ½at², v² = u² + 2as for constant acceleration.

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; work W = Fd·cosθ.

Ohm's law: V = IR; electric power P = VI = I²R = V²/R; resistors in series add, in parallel 1/R = Σ1/Rᵢ.

Wave relation: speed v = fλ, where f is frequency and λ is wavelength.

Density ρ = m/V; pressure P = F/A; pressure in a liquid at depth h is P = ρgh.

Conservation of momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ for an isolated system.

Heat: Q = mcΔT for temperature change and Q = mL for phase change, where L is latent heat.

Mole concept: 1 mol = 6.022×10²³ particles; number of moles n = mass / molar mass.

Molar volume of an ideal gas at STP is about 22.4 L/mol.

pH = −log[H⁺]; pH < 7 is acidic, pH = 7 neutral, pH > 7 basic at 25 °C.

Balancing combustion of a hydrocarbon CₓHᵧ: CₓHᵧ + (x + y/4)O₂ → xCO₂ + (y/2)H₂O.

Avogadro's law: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons.

Ideal gas law: PV = nRT, with R ≈ 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K).

Periodic trend: atomic radius decreases left-to-right across a period and increases down a group; electronegativity increases across a period.

Photosynthesis summary: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts.

Cellular respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP); glycolysis occurs in the cytoplasm.

DNA bases pair A–T and G–C; RNA replaces thymine with uracil and is single-stranded.

Mitosis produces two genetically identical diploid cells; meiosis produces four haploid gametes.

Human blood groups follow ABO: A and B are codominant, O is recessive; Rh factor is separate.

Mendel's law of segregation: allele pairs separate during gamete formation; law of independent assortment applies to unlinked genes.

The human heart has four chambers; oxygenated blood travels from lungs to left atrium to left ventricle to the aorta.

Enzymes are biological catalysts that lower activation energy and are specific to their substrates.

Dari is written right-to-left in a modified Arabic script; the alphabet has 32 letters, with Persian additions such as پ چ ژ گ.

Sentence parts: نهاد (subject), گزاره (predicate), مفعول (object); the verb normally comes at the end of the clause.

Ezafe (اضافه) links a noun to an adjective or possessor with an unstressed −e: کتابِ نو (new book), کتابِ احمد (Ahmad's book).

Past simple of بودن: بودم، بودی، بود، بودیم، بودید، بودند; present of بودن: هستم، هستی، است، هستیم، هستید، هستند.

Classical poets: Ferdowsi (Shahnameh), Rumi (Masnavi), Saadi (Gulistan, Bustan), Hafez (Divan), Jami and Attar.

The Shahnameh is an epic in couplets (مثنوی) recounting Iranian legendary and historical kings.

Common rhetorical devices: تشبیه (simile), استعاره (metaphor), کنایه (irony/allusion), جناس (pun).

Verb tense markers: میـ for imperfective present/past, بـ for subjunctive, and شده/بود for perfect and pluperfect forms.

Pashto is written right-to-left in a modified Arabic script; its alphabet adds retroflex letters such as ټ ډ ړ ږ ښ ڼ.

Pashto has grammatical gender: nouns are masculine or feminine, and adjectives agree with the noun.

Pashto has two main dialect groups: soft (نرم) western/southern and hard (سخت) eastern, differing in pronunciation of ښ and ږ.

Basic pronouns: زه (I), ته (you), هغه (he), هغه (she), مونږ (we), تاسو (you pl.), هغوی (they).

Classical Pashto poet Khushal Khan Khattak is celebrated for his poetry on honor, freedom, and Afghan unity.

Rahman Baba is a major Pashto mystic poet whose diwan is famous for Sufi themes.

Pashto folk literature includes the landay (لنډۍ), a short two-line folk couplet, and tappa.

Verb agreement in Pashto follows ergative patterns in past transitive constructions, where the object governs agreement.

The five pillars of Islam: Shahadah (testimony), Salah (prayer), Zakah (charity), Sawm (fasting in Ramadan), and Hajj (pilgrimage).

The Qur'an has 114 surahs; the longest is Al-Baqarah and the shortest is Al-Kawthar.

Salah is performed five times daily: Fajr, Zuhr, Asr, Maghrib, and Isha.

Zakah is an obligatory annual alms of 2.5% on qualifying wealth above the nisab.

Hajj takes place in the month of Dhu al-Hijjah and includes standing at Arafah on the 9th day.

The Hijrah (migration of the Prophet Muhammad from Makkah to Madinah) occurred in 622 CE and marks the start of the Islamic calendar.

The four rightly guided caliphs in order: Abu Bakr, Umar ibn al-Khattab, Uthman ibn Affan, and Ali ibn Abi Talib.

Fasting (Sawm) during Ramadan requires abstaining from food, drink, and other acts from dawn (Fajr) to sunset (Maghrib).

Afghanistan is a landlocked country in South-Central Asia; its capital is Kabul and its highest peak is Noshaq (about 7,492 m).

Major rivers: Amu Darya (north), Helmand (southwest), Kabul, and Hari Rud; the Helmand is the longest river within Afghanistan.

Afghanistan's neighbors: Iran to the west, Pakistan to the south and east, and Turkmenistan, Uzbekistan, and Tajikistan to the north; a narrow strip, the Wakhan Corridor, touches China.

Kabul lies at about 1,790 m elevation and has a semi-arid climate with cold winters and dry summers.

Afghanistan gained full independence from British influence in 1919 under King Amanullah Khan after the Third Anglo-Afghan War.

The Durrani Empire was founded by Ahmad Shah Durrani in 1747 and is often regarded as the origin of modern Afghanistan.

Civic concepts: a constitution defines state powers and citizens' rights; the separation of powers divides authority among executive, legislative, and judicial branches.

Geography terms: latitude measures north–south position, longitude measures east–west; Afghanistan lies roughly between 29°–38° N and 60°–75° E.