Afghan Air Force University Kankor cheat sheet

Quadratic formula: for ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / (2a); the discriminant b² − 4ac gives two real roots if positive, one if zero, none if negative.

Pythagorean theorem: in a right triangle with legs a, b and hypotenuse c, a² + b² = c².

Area formulas: triangle = ½bh; circle = πr²; trapezoid = ½(a + b)h; sphere surface = 4πr².

Volume formulas: cylinder = πr²h; cone = ⅓πr²h; sphere = (4/3)πr³.

sin²θ + cos²θ = 1 for every angle θ; also tanθ = sinθ / cosθ.

Arithmetic sequence: nth term aₙ = a₁ + (n − 1)d; sum Sₙ = n(a₁ + aₙ)/2.

Geometric sequence: nth term aₙ = a₁r^(n−1); sum Sₙ = a₁(1 − rⁿ)/(1 − r) when r ≠ 1.

Logarithm rules: log(xy) = log x + log y; log(x/y) = log x − log y; log(xⁿ) = n log x.

Probability of an event = (favorable outcomes) / (total equally likely outcomes); it always lies between 0 and 1.

Newton's second law: F = ma; force is measured in newtons (1 N = 1 kg·m/s²).

Kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as.

Weight vs mass: W = mg, where g ≈ 9.8 m/s² near Earth's surface.

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh.

Work = force × displacement × cosθ; power = work / time, measured in watts.

Ohm's law: V = IR; electrical power P = VI = I²R = V²/R.

Wave relation: speed = frequency × wavelength (v = fλ).

Density ρ = m/V; pressure P = F/A, measured in pascals.

Present perfect: have/has + past participle, used for past actions with present relevance (e.g., 'She has finished').

Simple past is used with finished time expressions such as yesterday, last year, in 2010.

Comparative adjectives: one-syllable words add -er (taller); longer words use 'more' (more beautiful).

Superlatives: one-syllable words add -est (tallest); longer words use 'most' (most beautiful).

Passive voice: form of 'be' + past participle (e.g., 'The letter was written by Ali').

Conditionals: first conditional = if + present simple, will + base verb; second conditional = if + past simple, would + base verb.

Subject–verb agreement: singular subject takes singular verb; 'each', 'every', and 'everyone' are singular.

Prepositions of time: 'in' for months/years, 'on' for days/dates, 'at' for clock times.

Mole concept: 1 mole = 6.022 × 10²³ particles (Avogadro's number).

Molar mass equals the sum of atomic masses in grams per mole; moles = mass / molar mass.

pH scale runs 0–14: pH < 7 is acidic, pH = 7 neutral, pH > 7 basic.

Acid + base → salt + water (neutralization); acid + metal → salt + hydrogen gas.

Atomic structure: protons (positive, atomic number Z), neutrons (neutral), electrons (negative) in shells.

Ionic bond forms by electron transfer between metal and nonmetal; covalent bond forms by electron sharing between nonmetals.

Balanced equations obey conservation of mass: the number of atoms of each element is equal on both sides.

Oxidation is loss of electrons; reduction is gain of electrons (OIL RIG).

Cell theory: all living things are made of cells; the cell is the basic unit of life; cells arise from existing cells.

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

Cellular respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP), mainly in mitochondria.

DNA is a double helix of nucleotides with bases adenine–thymine and guanine–cytosine.

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

Blood groups follow ABO rules: A and B are codominant, O is recessive.

Human circulatory system: heart → arteries → capillaries → veins → heart; arteries carry blood away from the heart.

Enzymes are proteins that speed up reactions and are specific to their substrates; they are affected by temperature and pH.

Dari (Afghan Persian) is written in a modified Arabic script, read right to left.

Pashto is written in a modified Arabic script with additional letters such as ښ, ږ, ړ, and ډ.

In both languages, nouns have grammatical gender in Dari (masculine/feminine), while Pashto nouns are classified by gender and number.

The Persian poet Rumi (Mawlana Balkhi), born in Balkh, wrote the Masnavi in Persian.

Hakim Abul-Qasim Firdawsi wrote the Shahnameh, the Persian national epic, in the late 10th–early 11th century.

Khushal Khan Khattak is a major classical Pashto poet known for his poetry and prose.

The ezafe construction (e.g., 'kitab-e' meaning 'book of') links nouns to modifiers in Dari.

Pashto verb agreement follows the split-ergative system: past transitive verbs agree with the object, present verbs with the subject.

The Five Pillars of Islam: Shahadah (testimony), Salah (prayer), Zakat (almsgiving), Sawm (fasting in Ramadan), and Hajj (pilgrimage).

The Qur'an has 114 surahs; the first surah is Al-Fatihah and the longest is Al-Baqarah.

Muslims pray five obligatory daily prayers: Fajr, Dhuhr, Asr, Maghrib, and Isha.

Zakat is generally 2.5% of qualifying wealth held for one lunar year.

Hajj is performed in the month of Dhu al-Hijjah and includes standing at Arafah.

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

The Qur'an was revealed to Prophet Muhammad over approximately 23 years.

Fasting (Sawm) during Ramadan is from dawn (Fajr) to sunset (Maghrib).

Afghanistan is a landlocked country in Central/South Asia bordered by Iran, Pakistan, Turkmenistan, Uzbekistan, Tajikistan, and China.

The Hindu Kush mountain range runs across central Afghanistan; its highest peak is Noshaq (about 7,492 m).

The Amu Darya (Oxus) forms part of Afghanistan's northern border; the Helmand is the longest river within Afghanistan.

Kabul is the capital of Afghanistan and lies at about 1,790 m elevation.

Afghanistan's climate is mostly arid to semi-arid with cold winters and hot summers; the lowlands are hotter than the highlands.

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

The Durrani Empire was founded by Ahmad Shah Durrani in 1747, often considered the beginning of modern Afghanistan.

Earth's latitude lines run east–west and measure distance north or south of the equator; the equator is at 0° latitude.