Afghanistan Kankor flashcards

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Quadratic formula

For ax²+bx+c=0, the roots are x = (−b ± √(b²−4ac)) / (2a). The discriminant b²−4ac determines how many real roots exist.

Sum of quadratic roots

If x₁ and x₂ are roots of ax²+bx+c=0, then x₁+x₂ = −b/a and x₁x₂ = c/a. These relations let you find roots without full factoring.

Law of cosines

In any triangle, a² = b² + c² − 2bc·cosA. It generalizes the Pythagorean theorem to triangles that are not right-angled.

Arithmetic sequence formula

The nth term is aₙ = a₁ + (n−1)d where d is the common difference. The sum of the first n terms is Sₙ = n(a₁+aₙ)/2.

Logarithm product rule

The logarithm of a product equals the sum of the logarithms: log(xy) = log x + log y. Related rules handle quotients and powers.

Newton's second law

The net force on an object equals its mass times its acceleration, F = ma. Weight is the special case W = mg with g about 9.8 m/s².

Ohm's law

The voltage across a conductor equals current times resistance, V = IR. Electric power is P = VI, which can also be written I²R or V²/R.

Wave speed relation

For any periodic wave, speed equals frequency times wavelength: v = fλ. Frequency is measured in hertz and wavelength in meters.

Conservation of momentum

In an isolated system, total momentum stays constant: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. This holds for collisions and explosions.

Mole concept

One mole contains 6.022×10²³ particles. The number of moles equals mass divided by molar mass, linking mass to particle count.

pH scale

pH = −log[H⁺]. At 25 °C, solutions with pH below 7 are acidic, pH equal to 7 is neutral, and pH above 7 is basic.

Ideal gas law

PV = nRT relates pressure, volume, moles, and temperature of a gas. R is about 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K).

Oxidation and reduction

Oxidation is loss of electrons and an increase in oxidation number; reduction is gain of electrons. The two always occur together in redox reactions.

Photosynthesis equation

Plants use light to convert carbon dioxide and water into glucose and oxygen: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂. This occurs in chloroplasts.

DNA base pairing

In DNA, adenine pairs with thymine and guanine pairs with cytosine. In RNA, uracil replaces thymine and the strand is single.

Mitosis versus meiosis

Mitosis produces two identical diploid cells for growth and repair. Meiosis produces four haploid gametes with genetic recombination for reproduction.

Mendel's law of segregation

During gamete formation, the two alleles of a gene separate so each gamete carries only one. This explains predictable inheritance ratios.

Ezafe construction

In Dari, an unstressed −e links a noun to a following modifier or possessor, as in کتابِ نو (new book) or کتابِ احمد (Ahmad's book).

Shahnameh

Ferdowsi's epic poem in rhymed couplets recounts the legendary and historical kings of Iran. It is a foundational work of Persian literature.

Dari verb final position

In a normal Dari clause the verb usually appears at the end, after the subject and object. Word order is typically subject–object–verb.

Pashto retroflex letters

Pashto's alphabet adds retroflex consonants such as ټ ډ ړ ږ ښ ڼ to the Arabic script. These distinguish Pashto from Dari and Urdu spelling.

Pashto grammatical gender

Pashto nouns are masculine or feminine, and adjectives agree with the noun in gender and number. Verb forms also reflect gender in many tenses.

Khushal Khan Khattak

A major classical Pashto poet known for poetry on honor, freedom, and Afghan unity. He is among the most celebrated figures in Pashto literature.

Landay

A landay is a short Pashto folk couplet, typically two lines with a fixed syllable pattern. It often expresses love, grief, or social commentary.

Five pillars of Islam

Shahadah (testimony of faith), Salah (prayer), Zakah (charity), Sawm (fasting in Ramadan), and Hajj (pilgrimage to Makkah). These are core obligations.

Zakah rate

Zakah is an obligatory annual alms of 2.5% on qualifying wealth held above the nisab threshold for a full lunar year.

Hijrah

The migration of the Prophet Muhammad from Makkah to Madinah in 622 CE. It marks the starting point of the Islamic lunar calendar.

Rightly guided caliphs

The first four caliphs in order: Abu Bakr, Umar ibn al-Khattab, Uthman ibn Affan, and Ali ibn Abi Talib. They led the early Muslim community.

Afghan independence 1919

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

Durrani Empire

Founded by Ahmad Shah Durrani in 1747, this empire is often regarded as the origin of the modern Afghan state. Its capital was Kandahar.

Afghanistan's neighbors

Iran to the west; Pakistan to the south and east; Turkmenistan, Uzbekistan, and Tajikistan to the north. The Wakhan Corridor touches China.

Separation of powers

A civic principle dividing state authority among executive, legislative, and judicial branches. Each branch checks the others to prevent concentration of power.