Konkur-e Farhangian cheat sheet

Persian meter (عروض): the eight main بحر families derive from repeated فعولن/مفاعیلن-type feet; a line's meter is fixed by the تقطیع of the first hemistich and must repeat in the second.

Major Persian epic: فردوسی's شاهنامه (~50,000 couplets, بحر متقارب); lyrical: نظامی's خمسه (مخزنالاسرار، خسرو و شیرین، لیلی و مجنون، هفتپیکر، اسکندرنامه); غزل master: حافظ; مثنوی معنوی: مولوی (بحر رمل).

Four canonical Persian prose classics: کلیله و دمنه (نصرالله منشی), گلستان (سعدی, ۸ باب, mixed prose/verse), تاریخ بیهقی (ابوالفضل بیهقی), سیاستنامه (خواجه نظامالملک).

Arabic grammar core: الإعراب states are رفع (ضمة), نصب (فتحة), جر (كسرة), جزم (سكون); الاسم يُرفع بالضمة ويُنصب بالفتحة ويُجر بالكسرة, and الأفعال الخمسة تُرفع بثبوت النون وتُنصب وتُجزم بحذفها.

Arabic morphology: الفعل الماضي مبني على الفتح, الأمر مبني على السكون, المضارع معرب إلا إذا اتصلت به نون التوكيد أو نون النساء فيُبنى على الفتح.

Quranic sciences: مكية vs مدنية distinction, أسباب النزول, الناسخ والمنسوخ, and the seven أحرف tradition; the Quran has 114 سورة and 30 جزء.

Islamic history markers: بعثت (610 CE), هجرت (622 CE = start of هجری calendar), فتح مکه (8 AH), and the split of شیعه/سنی traced to the question of خلافت after the Prophet.

فقه terminology: واجب (rewarded, punished if omitted), مستحب, حرام, مکروه, مباح; احکام تکلیفی vs احکام وضعی (صحیح, باطل, شرط, مانع).

Quadratic: for ax²+bx+c=0, Δ=b²−4ac; roots (−b±√Δ)/2a; sum = −b/a, product = c/a; Δ>0 two real roots, Δ=0 double, Δ<0 complex conjugates.

Logarithm rules: log_a(xy)=log_a x+log_a y; log_a(x/y)=log_a x−log_a y; log_a xⁿ=n·log_a x; log_a b = ln b/ln a; a^{log_a x}=x.

Trigonometry: sin²θ+cos²θ=1; sin2θ=2sinθcosθ; cos2θ=cos²θ−sin²θ=1−2sin²θ; law of cosines a²=b²+c²−2bc·cosA; law of sines a/sinA=2R.

Derivative rules: (xⁿ)′=n·xⁿ⁻¹; (sin x)′=cos x; (eˣ)′=eˣ; (ln x)′=1/x; product (uv)′=u′v+uv′; quotient (u/v)′=(u′v−uv′)/v².

Integral: ∫xⁿdx=xⁿ⁺¹/(n+1)+C (n≠−1); ∫dx/x=ln|x|+C; definite integral = F(b)−F(a); area between curves = ∫(upper−lower)dx.

Arithmetic progression: aₙ=a₁+(n−1)d, Sₙ=n(a₁+aₙ)/2; geometric: aₙ=a₁rⁿ⁻¹, Sₙ=a₁(1−rⁿ)/(1−r), infinite sum a₁/(1−r) when |r|<1.

Combinatorics: P(n,r)=n!/(n−r)!; C(n,r)=n!/(r!(n−r)!); probability P(A∪B)=P(A)+P(B)−P(A∩B); conditional P(A|B)=P(A∩B)/P(B).

Circle and line: distance from point (x₀,y₀) to ax+by+c=0 is |ax₀+by₀+c|/√(a²+b²); circle (x−h)²+(y−k)²=r²; tangent ⟺ distance equals r.

Newton's laws: F=ma; action–reaction pairs act on different bodies; friction f=μN; on an incline, component along slope = mg·sinθ, normal = mg·cosθ.

Kinematics: v=v₀+at; x=v₀t+½at²; v²=v₀²+2ax; projectile range R=v₀²sin2θ/g at launch angle θ.

Energy and momentum: KE=½mv²; PE=mgh; W=Fd·cosθ; momentum p=mv conserved in collisions absent external force; elastic collision also conserves KE.

Electricity: Ohm V=IR; power P=VI=I²R=V²/R; series R=R₁+R₂; parallel 1/R=1/R₁+1/R₂; Coulomb F=kq₁q₂/r².

Atomic structure: atomic number Z = protons; mass number A = protons+neutrons; isotopes differ in neutrons; electron configuration fills 1s2s2p3s3p4s3d4p by aufbau.

Mole concept: 1 mol = 6.022×10²³ particles = molar mass in grams; molarity M = mol solute / L solution; at STP 1 mol gas ≈ 22.4 L.

Acid–base: pH = −log[H⁺]; pH+pOH=14 at 25 °C; strong acid fully dissociates; neutralization acid+base→salt+water.

Biology essentials: photosynthesis 6CO₂+6H₂O→C₆H₁₂O₆+6O₂ in chloroplasts; cellular respiration in mitochondria yields ~36–38 ATP per glucose; DNA base pairing A–T, G–C.

Iran history timeline: ماد (۷۰۰–۵۵۰ ق.م), هخامنشی (۵۵۰–۳۳۰ ق.م, کوروش/داریوش), سلوکی, اشکانی (۲۴۷ ق.م–۲۲۴ م), ساسانی (۲۲۴–۶۵۱ م); constitutional revolution ۱۲۸۵ ش/1906.

Key modern dates: ۱۲۹۹ coup (Reza Khan), ۱۳۰۴ Pahlavi accession, ۱۳۲۰ abdication, ۱۳۳۲ coup (۲۸ مرداد), ۱۳۵۷ Islamic Revolution.

Geography of Iran: area ≈1,648,000 km²; highest peak دماوند (~5,610 m); longest river کارون; largest lake ارومیه; Caspian Sea to the north, Persian Gulf and Oman Sea to the south.

Climate controls: latitude, altitude, distance from sea, and pressure belts; Iran mostly arid/semi-arid with Mediterranean rainfall in the Zagros and Caspian lowlands.

Map skills: scale = map distance / ground distance; contour lines close together = steep slope; hachures point downhill; U-shaped valley = glacial, V-shaped = fluvial.

Social studies concepts: socialization agents (family, school, peers, media); norms vs values vs sanctions; primary vs secondary groups; social stratification by class, status, power.

Economic basics: scarcity → choice → opportunity cost; demand falls as price rises (ceteris paribus); GDP measures domestic output; inflation erodes purchasing power.

Ancient civilizations: Mesopotamia (Tigris–Euphrates, cuneiform), Egypt (Nile, hieroglyphs), Indus, Yellow River; writing, irrigation, and city-states as shared markers.

Piaget stages: sensorimotor (0–2, object permanence), preoperational (2–7, egocentrism, conservation lacking), concrete operational (7–11, conservation, classification), formal operational (11+, abstract/hypothetical reasoning).

Vygotsky: ZPD = gap between independent and assisted performance; scaffolding; language and social interaction drive cognitive development; inner speech as internalized dialogue.

Erikson psychosocial stages: trust/mistrust (infancy), autonomy/shame (1–3), initiative/guilt (3–6), industry/inferiority (6–12), identity/role confusion (adolescence).

Kohlberg moral development: preconventional (punishment/obedience, self-interest), conventional (good boy, law and order), postconventional (social contract, universal principles).

Bloom's taxonomy (revised): remember, understand, apply, analyze, evaluate, create - lower-order vs higher-order; objectives should use observable verbs.

Behaviorism: Pavlov classical conditioning (CS+UCS→CR); Skinner operant conditioning (reinforcement increases behavior, punishment decreases it); positive = adding stimulus, negative = removing.

Assessment concepts: formative (during learning, feedback) vs summative (end, grading); norm-referenced vs criterion-referenced; reliability = consistency, validity = measuring what is intended.

Motivation theories: Maslow hierarchy (physiological→safety→belonging→esteem→self-actualization); intrinsic vs extrinsic motivation; self-efficacy (Bandura) predicts persistence.

Lesson planning sequence: set induction → state objectives → present content in small steps → guided practice → independent practice → closure → assessment.

Questioning technique: wait time of 3–5 seconds after asking; distribute questions across the class; use probing and higher-order questions rather than choral answers.

Classroom management rules: establish routines early, use proximity and nonverbal cues before verbal correction, apply consequences consistently, and avoid whole-class punishment.

Assessment design: align each item with an objective (table of specifications); use a mix of selected-response and constructed-response; give rubrics before tasks.

Ethics: confidentiality of student records, fairness in grading, avoiding conflicts of interest, mandatory reporting of harm, respecting cultural and family diversity.

Teacher legal–professional duties: punctuality, safeguarding, avoiding corporal punishment (prohibited in Iranian schools), and maintaining an apolitical, non-discriminatory classroom.

Feedback principles: specific, timely, actionable, focused on the task not the person; praise effort and strategy to support a growth mindset.

Reflective practice: keep a teaching journal, use peer observation, and analyze student work samples to adjust instruction in the next cycle.

Number series: check differences, then ratios, then alternating or interleaved patterns; squares/cubes and ±1 offsets are common.

Percentage and ratio: percent change = (new−old)/old×100; successive changes multiply, not add (a% then b% → (1+a)(1+b)−1).

Work/rate: combined rate = 1/a+1/b; time together = ab/(a+b); distance = speed×time; average speed for equal distances = 2v₁v₂/(v₁+v₂).

Syllogism: valid only if the conclusion follows in every model satisfying the premises; "some A are B" does not imply "some B are not A".

Analogy and odd-one-out: identify the relation (category, function, part–whole, degree) before comparing options; the relation must match on both sides.

Coding–decoding: test letter shifts (+1, −1, reverse alphabet), positional sums, and letter-pair swaps; write the alphabet with positions 1–26 to verify quickly.

Logical deduction: conditional "if P then Q" is false only when P true and Q false; its contrapositive "if not Q then not P" is equivalent; converse is not.

Data interpretation: read axis units and totals first, compute required ratio directly, and estimate before exact calculation to save time.