Mongolia Upper Secondary State Exam cheat sheet

Quadratic formula: x = (-b ± √(b² − 4ac)) / (2a); discriminant D = b² − 4ac determines real roots (D ≥ 0).

Arithmetic sequence: aₙ = a₁ + (n−1)d; sum Sₙ = n(a₁ + aₙ)/2. Geometric: aₙ = a₁·rⁿ⁻¹; Sₙ = a₁(1−rⁿ)/(1−r) for r ≠ 1.

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

Trigonometric identity: sin²α + cos²α = 1; double angle: sin 2α = 2 sin α cos α, cos 2α = cos²α − sin²α.

Law of sines: a/sin A = b/sin B = c/sin C = 2R; law of cosines: c² = a² + b² − 2ab·cos C.

Probability of independent events: P(A∩B) = P(A)·P(B); complement: P(Ā) = 1 − P(A).

Volume formulas: sphere V = (4/3)πr³; cone V = (1/3)πr²h; cylinder V = πr²h.

Logarithm rules: logₐ(xy) = logₐx + logₐy; logₐ(xⁿ) = n·logₐx; logₐb = ln b / ln a.

Mongolian script is written vertically from top to bottom, with lines running left to right.

Vowel harmony: front vowels (э, ө, ү) and back vowels (а, о, у) generally do not mix within a native word.

The 2015 Law on Mongolian Language specifies the traditional Mongolian script be used alongside Cyrillic in official documents by 2025.

Case suffixes: genitive -ын/-ийн/-ны/-ний, dative -д/-т, accusative -ыг/-ийг, ablative -аас/-ээс, instrumental -аар/-ээр.

Classic literature: 'The Secret History of the Mongols' (Mongolyn Nuuts Tovchoo) is the oldest surviving literary monument, written after 1227.

Dashdorjiin Natsagdorj founded modern Mongolian literature; his poem 'My Native Land' (Nutag) is a landmark.

A sonnet has 14 lines; a haiku has 3 lines with 5-7-5 syllables; a limerick has 5 lines with AABBA rhyme.

Punctuation: Mongolian uses « » for quotations, and commas separate homogeneous parts but not the subject from predicate.

Present perfect: have/has + past participle, used for past actions with present relevance; time markers: since, for, already, yet.

Conditionals: Type 1 (if + present, will + verb), Type 2 (if + past, would + verb), Type 3 (if + had + past participle, would have + past participle).

Passive voice: be + past participle; the object of an active sentence becomes the subject (e.g., 'The book was written by him').

Reported speech: shift tense back one step (present → past, past → past perfect); pronouns and time expressions change (now → then, today → that day).

Relative clauses: defining clauses take no comma and use 'that' or 'which'; non-defining clauses use commas and 'which', never 'that'.

Common collocations: make a decision, do homework, take a break, pay attention, have an effect.

Prepositions of time: in (months, years, seasons), on (days, dates), at (exact times, night, weekend).

Modal verbs: must (obligation), should (advice), might (possibility), can't (deduction of impossibility).

Mongolia's Constitution (1992) establishes a parliamentary republic with a President as head of state and a Prime Minister as head of government.

The State Great Khural (Parliament) has 126 members elected for a 4-year term (amended from 76 in 2023).

Mongolia's territory is 1,564,116 km², the 19th largest country; it borders Russia to the north and China to the south.

Major rivers: Selenge, Orkhon, Kherlen; the highest peak is Khüiten Peak (4,374 m) in the Altai range.

Climate is strongly continental: long cold winters, short warm summers; Ulaanbaatar is the coldest capital city by average annual temperature.

Universal Declaration of Human Rights (1948) lists 30 articles; Mongolia ratified the ICCPR in 1974.

The Silk Road connected East Asia to the Mediterranean; the Mongol Empire under Genghis Khan unified the steppe in 1206.

Separation of powers: legislative (Khural), executive (government), judicial (courts); checks and balances prevent abuse.

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

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

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; conservation of mechanical energy holds without friction.

Mole concept: 1 mol = 6.022 × 10²³ particles; molar mass in g/mol; n = m/M.

pH scale: pH < 7 acidic, pH = 7 neutral, pH > 7 basic; pH = −log[H⁺].

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

DNA base pairing: adenine–thymine, guanine–cytosine; DNA replication is semi-conservative.

Cell organelles: mitochondria (ATP production), ribosomes (protein synthesis), nucleus (genetic control), chloroplasts (photosynthesis in plants).

Binary to decimal: each bit position has weight 2ⁿ, starting from 2⁰ on the right; e.g., 1011₂ = 11₁₀.

1 byte = 8 bits; 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB.

Logic gates: AND outputs 1 only if both inputs are 1; OR outputs 1 if any input is 1; NOT inverts.

Algorithm complexity: O(1) constant, O(log n) logarithmic, O(n) linear, O(n²) quadratic; binary search is O(log n).

Relational database keys: primary key uniquely identifies a row; foreign key references a primary key in another table.

IP addressing: IPv4 uses 32 bits, IPv6 uses 128 bits; DNS translates domain names to IP addresses.

HTML structure: , , ; CSS controls presentation; JavaScript adds interactivity.

Cybersecurity: phishing, malware, and weak passwords are common threats; strong passwords combine length and character variety.

1206: Temüjin was proclaimed Genghis Khan, unifying Mongol tribes at the kurultai on the Onon River.

1227: Genghis Khan died; the empire was divided among his sons into uluses (appanages).

1260–1294: Kublai Khan ruled; he founded the Yuan Dynasty in 1271 and moved the capital to Dadu (Beijing).

1368: Fall of the Yuan Dynasty in China; the Mongols retreated to the steppe (Northern Yuan).

1635: Ligden Khan's death marked the end of independent Mongol khanates; the Qing gradually incorporated Mongolia.

1911: Mongolian independence declared after the fall of the Qing; Bogd Khan became head of state.

1921: People's Revolution led by Damdin Sükhbaatar; 1924: Mongolian People's Republic proclaimed.

1990: Democratic revolution led to multi-party elections and the 1992 Constitution.

Economics: demand curve slopes downward; supply curve slopes upward; equilibrium where they intersect.

GDP = C + I + G + (X − M), where C is consumption, I investment, G government spending, X exports, M imports.

Accounting equation: Assets = Liabilities + Equity; double-entry bookkeeping keeps the equation balanced.

Geography elective: map scale 1:50,000 means 1 cm on map = 500 m on ground.

Business: break-even point where total revenue equals total cost; profit = revenue − cost.

Psychology: classical conditioning (Pavlov) pairs a neutral stimulus with an unconditioned one; operant conditioning uses reinforcement.

Art history: Renaissance (14th–17th c.) emphasized realism and perspective; Impressionism (19th c.) focused on light and momentary effect.

Environmental science: renewable resources (solar, wind, hydro) replenish naturally; non-renewable (coal, oil) are finite.