Tuzla Canton Secondary Matura cheat sheet

BCS has seven cases: nominative, genitive, dative, accusative, vocative, locative and instrumental; prepositions and verbs govern which case a noun takes.

Noun gender usually follows endings: masculine nouns often end in a consonant, feminine in -a, neuter in -o/-e; exceptions such as tata (masculine) and noć (feminine) override the ending rule.

Perfective verbs present an action as completed or bounded; imperfective verbs present it as ongoing, repeated or unbounded; aspect pairs include pisati/napisati.

Future I is formed with clitic ću, ćeš, će... plus an infinitive stem or da plus present: pisat ću / ću pisati; the negative future uses neću.

In the accusative singular, feminine nouns end in -u, masculine inanimate nouns match the nominative, and masculine animate nouns take genitive-like -a.

Clitic order is auxiliary (sam, si, je...) before dative before accusative/genitive: Dao sam mu je.

Ivo Andrić won the 1961 Nobel Prize in Literature; Na Drini ćuprija spans centuries of Bosnian history under Ottoman and Austro-Hungarian rule.

Hasanaginica is a Bosnian oral ballad recorded by Alberto Fortis in 1774; it narrates a noblewoman's separation, lament and death.

Mak Dizdar's Kameni spavač reworks stećak inscriptions; Meša Selimović's Derviš i smrt explores authority, guilt and conscience.

For ax² + bx + c = 0 with a ≠ 0, x = (-b ± √(b² - 4ac))/(2a); the discriminant D = b² - 4ac gives two, one or no real roots when D > 0, D = 0 or D < 0.

Vieta's formulas: for ax² + bx + c = 0, x₁ + x₂ = -b/a and x₁x₂ = c/a.

Arithmetic sequence: aₙ = a₁ + (n - 1)d; Sₙ = n(a₁ + aₙ)/2.

Geometric sequence: aₙ = a₁q^(n-1); for q ≠ 1, Sₙ = a₁(1 - qⁿ)/(1 - q).

Binomial theorem: (a + b)ⁿ = Σ C(n,k) a^(n-k)b^k, with C(n,k) = n!/(k!(n-k)!).

Derivatives: (xⁿ)' = nx^(n-1), (sin x)' = cos x, (cos x)' = -sin x, (eˣ)' = eˣ, (ln x)' = 1/x; chain rule: [f(g(x))]' = f'(g(x))g'(x).

Logarithms: log(ab) = log a + log b; log(a/b) = log a - log b; log(aⁿ) = n log a.

Probability: P(A∪B) = P(A) + P(B) - P(A∩B); for independent events, P(A∩B) = P(A)P(B).

Trigonometry: sin²x + cos²x = 1; sin 2x = 2 sin x cos x; cos 2x = cos²x - sin²x.

Present perfect (have/has + past participle) links a past action to the present; use it with for, since, just, already and yet, but not with finished time expressions such as yesterday.

Past simple marks completed past actions with a definite past time; irregular verb forms must be recalled individually.

First conditional: if + present simple, will + bare infinitive, for real future possibility; second conditional: if + past simple, would + bare infinitive, for unreal or hypothetical situations.

Passive voice: be + past participle; the tense is carried by be, and the by-agent is omitted when unknown or unimportant.

Reported speech after a past reporting verb usually backshifts one tense: present to past, will to would, can to could; pronouns and time expressions adjust.

Articles: a/an for singular countable indefinite nouns; the for specific or already known nouns; zero article for generic plurals and uncountable nouns.

Modals: must for obligation, should for advice, may for permission or possibility, can't for deduction of impossibility; modal verbs take a bare infinitive.

Defining relative clauses take no commas and may use that; non-defining clauses take commas, cannot use that, and cannot omit the relative pronoun as object.

Gerund follows prepositions and verbs such as enjoy, avoid and suggest; infinitive follows want, decide and hope.

German marks four cases: nominative, accusative, dative and genitive; definite articles change by case, gender and number (der, den, dem, des in masculine singular).

German main clauses place the finite verb in second position; subordinate clauses introduced by weil, dass or ob send the finite verb to the end.

German perfect tense uses haben or sein plus a past participle; sein is used with movement and change-of-state verbs such as gehen, kommen and werden.

Russian has six cases: nominative, genitive, dative, accusative, instrumental and prepositional; noun, adjective and pronoun endings depend on gender, number and declension class.

French passé composé uses avoir or être plus a past participle; être occurs with reflexive verbs and a small movement set, and the participle then agrees with the subject.

Italian passato prossimo uses avere or essere plus a past participle; with essere the participle agrees with the subject in gender and number.

Romance languages show noun-adjective agreement in gender and number, and French/Italian often use articles with general nouns where English omits them.

Formal address differs: German Sie, Russian вы, French vous and Italian Lei are used according to social distance and politeness.

Cell organelles: mitochondria produce ATP by aerobic respiration, ribosomes synthesize proteins, the nucleus stores DNA, and chloroplasts carry out photosynthesis.

Photosynthesis: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂; chlorophyll in chloroplasts converts light energy into chemical energy.

DNA base pairing: adenine pairs with thymine and guanine pairs with cytosine; complementary strands allow semi-conservative replication.

Periodic trends: atomic radius decreases across a period and increases down a group; electronegativity increases across a period and decreases down a group.

Mole concept: n = m/M; one mole contains 6.022 × 10²³ particles; molar volume of an ideal gas at STP is about 22.4 L.

pH = -log[H⁺]; at 25 °C pH < 7 is acidic, pH = 7 is neutral and pH > 7 is basic; strong acids dissociate completely.

Newton's laws: F = ma; action and reaction are equal and opposite; an object remains at rest or in uniform motion unless a net force acts.

Ohm's law: V = IR; series resistances add, R = R₁ + R₂ + ..., while parallel resistance satisfies 1/R = 1/R₁ + 1/R₂ + ...

Energy conservation: total energy remains constant; work W = Fd cos θ, kinetic energy is ½mv² and gravitational potential energy is mgh.

World War I was triggered by the assassination of Archduke Franz Ferdinand in Sarajevo on 28 June 1914, followed by the July Crisis.

Yugoslavia was invaded by Axis forces in April 1941; the Partisan resistance led by Tito prevailed and socialist Yugoslavia was established in 1945.

Yugoslavia's breakup began with 1991 independence declarations by Slovenia and Croatia; Bosnia and Herzegovina's independence was recognized in 1992, and the Dayton Agreement ended the war in 1995.

The Cold War opposed NATO and the United States to the Warsaw Pact and the USSR; the Berlin Wall stood from 1961 to 1989, and the USSR dissolved in 1991.

Tuzla Canton has a moderate continental climate; the Dinaric mountain system is characterized by karst landforms such as caves, sinkholes and poljes.

At convergent plate boundaries denser oceanic lithosphere subducts, producing earthquakes, volcanic arcs and mountain belts; divergent boundaries produce rifts.

Supply and demand: quantity demanded usually falls as price rises, quantity supplied usually rises, and equilibrium occurs where the curves intersect.

Separation of powers divides authority among legislative, executive and judicial branches, each able to check the others and reduce arbitrary rule.

Population pyramids show age and sex structure: broad bases indicate high birth rates, while narrow bases and large top segments indicate ageing populations.