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52 cardsDržavna Matura (Serbia)

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Flashcards reviewing mathematics formulas, Serbian grammar, and historical dates for the State Matura.

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Quadratic formula for

a x^{2} + b x + c = 0

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Quadratic formula for

a x^{2} + b x + c = 0

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

Vieta's formulas for

x^{2} + p x + q = 0

x_{1} + x_{2} = - p

and

x_{1} x_{2} = q

Sum of squares of the roots

x_{1}^{2} + x_{2}^{2} = (x_{1} + x_{2})^{2} - 2 x_{1} x_{2}

Product of

(a + bi) (a - bi)

a^{2} + b^{2}

n

th term of an arithmetic sequence

a_{n} = a_{1} + (n - 1) d

Sum of the first

n

terms of a geometric sequence

S_{n} = a_{1} \frac{q ^{n} - 1}{q - 1}

Derivative of

x^{n}

n x^{n - 1}

Heron's formula

s (s - a) (s - b) (s - c)

with

s = \frac{a + b + c}{2}

Volume of a sphere

\frac{4}{3} π r^{3}

Lateral area of a cone

π r l

, where

l

is the slant height

Space diagonal of a box

a^{2} + b^{2} + c^{2}

Sum of interior angles of an

n

-gon

(n - 2) \times 18 0^{\circ}

Vuk Karadžić

Reformed the Serbian language and alphabet; first dictionary in 1818.

Number of cases in Serbian

Seven, including the vocative.

Ivo Andrić

Nobel Prize in Literature 1961; The Bridge on the Drina.

Njegoš

Wrote the verse drama The Mountain Wreath, published in 1847.

Deseterac

The ten-syllable verse of Serbian epic folk poetry.

Battle of Kosovo

1389, Prince Lazar against the Ottomans.

Dušan, 1346

Crowned emperor; the Dušan Code followed in 1349.

First Serbian Uprising

1804, led by Karađorđe.

Second Serbian Uprising

1815, led by Miloš Obrenović.

Sretenje Constitution

1835, adopted in Kragujevac.

Congress of Berlin

1878, recognised Serbian independence.

Kingdom of Serbs, Croats and Slovenes

Proclaimed on 1 December 1918; renamed Yugoslavia in 1929.

Jotovanje (Iotation) in Serbian phonology

Consonant shift where non-palatals merge with 'j' to create palatals: c+j>č, d+j>đ, t+j>ć, z+j>ž, s+j>š, l+j>lj, n+j>nj.

Sibilarizacija (Second Palatalization) in Serbian

Consonant shift where velars k, g, h change into sibilants c, z, s before vowel 'i' (e.g. ruka -> ruci, noga -> nozi, svrha -> svrsi).

Palatalizacija (First Palatalization) in Serbian

Consonant shift where velars k, g, h change into palatals č, ž, š before front vowels e and sometimes i (e.g. vuk -> vuče, knez -> kneže).

Jednačenje suglasnika po zvučnosti (Voicing assimilation)

Consonants assimilate in voicing when in contact: voiced becomes voiceless before voiceless (b->p, d->t, z->s), and voiceless becomes voiced before voiced (p->b, t->d, s->z).

Nepostojano A (Fleeting A) in Serbian grammar

Vowel 'a' that appears in certain inflected forms (like nominative singular or genitive plural) and disappears in others (e.g. pas -> psa, momak -> momka).

Prevoj vokala (Vowel gradation / ablaut) in Serbian

Alternation of vowels in etymologically related roots signaling aspect or part of speech (e.g. plesti / plesti, rod / roditi / rađati).

Seven cases in Serbian grammar

Nominative (subject), Genitive (origin/possession), Dative (direction/indirect object), Accusative (direct object), Vocative (call/address), Instrumental (tool/company), Locative (location).

Gorski vijenac (The Mountain Wreath, 1847)

Written by Petar II Petrović Njegoš; philosophical poem and dramatic verse work in decasyllable (deseterac), central to Serbian literary canon.

Seobe (Migrations, 1929)

Masterpiece novel by Miloš Crnjanski recounting the tragic fate of Serbian regiments in the Slavonian-Danubian regiment under the Austrian Empire, centered on Vuk Isakovič.

Prokleta avlija (The Damned Yard, 1954)

Novella by Ivo Andrić (Nobel Prize in Literature 1961) depicting prisoners and power dynamics in an Ottoman Istanbul detention center, framed by Fra Petar.

Na Drini ćuprija (The Bridge on the Drina, 1945)

Chronicle novel by Ivo Andrić detailing four centuries of history around the Mehmed Paša Sokolović Bridge in Višegrad.

Koštana and Nečista krv (Bora Stanković)

Pioneering works of Serbian realism/modernism set in Vranje: 'Koštana' is a lyrical play of passion and sevdah; 'Nečista krv' (Impure Blood) explores the tragic fate of Sofka.

Derviš i smrt (Death and the Dervish, 1966)

Philosophical novel by Meša Selimović centered on Ahmed Nurudin, a Mevlevi dervish grappling with injustice and dogmatism in Ottoman Sarajevo.

Year 1847 in Serbian cultural history

Triumph of Vuk Karadžić's vernacular reform: marked by Njegoš's 'Gorski vijenac', Branko Radičević's 'Pesme', and Đuro Daničić's 'Rat za srpski jezik i pravopis'.

Stefan Nemanja (reigned 1166–1196)

Grand Prince of Serbia who unified Serbian lands, founded the Nemanjić dynasty, and established Studenica Monastery before taking monastic vows as Symeon.

Saint Sava (Rastko Nemanjić, 1174–1236)

First Archbishop of the autocephalous Serbian Orthodox Church (1219), author of the Karyes and Hilandar Typikons and the Nomocanon (Zakonopravilo).

Stefan the First-Crowned (Stefan Prvovenčani)

First crowned King of Serbia (1217), crowned by papal legate and anointed by Archbishop Saint Sava; builder of Žiča Monastery.

Emperor Stefan Dušan (Dušan the Mighty, r. 1331–1355)

Expanded Serbia into an empire, crowned Emperor of Serbs and Greeks in Skopje in 1346; promulgated Dušan's Code (Dušanov zakonik) in 1349 and 1354.

Battle of Kosovo (Boj na Kosovu, 1389)

Fought on Vidovdan (June 15/28, 1389) between Serbian forces led by Prince Lazar Hrebeljanović and the Ottoman army led by Sultan Murad I; both leaders died in the battle.

First Serbian Uprising (1804–1813)

Launched in Orašac under the leadership of Karađorđe Petrović against the Janissary Dahijas, sparking the Serbian Revolution and rebirth of modern statehood.

Second Serbian Uprising (1815)

Launched in Takovo under Miloš Obrenović; combined military victories with diplomacy to secure Serbian autonomy from the Ottoman Empire.

Congress of Berlin (1878) and Serbia

Formally recognized Serbia as an independent sovereign principality (later kingdom in 1882) and expanded its territory by four southern districts (Niš, Pirot, Vranje, Toplica).

Balkan Wars (1912–1913)

First Balkan War (1912) liberated Old Serbia and Macedonia from Ottoman rule; Second Balkan War (1913) defeated Bulgaria, securing the Vardar region.

Corfu Declaration (Krfska deklaracija, 1917)

Agreement between Nikola Pašić and Ante Trumbić (Yugoslav Committee) establishing the framework for a unified constitutional monarchy of Serbs, Croats, and Slovenes.

Addition formulas for sine and cosine

sin (α \pm β) = sin α cos β \pm cos α sin β

cos (α \pm β) = cos α cos β \mp sin α sin β

Distance between points

A (x_{1}, y_{1})

and

B (x_{2}, y_{2})

d (A, B) = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

Binomial theorem formula

(a + b)^{n} = \sum_{k = 0}^{n} (k n) a^{n - k} b^{k}

, where

(k n) = \frac{n !}{k ! ( n - k )!}

Area of an equilateral triangle with side

a

P = \frac{a ^{2} 3}{4}

, height

h = \frac{a 3}{2}

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