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52 cardsDržavna Matura (Montenegro)

State Matura Key Facts and Formulas

52 flashcards with core formulas, literary terms and dates of Montenegrin history. Study material written for practice, not an official test.

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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}

Discriminant of a quadratic equation

D = b^{2} - 4 a c

. If

D > 0

there are two real roots, if

D = 0

one, if

D < 0

none.

Vieta's formulas

For

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

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

and

x_{1} x_{2} = q

Sum of the first

n

terms of an arithmetic sequence

S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) d)

n

-th term of a geometric sequence

a_{n} = a_{1} q^{n - 1}

Sum of an infinite geometric series

S = \frac{a _{1}}{1 - q}

when

∣ q ∣ < 1

Pythagorean theorem

In a right triangle

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

, where

c

is the hypotenuse.

Law of cosines

c^{2} = a^{2} + b^{2} - 2 ab cos γ

Distance between

(x_{1}, y_{1})

and

(x_{2}, y_{2})

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

Derivative of

x^{n}

(x^{n})^{'} = n x^{n - 1}

Volume of a cylinder

V = r^{2} π h

Sum of interior angles of an

n

-gon

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

Number of diagonals of a convex

n

-gon

\frac{n ( n - 3 )}{2}

Number of combinations of

k

from

n

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

Logarithm rule for a product

lo g_{a} (x y) = lo g_{a} x + lo g_{a} y

Author and year of Gorski vijenac

Petar II Petrović Njegoš, printed in Vienna in 1847.

Verse form of Gorski vijenac

The decasyllable (deseterac), the ten-syllable line of the oral epic tradition.

The gusle

A one-stringed bowed instrument that accompanies the singing of epic poems.

Number of letters in the Montenegrin alphabet

32, with two added letters for the sounds written with s and z with an acute accent.

Number of grammatical cases

Seven: nominative, genitive, dative, accusative, vocative, locative and instrumental.

Simile versus metaphor

A simile compares with 'like' or 'as'. A metaphor says one thing is another.

Congress of Berlin, 1878

Recognised Montenegro as an independent state and enlarged its territory.

Proclamation of the Kingdom of Montenegro

1910, with Nikola I as king.

Independence referendum

21 May 2006. Independence Day is celebrated on that date.

Statehood Day

13 July, remembering the Treaty of Berlin of 1878 and the uprising of 1941.

Law of sines

\frac{a}{s i n α} = \frac{b}{s i n β} = \frac{c}{s i n γ} = 2 R

, where

R

is the circumradius.

Trigonometric identity

sin^{2} x + cos^{2} x

Equals

1

for all real

x

Double-angle formula for

sin (2 x)

sin (2 x) = 2 sin x cos x

Double-angle formula for

cos (2 x)

cos (2 x) = cos^{2} x - sin^{2} x = 2 cos^{2} x - 1 = 1 - 2 sin^{2} x

Derivative of

sin x

and

cos x

(sin x)^{'} = cos x

and

(cos x)^{'} = - sin x

Derivative of

e^{x}

and

ln x

(e^{x})^{'} = e^{x}

and

(ln x)^{'} = \frac{1}{x}

for

x > 0

Product rule for differentiation

(uv)^{'} = u^{'} v + u v^{'}

Quotient rule for differentiation

(\frac{u}{v})^{'} = \frac{u ^{'} v - u v ^{'}}{v ^{2}}

Equation of a circle with centre

(p, q)

and radius

r

(x - p)^{2} + (y - q)^{2} = r^{2}

Slope of a line through

(x_{1}, y_{1})

and

(x_{2}, y_{2})

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

for

x_{1} \neq = x_{2}

Midpoint formula in Cartesian plane

M = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

Volume and surface area of a sphere

V = \frac{4}{3} π r^{3}

and

A = 4 π r^{2}

Volume of a cone

V = \frac{1}{3} π r^{2} h

Logarithm rule for a quotient

lo g_{a} (\frac{x}{y}) = lo g_{a} x - lo g_{a} y

for

x, y > 0

Logarithm power rule

lo g_{a} (x^{k}) = k lo g_{a} x

for

x > 0

Oktoih Prvoglasnik (Octoechos)

Printed in 1494 at the Crnojević printing press in Cetinje, the first South Slavic incunabulum printed in Cyrillic.

Ljetopis Popa Dukljanina (Chronicle of the Priest of Duklja)

Medieval chronicle compiled in the 12th century describing the early history of Duklja and the South Slavs.

Petar I Petrović Njegoš (Saint Peter of Cetinje)

Prince-Bishop who unified Montenegrin clans and promulgated the first written legal code (Zakonik) in 1798.

Marko Miljanov

Montenegrin general and author known for 'Primjeri čojstva i junaštva' (Examples of Humanity and Heroism).

Battle of Vučji Do (1876)

Major victory of the Montenegrin-Herzegovinian forces over the Ottoman army, leading to recognition at the Congress of Berlin.

Battle of Grahovac (1858)

Decisive Montenegrin victory under Grand Duke Mirko Petrović against Ottoman forces, establishing border demarcation.

First printing press in Montenegro

Established by Đurađ Crnojević in Cetinje in 1493.

Tara River Canyon

The deepest canyon in Europe and part of Durmitor National Park, a UNESCO World Heritage site.

Bay of Kotor (Boka Kotorska)

A submerged river canyon on the Adriatic coast with historic towns Kotor and Perast, protected by UNESCO.

Lake Skadar (Skadarsko jezero)

The largest lake in Southern Europe, shared between Montenegro and Albania, known as a vital wetland reserve.

Alliteration versus assonance

Alliteration is the repetition of initial consonant sounds; assonance is the repetition of vowel sounds.

Hyperbole in literature

An intentional exaggeration used for rhetorical effect or emotional emphasis.

Državna Matura (Montenegro) in Montenegro

In Montenegro, Državna Matura (Montenegro) is part of: School-leaving exams.

Students on the same pathway also practise:

General Knowledge (Montenegro)

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