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37 cardsÉrettségi (Matura Hungary)

Erettsegi Key Facts and Formulas

37 flashcards with core formulas, literary facts and dates of Hungarian 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

Δ = b^{2} - 4 a c

. If

Δ > 0

there are two real roots, if

Δ = 0

one, if

Δ < 0

none.

Vieta's formulas for the roots

x_{1}, x_{2}

x_{1} + x_{2} = - \frac{b}{a}

and

x_{1} x_{2} = \frac{c}{a}

n

-th term of an arithmetic sequence

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

Sum of the first

n

terms of an arithmetic sequence

S_{n} = \frac{a _{1} + a _{n}}{2} \cdot n

n

-th term of a geometric sequence

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

Sum of the first

n

terms of a geometric sequence (

q e 1

)

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

Compound interest after

n

years at rate

p

K_{n} = K_{0} (1 + \frac{p}{100})^{n}

Number of permutations of

n

different objects

n! = n (n - 1) \dots 2 \cdot 1

Number of combinations of

k

from

n

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

Classical probability

P (A) = \frac{favourable outcomes}{all equally likely outcomes}

Pythagorean theorem

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

in a right triangle with hypotenuse

c

Law of cosines

c^{2} = a^{2} + b^{2} - 2 ab cos γ

Law of sines

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

Basic trigonometric identity

sin^{2} α + cos^{2} α = 1

Equation of a circle with centre

(u, v)

and radius

r

(x - u)^{2} + (y - v)^{2} = r^{2}

Distance between two points

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

Volume of a cylinder and a cone

V_{cy l} = π r^{2} h

and

V_{co n e} = \frac{1}{3} π r^{2} h

Logarithm of a product

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

Union of two finite sets

∣ A \cup B ∣ = ∣ A ∣ + ∣ B ∣ - ∣ A \cap B ∣

Conquest of the Carpathian Basin

895-896, led by Arpad.

Founding of the Christian kingdom

Stephen I was crowned around the year 1000; he was later made a saint.

Golden Bull

1222, a charter of King Andrew II that guaranteed rights to the nobility.

Battle of Mohacs

1526: the Ottomans defeated the Hungarian army and King Louis II died.

Rakoczi War of Independence

1703-1711 against the Habsburgs, led by Ferenc Rakoczi II.

Revolution of 1848

Began on 15 March 1848 in Pest; Kossuth led the government.

Compromise (Ausgleich)

1867: created Austria-Hungary, with Franz Joseph as king of Hungary.

Treaty of Trianon

Signed on 4 June 1920; Hungary lost about two thirds of its former territory.

Revolution of 1956

Began on 23 October 1956; crushed by Soviet forces on 4 November.

Change of system

1989: reburial of Imre Nagy, Round Table talks, Republic proclaimed on 23 October.

Hungarian language family

Uralic (Finno-Ugric); not related to its Slavic, Germanic and Romance neighbours.

Hymn (Himnusz)

Poem by Ferenc Kolcsey, 1823; music by Ferenc Erkel; the national anthem.

Petofi's National Song

Read on 15 March 1848; the anthem of the revolution.

Janos Arany

Author of the Toldi trilogy and the ballad The Bards of Wales.

The Tragedy of Man

Dramatic poem by Imre Madach, 1861, with Adam, Eve and Lucifer.

Nyugat

Literary journal founded in 1908; centre of Hungarian modernism (Ady, Babits, Kosztolanyi).

Imre Kertesz

Won the Nobel Prize in Literature in 2002; author of Fatelessness.

Érettségi (Matura Hungary) in Hungary

In Hungary, Érettségi (Matura Hungary) is part of: School-leaving exams.

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