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50 cardsYlioppilastutkinto (Finnish Matriculation)

Matriculation Key Facts Across Subjects

50 flashcards with key formulas for mathematics, dates from Finnish history and facts about the Finnish language and literature. Study material written for practice, not the official exam.

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Quadratic formula

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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}

Derivative of

x^{n}

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

Product rule

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

Chain rule

(f (g (x)))^{'} = f^{'} (g (x)) \cdot g^{'} (x)

Derivative of

ln x

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

Derivative of

e^{k x}

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

Derivative of

sin x

and

cos x

(sin x)^{'} = cos x

and

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

Integral of

x^{n}

\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + C

n \neq = - 1

Integration by parts

\int u d v = uv - \int v d u

Area between two curves

\int_{a}^{b} (f (x) - g (x)) d x

when

f \geq g

Volume of revolution about the

x

-axis

V = π \int_{a}^{b} (f (x))^{2} d x

Condition for a local maximum

f^{'} (x_{0}) = 0

and

f^{'}

changes from positive to negative

Arithmetic sum

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

Geometric sum

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

Infinite geometric series

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

for

∣ r ∣ < 1

Law of cosines

c^{2} = a^{2} + b^{2} - 2 ab cos C

Pythagorean identity

sin^{2} x + cos^{2} x = 1

Logarithm of a power

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

Combinations

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

Conditional probability

P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )}

Binomial distribution

P (X = k) = (k n) p^{k} (1 - p)^{n - k}

Dot product

a \cdot b = ∣ a ∣∣ b ∣ cos θ

Equation of a circle

(x - a)^{2} + (y - b)^{2} = r^{2}

Distance between two points

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

Year Finland became part of Russia

1809, in the Treaty of Hamina after the war between Sweden and Russia

Status of Finland 1809 to 1917

A grand duchy of the Russian Empire with its own laws and institutions

Capital from 1812

Helsinki, which replaced Turku

Independence Day

6 December 1917

Finnish Civil War

1918: the Whites, led by Mannerheim, defeated the Reds

Winter War

30 November 1939 to 13 March 1940, ended by the Moscow Peace Treaty

Continuation War

1941 to 1944, ended by the Moscow Armistice

Lapland War

1944 to 1945: Finland forced German troops out of the north

YYA treaty

1948 treaty of friendship, cooperation and mutual assistance with the Soviet Union

Helsinki Olympics

1952

Urho Kekkonen

President from 1956 to 1982

Finland joined the EU

1 January 1995

Finland joined NATO

4 April 2023

Women's suffrage

1906: Finland was the first in Europe to give women full political rights

Language family of Finnish

Uralic, in the Finno-Ugric branch

Compiler of the Kalevala

Elias Lönnrot, first version 1835 and final version 1849

Kalevala Day

28 February

Author of Seven Brothers

Aleksis Kivi, published in 1870

Author of The Unknown Soldier

Väinö Linna, published in 1954

Nobel laureate in literature, 1939

Frans Eemil Sillanpää

Father of written Finnish

Mikael Agricola, who published the first Finnish primer around 1543

Finnish inessive case

Means in, with the ending -ssa or -ssä: talossa

Finnish elative case

Means out of, with the ending -sta or -stä: talosta

Finnish illative case

Means into, as in taloon

Noun after a numeral above one

The singular partitive: kaksi taloa

Negation in Finnish

A negative verb that changes for person: en, et, ei

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