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52 cardsMaturität / Maturité (Switzerland)

Matura Key Formulas and Facts

52 flashcards with key formulas in mathematics and key facts in Swiss history, politics and culture for Matura revision. Original study material.

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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

Distance between

(x_{1}, y_{1})

and

(x_{2}, y_{2})

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

Circle with centre

(p, q)

and radius

r

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

Derivative of

x^{n}

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

Chain rule

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

Tangent to

f

x = a

y = f (a) + f^{'} (a) (x - a)

Local minimum test

f^{'} (a) = 0

and

f^{''} (a) > 0

Definite integral of a function

f

with antiderivative

F

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

Area between two curves

g \geq h

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

Product rule of logarithms

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

Sum of an arithmetic series

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

Sum of an infinite geometric series

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

, only if

∣ q ∣ < 1

Law of cosines

c^{2} = a^{2} + b^{2} - 2 ab cos γ

Arc length for angle

α

in degrees

l = \frac{α}{36 0 ^{\circ}} \cdot 2 π r

Volume of a sphere

V = \frac{4}{3} π r^{3}

Dot product of

(a_{1}, a_{2})

and

(b_{1}, b_{2})

a_{1} b_{1} + a_{2} b_{2}

Number of ways to choose

k

from

n

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

Mean and variance of a binomial variable

E (X) = n p

and

Var (X) = n p (1 - p)

Four national languages of Switzerland

German, French, Italian and Romansh.

Röstigraben

The cultural boundary between German-speaking and French-speaking Switzerland.

Author of The Visit and The Physicists

Friedrich Dürrenmatt.

Author of Homo Faber and Andorra

Max Frisch.

Author of Green Henry and Clothes Make the Man

Gottfried Keller.

Founding tradition of the Confederacy

The alliance of Uri, Schwyz and Unterwalden, dated 1291; national day on 1 August.

Federal constitution that created the modern state

The constitution of 1848, after the Sonderbund War of 1847.

Federal Council 'Magic Formula' (Zauberformel)

The traditional party composition of the 7-member Federal Council established in 1959 (2 FDP, 2 CVP/Mitte, 2 SP, 1 SVP; later modified as party strengths shifted).

Optional referendum signature threshold

50,000 valid citizens' signatures collected within 100 days to challenge a federal law in a popular vote.

Federal popular initiative signature threshold

100,000 valid citizens' signatures collected within 18 months to propose a total or partial revision of the Federal Constitution.

Cantons of Switzerland

26 cantons, including 6 half-cantons (Obwalden, Nidwalden, Appenzell Ausserrhoden, Appenzell Innerrhoden, Basel-Stadt, Basel-Landschaft) with half a cantonal vote each in federal votes.

Peace of Westphalia (1648) and Switzerland

Treaty of Münster formally recognised the Old Swiss Confederacy's legal independence from the Holy Roman Empire.

Congress of Vienna (1815) declaration on Switzerland

The European Great Powers formally recognised and guaranteed the perpetual neutrality and territorial integrity of Switzerland.

Opening of the Gotthard Railway Tunnel (1882)

Pioneering 15-kilometre alpine rail tunnel directed by engineer Louis Favre, linking northern Switzerland to Ticino and Italy.

Gotthard Base Tunnel (2016)

At 57 kilometres, the world's longest and deepest rail traffic tunnel, forming the core of the New Railway Link through the Alps (NEAT).

Foundation of the Red Cross (1863)

Founded in Geneva by Henri Dunant following his witness of the Battle of Solferino (1859); Dunant received the first Nobel Peace Prize in 1901.

Seat of the League of Nations and European UN Headquarters

Geneva (Palais des Nations), establishing Switzerland as a global diplomatic centre.

Johann Heinrich Pestalozzi

Influential Swiss educational reformer and philosopher of the Enlightenment whose holistic principles ('head, heart and hands') shaped modern pedagogy.

Carl Spitteler

Swiss poet and essayist who won the 1919 Nobel Prize in Literature for his epic poem Olympian Spring.

Hermann Hesse in Switzerland

German-born author of Steppenwolf, Siddhartha, and The Glass Bead Game who lived in Montagnola (Ticino) and became a Swiss citizen; 1946 Nobel laureate.

Robert Walser

Celebrated Swiss modernist novelist and short-story writer, author of Jakob von Gunten and The Assistant.

Ferdinand Hodler

Prominent Swiss symbolist and realist painter renowned for historical works (The Oath on the Rütli) and expressive alpine landscapes.

Albert Anker

Swiss national painter known as the 'painter of Swiss childhood' for his authentic portraits of 19th-century Bernese rural village life.

Le Corbusier (Charles-Édouard Jeanneret)

Swiss-born architect, designer and urban planner from La Chaux-de-Fonds, a pioneer of modern architecture.

Leonhard Euler

18th-century Basel-born mathematician and physicist, one of the greatest mathematicians in history; pioneer in calculus, graph theory and topology.

The Bernoulli family of Basel

Remarkable Swiss mathematical dynasty including Johann, Jakob and Daniel Bernoulli (known for the Bernoulli principle in fluid dynamics).

Paracelsus (Theophrastus von Hohenheim)

Swiss Renaissance physician and alchemist from Einsiedeln who pioneered toxicology and the use of chemicals in medicine ('the dose makes the poison').

Alberto Giacometti

World-famous Swiss sculptor and painter from Graubünden known for his slender, elongated bronze human figures.

Federal women's suffrage introduction (1971)

Accepted by Swiss male voters in a federal referendum on 7 February 1971; Appenzell Innerrhoden was the last canton to grant cantonal voting rights to women in 1990.

Creation of Canton Jura (1979)

Formed from parts of Canton Bern following popular votes and a constitutional amendment, becoming the 26th Swiss canton.

Swiss Federal Assembly structure

Bicameral parliament: the National Council (200 seats, representing the people by population) and the Council of States (46 seats, representing the cantons).

Seat of the Swiss Federal Supreme Court

Lausanne (with the social security law chambers located in Lucerne).

Mandate of the Swiss National Bank (SNB)

Independent central bank mandated to ensure price stability while taking due account of economic development.

Maturität / Maturité (Switzerland) in Switzerland

In Switzerland, Maturität / Maturité (Switzerland) is part of: School-leaving exams.

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