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Abitur Key Facts Across Subjects

28 flashcards with key formulas, facts and dates from mathematics, the sciences, German literature, history and politics. Study material written for practice, not the official exam.

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Product rule

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Product rule

(u \cdot v)^{'} = u^{'} v + u v^{'}

Chain rule

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

Necessary condition for a local extremum

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

; a sign change of

f^{'}

(or

f^{''} \neq = 0

) confirms it

Necessary condition for an inflection point

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

, with

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

as a sufficient condition

Fundamental theorem of calculus

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

where

F^{'} = f

Binomial probability

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

;

E (X) = n p

σ = n p (1 - p)

Newton's second law

F = ma

; the unit of force is the newton,

1 N = 1 kg\cdotm/s^{2}

Kinetic and potential energy

E_{k} = \frac{1}{2} m v^{2}

and

E_{p} = m g h

Ohm's law and power

U = R I

and

P = U I

Wave relation

c = f λ

Photoelectric effect

E_{k} = h f - W_{A}

; the electron energy depends on frequency, not intensity

Half-life

After

n

half-lives the amount left is

N_{0} \cdot (\frac{1}{2})^{n}

Hardy–Weinberg equation

p^{2} + 2 pq + q^{2} = 1

and

p + q = 1

Light-dependent reactions

Take place at the thylakoid membranes and produce ATP, NADPH and oxygen

Calvin cycle

Takes place in the stroma; RuBisCO fixes CO₂ onto RuBP

Semi-conservative replication

Each new DNA molecule has one old and one new strand

Mole and molar mass

n = \frac{m}{M}

; one mole contains about

6.02 \cdot 1 0^{23}

particles

pH = - lo g [H^{+}]

;

pH + pOH = 14

25^{\circ} C

Le Chatelier's principle

A system at equilibrium shifts to counteract a change in concentration, pressure or temperature

Gibbs free energy

Δ G = Δ H - T Δ S

; a reaction is spontaneous if

Δ G < 0

Goethe and Schiller

Main authors of Weimar Classicism (1794–1805)

Verfremdungseffekt

Brecht's alienation effect: keeps the audience critical of what happens on the stage

Years of German history

1871 German Empire, 1918 Republic, 1933 Nazi seizure of power, 1949 two states, 1990 reunification

Enabling Act (1933)

Allowed Hitler's government to make laws without the Reichstag

Basic Law, Article 1

Human dignity is inviolable (1949)

Personalised proportional representation

Two votes: a candidate (first vote) and a party list (second vote); 5 % threshold

Constructive vote of no confidence

The Bundestag can remove a Chancellor only by electing a successor at the same time

Social market economy

A market economy with state rules for competition and social balance

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