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Panhellenic Exams Key Facts

25 flashcards on the main theorems in calculus, literary and language terms and key events in Greek history. Study material written for practice, not an official test.

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Bolzano's theorem

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Bolzano's theorem

f

is continuous on

[a, b]

and

f (a) f (b) < 0

, then

f

has a root in

(a, b)

Rolle's theorem

f

is continuous on

[a, b]

, differentiable on

(a, b)

and

f (a) = f (b)

, then

f^{'} (ξ) = 0

for some

ξ \in (a, b)

Mean Value Theorem

f

is continuous on

[a, b]

and differentiable on

(a, b)

, then

f^{'} (ξ) = \frac{f ( b ) - f ( a )}{b - a}

for some

ξ

Fermat's theorem

f

has a local extremum at an interior point

x_{0}

and is differentiable there, then

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

Corollary of the Mean Value Theorem for

f^{'} = 0

f^{'} (x) = 0

on an interval, then

f

is constant on it.

Derivative of

ln u

\frac{u ^{'}}{u}

Derivative of

e^{u}

u^{'} e^{u}

Derivative of

sin u

u^{'} cos u

Quotient rule

(\frac{f}{g})^{'} = \frac{f ^{'} g - f g ^{'}}{g ^{2}}

Integration by parts

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

Fundamental Theorem of Calculus (derivative form)

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

with

f

continuous, then

F^{'} (x) = f (x)

Test for a local maximum at

x_{0}

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

and

f^{'}

changes sign from positive to negative.

Test for an inflection point

f^{''}

changes sign at the point.

Derivative of the inverse function at

f (x_{0})

(f^{- 1})^{'} (f (x_{0})) = \frac{1}{f ^{'} ( x _{0} )}

Dionysios Solomos

Poet of the Ionian School who wrote 'Hymn to Liberty', the basis of the Greek anthem.

Seferis and Elytis

The two Greek winners of the Nobel Prize in Literature, in 1963 and 1979.

Katharevousa and demotic

A purified formal language and the spoken popular language; demotic became the official language in 1976.

Monotonic system

The 1982 spelling reform that keeps one accent and drops the breathing marks.

Ethos, pathos, logos

Aristotle's three modes of persuasion: character, emotion and reason.

Greek War of Independence

Began in 1821; the allied victory at Navarino in 1827 helped the Greek cause.

Treaty of Lausanne (1923)

Provided for a compulsory exchange of populations between Greece and Turkey.

Oxi Day

28 October 1940: Greece rejected the Italian ultimatum.

Metapolitefsi

The return to democracy in 1974 after the fall of the junta.

Greece and the EU

Greece joined the EEC in 1981 and adopted the euro in 2001.

Megali Idea

The aim of uniting the Greek-inhabited lands in one state, ended by the defeat of 1922.

Panhellenic Examinations (Greece) in Greece

In Greece, Panhellenic Examinations (Greece) is part of: School-leaving exams.

Students on the same pathway also practise:

Greek General Knowledge

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