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25 cardsSelectividad / EvAU (Spain)

Selectividad Key Facts

25 flashcards on the main formulas, literary terms and historical events behind the Spanish university access exam. Study material written for practice, not an official test.

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Derivative of

ln u

with respect to

x

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Derivative of

ln u

with respect to

x

u^{'} / u

(the chain rule applied to the logarithm).

Derivative of

e^{u}

u^{'} e^{u}

Integration by parts formula

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

Condition for a local minimum at

x_{0}

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

and

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

Inflection point test

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

with a change of sign of

f^{''}

x_{0}

Determinant of

(a c b d)

a d - b c

Effect of multiplying an

n \times n

matrix by

k

on its determinant

The determinant is multiplied by

k^{n}

Rouché-Frobenius theorem

A linear system has a solution if and only if the rank of the coefficient matrix equals the rank of the augmented matrix.

Distance from point

(x_{0}, y_{0}, z_{0})

to the plane

a x + b y + cz + d = 0

\frac{∣ a x _{0} + b y _{0} + c z _{0} + d ∣}{a ^{2} + b ^{2} + c ^{2}}

Area of the parallelogram spanned by

u

and

v

∣ u \times v ∣

Bayes' theorem for two events

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

Binomial probability

P (X = k)

for

X \sim B (n, p)

(k n) p^{k} (1 - p)^{n - k}

Margin of error of a confidence interval for a mean (known

σ

)

z σ / n

Generation of 1898

Spanish writers, such as Unamuno, Machado and Baroja, who reflected on the national crisis after the loss of the last colonies.

Generation of 1927

A group of poets including Lorca, Alberti, Cernuda and Aleixandre.

Hendecasyllable

A line of eleven metrical syllables, used in the sonnet.

Spanish romance (verse form)

Lines of eight syllables with assonant rhyme in the even lines.

Esperpento

Valle-Inclán's style that deforms reality as in a concave mirror, as in Luces de bohemia.

Treaty of Utrecht (1713)

Ended the War of the Spanish Succession; Philip V kept the throne and Spain lost its European lands, Gibraltar and Menorca.

Constitution of 1812

Approved by the Cortes of Cádiz; set out national sovereignty and the separation of powers.

Turno pacífico

The agreed alternation in power of Conservatives and Liberals during the Restoration, helped by caciquismo.

Second Republic

Proclaimed on 14 April 1931; ended with the Civil War of 1936-1939.

Stabilisation Plan of 1959

Economic measures that opened Spain to foreign trade and investment and ended autarky.

Constitution of 1978

Approved by referendum on 6 December 1978; set up a parliamentary monarchy with autonomous communities.

Attempted coup of 23 February 1981

Lieutenant colonel Tejero entered the Congress with armed guards; the coup failed.

Selectividad / EvAU (Spain) in Spain

In Spain, Selectividad / EvAU (Spain) is part of: School-leaving exams.

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