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Matura Key Formulas and Facts

25 flashcards with key formulas in mathematics and key facts in Slovenian literature and history. Study material written for practice, not an official test.

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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}

Discriminant and the number of real roots

D = b^{2} - 4 a c

. If

D > 0

there are two roots, if

D = 0

one double root, if

D < 0

none.

Vertex of

y = a x^{2} + b x + c

x_{v} = - \frac{b}{2 a}

, then find

y_{v}

by substituting.

n

th term and sum of an arithmetic sequence

a_{n} = a_{1} + (n - 1) d

and

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

n

th term of a geometric sequence

a_{n} = a_{1} q^{n - 1}

Sum of an infinite geometric series

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

, only if

∣ q ∣ < 1

Basic trigonometric identity

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

Law of sines

\frac{a}{s i n α} = \frac{b}{s i n β} = \frac{c}{s i n γ}

Law of cosines

c^{2} = a^{2} + b^{2} - 2 ab cos γ

Area of a circle and its circumference

A = r^{2} π

and

C = 2 r π

Volume of a cone

V = \frac{1}{3} r^{2} π h

Distance from the point

(x_{0}, y_{0})

to the line

A x + B y + C = 0

d = \frac{∣ A x _{0} + B y _{0} + C ∣}{A ^{2} + B ^{2}}

Length of the vector

(a, b)

a^{2} + b^{2}

Product rule of logarithms

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

Derivative of

x^{n}

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

Product rule of derivatives

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

Definite integral with antiderivative

F

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

Number of ways to choose

k

from

n

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

Probability of independent events

P (A \cap B) = P (A) \cdot P (B)

Number of cases in Slovenian grammar

Six: nominative, genitive, dative, accusative, locative and instrumental. There is also a dual number.

Slovenian national poet

France Prešeren, author of Zdravljica, whose seventh stanza is the anthem.

First book printed in Slovenian

Catechismus and Abecedarium by Primož Trubar, 1550.

First Slovenian novel

Deseti brat by Josip Jurčič, 1866.

Author of Hlapec Jernej and his rights

Ivan Cankar.

Slovenian independence

Plebiscite 23 December 1990, declaration on 25 June 1991, Ten-Day War in the summer of 1991.

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