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State Matura Key Formulas and Facts

30 flashcards with key formulas and facts from mathematics, physics and language and literature. 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 of a quadratic and what it tells you

D = b^{2} - 4 a c

. If

D > 0

there are two real roots, if

D = 0

one, if

D < 0

none.

Sum and product of the roots of

a x^{2} + b x + c = 0

Sum

- \frac{b}{a}

and product

\frac{c}{a}

Distance between

(x_{1}, y_{1})

and

(x_{2}, y_{2})

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

Equation of a circle with centre

(p, q)

and radius

r

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

Sum of interior angles of an

n

-sided polygon

(n - 2) \cdot 18 0^{\circ}

Heron's formula

Area

= s (s - a) (s - b) (s - c)

with

s = \frac{a + b + c}{2}

Volume of a cone

V = \frac{1}{3} π r^{2} h

Arithmetic sequence:

n

th term and sum

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

and

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

Geometric sequence:

n

th term and sum

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

and

S_{n} = a_{1} \frac{r ^{n} - 1}{r - 1}

for

r \neq = 1

Logarithm rules

lo g (ab) = lo g a + lo g b

lo g \frac{a}{b} = lo g a - lo g b

lo g a^{k} = k lo g a

Number of ways to choose

k

n

(order irrelevant)

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

Derivative of

x^{n}

n x^{n - 1}

Product rule and chain rule

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

and

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

Integral of

x^{n}

for

n \neq = - 1

\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + C

Newton's second law

F = ma

: the net force equals mass times acceleration.

Kinetic energy and gravitational potential energy

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

and

E_{p} = m g h

Ohm's law and electrical power

V = I R

and

P = I V = I^{2} R

Resistors in series and in parallel

Series:

R = R_{1} + R_{2}

. Parallel:

\frac{1}{R} = \frac{1}{R _{1}} + \frac{1}{R _{2}}

Wave speed relation

v = f λ

, and the period is

T = \frac{1}{f}

Photon energy

E = h f

: doubling the frequency doubles the energy.

How many letters has the Macedonian alphabet, and which script is used?

31 letters, written in Cyrillic and codified in 1945.

Which author wrote Beli Mugri (1939)?

Koco Racin, whose poetry collection is seen as the first in modern Macedonian.

Where does stress usually fall in Macedonian words of three or more syllables?

On the third syllable from the end (the antepenultimate syllable).

Who wrote the classic narrative poem Serdarot (The Sirdar)?

Grigor Prličev, awarded the laurel wreath in Athens in 1860.

Which play by Vojdan Černodrinski is considered the foundational Macedonian drama?

Makedonska krvava svadba (Macedonian Blood Wedding, 1900).

What is the central metaphor of Petre M. Andreevski novel Pirej?

Couch grass (pirej), symbolizing the indestructible survival of the Macedonian people.

Coulomb's Law for electrostatic force

= k\frac{|q_1q_2|}{r^2}

, w i t h \approx 9 \times 1 0^{9} N \cdot m^{2} / C^{2}

Ideal gas law equation of state

= nRT$, relating pressure, volume, moles, and absolute temperature in Kelvin.

First derivative power rule

\frac{d}{d x} [x^{n}] = n x^{n - 1}

for any real exponent $.

Državna Matura (North Macedonia) in North Macedonia

In North Macedonia, Državna Matura (North Macedonia) is part of: School-leaving exams.

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