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Centralised Exams Key Formulas and Facts

30 flashcards with key formulas and facts from mathematics, Latvian language and literature, and Latvian 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}

Vieta's formulas for

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

Sum of the roots

- \frac{b}{a}

and product

\frac{c}{a}

Rules for logarithms

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

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

l g a^{k} = k l g a

Definition of the logarithm

l g x = y

means

x = 1 0^{y}

Basic trigonometric identity

sin^{2} α + cos^{2} α = 1

Heron's formula

Area

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

with

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

Interior angle of a regular

n

-gon

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

Volume of a sphere and of a cone

Sphere

\frac{4}{3} π r^{3}

and cone

\frac{1}{3} π r^{2} h

Midpoint of a segment

(\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

Distance between two points

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

Arithmetic progression sum

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

Geometric progression sum

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

for

q \neq = 1

Number of combinations

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

Derivative of

x^{n}

n x^{n - 1}

Integral of

x^{n}

for

n \neq = - 1

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

Local extrema test

Solve

f^{'} (x) = 0

. If

f^{''} > 0

at the point, it is a minimum; if

f^{''} < 0

, a maximum.

How many letters has the Latvian alphabet?

33 letters, a Latin alphabet with diacritics.

Where does the stress fall in Latvian words?

On the first syllable.

How many cases and genders does Latvian have?

Seven cases and two genders (masculine and feminine).

Who wrote the epic Lāčplēsis (1888)?

Andrejs Pumpurs.

What did Krišjānis Barons collect?

Latvian folk songs, the dainas, published as Latvju dainas.

When was independence proclaimed, and when restored?

Proclaimed on 18 November 1918; restoration declared on 4 May 1990.

What happened on 23 August 1989?

The Baltic Way, a human chain across Estonia, Latvia and Lithuania.

When did Latvia join NATO and the EU?

NATO on 29 March 2004 and the EU on 1 May 2004.

What was the first realistic novel in Latvian?

'Mērnieku laiki' (1879) by Reinis and Matīss Kaudzīte.

Who wrote the national symbolic plays Uguns un nakts and Zelta zirgs?

Rainis (Jānis Pliekšāns).

What psychological novella was written by Rūdolfs Blaumanis about fishermen on an ice floe?

'Nāves ēnā' (In the Shadow of Death).

When was the city of Riga founded, and by whom?

In 1201 by Bishop Albert of Buxhoeveden.

What historic event is commemorated on Lāčplēsis Day (11 November)?

The 1919 victory over the Bermontian army, liberating Riga in the War of Independence.

When was the Constitution of Latvia (Satversme) adopted?

On 15 February 1922 by the Constitutional Assembly.

Centralizētie Eksāmeni (Latvia) in Latvia

In Latvia, Centralizētie Eksāmeni (Latvia) is part of: School-leaving exams.

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Latvian General Knowledge

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