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52 cardsStúdentspróf (Iceland)

Studentspróf Key Facts Across Subjects

52 flashcards with key formulas for mathematics and essential dates and facts from Icelandic history and government for Studentspróf revision.

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Quadratic formula

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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 number of real roots

D = b^{2} - 4 a c

: two roots if

D > 0

, one if

D = 0

, none if

D < 0

Power rule for derivatives

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

Product rule

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

Quotient rule

(\frac{u}{v})^{'} = \frac{u ^{'} v - u v ^{'}}{v ^{2}}

Chain rule

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

Derivative of

e^{x}

and

ln x

(e^{x})^{'} = e^{x}

and

(ln x)^{'} = \frac{1}{x}

Derivative of

sin x

and

cos x

(sin x)^{'} = cos x

and

(cos x)^{'} = - sin x

Integral of

x^{n}

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

for

n \neq = - 1

Fundamental theorem of calculus

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

where

F^{'} = f

Sum of an arithmetic sequence

S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) d)

Sum of a geometric sequence

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

, and

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

∣ r ∣ < 1

Law of cosines

c^{2} = a^{2} + b^{2} - 2 ab cos C

Law of sines

\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}

Pythagorean identity

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

Logarithm product rule

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

Change of base

lo g_{a} x = \frac{l n x}{l n a}

Binomial coefficient

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

Probability of a complement

P (\overset{ˉ}{A}) = 1 - P (A)

Binomial probability

P (X = k) = (k n) p^{k} (1 - p)^{n - k}

Dot product of vectors

a \cdot b = a_{1} b_{1} + a_{2} b_{2} = ∣ a ∣∣ b ∣ cos θ

Distance between two points

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

Area of a circle and circumference

A = π r^{2}

and

C = 2 π r

Slope of a line through two points

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

Vertex of

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

x = - \frac{b}{2 a}

Traditional date of the settlement of Iceland

874, with Ingólfr Arnarson as the first permanent settler

Founding of the Althing

930, at Þingvellir

Conversion to Christianity

Around the year 1000, decided at the Althing by the law-speaker Þorgeir

Old Covenant (Gamli sáttmáli)

1262 to 1264: the chieftains accepted the king of Norway

Trade monopoly

1602 to 1787: only licensed Danish merchants could trade with Iceland

Móðuharðindin

Famine of 1783-84 after the Laki eruption

Restoration of the Althing

1845, as an advisory assembly, after it was abolished in 1800

Jón Sigurðsson

Leader of the independence movement, born on 17 June 1811

Home rule

1904, with Hannes Hafstein as the first minister

Act of Union

Took effect on 1 December 1918: Iceland became a sovereign kingdom in union with Denmark

Occupation in the Second World War

British forces landed in May 1940, and US forces took over in 1941

Proclamation of the republic

17 June 1944, at Þingvellir

First president

Sveinn Björnsson

NATO membership

Iceland was a founding member in 1949

Defence agreement with the United States

Signed in 1951, and US forces left Keflavík in 2006

Cod Wars

Three disputes with the United Kingdom, in 1958, 1972 and 1975 to 1976, over fishing limits

Women's Day Off

24 October 1975: many women left work for a day

Vigdís Finnbogadóttir

Elected president in 1980, the first democratically elected female president in the world

Reykjavik summit

October 1986: Reagan and Gorbachev met at Höfði

EEA agreement

In force from 1994: access to the single market without EU membership

Bank collapse

October 2008: the three largest banks failed

Manuscripts returned

From 1971 Denmark returned medieval manuscripts, such as Codex Regius

Skúli Magnússon

Eighteenth-century official who founded the Innréttingar workshops in Reykjavík

Number of seats in the Althing

The stúdentspróf

The upper-secondary school-leaving examination; each school sets its own final exams

Treaty of Kiel (1814)

Denmark ceded Norway to Sweden but retained Iceland, Greenland, and the Faroe Islands as Danish dependencies.

Cod Wars (Þorskastríðin)

A series of confrontations between the UK and Iceland from the 1950s to 1970s over fishing rights, resulting in Iceland expanding its Exclusive Economic Zone to 200 nautical miles.

Stúdentspróf (Iceland) in Iceland

In Iceland, Stúdentspróf (Iceland) is part of: School-leaving exams.

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