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30 cardsStudentereksamen STX (Denmark)

STX Key Formulas and Facts

30 flashcards with key formulas and facts from mathematics, Danish language and literature, and Danish 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 number of real roots

d = b^{2} - 4 a c

. Two roots if

d > 0

, one if

d = 0

, none if

d < 0

Exponential function and growth factor

f (x) = b \cdot a^{x}

. For growth rate

r

the growth factor is

a = 1 + r

Power function

f (x) = b \cdot x^{a}

. Doubling

x

multiplies

f (x)

2^{a}

Law of sines

\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}

Law of cosines

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

Area of a triangle from two sides and the angle between them

T = \frac{1}{2} ab sin C

Dot product of two plane vectors

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

, and it is zero when the vectors are perpendicular.

Length of a vector

∣ a ∣ = a_{1}^{2} + a_{2}^{2}

Equation of a circle with centre

(a, b)

and radius

r

(x - a)^{2} + (y - b)^{2} = r^{2}

Derivative of

x^{n}

and of

e^{x}

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

and

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

Product rule and chain rule

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

and

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

Derivative of

ln x

\frac{1}{x}

Integral of

x^{n}

for

n \neq = - 1

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

Differential equation

y^{'} = k y

y = c e^{k x}

, where

c = y (0)

Quartiles and interquartile range

The median splits the data in two halves.

Q_{1}

and

Q_{3}

are the medians of the halves, and the range is

Q_{3} - Q_{1}

Probability of the union of two events

P (A or B) = P (A) + P (B) - P (A and B)

Number of ways to choose

k

n

(order irrelevant)

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

How many letters does the Danish alphabet have?

29 letters, with Æ, Ø and Å added after Z.

Danish noun genders and definite endings

Common gender (en, definite -en: bogen) and neuter (et, definite -et: huset).

Who wrote Either/Or (1843)?

Søren Kierkegaard.

What did the 1849 constitution do?

It ended the absolute monarchy in Denmark; Constitution Day is 5 June.

What happened in 1864?

Denmark lost the duchies of Schleswig, Holstein and Lauenburg in the Second Schleswig War.

When did the German occupation of Denmark last?

From 9 April 1940 to 5 May 1945.

Logarithm product rule for natural and base-10 logarithms

ln (a \cdot b) = ln (a) + ln (b)

and

lo g (a \cdot b) = lo g (a) + lo g (b)

for all

a, b > 0

Logarithm quotient rule for natural and base-10 logarithms

ln (\frac{a}{b}) = ln (a) - ln (b)

and

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

for all

a, b > 0

Logarithm power rule for natural and base-10 logarithms

ln (a^{k}) = k \cdot ln (a)

and

lo g (a^{k}) = k \cdot lo g (a)

for all

a > 0

and real

k

Derivative of power function

f (x) = x^{n}

f^{'} (x) = n \cdot x^{n - 1}

for all real constants

n

Tangent line equation for a differentiable function

f (x)

x_{0}

y = f^{'} (x_{0}) (x - x_{0}) + f (x_{0})

Dot product of 2D vectors and orthogonality condition

a \cdot b = a_{x} b_{x} + a_{y} b_{y}

. Two non-zero vectors are orthogonal

⟺ a \cdot b = 0

Studentereksamen STX (Denmark) in Denmark

In Denmark, Studentereksamen STX (Denmark) is part of: School-leaving exams.

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