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Nach Nikomachos: Ermitteln der 5. Proportion

Questions on graph theory

This question displays one of 10 graphs. It asks the student to either 

(a) count the vertices, or

(b) count the edges, or

(c) state how many vertices a spanning tree would contain, or

(d) state how many edges a spanning tree would contain, or

(e) state the degree of a selected (randomly chosen) vertex.

Students are randomly shown one of two networks. They are shown four sub-networks, and asked to identify which one is a minimum spanning tree for the network. Thus, there are 2 versions of this question.

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.

https://numbas.mathcentre.ac.uk/question/22664/addition-and-subtraction-of-fractions/ by Lauren Richards

Translated to German and Part d) added.

Finde die Bruchzahl, deren Wert sich von den anderen unterscheidet. Die Nenner sind meistens zwei- oder dreistellig.

Angepasste und übersetzte Version von https://numbas.mathcentre.ac.uk/question/23234/select-the-fraction-not-equivalent-to-the-others-large-denominators/ von Christian Lawson-Perfect.

Solve for $x$: $\displaystyle \frac{px+s}{ax+b} = \frac{qx+t}{cx+d}$ with $pc=qa$.

German translation of https://numbas.mathcentre.ac.uk/question/12012/solve-an-equation-in-algebraic-fractions/ by Newcastle University Mathematics and Statistics

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Translated to German, minor changes to advice section.

Original: https://numbas.mathcentre.ac.uk/question/22497/surds-simplification/ by Lauren Richards.

Quadratwurzeln vereinfachen, Nenner rational machen

Deutsche Übersetzung von https://numbas.mathcentre.ac.uk/question/22587/using-surds-rationalising-the-denominator/ von Elliott Fletcher

Griechisch-römische Antike 3

Über den Weg des Lichts

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Rechnen mit der Näherungsformel und exakt.

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A simple ideal gas law question, using number of molecules, that asks the student to calculate one of the four variables. he question can ask for either L atm, or kPa m3, and either K or C for temp. As such the boltzmann constant is in either J/K or L atm/K.

Based on an activity tweeted by Richard Perring.

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

Error if torional stresses are calculated incorrectly 

Übungen zu Stellenwertsysteme, Euklidischer Algorithmus

Aufgabe zum schriftlichen Addieren in b-adischen Systemen

Aufgabe zum einfachen und erweiterten euklidischen Algorithmus (mit "schönen" Zahlen)

Zifferndarstellungen in b-adischen Systemen

Solve two quadratic equations (with real coefficients) in the complex numbers. The solutions have non-zero imaginary part, fractions can appear (but the denominators are rather small).

Equilibrium

Equilibrium

Equilibrium

Equilibrium

Equilibrium

Equilibrium