Find the determinant and inverse of three $2 \times 2$ invertible matrices.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$. 

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Crear una tabla de verdad para una expresión lógica de la forma :

                $( a \ {op1} \ b) \ {op2} \ (c \ {op} \ d) \ {op4} \ e $

donde cada una de $a, \; b, \; c, \; d, \; e, \; f $ puede ser una de las variables booleanas $ p, \; q, \; \neg q, \; \neg p $ y cada uno de los operados $\{op}$  puede ser uno de los operadores $\lor, \; \land, \; \to$.

Dados los primeros y últimos términos de una secuencia aritmética finita, calcule el número de elementos y luego la suma de la secuencia.

Cada parte se divide en pasos, con la fórmula dada.

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$. Finally, find all solutions of an equation $\mod b$.

Inputting algebraic expressions into Numbas. (Translation to German)

Kombinationen mit Wdh., einfache Einkleidung

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Solve a quadratic equation by completing the square. The roots are not pretty!

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.

Elementary Exercises in multiplying matrices. 

Used when running a test standalone outside a VLE. This version warns that their answer will show as incorrect.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

The student's answer is a fraction of two polynomials. First check that the student's answer is a fraction, then check that the numerator is of the form $x+a$.

To find the script, look in the Scripts tab of part a.

No description given

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