On a plusieurs ensembles dont les éléments sont des entiers tirés aléatoirement. Il faut faire des opérations élémentaires faisant intervenir  $\cap,\;\cup$ et la notion de complémentaire.

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

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.

Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.

Problem with solving the simultaneous equations gven by the constraints - too unwieldy and not given enough marks for doing so. Best if the point of intersection is given graphically by putting the mouse over the intersection.

Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.

Problem with solving the simultaneous equations gven by the constraints - too unwieldy and not given enough marks for doing so. Best if the point of intersection is given graphically by putting the mouse over the intersection.

Demo question: do some sneaky symbolic differentiation to check that the student's answer is the integral of the expression they're given.

Needs an advice section before it can be used.

Rationalise the denominator with increasingly difficult examples involving compound denominators. 

Translated to German, made some minor changes to Advice section.

Original: https://numbas.mathcentre.ac.uk/question/22555/rationalising-the-denominator-surds/ by Lauren Richards

Solve for $x$ each of the following equations: $n^{ax+b}=m^{cx}$ and $p^{rx^2}=q^{sx}$.

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Students are shown to intersecting lines in the context of comparing the costs of services from two companies. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

Students are shown to intersecting lines in the context of a gym visiting program. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

Students are shown a graph that simultaneously plots cost and revenue lines. They are asked to identify the break-even point.

They are asked to give the x- and y- coordinate values.

The graph is randomised, but it is set up so that the point of intersection lies on gridlines.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Divide $ f(x)=x ^ 4 + ax ^ 3 + bx^2 + cx+d$ by $g(x)=x^2+p $ so that:
$\displaystyle \frac{f(x)}{g(x)}=q(x)+\frac{r(x)}{g(x)}$

Solve for $x$ each of the following equations: $n^{ax+b}=m^{cx}$ and $p^{rx^2}=q^{sx}$.

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Algebraic manipulation/simplification.

Simplify $\displaystyle \frac{ax^4+bx^2+c}{a_1x^4+b_1x^2+c_1}$ by cancelling a a common degree 2 factor.

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

Rotate the graph of  $y=a\ln(bx)$  by $2\pi$ radians about the $y$-axis between $y=c$ and $y=d$. Find the volume of revolution.

Use the testing tab in the variables section to make sure the generated variables satisfy a condition

Given percentages of males and females working on a project, and the percentage of the total staff who are male (or female), find the percentage of all staff working on the project.

Based on question 3 from section 3 of the maths-aid workbook on numerical reasoning.

Adapted from section 7.3.1 in OpenIntro Statistics (4th ed).

Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

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

Given a pair of 3D position vectors, find the vector equation of the line through both.  Find two such lines and their point of intersection.

Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.

Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.