Questions around the notion of map, with underlying topic the statement of Goldbach's conjecture. The student has to write the conjecture (by filling in some gaps) as a surjectivity statement for a map, and compute some preimages of elements.

(In German)

More work on differentiation with trigonometric functions

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

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

A set of Numbas exercises for students transitioning from school to University. Designed to help students gain familiarity with using Numbas to enter mathematics, and as revision for algebra, geometry and calculus. 

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

Separable 1st order ODE with exponentials

Two trains arrive at the same platform with different periods. Compute the LCM of the two periods to find the time they clash.

This is a context question testing the student's ability to identify the lowest common multiple of two integer values which are not multiples of each other. 

Integrate Paris Law equation to estimate life to failure.

Exercises in solving simultaneous equations with 2 variables.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

This question is the one described in method 1 of the example "Apply a standard integral" in the Numbas documentation.

The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

Students are given a word problem with the distance travelled and the time taken by a cyclist. They need to choose the correct form for the linear equation, compute the gradient, and plot the line.

The distance travelled and time taken are randomised.

Speed, distance and time are all integer values.

This is a very simple question with no randomisation.

Students are asked to identify an inverse relationship equation.

This question shows how to use the GeoGebra extension to start with a blank worksheet, and add objects to it.

Simple Hertz contact without friction.

An example to help debug a problem with GeoGebra.

Questions used in a university course titled "Group theory".

The questions deal with permutations written in cycle or two-line notation.

Given a parcel's width, height and length, calculate its volume and surface area. Additionally, classify its size based on a formula inspired by a real delivery company (as mad as it sounds!).

The student must give units with each measurement.

Differentiate $\displaystyle ax^b, ax^b+cx^{1/d}, \frac{a}{x^{1/c}}+\frac{b}{x^{-1/d}}+c$ with respect to $x$.

Given sample data find mean, standard deviation, median, interquartile range.

Note that there are different versions of the upper and lower quartiles, so you may want to include your own versions - see the user defined functions in the question.

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

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

Differentiate $ (ax+b)^m(cx+d)^n$ using the product rule. The answer will be of the form $(ax+b)^{m-1}(cx+d)^{n-1}g(x)$ for a polynomial $g(x)$. Find $g(x)$.

Differentiate $ x ^ m(ax+b)^n$ using the product rule. The answer will be of the form $x^{m-1}(ax+b)^{n-1}g(x)$ for a polynomial $g(x)$. Find $g(x)$.