Evaluate a rational limit using algebra

Evaluate $\displaystyle \lim_{x\to 0} \frac{\sqrt{ax+b} - d}{cx}$ using algebra

Students will solve for x using algebraic maipulation.

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

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

Experimental question using JSXGraph to provide dynamic, interactive graphs.

Experimental question using JSXGraph to provide dynamic, interactive graphs.

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

Experimental question using JSXGraph to provide dynamic, interactive graphs.

Experimental question using JSXGraph to provide dynamic, interactive graphs.

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

The student is shown two number entry gaps on either side of a 'less than' sign. Their answer is marked correct if the first number is less than the second, using a custom marking algorithm.

This shows how to mark the gaps in a gap-fill part together, rather than independently.

This question uses the linear algebra extension to generate a system of linear equations which can be solved.

We want to produce an equation of the form $\mathrm{A}\mathbf{x} = \mathbf{y}$, where $\mathrm{A}$ and $\mathbf{y}$ are given, and $\mathbf{x}$ is to be found by the student.

First, we generate a linearly independent set of vectors to form $\mathrm{A}$, then freely pick the value of $\mathbf{x}$, and calculate the corresponding $\mathbf{y}$.

To generate $\mathrm{A}$, we generate more vectors we need, then pick a linearly independent subset of those using the subset_with_dimension function.

Tutorial questions focusing upon the Coulomb field, electrostatic potentials and parallel plate capacitors

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

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

Solving arithmetic progressions using simultaneous equations

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

No description given

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

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

Quadratwurzeln vereinfachen, Nenner rational machen

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

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.

Given a population size and data on a test for a condition on that population, use a tabular approach to find the increase in risk after a positive test in which there is a small chance of a false positive i.e. the probability that the test is positive even though  the condition is not present. See Advice for a graphical version.

This question uses the technique of allocating zero marks to gaps so that they act as holders of values input by the user but are not assessed. The values so input are then gathered using the code found in the preamble and suitable combinations are assigned as answers to gap fills which are then assessed to see if they meet the requirements of the question. Note that is a gap fill is created, but not addressed in the prompt of the part then it is hidden from the user.