Student is given a rational function, h(x), with randomised coefficients, and a linear function, k(x), also with randomised coeffieients and asked to find:

1. h(k(x)) or k(h(x)) (randomly selected) for a randomised value of x
2. The domain of h(x) - multiple choice part
3. A general expresion for k(h(x)) or h(k(x)) - opposite combination to first part.

Variables are constrained so that h(x) is not a degenerate form and that when evaluating h(x) denomiator is not 0.

Students need to rewrite a given trig espression in terms of one trig ratio only, Written as a scan solution and upload question, no randomisation.

Students need to rewrite a given trig espression in terms of one trig ratio only, Written as a scan solution and upload question, no randomisation.

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

Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.

Question asks students to find the time taken for an object thrown vertically upward from a platform to reach the ground. Set up randomly chooses environment to be on Earth, Mars or the Moon and uses appropriate acceleration due to gravity. The initial velocity of the body and height of the platform above the ground are randomly selected. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

Using given information to complete the equation $c= A \cos{ \left( \frac{2 \pi}{P} \left( t-H \right) \right) }+V $ that describes the concentration, $c$, of perscribed drug in a patient's drug over time, $t$. Calculating the maximum concentration and the concentration at a specific time. 

Calculating area under curves of the form $ax^2+bx$ and $ax^4+bx^3+cx^2+dx+e$ in a contextualised problem.

mass of tetrahedron via integration

Add, subtract, multiply and divide numerical fractions.

This question shows how to use the question's JavaScript preamble to request data from an external source, and use that data in question variables.

Note that this means the question only works when the external source is available. Use this very carefully, and avoid it if you possibly can!

A random proper fraction $a/b$ with denominator in the range 2 to 30 is picked, and the student must write $\frac{a}{b} \pi$.

The point of this question is to demonstrate that the correct answer is shown as a multiple of $\pi$ rather than a decimal.

A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.

If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.

Choice of 2 formulae. The first is a fraction of the form y=(r+x)(1-rx). The second is of the form y=sqrt[(1-x)/(1+x) ]. Rearrange to make x the subject.

Evaluate pi / (2r+s) given values for r and s (r>0, s positive or negative)

No description given

Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.   

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Vul de x-waarden van de extrema in.

Quiz designed to test integration of powers of x including negative powers, surds, fractions, etc.

This is the simplest demonstration of the "code" part type I could think of: write Python to assign x = 1.

An alternative answer gives a hint if the student's code doesn't define x at all.

This exam has a custom diagnostic algorithm which gives the progress as a rational value. At the moment, this means "NaN%" is displayed in the sidebar.

Separable equation for integration.

Solving first order differentials by separation of variables.

Practice question simplifying fractions for integration by using partial fractions.

No description given

Given a randomised rational function select the possible ways of writing the domain of the function.