Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Multiplying matrices (pre-defined sizes in answers)

This set is designed to emphasise non-commutativity.

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Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Set up so that sometimes it has infinitely many solutions (one free variable), sometimes unique solution. Scaffolded so meant for formative. The variable d determines the cases (d=1: unique solution, d-0: infinitely many solutions). The other variables are set up so that no entries become zero for some randomisations but not others.

Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.

Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.

Not randomised because it's the same as in our workbook.

Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.

Not randomised because it's the same as in our workbook.

Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.

Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.

Not randomised because it's the same as in our workbook.

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Introductory exercise about set equality

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A demonstration of the exam-level variable override feature. The student is shown the same question several times, but each instance is set up to suggest a different error in the process of computing the median of a sample. The first instance is very easy, and the last is pretty hard.

Test på om studentene kan:

• Dekomponere vektorer i et sett basisvektorer
• Forstå hvordan polare basisvektorer avhenger av posisjon

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Demonstrates how to set up a "choose one from a list" part where the number of choices is randomised.

The part is given a list of labels for the choices as well as a list specifying the marks to award for each choice.

A short demonstration of when the basic simplification rules are turned on, or off.

This question uses the vis.js library to plot 3D functions and data sets.

As well as JME functions to make plots, you can use javascript functions to get more control over how the plots are rendered.

This demonstrates how to render a set of tuples such as $\{(1,2),(3,4)\}$ in LaTeX, starting with a list of pairs of numbers.

Use attributes of the form eval-<name> to dynamically set an attribute on an element based on question variables.

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