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The student is given a triangle with one side running N-S. They are given bearings for the other two sides. They are given the length of the N-S side.

The bearings and the length are randomised.

They are then asked to find the area and the perimeter of the triangle.

This is a diagnostic test - we use it to determine where extra mathematical help is needed for the class as a whole and where you get to see specific areas where you may need to work on your mathematical skills. The diagnostic test DOES NOT count in any way towards your first year grade.

Students are given the bearings and distances of 2 consecutive straight line walks. They are asked to find the distance from the starting point to the endpoint. They are given a diagram to assist them.

The bearings and distances are randomised (any bearing, distances between 1.1 and 5.). Bearings can be given as either compass bearings or true bearings.

easy vector addition and scalar multiplication, for practice after Section 1 of lectures.

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Reconnaître des puissances positives

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.