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.

Derive the expressions for the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.

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Find the force required to produce a given moment, or vice-versa.

Find the moment of inertia of semi and quarter circles using the parallel axis theorem.

An A-frame structure supporting a force and a moment. The feet are at the different vertical positions so the solution will require simultaneous equations, unless you rotate the coordinate system.

Given the moment of inertia of an area about an arbitrary axis, find the centroidal moment of inertia and the moment of inertia about a second axis.

Write expressions for the moment of inertia of simple shapes about various axes.

Use the parallel axis theorem to find the area moment of inertia of a triangle and a rectangle about various axes.

Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.

Find moment of inertia wrt the x- and y- axes for a shape made up of two rectangles.

Find moment of inertia and radius of gyration for a built-up beam made of two channels and two plates.

Find moment of inertia of a composite shape consisting of a rectangle and two triangles with respect to the x-axis. Shapes rest on the x-axis so the parallel axis theorem is not required.

Find centroidal moments of inertia and radius of gyration for a beam composed of  two angle sections forming a box beam.

Use a table of properties to find the Area Moment of inertia for simple shapes: rectangle, triangle, circle, semicircle, and quarter circle.

 The parallel axis theorem is not required for any of these shapes.  One situation requires subtracting a triangle from a rectangle however.

Distinguish between centroidal and non-centroidal moments of inertia.

Euler-Bernoulli simply supported beam bending example with point force and moment.

A quick implementation of certainty-based marking: the student's score depends on how they rated their certainty in their answer before submission.

Because Numbas doesn't allow negative marking at the moment, scores are shifted upwards, so a high certainty incorrect answer scores 0, and a high certainty correct answer scores full credit.

The student has to compute $a^b$ and $b^a$, then decide which of the two is bigger.

This question shows how to set up a custom marking matrix for the "choose one from a list" part, based on values used elsewhere in the question. It could use adaptive marking to use the student's incorrect values for the comparison, but doesn't at the moment.

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

Write expressions for the moment of inertia of simple shapes about various axes.

Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.

Find the magnitude of the momentum of some objects, given mass and speed. Apply the formula $\rho = mv$.

Find the magnitude of the momentum of some objects, given mass and speed. Apply the formula $\rho = mv$.