Homework set.  Problems require finding centroid, then Moment of Inertia about a centroidal axis.

Homework set.  Application of Parallel Axis Theorem to find area Moment of Inertia

Homework set.  Basic concepts of Area Moment of Inertia.

Homework set.  Uniformly and uniformly varying distributed loads.

Homework set.  Use integration to find the centroid of shapes bounded by functions.

Homework set.  Use integration to find the centroid of shapes bounded by functions.

Homework set.  Find centroids of shapes by dividing them into simple subshapes.

Taken from question 37 of the book Problem Solving in GCSE Mathematics by Daniel Griller.

Given bearings and lengths of two straight lines, work out the bearing and distance back to the starting point.

A Eukleides diagram shows the setup visually.

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

Generates two sets of matrices that can be added and asks the student to add them. Will ensure that the dimensions in part a) are different to the dimensions in part b) to offer some variety.

Generates two sets of matrices that can be added and asks the student to add them. Will ensure that the dimensions in part a) are different to the dimensions in part b) to offer some variety.

Decide whether each of the described sets of data is drawn from a discrete or continuous distribution.

This question is about identifying what types of charts or visual representations of data you can use for different data sets.

No description given

Determine the correct parametric representation of a given curve.  Curve is randomly chosen from a set of 20.

The graph of the curve was not displayed on my machine.

The student is asked to find the square root of an integer of the form $\pm n^2$. If the root is not real, they should enter "nan".

A custom marking algorithm extends the built-in one to deal with "nan".

There's some custom javascript to set the expected answer correctly. In the future this will be possible in the marking algorithm - see https://github.com/numbas/Numbas/issues/856

Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

Things like "expand 4(5a-3)"

Basically expand an expression like "5y(-2z+3)" where the student types answer into a single gap.

A quick practice set of problems for education students to take in preparation for their numeracy test.

A quick practice set of problems for education students to take in preparation for their numeracy test.

This question plots a general amplitude modulated carrier signal defined by $v_s(t) = (V_{DC} + V_m \cos(2\pi f_m t))\cos(2\pi f_c t)$, where $V_{DC}$ is a DC offset, $V_m$ is the message amplitude, $f_m$ is the message frequency and $f_c$ is the carrier frequency ($f_c = 20f_m$ in this question). The student must identify the values of $V_{DC}$ and $V_m$ and enter these values into the appropriate gaps in the equation of the AM signal.

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

Find and compare means and standard deviation using EXCEL (downloadable randomised dataset)

A question to test understanding of set cardinality and intersections when limited information is known about the size of certain sets.

Student needs to solve a quadratic equation to calculate time taken for a diver to hit the water after diving from a diving board. Height of the board and initial upward velocity of the diver are randomly generated values. student needs to know that surface of the water is height 0, and only positive root of quadratic has physical meaning. Question is set to always give one positieve and one negative root.

The student has to enter three different letters of the alphabet in the three gaps. Their answer is marked as a set: repeated answers only count as one answer.

Each gap has the same custom marking algorithm which marks that gap as correct if the student's answer is in the set of acceptable answers.

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Schreibe $\displaystyle \frac{a} {b + \frac{c}{d}}$ als einen gekürzten Bruch $\displaystyle \frac{p}{q}$ mit ganzen Zahlen $p$ und $q$.

Angepasste, übersetzte und erweiterte Version von https://numbas.mathcentre.ac.uk/question/11701/simplifying-fractions/ von Newcastle University Mathematics and Statistics.

The student is shown a set of axes with three lines. They must move the lines so they match the given inequalities, then move a point inside the region satisfied by the inequalities.