$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Find the eigenfunctions of an irregular Sturm–Liouville problem and hence solve an inhomogeneous boundary value problem by writing the solution as an eigenfunction expansion.

Interpreting a p-value given the hypothesis.  Common misconceptions. 

Calculate the functional value at a point.

Calculate the functional value at a point.

This exercise will help you rearrange a linear equation to find the value of a given variable

When saving the data necessary to resume an attempt, Numbas only saves the values of variables which use the random number generator.

If you naively generate a large random sample in one variable, it'll be marked as a source of randomness so Numbas will save every value in the sample. Loading this value when you resume the attempt can be very slow.

Instead, you can generate a seed value in one variable and then use it with the seedrandom function in the variable that stores your random list. Only the value of the seed needs to be saved.

Reading a value from a simple bar chart.

Reading a value from a histogram.

Find principal stresses by finding the eigenvalues of the matrix

Calculating the amount of money in a savings account after a given amount of time, and calculating how long it will take for the amount of savings to exceed a given value. 

testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees but in radians

testing sin, cos, tan of angles that are negative or greater than 2pi radians that result in nice exact values. 

exact value of testing sin, cos, tan of angles that are negative or greater than 360 degrees that result in nice exact values. 

multiple choice testing sin, cos, tan of  random(pi/6, pi/4, pi/3) radians

multiple choice testing csc, sec, cot  of  random(pi/6, pi/4, pi/3) radians

exact value of sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees

multiple choice testing csc, sec, cot of random(30, 45, 60) degrees

multiple choice testing sin, cos, tan of  random(30, 45, 60) degrees

A random dataset given by a linear function with noise (gradient and y-intercept of the linear function are randomised as is distribution of x values).

Using the unit circle definition of sin, cos and tan, to calculate the exact value of trig functions evaluated at angles that depend on 0, 30, 45, 60 or 90 degrees.

Face, Place and actual value, adding, subtracting, multiplying, dividing and rounding decimals.

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Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.

The table uses the spreadsheet extension.

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.

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Shows two different ways

Collecting like terms, expanding a bracket (distributive law), substitution of values, finding factors, simplifying algebraic fractions.