Find $p$ and $q$ such that $ax^2+bx+c = a(x+p)^2+q$. 

Hence, or otherwise, find roots of  $ax^2+bx+c=0$.

Includes a video which shows how to solve a quadratic by completing the square.

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Choose from one of several pre-defined scenarios, and set variables to the corresponding values. 

This question has three variables: city, population, and percent_like_chocolate. These differ for each city. 

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Update: you can now use the conditional visibility button to do this more easily - see the documentation.

If the statement or advice for your question differs greatly depending on a random variable (for instance, if you're picking from a selection of scenarios), you only want to show content for the relevant scenario.

This question shows one way of doing that.

A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Break down the following numbers into component parts according to place value:

Download a file and scan the values into R to obtain a numeric vector of values. Then use R to explore your numeric vector in order to find the answers to these questions.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

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

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Substitute values into formulae for the area or volume of various geometric objects.

Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Choose from one of several pre-defined scenarios, and set variables to the corresponding values, defined in lists.

This question has three variables: city, population, and percent_like_chocolate. These differ for each city. We've defined a list for each variable, with the corresponding values. A variable called scenario picks a random position in the list, so the value of city, for example, is cities[scenario].

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

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.

A mathematical expression part whose answer is the product of two matrices, $X \times Y$.

By setting the "variable value generator" option for $X$ and $Y$ to produce random matrices, we can ensure that the order of the factors in the student's answer matters: $X \times Y \neq Y \times X$.

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.