Different methods of loading a geogebra applet.

Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.

Reduce a 5x6 matrix to row reduced form and using this find rank and nullity.

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A question to practise the following skills in the context of Earth Sciences:

• using a data set to deduce a linear relationship
• using the graph to make predictions

Given normal distribution $\operatorname{N}(m,\sigma^2)$ find $P(a \lt X \lt b),\; a \lt m,\;b \gt m$ and also find the value of $X$ corresponding to a given percentile $p$%. 

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This question uses the vis.js library to plot 3D functions and data sets.

As well as JME functions to make plots, you can use javascript functions to get more control over how the plots are rendered.

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Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Compute a table of values for an exponential function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Doesn't work - used the old extension.

Mark a GeoGebra worksheet.

Needs a worked solution.

A sneak peek at a really clever integration of GeoGebra with Numbas.

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

Given data on population mean and population standard deviation and three sampling sizes, calculate the probabilities that the sample means are within a specified distance from the population mean.

Pick four numbers from $1900\dots 2015$ and ask the student to factorise them.

Custom marking scripts make sure the student has entered a complete factorisation.

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA

A box contains $n$ balls, $m$ of these are red the rest white.

$r$ are drawn without replacement.

What is the probability that at least one of the $r$ is red?

Trying out something: get the student to enter a set for each of "regular singular points" and "essential singular points".

Find and classify singular points of a second-order ordinary differential equation.  One equation is chosen from a selection of 10.

Given a matrix in row reduced form use this to find bases for the null, column and row spaces of the matrix.

Given $6$ vectors in $\mathbb{R^4}$ and given that they span $\mathbb{R^4}$ find a  basis.

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.

Cofactors Determinant and inverse of a 3x3 matrix.