Differentiation of trigonometric functions

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

Matrix multiplication. Contains a function that will let you print the calculation steps of matrix multiplication, e.g. in the Advice.

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Obosolete: there's now a built-in function sort_by.

Defines a custom function sort_by to sort a list of lists by the elements at the given index.

You could do a similar thing to sort lists of dictionaries.

Should not be used: there's now a built-in function frequencies.

This question randomly generates a list of 100 items, each chosen from a list of strings.

It then computes the number of occurrences of each distinct item in the list. The statement shows the frequencies in a table.

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.

Shows how to use the JME function lpad to add zeros to the beginning of a number so it's always displayed using two digits.

Demo showing how to write a custom function in javascript.

Call a custom function from another javascript custom function by using scope.evaluate

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Demo question showing how to use the matrix maths functions in JavaScript.

This shows how to implement a recursive function in JavaScript with a nested function definition.

Ask for the squares of five randomly-chosen numbers between 0 and 15.

The shuffle function puts a list in random order.

This question shows how to use the currency function to display amounts of currency with the correct symbols.

This question shows how to display a number like "1234" as "1,234", or "1 234", using the formatNumber function.

A method of randomly choosing variable names - use the expression() JME function to create a variable name from a randomly chosen string.

(This question also uses a custom marking script to check that the student has simplified the expression)

Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

More work on differentiation with trigonometric functions

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

This question demonstrates defining an 'unknown' function $F(x)$ as a custom function so that it can be used in marking.

The definition of $F$ is arbitrary, so care must be taken to ensure it doesn't have more properties, such as evenness, than necessary.

This shows how to use captured groups in a mathematical expression part's pattern restriction to mark an answer involving multiple occurrences of an undefined function.

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

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 negative gradient.

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.