A function which renders the factorisation of a number in LaTeX.

Show a list of the factors of a number.

Works by testing each number up to $n$ for divisibility by $n$, so won't do well with really big numbers. Certainly fast enough for numbers up to 4 or 5 digits.

One method of randomly choosing names for variables. For each variable, we have 4 options. Create a list of 4 numbers, which is 1 for the name we want to use, and 0 otherwise.

Then, whenever we use that variable, multiply each of the possible names by the corresponding number in the list. When the expression is simplified, the unwanted names will cancel to 0, leaving only the name we want.

This is quite clunky!

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

Some custom CSS restyles the matrix input so it looks like a fraction, with input boxes on top and bottom.

Ideally, there should be a fraction input part type, or an option for the number entry part to display a fraction input.

Numbas can now understand and use several different styles of notation for numbers.

This question shows off all the supported styles, both for display in text and in the answers to number entry parts.

Student is given a few numbers to choose from. They must pick at least two, and then give the sum of their chosen numbers.

This question shows how to ask for a number in scientific notation, by asking for the significand and exponent separately and using a custom marking algorithm in the gap-fill part to put the two pieces together.

Answers not in standard form, i.e. with a significand not in $[1,10)$, are accepted but given partial marks.

A randomly generated list of numbers is shown to the student. They must tick every occurrence of the lowest number. The number of occurrences isn't always the same - sometimes the minimum is unique and sometimes it is repeated. The map function makes it easy to construct a marking matrix.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.
This version of the question asks for 10 fields to be filled rather than the full 25, although the question statement asks for 25. I am sure that the first version asked for all 25.

Find upper and lower bounds on the number of codewords in three maximal codes given their codeword lengths and minimum distances.

Uses Hamming, Singleton and Gilbert-Varshamov bounds.

Find angle between plane $\Pi_1$, given by three points, and the plane $\Pi_2$ given in Cartesian form.

The calculation of $cos(\alpha)$ at the end of Advice has fractionNumbers switched on and so the result is presented as a fraction, which can be misleading. Best if calculation is followed through without using fractionNumbers.

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Approximating integral of a quadratic by Riemann sums . Will include an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

$x_n=n^k t^n$ where $k$ is a positive integer and $t$ a real number with $0 < t<1$. Find the smallest integer $N$ such that $(m+1)^k t^{m+1} \leq m^k t^m$ for all $m \geq N$. 

Entering numbers in Numbas, Part 1.

Details on inputting numbers into Numbas.

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

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

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

Independent events in probability. Choose whether given three given pairs of events are independent or not.

Find a regression equation.

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

Number Theory. 

Given $n \in \mathbb{N}$ find $\mu(n),\;\tau(n),\;\sigma(n),\;\phi(n).$

Given $\frac{a}{b} \in \mathbb{Q}$ for suitable choices of $a$ and $b$, find all $n \in \mathbb{N}$ such that $\phi(n)=\frac{a}{b}n$.

Given $m \in \mathbb{N}$, find values of $n\in \mathbb{N}$ such that $\sigma(n)=m$.

There are at most two such solutions in this question.