Christian Lawson-Perfect

The custom function rectangle(width,height) draws a rectangle with the given dimensions, along with some labels.

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.

Apply formulas to calculate the areas of various shapes.

Given mass and volume of an object in SI units, calculate its density. The units are given at different orders of magnitude.

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Give the student three points lying on a quadratic, and ask them to find the roots.

Then ask them to find the equation of the quadratic, using their roots. Error in calculating the roots is carried forward.

Finally, ask them to find the midpoint of the roots (just for fun). Error is carried forward again.

Ask the student to find a matrix corresponding to a given rotation about the origin.

Then ask them to find the determinant. Their answer is marked against the matrix they gave, not just the correct one.

Finally, ask them to find the inverse of their matrix. Marking is against the matrix and determinant they gave.

Some questions which demonstrate the adaptive marking feature.

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

The student must enter a number in scientific notation, with separate boxes for significand and exponent. They only get the marks if both elements are correct.

These questions show how to use JSON data to represent structured information.

Create a list of records for randomly-generated people. Each record contains the person's name, age, and list of hobbies.

The names and hobbies are generated from JSON data.

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.

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].

Some clever variable-substitution trickery to randomly pick two sides of a right-angled triangle to give to a student, and ask for the other.

The sides are set up so they're always Pythagorean triples, and the opposite side is always odd.

As ever, most of the tricky stuff is in the advice. 

Because this was created quickly to show how to set up the randomisation, there's no diagram. It would benefit greatly from a diagram.

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)

Load data about members of the Scottish parliament from a JSON object, and display a table of 5 randomly picked MSPs.

Load data on some items held in the Cooper Hewitt collection, and show a table of 5 randomly picked items.

Identify parts of statistical formulas, and answer questions about how changing one variable affects the statistic.

This question adds a CSS rule to hide the brackets around the matrix input.

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.

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.

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