Shows how to use the programming extension's preload function to load files from the question resources into the Python or R code runners.

Look at the question's JavaScript preamble.

Calculate the heat losses from a model building based on the U values, dimensions and other parameters specified. In addition calculate the annual running costs and payback period for improvements to the building Fabric.

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rebelmaths

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

A set of practice questions for primary teaching students studying Mathematical Patterns and Relationships

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

rebelmaths

In the first part, the student must write any linear equation in three unknowns. Each distinct variable can occur more than once, and on either side of the equals sign. It doesn't check that the equation has a unique solution.

In the second part, they must write three equations in two unknowns. It doesn't check that they're independent or that the system has a solution. The marking algorithm on each of the gaps just checks that they're valid linear equations, and the marking algorithm for the whole gap-fill checks the number of unknowns.

The student must solve a pair of simultaneous equations in $x$ and $y$.

The variables are generated backwards: first $x$ and $y$ are picked, then values for the coefficients of the equations are chosen satisfying those values.

Shows how to use JSXGraph to make a sine graph with amplitude, frequency and phase controlled by sliders.

This shows how to define a list of LaTeX strings, and pick a couple of them at random to display.

The "JSON data" type is used to define the available strings, so they're automatically marked as "safe" and curly braces aren't interpreted as variable substitution.

This question shows how to generate a random set of $(x,y)$ samples, where $y = mx + c + \mathrm{noise}$.

The JSXGraph extension is used to show a scatter plot of the data. This isn't necessary if you just want to generate the data.

This shows how to use a variable name annotation to put a hat on a variable name inside the \simplify command.

A mathematical expression part with a pattern restriction to ensure that the student has extracted the highest common factor of two terms.

The answer must be of the form $a(b+cx)$, where $b$ and $c$ are coprime.

The student is asked to give the roots of a quadratic equation. They should be able to enter the numbers in any order, and each correct number should earn a mark.

When there's only one root, the student can only fill in one of the answer fields.

This is implemented with a gap-fill with two number entry gaps. The gaps have a custom marking algorithm to allow an empty answer. The gap-fill considers the student's two answers as a set, and compares with the set of correct answers.

The marking corresponds to this table:

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm evaluates the exponential of the student's answer and the expected answer, and compares those.

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm checks that the student's answer differs from the expected answer by a multiple of $2\pi$.

There's one question, which you have to get right 5 times in a row. If you get it wrong, you have to start again.

This makes more sense if the question is randomised!

This shows one way of laying out matrix cells in a table, so that some cells can be filled in by the student.

At the time this was written, there's an open issue for allowing some entries in the matrix entry part to be filled-in, which would make this technique redundant.

Some CSS in the preamble adds the brackets around the table - it has to have the attribute class="matrix-gaps"

This question shows how to use the question's JavaScript preamble to request data from an external source, and use that data in question variables.

Note that this means the question only works when the external source is available. Use this very carefully, and avoid it if you possibly can!

Shows that you can embed a 3D GeoGebra applet in a content area.

The student is shown a passage of code in the prompt to a "choose several from a list" part.

A random proper fraction $a/b$ with denominator in the range 2 to 30 is picked, and the student must write $\frac{a}{b} \pi$.

The point of this question is to demonstrate that the correct answer is shown as a multiple of $\pi$ rather than a decimal.

The number entry part in this question has an alternative answer which is marked correct if the student's number satisfies an equation specified in the custom marking algorithm.

A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.

If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.

HELM Book 1.5 Formulae and substitution exercises.

Copy the problem parameters into the handout provided and solve the Building Fabric heat loss problem by hand. Enter your answers into this quiz to get your score. Upload a copy of your written answer to the submission on Brightspace. Good Luck!

HELM Book 1.5.1: using formulae and substitution: task 1

The student is asked to calculate a division by the method of long division, which they should enter in a grid.

The process is simulated and the order in which cells are filled in is recorded, so the marking feedback tries to identify the first cell that the student got wrong, or should try to fill in next.

They're asked to give the quotient as a plain number in a second part, to check that they can interpret the finished grid properly.

Shows how the "give a number which satisfies an equation" part type can be used to makr the student's number correct if it satisfies an equation of the form $f(x) = 0$.