The student is shown two labelled graphs. They are asked:

• Number of vertices in each
• Number of edges in each
• Degree sequences for each
• Is there an isomorphism between them? If so, write one.

The number of vertices is always equal, so this is a gimme.

If the edges or degree sequences are different, the student is expected to realise that there cannot be an isomorphism.

If these values are the same, then there will be an isomorphism (else the question is a bit too tricky).

Numbas expects a particular isomorphism, but there may be more than one, all of which would be accepted.

This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".

sin horizontal shifted Working 1_11_16

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

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How to find solutions to a second order recurrence relation.

This exam includes the formulas students need to memorize for the SAT Math exam.

Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.

Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. SP = Statistics & Probability strand. Students read the annual hours worked from the chart and calculate the weekly hours given the number of weeks annual leave. There are 7 different versions of this question.

Calculate the conduction heat loss through a concrete slab

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

An A-frame structure supporting a force and a moment. The feet are at the different vertical positions so the solution will require simultaneous equations, unless you rotate the coordinate system.

This question assesses learners' ability to:

- construct a confidence interval for a proportion given corresponding summarised data;

- predict the sample size required to limit the margin of error to a given value.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given a ratio, and the total number of dancers. They must calculate the number of girls (the larger share). The ratio, and total number are randomly generated.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students need to read the speed of the given object from the table, then convert from m/s to km/h. There are 7 objects, and hence 7 different possible questions.

Definite integation of basic functions.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given a height (in cm) and weight (kg), then need to calculate the BMI given the formula (first converting height to m), then determine the weight range from the table. Weight and height are randomised.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. NC = Non Calculator. The start time for Period 1 (randomised) and the end time for Period 2 (randomised) are given, and students are asked to find the middle of those two times. 

Out of three options, you need to choose the best pokemon type to use to defeat a given pokemon type.

Info is taken from https://www.eurogamer.net/articles/2018-12-21-pokemon-go-type-chart-effectiveness-weaknesses  

Icons are taken from https://bulbapedia.bulbagarden.net/wiki/Main_Page

Consider a binary tree with $2^n$ nodes.

We give generators for the isomorphisms of the tree: at each non-leaf vertex, swap the branches descending from that node.

• What is the action of a given word?
• Write a word which produces the required isomorphism
• Which generators commute?
• What is the order of each generator?
• Write one of the (non-root) generators in terms of the others.
• Which permutations of the leaves are possible?
• What is the order of the group of isomorphisms?
• What is the order of the quotient group obtained by identifying all the leaves of one branch?

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The student is given a number in base 10 and asked to write it in a given base, between 2 and 16. The number has at most 3 digits in the other base.

Until it's possible to derive the expected answer for a part in the marking algorithm (see the issue tracker), this question has "show expected answer" turned off, because it just shows the base 10 number.

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