Matrix multiplication. Has automatically generated "unresolved" matrix product to write in the solution, which is the interesting part of this implementation.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

The interesting part about the implementation is the way the output is generated for "Advice".

Educational calculation tool rather than "question".

This allows the student to input a square matrix (max rows 5). 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 matrix and the identity matrix (or what it has got to). This question has no marks and no feedback as it's just meant as a "calculator". It has some checks in so students know when they are not entering a square matrix or a valid row number etc.

It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.

It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.

Student decides on four different examples whether two subspaces form a direct sum and whether the sum is the whole vectorspace.

No randomisation, just the four examples. The question is set in explore mode, so that after deciding, students are asked to give reasons for their choices.

FY001 Exam

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

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.

No description given

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.