Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given the total cost, insurance fee and daily hire charge (all randomly generated). They need to calculate the number of days hired.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are shown a personal income tax table and given a randomly generated taxable income. They are required to calculate the tax payable.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. The total amount raised and the number of participants is supplied (and both are randomly generated). Students must calculate the average per participant. 

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. The width and length of each vege bed are given in cm (randomised) as well as the path width in mm (randomised). Students are asked to find the perimeter of the whole vege patch in metres.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Students must calculate the area of the classroom excluding the storeroom. The length and width of the classroom and the area of the storeroom are randomly generated.

Solving cosx in given interval. With random variation and worked solutions.

Solving sinx in given interval. With random variation and worked solutions.

Solving tanx in given interval. With random variation and worked solutions.

Simple multiplication of complex conjugates. Complex numbers are of the form $a+bi$ where $a$ and $b$ are randomised between 1 and 9 inclusive. 

Horizontal and vertical shifts and scales of a random cubic spline

Simple questions on interval notation. If you are not randomising the order of your questions please turn on randomise choices in these questions.

In this assignment, try and find the roots of a randomly generated polynomial, using the quadratic equation.

A test assignment to see if it integrates properly into Canvas.

A simple test for practicing division with remainder. Numbers are randomised, and ranges for divisor and quotient can be specified.

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

Simple questions on interval notation. If you are not randomising the order of your questions please turn on randomise choices in these questions.

Simple questions on interval notation. If you are not randomising the order of your questions please turn on randomise choices in these questions.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Set up so that sometimes it has infinitely many solutions (one free variable), sometimes unique solution. Scaffolded so meant for formative. The variable d determines the cases (d=1: unique solution, d-0: infinitely many solutions). The other variables are set up so that no entries become zero for some randomisations but not others.

Adding matrices of random size: two to four rows and two to four columns. Advice (i.e. solution) has conditional visibility to show only the correct size.

Adding vectors of random size. Advice (i.e. solution) has conditional visibility to show only the correct size.

Adding and subtracting vectors of random size, including resolving brackets. Advice (i.e. solution) has conditional visibility to show only the correct size.

Simple vector addition and scalar multiplication in \(\mathbb{R}^2\).

Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.

Calculating with vectors of random size, including resolving brackets. Advice (i.e. solution) has conditional visibility to show only the correct size.

Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.

Not randomised because it's the same as in our workbook.

give the negative of each of two vectors. One always has 5 entries, the other has a random number of entries.

Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.

Not randomised because it's the same as in our workbook.

Simple scalar multiplication of a general vector with the important scalars 0, 1, -1. Just the variable name is randomised.

Calculate trace of a matrix.