Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Not randomized because it's the same as in our workbook. But the variables are made in a way that it should be easy to randomise the size of the matrix, and the to change the formula for the input in not too many places.

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.

Calculate matrix times vector.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

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.

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.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

Calculate matrix times vector.

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.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

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

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Pick from the range -5..5, but make 0 more likely.

Demonstrates how to set up a "choose one from a list" part where the number of choices is randomised.

The part is given a list of labels for the choices as well as a list specifying the marks to award for each choice.

Should not be used: there's now a built-in function frequencies.

This question randomly generates a list of 100 items, each chosen from a list of strings.

It then computes the number of occurrences of each distinct item in the list. The statement shows the frequencies in a table.

No description given

No description given

Ask for the squares of five randomly-chosen numbers between 0 and 15.

The shuffle function puts a list in random order.

A table showing how to substitute raw LaTeX code into question text.

NOTE: You probably don't want to do this! There's usually a more robust way, where you get Numbas to make the expression for you.

Demonstrates how to create variables containing LaTeX commands, and how to use them in the question text.

A method of randomly choosing variable names - use the expression() JME function to create a variable name from a randomly chosen string.

(This question also uses a custom marking script to check that the student has simplified the expression)

A randomised table is contained in a div tag with the id #sales-table, so it can be styled using the CSS preamble.