The student is shown a circuit diagram with three logic gates. It's always in the form (a OP b) OP (b OP c).

They have to fill in a truth table for the circuit. There is a step which expands the truth table, adding a column for each of the first two gates.

Calculate the product of two 3D vectors in column notation.

Part 1: multiply a 3D vector by an integer scalar
Part 2: perform scalar multiplication and subtraction in one expression with two 3D vectors

No description given

Issues: alignment in columns in the working - not sure what to do about it

Decimal divided by a decimal. Multiply by a power of ten to get an integer divisor. Long and short division process. There is a remainder which we express as a decimal by continuing the division process. Rounding is required to some number of decimal places.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are asked a multiple choice question based on a series of bar charts. The question is randomly selected from a pool of seven questions.

Uses the $\chi^2$ test to see if there is any significant difference in preferences.

This demonstrates how to:

• Generate a fixed number of observations of data in two categories.
• Display the data in a table, with row and column totals.
• Ask the student to enter the data in a spreadsheet which is automatically marked.

Issues: alignment in columns in the working - not sure what to do about it

Decimal divided by a decimal. Multiply by a power of ten to get an integer divisor. Long and short division process. There is a remainder which we express as a decimal by continuing the division process. Rounding is required to some number of decimal places.

The purpose of this question is to ask the students to go through one Rijndael round from the AES algorithm.

Recovering original function given some information such as derivative and value at some point.

The student is shown a table with rows for each class in a school, and two columns of numbers: books, and children. They have to work out the column totals, and the number of books per child, and enter them in the table.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown a column graph and asked to calculate the net benefit given the amount invested (randomly generated) and the intervention type (one of seven possible).

Student finds a basis for kernel and image of a matrix transformation. Any basis can be entered; there is a custom marking algorithm which checks if it is a correct basis.

There are options to adjust this question fairly easily, for example to get different variants for practice and for a test, by changing the options in the "pivot columns" in the variables. You should be careful to think about and test your pivot options, as some are easier or harder than others, and some don't work very well.

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".

Based on Chapter 8, quite loosley.Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

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.

Easy true/false questions to check if the meaning of a size of a matrix is understood, in terms of numbers of rows and columns.

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.

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.

To understand matrix multiplication in terms of linear combinations of column vectors.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Finding probabilities from a survey giving a table of data on the alcohol consumption of males. This can be easily adapted to data from other types of surveys.

Given a matrix in row reduced form use this to find bases for the null, column and row spaces of the matrix.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Finding probabilities from a survey giving a table of data on the alcohol consumption of males. This can be easily adapted to data from other types of surveys.