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".

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

Given a sum of logs, all numbers are integers,

$\log_b(a_1)+\alpha\log_b(a_2)+\beta\log_b(a_3)$ write as $\log_b(a)$ for some fraction $a$.

Also calculate to 3 decimal places $\log_b(a)$. 

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Identify co-efficients, then use quadratic formula to find roots.

All set to be distinct and real. Some can be non-integer (0.5 steps)

Solve quadratic equations (non-simple case, two real, discrete roots) using the formula. Some, random, non integer roots.

Simple application of "Power Rule" to differentiate polynomials.

Some co-efficients and powers are non-integer and some may be negative.

Simple application of "Power Rule" to differentiate single term functions.

Some co-efficients and powers are non-integer and some may be negative.

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Given two distributions, calculate the measures of average and spread and make some decisions based on the results.

Some quadratics are to be solved by factorising

11 questions that test trig equations including use of identities and those needing stretches and translations. Also some questions related to trig graph shapes and applications.

A couple of different ways of showing the correct answer to a single part as soon as the student submits an answer. One way allows the student to change their answer, while the other locks the part.

A third part includes a "reveal answers to this part" button, which allows the student to choose to reveal the answer to the part.

Think very carefully before using this: by revealing the answer, you are removing the opportunity for the student to later on realise they've got that step wrong, as a consequence of some further work. It's often possible to use adaptive marking to use the student's answer in place of the correct answer in later parts.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Some questions demonstrating the JSXGraph extension, for my talk at the JSXGraph conference 2021.

Some basic tests of adding, scaling, and multiplying matrices.

Demo of automatically generating latex strings to out put vectors/matrices of variable size and that are calculated by some formula.

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.

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.

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".

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.

Asking the student to create examples of two matrices which multiply to zero but are not themselves the zero matrix. Then getting the student to think about some features of these examples.

This exam covers some of the techniques seen in the Psychology page on the wiki.

Because JavaScript numbers lose precision as they get bigger, you get some unexpected results.

See the variable "two" - the difference should be 2, but because the JavaScript representation of each of the two numbers is the same, it thinks the difference is 0.

Using the decimal data type, there's no loss of precision, so the correct value is produced.

Give the student a larger area to write some free-form text, which isn't marked.

This question shows how to run some JavaScript code when the question's HTML is displayed on the page.

This question shows how to use the 'adviceDisplayed' signal to run some javascript when the question's advice is revealed to the student.