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Two shops each have different numbers of jumper designs and colours. How many choices of jumper are there?

Inverse and division of complex numbers.  Four parts.

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

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First- and second order recurrence equations, homogenous and nonhomogenous

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No time limit - unlimited regeneration of questions allowed from these groups:

• Notation and Algebra
• Calculus - Differentiation
• Calculus - Integration
• Trigonometry and Matrices

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Addition and subtraction of matrices; multiplication by scalar.

Simple trig equations with radians

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Algebra Test 1

This question demonstrates a few ways of interacting with a Venn diagram drawn using JSXGraph.

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Compute the experimental probability of a particular score on a die given a sample of throws, and compare it with the theoretical probability.

The last part asks what you expect to happen to the experimental probability as the sample size increases.

FY001 Exam

Some quadratics are to be solved by factorising

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.

Educational calculation tool rather than "question".

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".

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.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

A bag contains balls of three different colours. You're told how many there are of each, and asked the probability of picking a ball of a particular colour.

Gives a plot of a velocity-time graph using JSXgraph, and a description of the motion shown in the graph. The student is asked to calculate the acceleration at different stages of the motion, and the displacement at the end of the motion.