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Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students are given a height in centimetres and another height in metres, and are asked to write the ratio of the two heights in simplest form. There are 16 versions of this question.

Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students are given the number of bagels baked, in a number of hours, and need to calculate the number baked per half-hour. There are 6 different versions of this question.

Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students are given a proportion of staff who either have or haven't completed their reports. They are asked to find the complement, as a percentage. There are 6 different versions of this question. 

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students calculate the cost of the halogen globes given electricity cost, number of globes, number of years, replacement cost and lifespan of globes. Some of these variables are randomly selected. There are more than 10 different versions of this question.

Metric Unit conversion - division by 1000. 

Simple unit conversion with metric units. 

Unit conversion between two compound units.

Using the various versions of $\cos{2x}$ identity to integrate $\sin^2{x}$ and $\cos^2{x}$.

Add (a/b).x +/- (c/d) where a,b,c,d are randomised positive integers, and x is a randomised letter.

Alternative version of Graphs: Match graph to its adjacency matrix, where the student must match an adjacency matrix to a graph.

Multiple choice. Students need to select the correct simplification for a given expression. 

This question has four versions. Skills required are: using Pythagorean identities, converting to sine or cosine. Some also require fraction division.

Use Pythagoras' Theorem to find the length of a side on a right-angled triangle.

Converting millilitres to litres and kg to mg.

Convert a number given in base 10 to a different base.

Convert a number given in base 10 to a different base.

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".

Extra practice on some basic algebra skills, including solving linear equations. You can try as many times as you like and also generate new versions of the questions for extra practice.

Schreibe $\displaystyle \frac{a} {b + \frac{c}{d}}$ als einen gekürzten Bruch $\displaystyle \frac{p}{q}$ mit ganzen Zahlen $p$ und $q$.

Angepasste, übersetzte und erweiterte Version von https://numbas.mathcentre.ac.uk/question/11701/simplifying-fractions/ von Newcastle University Mathematics and Statistics.

This is a copy of a question from the Numbas demos project, with references to the editor removed.

The student is shown a plot of a mystery function. They can enter values of $x$ check, within the bounds of the plot.

They're asked to give the formula for the function, and then asked for its value at a very large value of $x$.

A plot of the student's function updates automatically as they type. Adaptive marking is used for the final part to award credit if the student gives the right value for their incorrect function.

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This exercise will help you round off decimals to given decimal places.

This exercise will help you round off decimals to given decimal places.

This question is a variation on another version which asks the student to find the height of a bridge arch and width of the river given a formula for the arch of the bridge (also available in the Numbas database)

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to rewrite the solution correctly. No variables but this is version 5 of 5 versions of the question. This version uses a much more mangled AI generated solution that the other 4 versions and does not ask for the line with the first error, just for the student to rewrite the solution correctly.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is version 4 of 5 versions of the question.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is version 2 of 5 versions of the question.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is 1 of 5 versions of the question.