old question, way too many things in one question! I have made better questions out of each part now.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

The student is asked to give the roots of a quadratic equation. They should be able to enter the numbers in any order, and each correct number should earn a mark.

When there's only one root, the student can only fill in one of the answer fields.

This is implemented with a gap-fill with two number entry gaps. The gaps have a custom marking algorithm to allow an empty answer. The gap-fill considers the student's two answers as a set, and compares with the set of correct answers.

The marking corresponds to this table:

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm evaluates the exponential of the student's answer and the expected answer, and compares those.

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm checks that the student's answer differs from the expected answer by a multiple of $2\pi$.

There's one question, which you have to get right 5 times in a row. If you get it wrong, you have to start again.

This makes more sense if the question is randomised!

This shows one way of laying out matrix cells in a table, so that some cells can be filled in by the student.

At the time this was written, there's an open issue for allowing some entries in the matrix entry part to be filled-in, which would make this technique redundant.

Some CSS in the preamble adds the brackets around the table - it has to have the attribute class="matrix-gaps"

A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.

If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.

Simplify a fraction where the numerator and denominator are factorised and have common products, and one of the common factors is powered. Part of HELM book 1.4

In this question the students are given the public and private keys for El Gamal through Elliptic Curve and a message to decrypt. They have to decrypt the message.

Factorise two algebraic terms that have a numerical gcd > 1. Part of HELM book 1.3

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.

The student is shown a diagram with measurements of rooms in a house. They have to enter the measurements in a spreadsheet, then the area of each room, and finally the total area of the house.

This practice exam shows you the style and format of the real exam.

In this practice exam there are only 6 questions. The real exam will have 15-20 questions.

DIAGNOSYS is a knowledge-based test of mathematics background knowledge for first-year university students, created by John Appleby at Newcastle University.

The questions have been translated directly into Numbas, with as few changes as possible.

Students have to match four receptacles of varying sizes with the following fractions of a litre: 1 whole, 1/10, 1/100 and 1/1000.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

Given n-1 angles inside a polygon, students have to calculate the value of the last internal angle.

Students are given an exponential equation and asked to identify the y-intercept from a list of choices.

The constants in the exponential equation have been randomised.

Shows an exponential graph displaying the value of an investment under compound interest. Students have to identify the type of graph and answer 3 questions about the value of the investment from the graph.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown an infographic, given the details of one man and asked how many routine screenings they should have. There are seven possible questions.

Guides the student through the process of writing an integer in binary. They can pick any number they like, then choose from a selection of methods, or just do their own method and have the answer checked.

A line with random $x$- and $y$- intercepts is plotted, and you have to drag two dots over the points where the line crosses the $x$ and $y$ axes.

Topics: Trigonometeric equations and complex numbers
Students must complete the exam within 90 mins (standard time).
Questions have variables to produce randomised questions.

A first exam that I have created to see if I can get Numbas working. Not something to be used by anyone else.

Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.

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

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".

Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.