The student has to enter `diff(y,x,2)`, equivalent to $\frac{\mathrm{d}^2y}{\mathrm{d}x^2}$, as their answer. It's marked by pattern matching, using a custom marking algorithm.

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

This easy exam is intended to be used by administrators to check the integration of Numbas with a leaarning environment.

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.

Asks students to find the partil fraction decomposition for a rational function Denominator is a quadratic with distinct factors.

Convert numbers greater than 1 into standard form/scientific notation.

Some questions for our open day, to give students a first taste of Numbas.

The student is given the equations of a line and a circle, and has to find the coordinates of the points of intersection. They're always at integer coordinates.

Expand $(az^2+bz+c)(pz+q)$.

The student is shown a set of axes with three lines. They must move the lines so they match the given inequalities, then move a point inside the region satisfied by the inequalities.

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.

Solving a system of simultaneous congruences using the Chinese Remainder Theorem.

An explore mode question which allows you to write a solution straight away, or break it down into steps.

After solving a system of three congruences, you can ask for a new problem with more congruences.

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This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

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This exam test students understanding of determinants and inverses of 3x3 matrices.

This exam looks at the determinatns and inverses of 2x2 matrices

Cofactors Determinant and inverse of a 3x3 matrix.

Exercises on calculating the determinant of 2x2 and 3x3 matrices.

Exercises on calculating the determinant of 3x3 matrices.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

This question tests learner's knowledge of the inverse matrix method for a 3x3 matrix.

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

This exam gives an overview of skills studnets require to be able to add and subtract matrices.

Exam to test students understanding of matrices multiplied by a scalar.

This exam gives tests for an overview of the skills students need to be able to perfom matrix multiplications.