Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. 

The student is asked to enter a given matrix, but they're only required to fill in the upper triangle.

A custom marking algorithm fills in any empty cells in the lower triangle of the student's answer with the corresponding cell in the upper triangle.

The student is still warned if they leave any cells empty in the upper triangle.

Tags: algebra, equations (linear), equations (quadratic)

Last updated Sep 2019

This demonstrates how to:

• Generate a fixed number of observations of data in two categories.
• Display the data in a table, with row and column totals.
• Ask the student to enter the data in a spreadsheet which is automatically marked.

Find and compare means and standard deviation using EXCEL (downloadable randomised dataset)

FoES Electronics Written Assessment

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

Linear combinations of $2 \times 2$ matrices. Three examples.

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Practice using the log rules to add and subtract logarithms

Zet de decimale getallen naar breukvorm om en omgekeerd

The CSS preamble adds a vertical line down the input for part b, to separate the two parts of the matrix.

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.

A practice test to get used to the NUMBAS environment.

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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.