Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

Given a circle with radius between 2 and 6 units, students are given a set of 8 points and asked to identify whether they are on, inside or outside the circle locus.

Find the equation of a line passing through two points in the form y=mx+b. The question is set up so that m and b will be integers.

This uses an embedded Geogebra graph of a polar function with random coefficients set by NUMBAS.

This question models an experiment: the student must collect some data and enter it at the start of the question, and the expected answers to subsequent parts are marked based on that data.

A downside of working this way is that you have to set up the variable replacements on each part of the question. You could avoid this by using explore mode.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Question asks students to find the time taken for an object thrown vertically upward from a platform to reach the ground. Set up randomly chooses environment to be on Earth, Mars or the Moon and uses appropriate acceleration due to gravity. The initial velocity of the body and height of the platform above the ground are randomly selected. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

No description given

set of exercises on double and triple integrals

A set of practice questions for primary teaching students studying Mathematical Patterns and Relationships

This question shows how to generate a random set of $(x,y)$ samples, where $y = mx + c + \mathrm{noise}$.

The JSXGraph extension is used to show a scatter plot of the data. This isn't necessary if you just want to generate the data.

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:

Should not be used: this relies on a custom JavaScript which is not guaranteed to continue working.

Wrap the student's answer in set() so it's marked as a set.

This demonstrates how to set xmin, ymin, xmax and ymax for an embedded geogebra diagram.

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

Several questions on interrogating the mtcars dataset built in to R.

The statement contains two blank geogebra applets: one with the computer algebra view, which can be used as a calculator, and the other with algebra and geometry views.

There are custom functions which set the perspective of a geogebra applet and show the toolbar or algebra input line. These will probably be included in the geogebra extension eventually.

The statement contains two blank geogebra applets: one with the computer algebra view, which can be used as a calculator, and the other with algebra and geometry views.

There are custom functions which set the perspective of a geogebra applet and show the toolbar or algebra input line. These will probably be included in the geogebra extension eventually.

Asks students to add and multiply two integers modulo another integer.  The modulus is a random number between 30 and 70, the summands are set to be large enough that modular reduction will be necessary.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of amodulus function with random coefficients set by NUMBAS.