Solve $\displaystyle ay + b = cy + d$ for $y$.

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Solve an exponential equation

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Introduces students to the floor and ceiling functions

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

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This question summarizes the definitions of surjective and injective, and applies them to prove the existance of an inverse.

This question demonstrates sending commands to geogebra and getting geogebra values and using them as part of a marking algorithm.

Slightly harder introductory exercises about the power set.

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

Converting between metres (m) and centimetres (cm). 

Round random numbers to the closest whole number, 1 to 3 decimals places. Also rounding that could show common misunderstandings.

A simple situational question about a box of chocolates, asking how many of each type there are, what percentage of the box they represent, the probability of picking one and ratios of different types.

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.

This question is a simple example to show how to input value from numbas to geogebra applet, and get a value back from geogebra to numbas for marking.

Questions used in a university course titled "Group theory".

The questions deal with permutations written in cycle or two-line notation.

Substitute values into formulae for the area or volume of various geometric objects.

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Work out \(k\) when \( y = kx^2\).

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Given a sum of logs, all numbers are integers,

$\log_b(a_1)+\alpha\log_b(a_2)+\beta\log_b(a_3)$ write as $\log_b(a)$ for some fraction $a$.

Also calculate to 3 decimal places $\log_b(a)$. 

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve $\displaystyle ax + b = cx + d$ for $x$.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$