Finding the area of a circle when given the diameter of the circle.

Find the diagonal or one side of a rectangle using Pythagoras' theorem.

Find the missing angle in a triangle using the fact that the angles add to 180 degrees.

Finding the stationary points of a cubic equation and determining their nature.

Find the derivative of a function of the form $y=a \tan(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \cos(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

Solving an equation of the form $a^x=b$ using logarithms to find $x$.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

Finding composite functions of 2 linear functions.

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x+a},\,x\neq-a$.

Calculating gradient and finding intercept from a geogebra graph.

Find roots and the area under a parabola

Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration. 

Find the centroid and the centroidal moments of inertia for a beam composed of a flat plate and two angle sections.

Find all forces on a two-part, symmetrical frame supporting a load. 

Find the highest scoring people over a course of days using the MAX, MATCH and INDEX functions

Classic machine problem.  Find the mechanical advantage of a pair of pliers and the force on the hinge pin.

Find the centroidal moment of inertia of a sideways T shape. This requires first locating the centroid, then applying the parallel axis theorem.

Solving simple linear equations in $\mathbb{Q}$ and $\mathbb{Z}_n$ for $n= 13, \;17$ or $19$.

Given $f(x)=(x+b)^n$. Find the gradient and equation of the chord between $(a,f(a))$ and $(a+h,f(a+h))$ for randomised values of $a$, $b$ and $h$.

In this question the students have to solve a linear recurrence of order 1. The sequence is asked in recurrence form and the goal is to find its closed form.

In this question the students have to solve a linear recurrence of order 2. The sequence is asked in recurrence form and the goal is to find its closed form.

Use Pythagoras' Theorem to find the length of a side on a right-angled triangle.

Part (a) - dividing a total quantity given a ratio

Part (b) - given the value of one part of the ratio to find the total quantity.

The student is asked to find the square root of an integer of the form $\pm n^2$. If the root is not real, they should enter "nan".

A custom marking algorithm extends the built-in one to deal with "nan".

There's some custom javascript to set the expected answer correctly. In the future this will be possible in the marking algorithm - see https://github.com/numbas/Numbas/issues/856

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.