Finding the current in a simple series RL circuit.

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

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

Find the number of people with heights greater then mean plus two times the standard deviation.

Finding the stationary points of a cubic with two turning points

Finding lengths of sides of triangles

Finding the volumes of basic 3D shapes

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

Find the gradient of  $ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=n$

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

Find the gradient of  $ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=n$

Find the gradient of  $ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=n$

Finding the stationary points of a cubic with two turning points

Find the area under a curve. The step is given.

Find the area under a porabola.

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.

Find the rectangular (scalar) components of a force for two coordinates systems.

This question is a variation on another version which asks the student to find the height of a bridge arch and width of the river given a formula for the arch of the bridge (also available in the Numbas database)

Find the missing whole number power in an equation.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

An application of quadratic functions based on the Gladesville Bridge in Sydney, Australia. Student is given an equation representing the arch of the bridge and asked to find the height of the arch and the width of the river. Requires and understanding of the quadratic function and where and how to apply correct formulae.

An application of quadratic functions based on the Gateshead Bridge in the UK city of Newcastle. Student is given an equation representing the arch of the bridge and asked to find the height of the arch and the width of the river. Requires and understanding of the quadratic function and where and how to apply correct formulae.

Student is given a rational function, h(x), with randomised coefficients, and a linear function, k(x), also with randomised coeffieients and asked to find:

1. h(k(x)) or k(h(x)) (randomly selected) for a randomised value of x
2. The domain of h(x) - multiple choice part
3. A general expresion for k(h(x)) or h(k(x)) - opposite combination to first part.

Variables are constrained so that h(x) is not a degenerate form and that when evaluating h(x) denomiator is not 0.

This question gives the student the formula for the charge on a capacitor as a function of time then asks them to find the value of k, the exponential constant given other values and hence write out the formula for the given case. A custom function (in Extensions & scripts) extracts the student's formula and plots it on a JSXGraph object in the question. The student is then asked to evaluate the function at a given point using the plot or other methods. The value of the capacitor (Q_0), time (t) and charge at time t are randomised as is the value at which the formula is to be evaluated.

Calculation of the length and alternative form of the parameteric representation of a curve, involving trigonometric functions.

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

Basic trigonometry question, students are asked to find the diameter of a circular tunnel given distance from edge of a roadway to centre top of tunnel (randomised) and angle from edge of road to centre top of tunnel (randomised).

Basic trigonometry question, students are asked to find the width of a roadway in a circular tunnel given distance from edge of road to centre top of tunnel (randomised) and angle from edge of road to centre top of tunnel (randomised).