A basic introduction to differentiation

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More work on differentiation with trigonometric functions

Using the chain rule with polynomials

Finding the stationary points of a cubic with two turning points

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 2 with parts' by Joshua Boddy.

These questions deal with vector operations and its application in geology.

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.

Shear and Bending Moment diagram for a beam with several concentrated loads.  Student can't see V & M diagrams a hints.

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

This easy question is intended to be used by administrators to test the integration of Numbas with a learning environment.

Determine the principal stresses for a 3D stress state (with null third invariant).

Skills Audit for Maths and Stats for MAS003 SEFY students without a prerequisite of A-level Maths.

Find the missing whole number power in an equation.

Calculating with indices.

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.

Rationalise the denominator with increasingly difficult examples involving compound denominators. 

Unmarked question, with advice.

Write down an example of a polynomial of given degree and given variable.

Write down a non-polynomial function.

Explain why a polynomial with a fractional index is not a polynomial.

The question includes a quadratic graph depicting the relationship between the frequency of an allele A at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A. The aim is to estimate the maximum and minimum fitness of the population and the corresponding frequency of allele A.

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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.

Solving a separable differential equation that describes the rate of decay of radioactive isotopes over time with a known initial condition to calculate the mass of the isotope after a given time and the time taken for the mass to reach $m$ grams. 

Decay Constant - Radioactivity - Nuclear Power (nuclear-power.com)

Simple Veriosn of Exam with randomised values

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.