In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

Get further into power series using the fascinating Bessel's equation.

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

Here are several equations from real life. Can you work out which measurements are possible from each equation?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Use vectors and matrices to explore the symmetries of crystals.

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

When you change the units, do the numbers get bigger or smaller?

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Which dilutions can you make using only 10ml pipettes?

Which units would you choose best to fit these situations?

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Work out the numerical values for these physical quantities.

Explore the relationship between resistance and temperature

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Explore the properties of matrix transformations with these 10 stimulating questions.

Formulate and investigate a simple mathematical model for the design of a table mat.

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

Which line graph, equations and physical processes go together?

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Get some practice using big and small numbers in chemistry.

Can you make matrices which will fix one lucky vector and crush another to zero?

Explore the meaning of the scalar and vector cross products and see how the two are related.

Go on a vector walk and determine which points on the walk are closest to the origin.

Can you sketch these difficult curves, which have uses in mathematical modelling?

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Use trigonometry to determine whether solar eclipses on earth can be perfect.

Explore the shape of a square after it is transformed by the action of a matrix.

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Invent scenarios which would give rise to these probability density functions.

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Can you work out which processes are represented by the graphs?

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Simple models which help us to investigate how epidemics grow and die out.