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

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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

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

Which units would you choose best to fit these situations?

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

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

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

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.

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Analyse these beautiful biological images and attempt to rank them in size order.

This problem explores the biology behind Rudolph's glowing red nose.

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

Which dilutions can you make using only 10ml pipettes?

Get some practice using big and small numbers in chemistry.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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