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

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

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

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

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

How would you go about estimating populations of dolphins?

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

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

Can you match the charts of these functions to the charts of their integrals?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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

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

Can you construct a cubic equation with a certain distance between its turning points?

Which of these infinitely deep vessels will eventually full up?

How do you choose your planting levels to minimise the total loss at harvest time?

Was it possible that this dangerous driving penalty was issued in error?

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

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

Match the descriptions of physical processes to these differential equations.

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?

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

Look at the advanced way of viewing sin and cos through their power series.

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

Is it really greener to go on the bus, or to buy local?

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

Can you draw the height-time chart as this complicated vessel fills with water?

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