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

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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

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?

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

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

Why MUST these statistical statements probably be at least a little bit wrong?

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

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

Which of these infinitely deep vessels will eventually full up?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

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

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

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

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Build up the concept of the Taylor series

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

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

Match the descriptions of physical processes to these differential equations.

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.

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

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

How would you go about estimating populations of dolphins?

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?