Match the charts of these functions to the charts of their integrals.

How would you go about estimating populations of dolphins?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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?

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

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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.

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

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

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

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

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

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

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

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

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

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

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

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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

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

Work out the numerical values for these physical quantities.

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

Explore the relationship between resistance and temperature

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

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

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

Get some practice using big and small numbers in chemistry.

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?