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

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

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

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

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

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

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

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?

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?

How would you go about estimating populations of dolphins?

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

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

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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?

Which dilutions can you make using only 10ml pipettes?

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

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

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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

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

Use vectors and matrices to explore the symmetries of crystals.

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 calulate various quantities in biological contexts.

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

Match the descriptions of physical processes to these differential equations.

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

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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.

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

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

Get some practice using big and small numbers in chemistry.

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

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.

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