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

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

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

Which line graph, equations and physical processes go together?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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?

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?

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

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

How would you go about estimating populations of dolphins?

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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.

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

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

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

Build up the concept of the Taylor series

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

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

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

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 Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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.

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

Which dilutions can you make using only 10ml pipettes?

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.

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

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

Work out the numerical values for these physical quantities.

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

Explore the relationship between resistance and temperature