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

Explore the relationship between resistance and temperature

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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

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

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

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

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.

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

Build up the concept of the Taylor series

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.

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

Which line graph, equations and physical processes go together?

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

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

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

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

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.

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

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.

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

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

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?

Simple models which help us to investigate how epidemics grow and die out.

Where should runners start the 200m race so that they have all run the same distance by the finish?

Which dilutions can you make using only 10ml pipettes?

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.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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

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

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?

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

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

Get some practice using big and small numbers in chemistry.

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

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