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

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Explore the relationship between resistance and temperature

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

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

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

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

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

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

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

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

Build up the concept of the Taylor series

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

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

Get some practice using big and small numbers in chemistry.

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

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

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?

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

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

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

Which line graph, equations and physical processes go together?

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

Work out the numerical values for these physical quantities.

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

Match the descriptions of physical processes to these differential equations.

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

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?

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

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?

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

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

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

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.

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

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

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

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

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.

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