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?

Explore the relationship between resistance and temperature

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

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.

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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.

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

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

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

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

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

Work out the numerical values for these physical quantities.

Which line graph, equations and physical processes go together?

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

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

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

Get some practice using big and small numbers in chemistry.

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

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.

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

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.

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

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

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.

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

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

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

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

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.

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