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?

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

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

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

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

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

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

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 calulate various quantities in biological contexts.

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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

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.

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.

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

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

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

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

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?

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

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.

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

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

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

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

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

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.

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.

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