Can you match the charts of these functions to the charts of their integrals?

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

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

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

Which line graph, equations and physical processes go together?

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

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

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

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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

Build up the concept of the Taylor series

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

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 relationship between resistance and temperature

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

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

Which of these infinitely deep vessels will eventually full up?

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

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?

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.

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

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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?

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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