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

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

Which line graph, equations and physical processes go together?

Use vectors and matrices to explore the symmetries of crystals.

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?

Build up the concept of the Taylor series

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

Explore the relationship between resistance and temperature

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

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

Work out the numerical values for these physical quantities.

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

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

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

Which of these infinitely deep vessels will eventually full up?

How do you choose your planting levels to minimise the total loss at harvest time?

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

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

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?

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

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

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

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

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