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

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

Use vectors and matrices to explore the symmetries of crystals.

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

How would you go about estimating populations of dolphins?

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

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

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

Can you make matrices which will fix one lucky vector and crush another to zero?

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

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

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

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

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

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

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

Use your skill and judgement to match the sets of random data.

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.

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

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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

Build up the concept of the Taylor series

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?

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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

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

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

Explore the relationship between resistance and temperature

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?

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

Get some practice using big and small numbers in chemistry.

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

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