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

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

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

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

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

Which line graph, equations and physical processes go together?

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.

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

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?

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

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

Work out the numerical values for these physical quantities.

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

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

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

Simple models which help us to investigate how epidemics grow and die out.

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

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

Which units would you choose best to fit these situations?

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

Get some practice using big and small numbers in chemistry.

When you change the units, do the numbers get bigger or smaller?

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

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

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

Explore the relationship between resistance and temperature