Which line graph, equations and physical processes go together?

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

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

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

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

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

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

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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

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

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

Which units would you choose best to fit these situations?

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?

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

Work out the numerical values for these physical quantities.

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

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?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

Explore the relationship between resistance and temperature

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

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

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

Which dilutions can you make using only 10ml pipettes?

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

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

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

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

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

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

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.

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