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 physical contexts.

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

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

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

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?

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

Which dilutions can you make using only 10ml pipettes?

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

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

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

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

Build up the concept of the Taylor series

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

Which line graph, equations and physical processes go together?

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

Which units would you choose best to fit these situations?

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

Work out the numerical values for these physical quantities.

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

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.

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

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

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

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

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

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

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

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

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

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

Explore the relationship between resistance and temperature

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.

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

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