Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
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?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Can you draw the height-time chart as this complicated vessel fills
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Analyse these beautiful biological images and attempt to rank them in size order.
Work out the numerical values for these physical quantities.
Which line graph, equations and physical processes go together?
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.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
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?
Which pdfs match the curves?
Which countries have the most naturally athletic populations?
Explore the properties of perspective drawing.
Can you construct a cubic equation with a certain distance between
its turning points?
How do you choose your planting levels to minimise the total loss
at harvest time?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Which dilutions can you make using only 10ml pipettes?
Why MUST these statistical statements probably be at least a little
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
A problem about genetics and the transmission of disease.
Get some practice using big and small numbers in chemistry.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Can you sketch these difficult curves, which have uses in
Explore the meaning of the scalar and vector cross products and see how the two are related.
Formulate and investigate a simple mathematical model for the design of a table mat.
Go on a vector walk and determine which points on the walk are
closest to the origin.
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.
Can you work out which processes are represented by the graphs?
How much energy has gone into warming the planet?
Use your skill and judgement to match the sets of random data.
Match the descriptions of physical processes to these differential
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
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.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Who will be the first investor to pay off their debt?
Estimate areas using random grids
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.