Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
Can you draw the height-time chart as this complicated vessel fills
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
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.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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.
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?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Which line graph, equations and physical processes go together?
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Which dilutions can you make using only 10ml pipettes?
Why MUST these statistical statements probably be at least a little
Explore the meaning of the scalar and vector cross products and see how the two are related.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
A problem about genetics and the transmission of disease.
Formulate and investigate a simple mathematical model for the design of a table mat.
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...
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Can you sketch these difficult curves, which have uses in
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Can you work out which processes are represented by the graphs?
How much energy has gone into warming the planet?
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.
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign.
Estimate areas using random grids
Who will be the first investor to pay off their debt?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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?