Match the descriptions of physical processes to these differential equations.
Who will be the first investor to pay off their debt?
Explore the properties of matrix transformations with these 10 stimulating questions.
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Get further into power series using the fascinating Bessel's equation.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Are these estimates of physical quantities accurate?
How would you go about estimating populations of dolphins?
Can you find the volumes of the mathematical vessels?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore the shape of a square after it is transformed by the action of a matrix.
Which of these infinitely deep vessels will eventually full up?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you match these equations to these graphs?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
How do you choose your planting levels to minimise the total loss at harvest time?
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?
Was it possible that this dangerous driving penalty was issued in error?
Match the charts of these functions to the charts of their integrals.
Can you construct a cubic equation with a certain distance between its turning points?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore how matrices can fix vectors and vector directions.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Invent scenarios which would give rise to these probability density functions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Build up the concept of the Taylor series
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.
Estimate areas using random grids
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
This problem explores the biology behind Rudolph's glowing red nose.
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.
A problem about genetics and the transmission of disease.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Why MUST these statistical statements probably be at least a little bit wrong?
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
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?
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
Explore the properties of perspective drawing.