In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Which pdfs match the curves?
Explore the meaning of the scalar and vector cross products and see how the two are related.
How would you go about estimating populations of dolphins?
Can you find the volumes of the mathematical vessels?
Who will be the first investor to pay off their debt?
Can you make matrices which will fix one lucky vector and crush another to zero?
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Match the charts of these functions to the charts of their integrals.
Explore the properties of perspective drawing.
Which of these infinitely deep vessels will eventually full up?
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?
Invent scenarios which would give rise to these probability density functions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
Are these estimates of physical quantities accurate?
How do you choose your planting levels to minimise the total loss at harvest time?
How much energy has gone into warming the planet?
Match the descriptions of physical processes to these differential equations.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Can you construct a cubic equation with a certain distance between its turning points?
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?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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 how matrices can fix vectors and vector directions.
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?
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
This problem explores the biology behind Rudolph's glowing red nose.
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.
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you match these equations to these graphs?
Was it possible that this dangerous driving penalty was issued in error?
Analyse these beautiful biological images and attempt to rank them in size order.
How efficiently can you pack together disks?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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?