Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Which pdfs match the curves?
Can you find the volumes of the mathematical vessels?
How would you go about estimating populations of dolphins?
Who will be the first investor to pay off their debt?
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Go on a vector walk and determine which points on the walk are closest to the origin.
Match the charts of these functions to the charts of their integrals.
Explore the shape of a square after it is transformed by the action of a matrix.
Are these estimates of physical quantities accurate?
How do you choose your planting levels to minimise the total loss at harvest time?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Explore the properties of perspective drawing.
Invent scenarios which would give rise to these probability density functions.
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 of these infinitely deep vessels will eventually full up?
How much energy has gone into warming the planet?
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 biological contexts.
Match the descriptions of physical processes to these differential equations.
Why MUST these statistical statements probably be at least a little bit wrong?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which line graph, equations and physical processes go together?
Can you sketch these difficult curves, which have uses in mathematical modelling?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
This problem explores the biology behind Rudolph's glowing red nose.
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?
Get further into power series using the fascinating Bessel's equation.
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.
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?
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?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Estimate areas using random grids
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Build up the concept of the Taylor series
How efficiently can you pack together disks?
Formulate and investigate a simple mathematical model for the design of a table mat.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get some practice using big and small numbers in chemistry.
A problem about genetics and the transmission of disease.
Analyse these beautiful biological images and attempt to rank them in size order.