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.
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you make matrices which will fix one lucky vector and crush another to zero?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Who will be the first investor to pay off their debt?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Use vectors and matrices to explore the symmetries of crystals.
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
Which pdfs match the curves?
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.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Which of these infinitely deep vessels will eventually full up?
How do you choose your planting levels to minimise the total loss at harvest time?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
How much energy has gone into warming the planet?
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?
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
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?
Can you find the volumes of the mathematical vessels?
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Explore the shape of a square after it is transformed by the action of a matrix.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
Explore the properties of perspective drawing.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you construct a cubic equation with a certain distance between its turning points?
Can you draw the height-time chart as this complicated vessel fills with water?
A problem about genetics and the transmission of disease.
How efficiently can you pack together disks?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How would you go about estimating populations of dolphins?
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Can you work out which processes are represented by the graphs?
Get further into power series using the fascinating Bessel's equation.